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- 2019-07-12T12:47:53+02:00 (5 years ago)
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- NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc
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r10146 r11263 1 1 #!/bin/bash 2 2 3 ./inc/clean.sh4 ./inc/build.sh3 #./inc/clean.sh 4 #./inc/build.sh 5 5 6 cd tex_main 7 sed -i -e 's#\\documentclass#%\\documentclass#' -e '/{document}/ s/^/%/' \ 8 ../tex_sub/*.tex 9 sed -i 's#\\subfile{#\\include{#g' \ 10 NEMO_manual.tex 11 latex2html -local_icons -no_footnode -split 4 -link 2 -mkdir -dir ../html_LaTeX2HTML \ 12 $* \ 13 NEMO_manual 14 sed -i -e 's#%\\documentclass#\\documentclass#' -e '/{document}/ s/^%//' \ 15 ../tex_sub/*.tex 16 sed -i 's#\\include{#\\subfile{#g' \ 17 NEMO_manual.tex 6 sed -i -e 's#utf8#latin1#' \ 7 -e 's#\[outputdir=../build\]{minted}#\[\]{minted}#' \ 8 -e '/graphicspath/ s#{../#{../../#g' \ 9 global/packages.tex 10 11 cd ./NEMO/main 12 sed -i -e 's#\\documentclass#%\\documentclass#' -e '/{document}/ s#^#%#' ../subfiles/*.tex 13 sed -i 's#\\subfile{#\\input{#' chapters.tex appendices.tex 14 15 #latex2html -noimages -local_icons -no_footnode -split 4 -link 2 -dir ../html_LaTeX2HTML $* NEMO_manual 16 latex2html -debug -noreuse -init_file ../../l2hconf.pm -local_icons -dir ../build/html NEMO_manual 17 18 sed -i -e 's#%\\documentclass#\\documentclass#' -e '/{document}/ s#^%##' ../subfiles/*.tex 19 sed -i 's#\\input{#\\subfile{#' chapters.tex appendices.tex 18 20 cd - 19 21 22 sed -i -e 's#latin1#utf8#' \ 23 -e 's#\[\]{minted}#\[outputdir=../build\]{minted}#' \ 24 -e '/graphicspath/ s#{../../#{../#g' \ 25 global/packages.tex 26 20 27 exit 0 -
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NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_A.tex
r10442 r11263 79 79 { 80 80 \begin{array}{*{20}l} 81 \nabla \cdot {\ rm {\bf U}}81 \nabla \cdot {\mathrm {\mathbf U}} 82 82 &= \frac{1}{e_1 \,e_2 } \left[ \left. {\frac{\partial (e_2 \,u)}{\partial i}} \right|_z 83 83 +\left. {\frac{\partial(e_1 \,v)}{\partial j}} \right|_z \right] … … 115 115 $, it becomes:} 116 116 % 117 \nabla \cdot {\ rm {\bf U}}117 \nabla \cdot {\mathrm {\mathbf U}} 118 118 & = \frac{1}{e_1 \,e_2 \,e_3 } \left[ 119 119 \left. \frac{\partial (e_2 \,e_3 \,u)}{\partial i} \right|_s … … 144 144 { 145 145 \begin{array}{*{20}l} 146 \nabla \cdot {\ rm {\bf U}}146 \nabla \cdot {\mathrm {\mathbf U}} 147 147 &= \frac{1}{e_1 \,e_2 \,e_3 } \left[ 148 148 \left. \frac{\partial (e_2 \,e_3 \,u)}{\partial i} \right|_s … … 346 346 % 347 347 &= \left. {\frac{\partial u }{\partial t}} \right|_s 348 &+ \left. \nabla \cdot \left( {{\ rm {\bf U}}\,u} \right) \right|_s348 &+ \left. \nabla \cdot \left( {{\mathrm {\mathbf U}}\,u} \right) \right|_s 349 349 + \,u \frac{1}{e_3 } \frac{\partial e_3}{\partial t} 350 350 - \frac{v}{e_1 e_2 }\left( v \;\frac{\partial e_2 }{\partial i} … … 359 359 \label{apdx:A_sco_Dt_flux} 360 360 \left. \frac{D u}{D t} \right|_s = \frac{1}{e_3} \left. \frac{\partial ( e_3\,u)}{\partial t} \right|_s 361 + \left. \nabla \cdot \left( {{\ rm {\bf U}}\,u} \right) \right|_s361 + \left. \nabla \cdot \left( {{\mathrm {\mathbf U}}\,u} \right) \right|_s 362 362 - \frac{v}{e_1 e_2 }\left( v \;\frac{\partial e_2 }{\partial i} 363 363 -u \;\frac{\partial e_1 }{\partial j} \right) … … 399 399 400 400 As in $z$-coordinate, 401 the horizontal pressure gradient can be split in two parts following \citet{ Marsaleix_al_OM08}.401 the horizontal pressure gradient can be split in two parts following \citet{marsaleix.auclair.ea_OM08}. 402 402 Let defined a density anomaly, $d$, by $d=(\rho - \rho_o)/ \rho_o$, 403 403 and a hydrostatic pressure anomaly, $p_h'$, by $p_h'= g \; \int_z^\eta d \; e_3 \; dk$. … … 483 483 \label{apdx:A_PE_dyn_flux_u} 484 484 \frac{1}{e_3} \frac{\partial \left( e_3\,u \right) }{\partial t} = 485 \nabla \cdot \left( {{\ rm {\bf U}}\,u} \right)485 \nabla \cdot \left( {{\mathrm {\mathbf U}}\,u} \right) 486 486 + \left\{ {f + \frac{1}{e_1 e_2 }\left( v \;\frac{\partial e_2 }{\partial i} 487 487 -u \;\frac{\partial e_1 }{\partial j} \right)} \right\} \,v \\ … … 493 493 \label{apdx:A_dyn_flux_v} 494 494 \frac{1}{e_3}\frac{\partial \left( e_3\,v \right) }{\partial t}= 495 - \nabla \cdot \left( {{\ rm {\bf U}}\,v} \right)495 - \nabla \cdot \left( {{\mathrm {\mathbf U}}\,v} \right) 496 496 + \left\{ {f + \frac{1}{e_1 e_2 }\left( v \;\frac{\partial e_2 }{\partial i} 497 497 -u \;\frac{\partial e_1 }{\partial j} \right)} \right\} \,u \\ -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_B.tex
r10442 r11263 162 162 the ($i$,$j$,$k$) curvilinear coordinate system in which 163 163 the equations of the ocean circulation model are formulated, 164 takes the following form \citep{ Redi_JPO82}:164 takes the following form \citep{redi_JPO82}: 165 165 166 166 \begin{equation} … … 184 184 185 185 In practice, isopycnal slopes are generally less than $10^{-2}$ in the ocean, 186 so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{ Cox1987}:186 so $\textbf {A}_{\textbf I}$ can be simplified appreciably \citep{cox_OM87}: 187 187 \begin{subequations} 188 188 \label{apdx:B4} … … 236 236 { 237 237 \begin{array}{*{20}l} 238 \nabla T\;.\left( {{\ rm {\bf A}}_{\rm {\bf I}} \nabla T}238 \nabla T\;.\left( {{\mathrm {\mathbf A}}_{\mathrm {\mathbf I}} \nabla T} 239 239 \right)&=A^{lT}\left[ {\left( {\frac{\partial T}{\partial i}} \right)^2-2a_1 240 240 \frac{\partial T}{\partial i}\frac{\partial T}{\partial k}+\left( … … 379 379 - \nabla _h \times \left( {A^{lm}\;\zeta \;{\textbf{k}}} \right) 380 380 + \frac{1}{e_3 }\frac{\partial }{\partial k}\left( {\frac{A^{vm}\;}{e_3 } 381 \frac{\partial {\ rm {\bf U}}_h }{\partial k}} \right) \\381 \frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}} \right) \\ 382 382 \end{equation} 383 383 that is, in expanded form: -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_D.tex
r10442 r11263 32 32 33 33 To satisfy part of these aims, \NEMO is written with a coding standard which is close to the ECMWF rules, 34 named DOCTOR \citep{ Gibson_TR86}.34 named DOCTOR \citep{gibson_rpt86}. 35 35 These rules present some advantages like: 36 36 -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_E.tex
r10442 r11263 49 49 50 50 This results in a dissipatively dominant (\ie hyper-diffusive) truncation error 51 \citep{ Shchepetkin_McWilliams_OM05}.52 The overall performance of the advection scheme is similar to that reported in \cite{ Farrow1995}.51 \citep{shchepetkin.mcwilliams_OM05}. 52 The overall performance of the advection scheme is similar to that reported in \cite{farrow.stevens_JPO95}. 53 53 It is a relatively good compromise between accuracy and smoothness. 54 54 It is not a \emph{positive} scheme meaning false extrema are permitted but … … 65 65 the second term which is the diffusive part of the scheme, is evaluated using the \textit{before} velocity 66 66 (forward in time). 67 This is discussed by \citet{ Webb_al_JAOT98} in the context of the Quick advection scheme.67 This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme. 68 68 UBS and QUICK schemes only differ by one coefficient. 69 Substituting 1/6 with 1/8 in (\autoref{eq:tra_adv_ubs}) leads to the QUICK advection scheme \citep{ Webb_al_JAOT98}.69 Substituting 1/6 with 1/8 in (\autoref{eq:tra_adv_ubs}) leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 70 70 This option is not available through a namelist parameter, since the 1/6 coefficient is hard coded. 71 71 Nevertheless it is quite easy to make the substitution in \mdl{traadv\_ubs} module and obtain a QUICK scheme. … … 80 80 $\tau_w^{ubs}$ will be evaluated using either \textit{(a)} a centered $2^{nd}$ order scheme, 81 81 or \textit{(b)} a TVD scheme, or \textit{(c)} an interpolation based on conservative parabolic splines following 82 \citet{ Shchepetkin_McWilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS.82 \citet{shchepetkin.mcwilliams_OM05} implementation of UBS in ROMS, or \textit{(d)} an UBS. 83 83 The $3^{rd}$ case has dispersion properties similar to an eight-order accurate conventional scheme. 84 84 … … 255 255 \subsection{Griffies iso-neutral diffusion operator} 256 256 257 Let try to define a scheme that get its inspiration from the \citet{ Griffies_al_JPO98} scheme,257 Let try to define a scheme that get its inspiration from the \citet{griffies.gnanadesikan.ea_JPO98} scheme, 258 258 but is formulated within the \NEMO framework 259 259 (\ie using scale factors rather than grid-size and having a position of $T$-points that … … 272 272 Nevertheless, this technique works fine for $T$ and $S$ as they are active tracers 273 273 (\ie they enter the computation of density), but it does not work for a passive tracer. 274 \citep{ Griffies_al_JPO98} introduce a different way to discretise the off-diagonal terms that274 \citep{griffies.gnanadesikan.ea_JPO98} introduce a different way to discretise the off-diagonal terms that 275 275 nicely solve the problem. 276 276 The idea is to get rid of combinations of an averaged in one direction combined with … … 308 308 \begin{figure}[!ht] 309 309 \begin{center} 310 \includegraphics[width= 0.70\textwidth]{Fig_ISO_triad}310 \includegraphics[width=\textwidth]{Fig_ISO_triad} 311 311 \caption{ 312 312 \protect\label{fig:ISO_triad} … … 508 508 \] 509 509 510 \citep{ Griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form.510 \citep{griffies_JPO98} introduces another way to implement the eddy induced advection, the so-called skew form. 511 511 It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. 512 512 For example in the (\textbf{i},\textbf{k}) plane, the tracer advective fluxes can be transformed as follows: … … 574 574 The horizontal component reduces to the one use for an horizontal laplacian operator and 575 575 the vertical one keeps the same complexity, but not more. 576 This property has been used to reduce the computational time \citep{ Griffies_JPO98},576 This property has been used to reduce the computational time \citep{griffies_JPO98}, 577 577 but it is not of practical use as usually $A \neq A_e$. 578 578 Nevertheless this property can be used to choose a discret form of \autoref{eq:eiv_skew_continuous} which -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/annex_iso.tex
r10442 r11263 4 4 \newcommand{\rML}[1][i]{\ensuremath{_{\mathrm{ML}\,#1}}} 5 5 \newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}} 6 \newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}} 6 %% Move to ../../global/new_cmds.tex to avoid error with \listoffigures 7 %\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}} 7 8 \newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}} 8 9 \newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}} … … 52 53 the vertical skew flux is further reduced to ensure no vertical buoyancy flux, 53 54 giving an almost pure horizontal diffusive tracer flux within the mixed layer. 54 This is similar to the tapering suggested by \citet{ Gerdes1991}. See \autoref{subsec:Gerdes-taper}55 This is similar to the tapering suggested by \citet{gerdes.koberle.ea_CD91}. See \autoref{subsec:Gerdes-taper} 55 56 \item[\np{ln\_botmix\_triad}] 56 57 See \autoref{sec:iso_bdry}. … … 71 72 \label{sec:iso} 72 73 73 We have implemented into \NEMO a scheme inspired by \citet{ Griffies_al_JPO98},74 We have implemented into \NEMO a scheme inspired by \citet{griffies.gnanadesikan.ea_JPO98}, 74 75 but formulated within the \NEMO framework, using scale factors rather than grid-sizes. 75 76 … … 194 195 \subsection{Expression of the skew-flux in terms of triad slopes} 195 196 196 \citep{ Griffies_al_JPO98} introduce a different discretization of the off-diagonal terms that197 \citep{griffies.gnanadesikan.ea_JPO98} introduce a different discretization of the off-diagonal terms that 197 198 nicely solves the problem. 198 199 % Instead of multiplying the mean slope calculated at the $u$-point by … … 201 202 \begin{figure}[tb] 202 203 \begin{center} 203 \includegraphics[width= 1.05\textwidth]{Fig_GRIFF_triad_fluxes}204 \includegraphics[width=\textwidth]{Fig_GRIFF_triad_fluxes} 204 205 \caption{ 205 206 \protect\label{fig:ISO_triad} … … 265 266 \begin{figure}[tb] 266 267 \begin{center} 267 \includegraphics[width= 0.80\textwidth]{Fig_GRIFF_qcells}268 \includegraphics[width=\textwidth]{Fig_GRIFF_qcells} 268 269 \caption{ 269 270 \protect\label{fig:qcells} … … 473 474 474 475 To complete the discretization we now need only specify the triad volumes $_i^k\mathbb{V}_{i_p}^{k_p}$. 475 \citet{ Griffies_al_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells,476 \citet{griffies.gnanadesikan.ea_JPO98} identifies these $_i^k\mathbb{V}_{i_p}^{k_p}$ as the volumes of the quarter cells, 476 477 defined in terms of the distances between $T$, $u$,$f$ and $w$-points. 477 478 This is the natural discretization of \autoref{eq:cts-var}. … … 658 659 \begin{figure}[h] 659 660 \begin{center} 660 \includegraphics[width= 0.60\textwidth]{Fig_GRIFF_bdry_triads}661 \includegraphics[width=\textwidth]{Fig_GRIFF_bdry_triads} 661 662 \caption{ 662 663 \protect\label{fig:bdry_triads} … … 685 686 As discussed in \autoref{subsec:LDF_slp_iso}, 686 687 iso-neutral slopes relative to geopotentials must be bounded everywhere, 687 both for consistency with the small-slope approximation and for numerical stability \citep{ Cox1987, Griffies_Bk04}.688 both for consistency with the small-slope approximation and for numerical stability \citep{cox_OM87, griffies_bk04}. 688 689 The bound chosen in \NEMO is applied to each component of the slope separately and 689 690 has a value of $1/100$ in the ocean interior. … … 732 733 \[ 733 734 % \label{eq:iso_tensor_ML} 734 D^{lT}=\nabla {\ rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad735 D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 735 736 \mbox{with}\quad \;\;\Re =\left( {{ 736 737 \begin{array}{*{20}c} … … 829 830 (\eg the green triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.} 830 831 % } 831 \includegraphics[width= 0.60\textwidth]{Fig_GRIFF_MLB_triads}832 \includegraphics[width=\textwidth]{Fig_GRIFF_MLB_triads} 832 833 \end{figure} 833 834 % >>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 847 848 \[ 848 849 % \label{eq:iso_tensor_ML2} 849 D^{lT}=\nabla {\ rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad850 D^{lT}=\nabla {\mathrm {\mathbf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad 850 851 \mbox{with}\quad \;\;\Re =\left( {{ 851 852 \begin{array}{*{20}c} … … 859 860 \footnote{ 860 861 To ensure good behaviour where horizontal density gradients are weak, 861 we in fact follow \citet{ Gerdes1991} and862 we in fact follow \citet{gerdes.koberle.ea_CD91} and 862 863 set $\rML^*=\mathrm{sgn}(\tilde{r}_i)\min(|\rMLt^2/\tilde{r}_i|,|\tilde{r}_i|)-\sigma_i$. 863 864 } … … 865 866 This approach is similar to multiplying the iso-neutral diffusion coefficient by 866 867 $\tilde{r}_{\mathrm{max}}^{-2}\tilde{r}_i^{-2}$ for steep slopes, 867 as suggested by \citet{ Gerdes1991} (see also \citet{Griffies_Bk04}).868 as suggested by \citet{gerdes.koberle.ea_CD91} (see also \citet{griffies_bk04}). 868 869 Again it is applied separately to each triad $_i^k\mathbb{R}_{i_p}^{k_p}$ 869 870 … … 925 926 926 927 However, when \np{ln\_traldf\_triad} is set true, 927 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{ Griffies_JPO98}.928 \NEMO instead implements eddy induced advection according to the so-called skew form \citep{griffies_JPO98}. 928 929 It is based on a transformation of the advective fluxes using the non-divergent nature of the eddy induced velocity. 929 930 For example in the (\textbf{i},\textbf{k}) plane, … … 1139 1140 it is equivalent to a horizontal eiv (eddy-induced velocity) that is uniform within the mixed layer 1140 1141 \autoref{eq:eiv_v}. 1141 This ensures that the eiv velocities do not restratify the mixed layer \citep{ Treguier1997,Danabasoglu_al_2008}.1142 This ensures that the eiv velocities do not restratify the mixed layer \citep{treguier.held.ea_JPO97,danabasoglu.ferrari.ea_JC08}. 1142 1143 Equivantly, in terms of the skew-flux formulation we use here, 1143 1144 the linear slope tapering within the mixed-layer gives a linearly varying vertical flux, … … 1153 1154 $uw$ (integer +1/2 $i$, integer $j$, integer +1/2 $k$) and $vw$ (integer $i$, integer +1/2 $j$, integer +1/2 $k$) 1154 1155 points (see Table \autoref{tab:cell}) respectively. 1155 We follow \citep{ Griffies_Bk04} and calculate the streamfunction at a given $uw$-point from1156 We follow \citep{griffies_bk04} and calculate the streamfunction at a given $uw$-point from 1156 1157 the surrounding four triads according to: 1157 1158 \[ -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_ASM.tex
r10442 r11263 37 37 it may be preferable to introduce the increment gradually into the ocean model in order to 38 38 minimize spurious adjustment processes. 39 This technique is referred to as Incremental Analysis Updates (IAU) \citep{ Bloom_al_MWR96}.39 This technique is referred to as Incremental Analysis Updates (IAU) \citep{bloom.takacs.ea_MWR96}. 40 40 IAU is a common technique used with 3D assimilation methods such as 3D-Var or OI. 41 41 IAU is used when \np{ln\_asmiau} is set to true. 42 42 43 With IAU, the model state trajectory ${\ bf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$)43 With IAU, the model state trajectory ${\mathbf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$) 44 44 is corrected by adding the analysis increments for temperature, salinity, horizontal velocity and SSH as 45 45 additional tendency terms to the prognostic equations: 46 46 \begin{align*} 47 47 % \label{eq:wa_traj_iau} 48 {\ bf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\bf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\bf x}^{a}48 {\mathbf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\mathbf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\mathbf x}^{a} 49 49 \end{align*} 50 where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\ bf x}^{a}$ defined such that50 where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\mathbf x}^{a}$ defined such that 51 51 $\sum_{i=1}^{N} F_{i}=1$. 52 ${\ bf x}^b$ denotes the model initial state and ${\bf x}^a$ is the model state after the increments are applied.52 ${\mathbf x}^b$ denotes the model initial state and ${\mathbf x}^a$ is the model state after the increments are applied. 53 53 To control the adjustment time of the model to the increment, 54 54 the increment can be applied over an arbitrary sub-window, $t_{m} \leq t_{i} \leq t_{n}$, … … 62 62 =\left\{ 63 63 \begin{array}{ll} 64 0 & {\ rm if} \; \; \; t_{i} < t_{m} \\65 1/M & {\ rm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\66 0 & {\ rm if} \; \; \; t_{i} > t_{n}64 0 & {\mathrm if} \; \; \; t_{i} < t_{m} \\ 65 1/M & {\mathrm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\ 66 0 & {\mathrm if} \; \; \; t_{i} > t_{n} 67 67 \end{array} 68 68 \right. … … 76 76 =\left\{ 77 77 \begin{array}{ll} 78 0 & {\ rm if} \; \; \; t_{i} < t_{m} \\79 \alpha \, i & {\ rm if} \; \; \; t_{m} \leq t_{i} \leq t_{M/2} \\80 \alpha \, (M - i +1) & {\ rm if} \; \; \; t_{M/2} < t_{i} \leq t_{n} \\81 0 & {\ rm if} \; \; \; t_{i} > t_{n}78 0 & {\mathrm if} \; \; \; t_{i} < t_{m} \\ 79 \alpha \, i & {\mathrm if} \; \; \; t_{m} \leq t_{i} \leq t_{M/2} \\ 80 \alpha \, (M - i +1) & {\mathrm if} \; \; \; t_{M/2} < t_{i} \leq t_{n} \\ 81 0 & {\mathrm if} \; \; \; t_{i} > t_{n} 82 82 \end{array} 83 83 \right. … … 118 118 This type of the initialisation reduces the vertical velocity magnitude and 119 119 alleviates the problem of the excessive unphysical vertical mixing in the first steps of the model integration 120 \citep{ Talagrand_JAS72, Dobricic_al_OS07}.120 \citep{talagrand_JAS72, dobricic.pinardi.ea_OS07}. 121 121 Diffusion coefficients are defined as $A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. 122 122 The divergence damping is activated by assigning to \np{nn\_divdmp} in the \textit{nam\_asminc} namelist -
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r10442 r11263 18 18 \label{sec:CFG_intro} 19 19 20 The purpose of this part of the manual is to introduce the \NEMO reference configurations.20 The purpose of this part of the manual is to introduce the NEMO reference configurations. 21 21 These configurations are offered as means to explore various numerical and physical options, 22 22 thus allowing the user to verify that the code is performing in a manner consistent with that we are running. … … 24 24 The reference configurations also provide a sense for some of the options available in the code, 25 25 though by no means are all options exercised in the reference configurations. 26 Configuration is defined manually through the \textit{namcfg} namelist variables. 26 27 27 28 %------------------------------------------namcfg---------------------------------------------------- … … 33 34 % 1D model configuration 34 35 % ================================================================ 35 \section{C1D: 1D Water column model (\protect\key{c1d}) } 36 \section[C1D: 1D Water column model (\texttt{\textbf{key\_c1d}})] 37 {C1D: 1D Water column model (\protect\key{c1d})} 36 38 \label{sec:CFG_c1d} 37 39 38 BE careful: to be re-written according to suppression of jpizoom and jpjzoom !!!! 39 40 The 1D model option simulates a stand alone water column within the 3D \NEMO system. 40 The 1D model option simulates a stand alone water column within the 3D NEMO system. 41 41 It can be applied to the ocean alone or to the ocean-ice system and can include passive tracers or a biogeochemical model. 42 42 It is set up by defining the position of the 1D water column in the grid 43 (see \textit{ CONFIG/SHARED/namelist\_ref}).43 (see \textit{cfgs/SHARED/namelist\_ref}). 44 44 The 1D model is a very useful tool 45 45 \textit{(a)} to learn about the physics and numerical treatment of vertical mixing processes; … … 50 50 \textit{(d)} to produce extra diagnostics, without the large memory requirement of the full 3D model. 51 51 52 The methodology is based on the use of the zoom functionality over the smallest possible domain: 53 a 3x3 domain centered on the grid point of interest, with some extra routines. 54 There is no need to define a new mesh, bathymetry, initial state or forcing, 55 since the 1D model will use those of the configuration it is a zoom of. 56 The chosen grid point is set in \textit{\ngn{namcfg}} namelist by 57 setting the \np{jpizoom} and \np{jpjzoom} parameters to the indices of the location of the chosen grid point. 52 The methodology is based on the configuration of the smallest possible domain: 53 a 3x3 domain with 75 vertical levels. 58 54 59 55 The 1D model has some specifies. First, all the horizontal derivatives are assumed to be zero, 60 56 and second, the two components of the velocity are moved on a $T$-point. 61 Therefore, defining \key{c1d} changes five mainthings in the code behaviour:57 Therefore, defining \key{c1d} changes some things in the code behaviour: 62 58 \begin{description} 63 59 \item[(1)] 64 the lateral boundary condition routine (\rou{lbc\_lnk}) set the value of the central column of65 the 3x3 domain is imposed over the whole domain;66 \item[(3)]67 a call to \rou{lbc\_lnk} is systematically done when reading input data (\ie in \mdl{iom});68 \item[(3)]69 60 a simplified \rou{stp} routine is used (\rou{stp\_c1d}, see \mdl{step\_c1d} module) in which 70 61 both lateral tendancy terms and lateral physics are not called; 71 \item[( 4)]62 \item[(2)] 72 63 the vertical velocity is zero 73 64 (so far, no attempt at introducing a Ekman pumping velocity has been made); 74 \item[( 5)]65 \item[(3)] 75 66 a simplified treatment of the Coriolis term is performed as $U$- and $V$-points are the same 76 67 (see \mdl{dyncor\_c1d}). 77 68 \end{description} 78 All the relevant \textit{\_c1d} modules can be found in the NEMOGCM/NEMO/OPA\_SRC/C1D directory of79 the \NEMO distribution.69 All the relevant \textit{\_c1d} modules can be found in the src/OCE/C1D directory of 70 the NEMO distribution. 80 71 81 72 % to be added: a test case on the yearlong Ocean Weather Station (OWS) Papa dataset of Martin (1985) … … 88 79 89 80 The ORCA family is a series of global ocean configurations that are run together with 90 the LIM sea-ice model (ORCA-LIM) and possibly with PISCES biogeochemical model (ORCA-LIM-PISCES), 91 using various resolutions. 92 An appropriate namelist is available in \path{CONFIG/ORCA2_LIM3_PISCES/EXP00/namelist_cfg} for ORCA2. 81 the SI3 model (ORCA-ICE) and possibly with PISCES biogeochemical model (ORCA-ICE-PISCES). 82 An appropriate namelist is available in \path{cfgs/ORCA2_ICE_PISCES/EXPREF/namelist_cfg} for ORCA2. 93 83 The domain of ORCA2 configuration is defined in \ifile{ORCA\_R2\_zps\_domcfg} file, 94 this file is available in tar file in the wiki of NEMO: \\ 95 https://forge.ipsl.jussieu.fr/nemo/wiki/Users/ReferenceConfigurations/ORCA2\_LIM3\_PISCES \\ 84 this file is available in tar file on the NEMO community zenodo platform: \\ 85 https://doi.org/10.5281/zenodo.2640723 86 96 87 In this namelist\_cfg the name of domain input file is set in \ngn{namcfg} block of namelist. 97 88 … … 99 90 \begin{figure}[!t] 100 91 \begin{center} 101 \includegraphics[width= 0.98\textwidth]{Fig_ORCA_NH_mesh}92 \includegraphics[width=\textwidth]{Fig_ORCA_NH_mesh} 102 93 \caption{ 103 94 \protect\label{fig:MISC_ORCA_msh} … … 106 97 The two "north pole" are the foci of a series of embedded ellipses (blue curves) which 107 98 are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes). 108 Then, following \citet{ Madec_Imbard_CD96}, the normal to the series of ellipses (red curves) is computed which99 Then, following \citet{madec.imbard_CD96}, the normal to the series of ellipses (red curves) is computed which 109 100 provides the j-lines of the mesh (pseudo longitudes). 110 101 } … … 119 110 \label{subsec:CFG_orca_grid} 120 111 121 The ORCA grid is a tripolar is based on the semi-analytical method of \citet{Madec_Imbard_CD96}.112 The ORCA grid is a tripolar grid based on the semi-analytical method of \citet{madec.imbard_CD96}. 122 113 It allows to construct a global orthogonal curvilinear ocean mesh which has no singularity point inside 123 114 the computational domain since two north mesh poles are introduced and placed on lands. … … 131 122 \begin{figure}[!tbp] 132 123 \begin{center} 133 \includegraphics[width= 1.0\textwidth]{Fig_ORCA_NH_msh05_e1_e2}134 \includegraphics[width= 0.80\textwidth]{Fig_ORCA_aniso}124 \includegraphics[width=\textwidth]{Fig_ORCA_NH_msh05_e1_e2} 125 \includegraphics[width=\textwidth]{Fig_ORCA_aniso} 135 126 \caption { 136 127 \protect\label{fig:MISC_ORCA_e1e2} … … 158 149 159 150 % ------------------------------------------------------------------------------------------------------------- 160 % ORCA- LIM(-PISCES) configurations151 % ORCA-ICE(-PISCES) configurations 161 152 % ------------------------------------------------------------------------------------------------------------- 162 153 \subsection{ORCA pre-defined resolution} … … 199 190 The ORCA\_R2 configuration has the following specificity: starting from a 2\deg~ORCA mesh, 200 191 local mesh refinements were applied to the Mediterranean, Red, Black and Caspian Seas, 201 so that the resolution is 1\deg \time 1\degthere.192 so that the resolution is 1\deg~ there. 202 193 A local transformation were also applied with in the Tropics in order to refine the meridional resolution up to 203 0.5\deg at the Equator.194 0.5\deg~ at the Equator. 204 195 205 196 The ORCA\_R1 configuration has only a local tropical transformation to refine the meridional resolution up to … … 211 202 For ORCA\_R1 and R025, setting the configuration key to 75 allows to use 75 vertical levels, otherwise 46 are used. 212 203 In the other ORCA configurations, 31 levels are used 213 (see \autoref{tab:orca_zgr} %\sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}).214 215 Only the ORCA\_R2 is provided with all its input files in the \NEMO distribution.216 It is very similar to that used as part of the climate model developed at IPSL for the 4th IPCC assessment of217 climate change (Marti et al., 2009).218 It is also the basis for the \NEMO contribution to the Coordinate Ocean-ice Reference Experiments (COREs)219 documented in \citet{Griffies_al_OM09}.204 (see \autoref{tab:orca_zgr}). %\sfcomment{HERE I need to put new table for ORCA2 values} and \autoref{fig:zgr}). 205 206 Only the ORCA\_R2 is provided with all its input files in the NEMO distribution. 207 %It is very similar to that used as part of the climate model developed at IPSL for the 4th IPCC assessment of 208 %climate change (Marti et al., 2009). 209 %It is also the basis for the \NEMO contribution to the Coordinate Ocean-ice Reference Experiments (COREs) 210 %documented in \citet{griffies.biastoch.ea_OM09}. 220 211 221 212 This version of ORCA\_R2 has 31 levels in the vertical, with the highest resolution (10m) in the upper 150m 222 213 (see \autoref{tab:orca_zgr} and \autoref{fig:zgr}). 223 214 The bottom topography and the coastlines are derived from the global atlas of Smith and Sandwell (1997). 224 The default forcing uses the boundary forcing from \citet{ Large_Yeager_Rep04} (see \autoref{subsec:SBC_blk_core}),215 The default forcing uses the boundary forcing from \citet{large.yeager_rpt04} (see \autoref{subsec:SBC_blk_core}), 225 216 which was developed for the purpose of running global coupled ocean-ice simulations without 226 217 an interactive atmosphere. 227 This \citet{ Large_Yeager_Rep04} dataset is available through218 This \citet{large.yeager_rpt04} dataset is available through 228 219 the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. 229 The "normal year" of \citet{ Large_Yeager_Rep04} has been chosen of the \NEMO distribution since release v3.3.230 231 ORCA\_R2 pre-defined configuration can also be run with an AGRIF zoom over the Agulhas current area232 (\key{agrif} defined) and, by setting the appropriate variables, see \path{CONFIG/SHARED/namelist_ref}. 220 The "normal year" of \citet{large.yeager_rpt04} has been chosen of the NEMO distribution since release v3.3. 221 222 ORCA\_R2 pre-defined configuration can also be run with multiply online nested zooms (\ie with AGRIF, \key{agrif} defined). This is available as the AGRIF\_DEMO configuration that can be found in the \path{cfgs/AGRIF_DEMO/} directory. 223 233 224 A regional Arctic or peri-Antarctic configuration is extracted from an ORCA\_R2 or R05 configurations using 234 225 sponge layers at open boundaries. … … 237 228 % GYRE family: double gyre basin 238 229 % ------------------------------------------------------------------------------------------------------------- 239 \section{GYRE family: double gyre basin 230 \section{GYRE family: double gyre basin} 240 231 \label{sec:CFG_gyre} 241 232 242 The GYRE configuration \citep{ Levy_al_OM10} has been built to233 The GYRE configuration \citep{levy.klein.ea_OM10} has been built to 243 234 simulate the seasonal cycle of a double-gyre box model. 244 It consists in an idealized domain similar to that used in the studies of \citet{ Drijfhout_JPO94} and245 \citet{ Hazeleger_Drijfhout_JPO98, Hazeleger_Drijfhout_JPO99, Hazeleger_Drijfhout_JGR00, Hazeleger_Drijfhout_JPO00},235 It consists in an idealized domain similar to that used in the studies of \citet{drijfhout_JPO94} and 236 \citet{hazeleger.drijfhout_JPO98, hazeleger.drijfhout_JPO99, hazeleger.drijfhout_JGR00, hazeleger.drijfhout_JPO00}, 246 237 over which an analytical seasonal forcing is applied. 247 238 This allows to investigate the spontaneous generation of a large number of interacting, transient mesoscale eddies 248 239 and their contribution to the large scale circulation. 249 240 241 The GYRE configuration run together with the PISCES biogeochemical model (GYRE-PISCES). 250 242 The domain geometry is a closed rectangular basin on the $\beta$-plane centred at $\sim$ 30\deg{N} and 251 243 rotated by 45\deg, 3180~km long, 2120~km wide and 4~km deep (\autoref{fig:MISC_strait_hand}). … … 253 245 The configuration is meant to represent an idealized North Atlantic or North Pacific basin. 254 246 The circulation is forced by analytical profiles of wind and buoyancy fluxes. 255 The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{ Levy_al_OM10}.247 The applied forcings vary seasonally in a sinusoidal manner between winter and summer extrema \citep{levy.klein.ea_OM10}. 256 248 The wind stress is zonal and its curl changes sign at 22\deg{N} and 36\deg{N}. 257 249 It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain and … … 266 258 The GYRE configuration is set like an analytical configuration. 267 259 Through \np{ln\_read\_cfg}\forcode{ = .false.} in \textit{namcfg} namelist defined in 268 the reference configuration \path{ CONFIG/GYRE/EXP00/namelist_cfg}260 the reference configuration \path{cfgs/GYRE_PISCES/EXPREF/namelist_cfg} 269 261 analytical definition of grid in GYRE is done in usrdef\_hrg, usrdef\_zgr routines. 270 262 Its horizontal resolution (and thus the size of the domain) is determined by 271 263 setting \np{nn\_GYRE} in \ngn{namusr\_def}: \\ 264 272 265 \np{jpiglo} $= 30 \times$ \np{nn\_GYRE} + 2 \\ 266 273 267 \np{jpjglo} $= 20 \times$ \np{nn\_GYRE} + 2 \\ 268 274 269 Obviously, the namelist parameters have to be adjusted to the chosen resolution, 275 see the Configurations pages on the NEMO web site ( Using NEMO\/Configurations).270 see the Configurations pages on the NEMO web site (NEMO Configurations). 276 271 In the vertical, GYRE uses the default 30 ocean levels (\jp{jpk}\forcode{ = 31}) (\autoref{fig:zgr}). 277 272 … … 281 276 even though the physical integrity of the solution can be compromised. 282 277 Benchmark is activate via \np{ln\_bench}\forcode{ = .true.} in \ngn{namusr\_def} in 283 namelist \path{ CONFIG/GYRE/EXP00/namelist_cfg}.278 namelist \path{cfgs/GYRE_PISCES/EXPREF/namelist_cfg}. 284 279 285 280 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 286 281 \begin{figure}[!t] 287 282 \begin{center} 288 \includegraphics[width= 1.0\textwidth]{Fig_GYRE}283 \includegraphics[width=\textwidth]{Fig_GYRE} 289 284 \caption{ 290 285 \protect\label{fig:GYRE} 291 286 Snapshot of relative vorticity at the surface of the model domain in GYRE R9, R27 and R54. 292 From \citet{ Levy_al_OM10}.287 From \citet{levy.klein.ea_OM10}. 293 288 } 294 289 \end{center} … … 304 299 The AMM, Atlantic Margins Model, is a regional model covering the Northwest European Shelf domain on 305 300 a regular lat-lon grid at approximately 12km horizontal resolution. 306 The appropriate \textit{\&namcfg} namelist is available in \textit{ CONFIG/AMM12/EXP00/namelist\_cfg}.301 The appropriate \textit{\&namcfg} namelist is available in \textit{cfgs/AMM12/EXPREF/namelist\_cfg}. 307 302 It is used to build the correct dimensions of the AMM domain. 308 303 309 304 This configuration tests several features of NEMO functionality specific to the shelf seas. 310 In particular, the AMM uses $S$-coordinates in the vertical rather than $z$-coordinates and 311 is forced with tidal lateral boundary conditions using a flather boundary condition from the BDY module. 312 The AMM configuration uses the GLS (\key{zdfgls}) turbulence scheme, 313 the VVL non-linear free surface(\key{vvl}) and time-splitting (\key{dynspg\_ts}). 305 In particular, the AMM uses $s$-coordinates in the vertical rather than $z$-coordinates and 306 is forced with tidal lateral boundary conditions using a Flather boundary condition from the BDY module. 307 Also specific to the AMM configuration is the use of the GLS turbulence scheme (\np{ln\_zdfgls} \forcode{= .true.}). 314 308 315 309 In addition to the tidal boundary condition the model may also take open boundary conditions from -
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r10509 r11263 25 25 the same run performed in one step. 26 26 It should be noted that this requires that the restart file contains two consecutive time steps for 27 all the prognostic variables, and that it is saved in the same binary format as the one used by the computer that 28 is to read it (in particular, 32 bits binary IEEE format must not be used for this file). 27 all the prognostic variables. 29 28 30 29 The output listing and file(s) are predefined but should be checked and eventually adapted to the user's needs. … … 38 37 the writing work is distributed over the processors in massively parallel computing. 39 38 A complete description of the use of this I/O server is presented in the next section. 40 41 By default, \key{iomput} is not defined,42 NEMO produces NetCDF with the old IOIPSL library which has been kept for compatibility and its easy installation.43 However, the IOIPSL library is quite inefficient on parallel machines and, since version 3.2,44 many diagnostic options have been added presuming the use of \key{iomput}.45 The usefulness of the default IOIPSL-based option is expected to reduce with each new release.46 If \key{iomput} is not defined, output files and content are defined in the \mdl{diawri} module and47 contain mean (or instantaneous if \key{diainstant} is defined) values over a regular period of48 nn\_write time-steps (namelist parameter).49 39 50 40 %\gmcomment{ % start of gmcomment … … 91 81 in a very easy way. 92 82 All details of iomput functionalities are listed in the following subsections. 93 Examples of the XML files that control the outputs can be found in: \path{NEMOGCM/CONFIG/ORCA2_LIM/EXP00/iodef.xml}, 94 \path{NEMOGCM/CONFIG/SHARED/field_def.xml} and \path{NEMOGCM/CONFIG/SHARED/domain_def.xml}. \\ 83 Examples of the XML files that control the outputs can be found in: 84 \path{cfgs/ORCA2_ICE_PISCES/EXPREF/iodef.xml}, 85 \path{cfgs/SHARED/field_def_nemo-oce.xml}, 86 \path{cfgs/SHARED/field_def_nemo-pisces.xml}, 87 \path{cfgs/SHARED/field_def_nemo-ice.xml} and \path{cfgs/SHARED/domain_def_nemo.xml}. \\ 95 88 96 89 The second functionality targets output performance when running in parallel (\key{mpp\_mpi}). … … 101 94 102 95 In version 3.6, the iom\_put interface depends on 103 an external code called \href{https://forge.ipsl.jussieu.fr/ioserver/browser/XIOS/branchs/xios- 1.0}{XIOS-1.0}96 an external code called \href{https://forge.ipsl.jussieu.fr/ioserver/browser/XIOS/branchs/xios-2.5}{XIOS-2.5} 104 97 (use of revision 618 or higher is required). 105 98 This new IO server can take advantage of the parallel I/O functionality of NetCDF4 to … … 168 161 \xmlline|<variable id="using_server" type="bool"></variable>| 169 162 170 The {\tt using\_server} setting determines whether or not the server will be used in \textit{attached mode}171 (as a library) [{\tt > false <}] or in \textit{detached mode}172 (as an external executable on N additional, dedicated cpus) [{\tt > true <}].163 The {\ttfamily using\_server} setting determines whether or not the server will be used in \textit{attached mode} 164 (as a library) [{\ttfamily> false <}] or in \textit{detached mode} 165 (as an external executable on N additional, dedicated cpus) [{\ttfamily > true <}]. 173 166 The \textit{attached mode} is simpler to use but much less efficient for massively parallel applications. 174 167 The type of each file can be either ''multiple\_file'' or ''one\_file''. … … 207 200 \subsubsection{Control of XIOS: the context in iodef.xml} 208 201 209 As well as the {\tt using\_server} flag, other controls on the use of XIOS are set in the XIOS context in iodef.xml.202 As well as the {\ttfamily using\_server} flag, other controls on the use of XIOS are set in the XIOS context in iodef.xml. 210 203 See the XML basics section below for more details on XML syntax and rules. 211 204 … … 257 250 See the installation guide on the \href{http://forge.ipsl.jussieu.fr/ioserver/wiki}{XIOS} wiki for help and guidance. 258 251 NEMO will need to link to the compiled XIOS library. 259 The \href{https://forge.ipsl.jussieu.fr/nemo/ wiki/Users/ModelInterfacing/InputsOutputs#Inputs-OutputsusingXIOS}260 { XIOS with NEMO} guide provides an example illustration of how this can be achieved.252 The \href{https://forge.ipsl.jussieu.fr/nemo/chrome/site/doc/NEMO/guide/html/install.html#extract-and-install-xios} 253 {Extract and install XIOS} guide provides an example illustration of how this can be achieved. 261 254 262 255 \subsubsection{Add your own outputs} … … 269 262 \begin{enumerate} 270 263 \item[1.] 271 in NEMO code, add a \forcode{CALL iom \_put( 'identifier', array )} where you want to output a 2D or 3D array.264 in NEMO code, add a \forcode{CALL iom_put( 'identifier', array )} where you want to output a 2D or 3D array. 272 265 \item[2.] 273 266 If necessary, add \forcode{USE iom ! I/O manager library} to the list of used modules in … … 442 435 \xmlline|<context src="./nemo_def.xml" />| 443 436 444 \noindent In NEMO, by default, the field and domain definition is done in 2 separate files: 445 \path{NEMOGCM/CONFIG/SHARED/field_def.xml} and \path{NEMOGCM/CONFIG/SHARED/domain_def.xml} that 437 \noindent In NEMO, by default, the field definition is done in 3 separate files ( 438 \path{cfgs/SHARED/field_def_nemo-oce.xml}, 439 \path{cfgs/SHARED/field_def_nemo-pisces.xml} and 440 \path{cfgs/SHARED/field_def_nemo-ice.xml} ) and the domain definition is done in another file ( \path{cfgs/SHARED/domain_def_nemo.xml} ) 441 that 446 442 are included in the main iodef.xml file through the following commands: 447 443 \begin{xmllines} 448 <field_definition src="./field_def.xml" /> 449 <domain_definition src="./domain_def.xml" /> 444 <context id="nemo" src="./context_nemo.xml"/> 450 445 \end{xmllines} 451 446 … … 508 503 509 504 Secondly, the group can be used to replace a list of elements. 510 Several examples of groups of fields are proposed at the end of the file \path{CONFIG/SHARED/field_def.xml}. 505 Several examples of groups of fields are proposed at the end of the XML field files ( 506 \path{cfgs/SHARED/field_def_nemo-oce.xml}, 507 \path{cfgs/SHARED/field_def_nemo-pisces.xml} and 508 \path{cfgs/SHARED/field_def_nemo-ice.xml} ) . 511 509 For example, a short list of the usual variables related to the U grid: 512 510 … … 514 512 <field_group id="groupU" > 515 513 <field field_ref="uoce" /> 516 <field field_ref="s uoce" />514 <field field_ref="ssu" /> 517 515 <field field_ref="utau" /> 518 516 </field_group> … … 538 536 the tag family domain. 539 537 It must therefore be done in the domain part of the XML file. 540 For example, in \path{ CONFIG/SHARED/domain_def.xml}, we provide the following example of a definition of538 For example, in \path{cfgs/SHARED/domain_def.xml}, we provide the following example of a definition of 541 539 a 5 by 5 box with the bottom left corner at point (10,10). 542 540 543 541 \begin{xmllines} 544 <domain _group id="grid_T">545 < domain id="myzoom" zoom_ibegin="10" zoom_jbegin="10" zoom_ni="5" zoom_nj="5" />542 <domain id="myzoomT" domain_ref="grid_T"> 543 <zoom_domain ibegin="10" jbegin="10" ni="5" nj="5" /> 546 544 \end{xmllines} 547 545 … … 551 549 \begin{xmllines} 552 550 <file id="myfile_vzoom" output_freq="1d" > 553 <field field_ref="toce" domain_ref="myzoom "/>551 <field field_ref="toce" domain_ref="myzoomT"/> 554 552 </file> 555 553 \end{xmllines} … … 576 574 \subsubsection{Define vertical zooms} 577 575 578 Vertical zooms are defined through the attributs zoom\_begin and zoom\_ endof the tag family axis.576 Vertical zooms are defined through the attributs zoom\_begin and zoom\_n of the tag family axis. 579 577 It must therefore be done in the axis part of the XML file. 580 For example, in \path{NEMOGCM/CONFIG/ORCA2_LIM/iodef_demo.xml}, we provide the following example: 581 582 \begin{xmllines} 583 <axis_group id="deptht" long_name="Vertical T levels" unit="m" positive="down" > 584 <axis id="deptht" /> 585 <axis id="deptht_myzoom" zoom_begin="1" zoom_end="10" /> 578 For example, in \path{cfgs/ORCA2_ICE_PISCES/EXPREF/iodef_demo.xml}, we provide the following example: 579 580 \begin{xmllines} 581 <axis_definition> 582 <axis id="deptht" long_name="Vertical T levels" unit="m" positive="down" /> 583 <axis id="deptht_zoom" azix_ref="deptht" > 584 <zoom_axis zoom_begin="1" zoom_n="10" /> 585 </axis> 586 586 \end{xmllines} 587 587 … … 765 765 \end{xmllines} 766 766 767 Note that, then the code is crashing, writting real4 variables forces a numerical conve ction from767 Note that, then the code is crashing, writting real4 variables forces a numerical conversion from 768 768 real8 to real4 which will create an internal error in NetCDF and will avoid the creation of the output files. 769 769 Forcing double precision outputs with prec="8" (for example in the field\_definition) will avoid this problem. … … 938 938 \hline 939 939 \end{tabularx} 940 \caption{Field tags ("\tt {field\_*}")}940 \caption{Field tags ("\ttfamily{field\_*}")} 941 941 \end{table} 942 942 … … 974 974 \hline 975 975 \end{tabularx} 976 \caption{File tags ("\tt {file\_*}")}976 \caption{File tags ("\ttfamily{file\_*}")} 977 977 \end{table} 978 978 … … 1007 1007 \hline 1008 1008 \end{tabularx} 1009 \caption{Axis tags ("\tt {axis\_*}")}1009 \caption{Axis tags ("\ttfamily{axis\_*}")} 1010 1010 \end{table} 1011 1011 … … 1040 1040 \hline 1041 1041 \end{tabularx} 1042 \caption{Domain tags ("\tt {domain\_*)}"}1042 \caption{Domain tags ("\ttfamily{domain\_*)}"} 1043 1043 \end{table} 1044 1044 … … 1073 1073 \hline 1074 1074 \end{tabularx} 1075 \caption{Grid tags ("\tt {grid\_*}")}1075 \caption{Grid tags ("\ttfamily{grid\_*}")} 1076 1076 \end{table} 1077 1077 … … 1114 1114 \hline 1115 1115 \end{tabularx} 1116 \caption{Reference attributes ("\tt {*\_ref}")}1116 \caption{Reference attributes ("\ttfamily{*\_ref}")} 1117 1117 \end{table} 1118 1118 … … 1150 1150 \hline 1151 1151 \end{tabularx} 1152 \caption{Domain attributes ("\tt {zoom\_*}")}1152 \caption{Domain attributes ("\ttfamily{zoom\_*}")} 1153 1153 \end{table} 1154 1154 … … 1318 1318 \subsection{CF metadata standard compliance} 1319 1319 1320 Output from the XIOS -1.0IO server is compliant with1320 Output from the XIOS IO server is compliant with 1321 1321 \href{http://cfconventions.org/Data/cf-conventions/cf-conventions-1.5/build/cf-conventions.html}{version 1.5} of 1322 1322 the CF metadata standard. … … 1332 1332 % NetCDF4 support 1333 1333 % ================================================================ 1334 \section{NetCDF4 support (\protect\key{netcdf4})} 1334 \section[NetCDF4 support (\texttt{\textbf{key\_netcdf4}})] 1335 {NetCDF4 support (\protect\key{netcdf4})} 1335 1336 \label{sec:DIA_nc4} 1336 1337 … … 1340 1341 Chunking and compression can lead to significant reductions in file sizes for a small runtime overhead. 1341 1342 For a fuller discussion on chunking and other performance issues the reader is referred to 1342 the NetCDF4 documentation found \href{http ://www.unidata.ucar.edu/software/netcdf/docs/netcdf.html#Chunking}{here}.1343 the NetCDF4 documentation found \href{https://www.unidata.ucar.edu/software/netcdf/docs/netcdf_perf_chunking.html}{here}. 1343 1344 1344 1345 The new features are only available when the code has been linked with a NetCDF4 library … … 1389 1390 \end{forlines} 1390 1391 1391 \noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\tt 46x38x1} respectively in1392 the mono-processor case (\ie global domain of {\small\tt 182x149x31}).1392 \noindent for a standard ORCA2\_LIM configuration gives chunksizes of {\small\ttfamily 46x38x1} respectively in 1393 the mono-processor case (\ie global domain of {\small\ttfamily 182x149x31}). 1393 1394 An illustration of the potential space savings that NetCDF4 chunking and compression provides is given in 1394 1395 table \autoref{tab:NC4} which compares the results of two short runs of the ORCA2\_LIM reference configuration with … … 1450 1451 % Tracer/Dynamics Trends 1451 1452 % ------------------------------------------------------------------------------------------------------------- 1452 \section{Tracer/Dynamics trends (\protect\ngn{namtrd})} 1453 \section[Tracer/Dynamics trends (\texttt{namtrd})] 1454 {Tracer/Dynamics trends (\protect\ngn{namtrd})} 1453 1455 \label{sec:DIA_trd} 1454 1456 … … 1462 1464 (\ie at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). 1463 1465 This capability is controlled by options offered in \ngn{namtrd} namelist. 1464 Note that the output are done with xIOS, and therefore the \key{IOM} is required.1466 Note that the output are done with XIOS, and therefore the \key{iomput} is required. 1465 1467 1466 1468 What is done depends on the \ngn{namtrd} logical set to \forcode{.true.}: … … 1488 1490 1489 1491 Note that the mixed layer tendency diagnostic can also be used on biogeochemical models via 1490 the \key{trdtrc} and \key{trdm ld\_trc} CPP keys.1492 the \key{trdtrc} and \key{trdmxl\_trc} CPP keys. 1491 1493 1492 1494 \textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested. … … 1497 1499 % On-line Floats trajectories 1498 1500 % ------------------------------------------------------------------------------------------------------------- 1499 \section{FLO: On-Line Floats trajectories (\protect\key{floats})} 1501 \section[FLO: On-Line Floats trajectories (\texttt{\textbf{key\_floats}})] 1502 {FLO: On-Line Floats trajectories (\protect\key{floats})} 1500 1503 \label{sec:FLO} 1501 1504 %--------------------------------------------namflo------------------------------------------------------- … … 1506 1509 The on-line computation of floats advected either by the three dimensional velocity field or constraint to 1507 1510 remain at a given depth ($w = 0$ in the computation) have been introduced in the system during the CLIPPER project. 1508 Options are defined by \ngn{namflo} namelis variables.1509 The algorithm used is based either on the work of \cite{ Blanke_Raynaud_JPO97} (default option),1511 Options are defined by \ngn{namflo} namelist variables. 1512 The algorithm used is based either on the work of \cite{blanke.raynaud_JPO97} (default option), 1510 1513 or on a $4^th$ Runge-Hutta algorithm (\np{ln\_flork4}\forcode{ = .true.}). 1511 Note that the \cite{ Blanke_Raynaud_JPO97} algorithm have the advantage of providing trajectories which1514 Note that the \cite{blanke.raynaud_JPO97} algorithm have the advantage of providing trajectories which 1512 1515 are consistent with the numeric of the code, so that the trajectories never intercept the bathymetry. 1513 1516 … … 1519 1522 In case of Ariane convention, input filename is \np{init\_float\_ariane}. 1520 1523 Its format is: \\ 1521 {\scriptsize \texttt{I J K nisobfl itrash itrash}}1524 {\scriptsize \texttt{I J K nisobfl itrash}} 1522 1525 1523 1526 \noindent with: … … 1577 1580 In that case, output filename is trajec\_float. 1578 1581 1579 Another possiblity of writing format is Netcdf (\np{ln\_flo\_ascii}\forcode{ = .false.}). 1580 There are 2 possibilities: 1581 1582 - if (\key{iomput}) is used, outputs are selected in iodef.xml. 1582 Another possiblity of writing format is Netcdf (\np{ln\_flo\_ascii}\forcode{ = .false.}) with 1583 \key{iomput} and outputs selected in iodef.xml. 1583 1584 Here it is an example of specification to put in files description section: 1584 1585 … … 1597 1598 \end{xmllines} 1598 1599 1599 - if (\key{iomput}) is not used, a file called \ifile{trajec\_float} will be created by IOIPSL library.1600 1601 See also \href{http://stockage.univ-brest.fr/~grima/Ariane/}{here} the web site describing the off-line use of1602 this marvellous diagnostic tool.1603 1600 1604 1601 % ------------------------------------------------------------------------------------------------------------- 1605 1602 % Harmonic analysis of tidal constituents 1606 1603 % ------------------------------------------------------------------------------------------------------------- 1607 \section{Harmonic analysis of tidal constituents (\protect\key{diaharm}) } 1604 \section[Harmonic analysis of tidal constituents (\texttt{\textbf{key\_diaharm}})] 1605 {Harmonic analysis of tidal constituents (\protect\key{diaharm})} 1608 1606 \label{sec:DIA_diag_harm} 1609 1607 1610 %------------------------------------------nam dia_harm----------------------------------------------------1608 %------------------------------------------nam_diaharm---------------------------------------------------- 1611 1609 % 1612 1610 \nlst{nam_diaharm} … … 1616 1614 This on-line Harmonic analysis is actived with \key{diaharm}. 1617 1615 1618 Some parameters are available in namelist \ngn{nam dia\_harm}:1616 Some parameters are available in namelist \ngn{nam\_diaharm}: 1619 1617 1620 1618 - \np{nit000\_han} is the first time step used for harmonic analysis … … 1652 1650 % Sections transports 1653 1651 % ------------------------------------------------------------------------------------------------------------- 1654 \section{Transports across sections (\protect\key{diadct}) } 1652 \section[Transports across sections (\texttt{\textbf{key\_diadct}})] 1653 {Transports across sections (\protect\key{diadct})} 1655 1654 \label{sec:DIA_diag_dct} 1656 1655 … … 1664 1663 1665 1664 Each section is defined by the coordinates of its 2 extremities. 1666 The pathways between them are contructed using tools which can be found in \texttt{ NEMOGCM/TOOLS/SECTIONS\_DIADCT}1667 and are written in a binary file \texttt{section\_ijglobal.diadct \_ORCA2\_LIM} which is later read in by1665 The pathways between them are contructed using tools which can be found in \texttt{tools/SECTIONS\_DIADCT} 1666 and are written in a binary file \texttt{section\_ijglobal.diadct} which is later read in by 1668 1667 NEMO to compute on-line transports. 1669 1668 … … 1684 1683 \subsubsection{Creating a binary file containing the pathway of each section} 1685 1684 1686 In \texttt{ NEMOGCM/TOOLS/SECTIONS\_DIADCT/run},1685 In \texttt{tools/SECTIONS\_DIADCT/run}, 1687 1686 the file \textit{ {list\_sections.ascii\_global}} contains a list of all the sections that are to be computed 1688 1687 (this list of sections is based on MERSEA project metrics). … … 1733 1732 1734 1733 The script \texttt{job.ksh} computes the pathway for each section and creates a binary file 1735 \texttt{section\_ijglobal.diadct \_ORCA2\_LIM} which is read by NEMO. \\1734 \texttt{section\_ijglobal.diadct} which is read by NEMO. \\ 1736 1735 1737 1736 It is possible to use this tools for new configuations: \texttt{job.ksh} has to be updated with … … 1809 1808 The steric effect is therefore not explicitely represented. 1810 1809 This approximation does not represent a serious error with respect to the flow field calculated by the model 1811 \citep{ Greatbatch_JGR94}, but extra attention is required when investigating sea level,1810 \citep{greatbatch_JGR94}, but extra attention is required when investigating sea level, 1812 1811 as steric changes are an important contribution to local changes in sea level on seasonal and climatic time scales. 1813 1812 This is especially true for investigation into sea level rise due to global warming. 1814 1813 1815 1814 Fortunately, the steric contribution to the sea level consists of a spatially uniform component that 1816 can be diagnosed by considering the mass budget of the world ocean \citep{ Greatbatch_JGR94}.1815 can be diagnosed by considering the mass budget of the world ocean \citep{greatbatch_JGR94}. 1817 1816 In order to better understand how global mean sea level evolves and thus how the steric sea level can be diagnosed, 1818 1817 we compare, in the following, the non-Boussinesq and Boussinesq cases. … … 1888 1887 the ocean surface, not by changes in mean mass of the ocean: the steric effect is missing in a Boussinesq fluid. 1889 1888 1890 Nevertheless, following \citep{ Greatbatch_JGR94}, the steric effect on the volume can be diagnosed by1889 Nevertheless, following \citep{greatbatch_JGR94}, the steric effect on the volume can be diagnosed by 1891 1890 considering the mass budget of the ocean. 1892 1891 The apparent changes in $\mathcal{M}$, mass of the ocean, which are not induced by surface mass flux 1893 1892 must be compensated by a spatially uniform change in the mean sea level due to expansion/contraction of the ocean 1894 \citep{ Greatbatch_JGR94}.1893 \citep{greatbatch_JGR94}. 1895 1894 In others words, the Boussinesq mass, $\mathcal{M}_o$, can be related to $\mathcal{M}$, 1896 1895 the total mass of the ocean seen by the Boussinesq model, via the steric contribution to the sea level, … … 1924 1923 This value is a sensible choice for the reference density used in a Boussinesq ocean climate model since, 1925 1924 with the exception of only a small percentage of the ocean, density in the World Ocean varies by no more than 1926 2$\%$ from this value (\cite{ Gill1982}, page 47).1925 2$\%$ from this value (\cite{gill_bk82}, page 47). 1927 1926 1928 1927 Second, we have assumed here that the total ocean surface, $\mathcal{A}$, … … 1954 1953 so that there are no associated ocean currents. 1955 1954 Hence, the dynamically relevant sea level is the effective sea level, 1956 \ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{ Campin_al_OM08}.1955 \ie the sea level as if sea ice (and snow) were converted to liquid seawater \citep{campin.marshall.ea_OM08}. 1957 1956 However, in the current version of \NEMO the sea-ice is levitating above the ocean without mass exchanges between 1958 1957 ice and ocean. … … 1976 1975 % Other Diagnostics 1977 1976 % ------------------------------------------------------------------------------------------------------------- 1978 \section{Other diagnostics (\protect\key{diahth}, \protect\key{diaar5})} 1977 \section[Other diagnostics (\texttt{\textbf{key\_diahth}}, \texttt{\textbf{key\_diaar5}})] 1978 {Other diagnostics (\protect\key{diahth}, \protect\key{diaar5})} 1979 1979 \label{sec:DIA_diag_others} 1980 1980 … … 1982 1982 The available ready-to-add diagnostics modules can be found in directory DIA. 1983 1983 1984 \subsection{Depth of various quantities (\protect\mdl{diahth})} 1984 \subsection[Depth of various quantities (\textit{diahth.F90})] 1985 {Depth of various quantities (\protect\mdl{diahth})} 1985 1986 1986 1987 Among the available diagnostics the following ones are obtained when defining the \key{diahth} CPP key: 1987 1988 1988 - the mixed layer depth (based on a density criterion \citep{de _Boyer_Montegut_al_JGR04}) (\mdl{diahth})1989 - the mixed layer depth (based on a density criterion \citep{de-boyer-montegut.madec.ea_JGR04}) (\mdl{diahth}) 1989 1990 1990 1991 - the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) … … 1998 1999 % ----------------------------------------------------------- 1999 2000 2000 \subsection{Poleward heat and salt transports (\protect\mdl{diaptr})} 2001 \subsection[Poleward heat and salt transports (\textit{diaptr.F90})] 2002 {Poleward heat and salt transports (\protect\mdl{diaptr})} 2001 2003 2002 2004 %------------------------------------------namptr----------------------------------------- … … 2016 2018 \begin{figure}[!t] 2017 2019 \begin{center} 2018 \includegraphics[width= 1.0\textwidth]{Fig_mask_subasins}2020 \includegraphics[width=\textwidth]{Fig_mask_subasins} 2019 2021 \caption{ 2020 2022 \protect\label{fig:mask_subasins} … … 2032 2034 % CMIP specific diagnostics 2033 2035 % ----------------------------------------------------------- 2034 \subsection{CMIP specific diagnostics (\protect\mdl{diaar5})} 2036 \subsection[CMIP specific diagnostics (\textit{diaar5.F90})] 2037 {CMIP specific diagnostics (\protect\mdl{diaar5})} 2035 2038 2036 2039 A series of diagnostics has been added in the \mdl{diaar5}. -
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r10442 r11263 33 33 (\ie from the temperature of the top few model levels) or from some other source. 34 34 It must be noted that both the cool skin and warm layer models produce estimates of the change in temperature 35 ($\Delta T_{\ rm{cs}}$ and $\Delta T_{\rm{wl}}$) and35 ($\Delta T_{\mathrm{cs}}$ and $\Delta T_{\mathrm{wl}}$) and 36 36 both must be added to a foundation SST to obtain the true skin temperature. 37 37 … … 60 60 %=============================================================== 61 61 62 The warm layer is calculated using the model of \citet{ Takaya_al_JGR10} (TAKAYA10 model hereafter).62 The warm layer is calculated using the model of \citet{takaya.bidlot.ea_JGR10} (TAKAYA10 model hereafter). 63 63 This is a simple flux based model that is defined by the equations 64 64 \begin{align} 65 \frac{\partial{\Delta T_{\ rm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p65 \frac{\partial{\Delta T_{\mathrm{wl}}}}{\partial{t}}&=&\frac{Q(\nu+1)}{D_T\rho_w c_p 66 66 \nu}-\frac{(\nu+1)ku^*_{w}f(L_a)\Delta T}{D_T\Phi\!\left(\frac{D_T}{L}\right)} \mbox{,} 67 67 \label{eq:ecmwf1} \\ 68 68 L&=&\frac{\rho_w c_p u^{*^3}_{w}}{\kappa g \alpha_w Q }\mbox{,}\label{eq:ecmwf2} 69 69 \end{align} 70 where $\Delta T_{\ rm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal.70 where $\Delta T_{\mathrm{wl}}$ is the temperature difference between the top of the warm layer and the depth $D_T=3$\,m at which there is assumed to be no diurnal signal. 71 71 In equation (\autoref{eq:ecmwf1}) $\alpha_w=2\times10^{-4}$ is the thermal expansion coefficient of water, 72 72 $\kappa=0.4$ is von K\'{a}rm\'{a}n's constant, $c_p$ is the heat capacity at constant pressure of sea water, 73 73 $\rho_w$ is the water density, and $L$ is the Monin-Obukhov length. 74 74 The tunable variable $\nu$ is a shape parameter that defines the expected subskin temperature profile via 75 $T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\ rm{wl}}$,75 $T(z) = T(0) - \left( \frac{z}{D_T} \right)^\nu \Delta T_{\mathrm{wl}}$, 76 76 where $T$ is the absolute temperature and $z\le D_T$ is the depth below the top of the warm layer. 77 77 The influence of wind on TAKAYA10 comes through the magnitude of the friction velocity of the water $u^*_{w}$, … … 82 82 the diurnal layer, \ie 83 83 \[ 84 Q = Q_{\ rm{sol}} + Q_{\rm{lw}} + Q_{\rm{h}}\mbox{,}84 Q = Q_{\mathrm{sol}} + Q_{\mathrm{lw}} + Q_{\mathrm{h}}\mbox{,} 85 85 % \label{eq:e_flux_eqn} 86 86 \] 87 where $Q_{\ rm{h}}$ is the sensible and latent heat flux, $Q_{\rm{lw}}$ is the long wave flux,88 and $Q_{\ rm{sol}}$ is the solar flux absorbed within the diurnal warm layer.89 For $Q_{\ rm{sol}}$ the 9 term representation of \citet{Gentemann_al_JGR09} is used.87 where $Q_{\mathrm{h}}$ is the sensible and latent heat flux, $Q_{\mathrm{lw}}$ is the long wave flux, 88 and $Q_{\mathrm{sol}}$ is the solar flux absorbed within the diurnal warm layer. 89 For $Q_{\mathrm{sol}}$ the 9 term representation of \citet{gentemann.minnett.ea_JGR09} is used. 90 90 In equation \autoref{eq:ecmwf1} the function $f(L_a)=\max(1,L_a^{\frac{2}{3}})$, 91 91 where $L_a=0.3$\footnote{ … … 118 118 %=============================================================== 119 119 120 The cool skin is modelled using the framework of \citet{ Saunders_JAS82} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$.121 As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\ rm{cs}}$ becomes120 The cool skin is modelled using the framework of \citet{saunders_JAS67} who used a formulation of the near surface temperature difference based upon the heat flux and the friction velocity $u^*_{w}$. 121 As the cool skin is so thin (~1\,mm) we ignore the solar flux component to the heat flux and the Saunders equation for the cool skin temperature difference $\Delta T_{\mathrm{cs}}$ becomes 122 122 \[ 123 123 % \label{eq:sunders_eqn} 124 \Delta T_{\ rm{cs}}=\frac{Q_{\rm{ns}}\delta}{k_t} \mbox{,}124 \Delta T_{\mathrm{cs}}=\frac{Q_{\mathrm{ns}}\delta}{k_t} \mbox{,} 125 125 \] 126 where $Q_{\ rm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and126 where $Q_{\mathrm{ns}}$ is the, usually negative, non-solar heat flux into the ocean and 127 127 $k_t$ is the thermal conductivity of sea water. 128 128 $\delta$ is the thickness of the skin layer and is given by … … 132 132 \end{equation} 133 133 where $\mu$ is the kinematic viscosity of sea water and $\lambda$ is a constant of proportionality which 134 \citet{ Saunders_JAS82} suggested varied between 5 and 10.134 \citet{saunders_JAS67} suggested varied between 5 and 10. 135 135 136 The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{ Artale_al_JGR02},137 which is shown in \citet{ Tu_Tsuang_GRL05} to outperform a number of other parametrisations at136 The value of $\lambda$ used in equation (\autoref{eq:sunders_thick_eqn}) is that of \citet{artale.iudicone.ea_JGR02}, 137 which is shown in \citet{tu.tsuang_GRL05} to outperform a number of other parametrisations at 138 138 both low and high wind speeds. 139 139 Specifically, -
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r10502 r11263 40 40 \begin{figure}[!tb] 41 41 \begin{center} 42 \includegraphics[ ]{Fig_cell}42 \includegraphics[width=\textwidth]{Fig_cell} 43 43 \caption{ 44 44 \protect\label{fig:cell} … … 60 60 the centre of each face of the cells (\autoref{fig:cell}). 61 61 This is the generalisation to three dimensions of the well-known ``C'' grid in Arakawa's classification 62 \citep{ Mesinger_Arakawa_Bk76}.62 \citep{mesinger.arakawa_bk76}. 63 63 The relative and planetary vorticity, $\zeta$ and $f$, are defined in the centre of each vertical edge and 64 64 the barotropic stream function $\psi$ is defined at horizontal points overlying the $\zeta$ and $f$-points. … … 218 218 \begin{figure}[!tb] 219 219 \begin{center} 220 \includegraphics[ ]{Fig_index_hor}220 \includegraphics[width=\textwidth]{Fig_index_hor} 221 221 \caption{ 222 222 \protect\label{fig:index_hor} … … 272 272 \begin{figure}[!pt] 273 273 \begin{center} 274 \includegraphics[ ]{Fig_index_vert}274 \includegraphics[width=\textwidth]{Fig_index_vert} 275 275 \caption{ 276 276 \protect\label{fig:index_vert} … … 345 345 % Domain: Horizontal Grid (mesh) 346 346 % ================================================================ 347 \section{Horizontal grid mesh (\protect\mdl{domhgr})} 347 \section[Horizontal grid mesh (\textit{domhgr.F90})] 348 {Horizontal grid mesh (\protect\mdl{domhgr})} 348 349 \label{sec:DOM_hgr} 349 350 … … 397 398 (\ie as the analytical first derivative of the transformation that 398 399 gives $(\lambda,\varphi,z)$ as a function of $(i,j,k)$) 399 is specific to the \NEMO model \citep{ Marti_al_JGR92}.400 is specific to the \NEMO model \citep{marti.madec.ea_JGR92}. 400 401 As an example, $e_{1t}$ is defined locally at a $t$-point, 401 402 whereas many other models on a C grid choose to define such a scale factor as … … 405 406 since they are first introduced in the continuous equations; 406 407 secondly, analytical transformations encourage good practice by the definition of smoothly varying grids 407 (rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{ Treguier1996}.408 (rather than allowing the user to set arbitrary jumps in thickness between adjacent layers) \citep{treguier.dukowicz.ea_JGR96}. 408 409 An example of the effect of such a choice is shown in \autoref{fig:zgr_e3}. 409 410 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 410 411 \begin{figure}[!t] 411 412 \begin{center} 412 \includegraphics[ ]{Fig_zgr_e3}413 \includegraphics[width=\textwidth]{Fig_zgr_e3} 413 414 \caption{ 414 415 \protect\label{fig:zgr_e3} … … 451 452 % Domain: Vertical Grid (domzgr) 452 453 % ================================================================ 453 \section{Vertical grid (\protect\mdl{domzgr})} 454 \section[Vertical grid (\textit{domzgr.F90})] 455 {Vertical grid (\protect\mdl{domzgr})} 454 456 \label{sec:DOM_zgr} 455 457 %-----------------------------------------nam_zgr & namdom------------------------------------------- … … 471 473 \begin{figure}[!tb] 472 474 \begin{center} 473 \includegraphics[ ]{Fig_z_zps_s_sps}475 \includegraphics[width=\textwidth]{Fig_z_zps_s_sps} 474 476 \caption{ 475 477 \protect\label{fig:z_zps_s_sps} … … 480 482 (d) hybrid $s-z$ coordinate, 481 483 (e) hybrid $s-z$ coordinate with partial step, and 482 (f) same as (e) but in the non-linear free surface (\protect\np{ln\_linssh} ~\forcode{= .false.}).484 (f) same as (e) but in the non-linear free surface (\protect\np{ln\_linssh}\forcode{ = .false.}). 483 485 Note that the non-linear free surface can be used with any of the 5 coordinates (a) to (e). 484 486 } … … 491 493 It is not intended as an option which can be enabled or disabled in the middle of an experiment. 492 494 Three main choices are offered (\autoref{fig:z_zps_s_sps}): 493 $z$-coordinate with full step bathymetry (\np{ln\_zco} ~\forcode{= .true.}),494 $z$-coordinate with partial step bathymetry (\np{ln\_zps} ~\forcode{= .true.}),495 or generalized, $s$-coordinate (\np{ln\_sco} ~\forcode{= .true.}).495 $z$-coordinate with full step bathymetry (\np{ln\_zco}\forcode{ = .true.}), 496 $z$-coordinate with partial step bathymetry (\np{ln\_zps}\forcode{ = .true.}), 497 or generalized, $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}). 496 498 Hybridation of the three main coordinates are available: 497 499 $s-z$ or $s-zps$ coordinate (\autoref{fig:z_zps_s_sps} and \autoref{fig:z_zps_s_sps}). 498 500 By default a non-linear free surface is used: the coordinate follow the time-variation of the free surface so that 499 501 the transformation is time dependent: $z(i,j,k,t)$ (\autoref{fig:z_zps_s_sps}). 500 When a linear free surface is assumed (\np{ln\_linssh} ~\forcode{= .true.}),502 When a linear free surface is assumed (\np{ln\_linssh}\forcode{ = .true.}), 501 503 the vertical coordinate are fixed in time, but the seawater can move up and down across the $z_0$ surface 502 504 (in other words, the top of the ocean in not a rigid-lid). … … 513 515 N.B. in full step $z$-coordinate, a \ifile{bathy\_level} file can replace the \ifile{bathy\_meter} file, 514 516 so that the computation of the number of wet ocean point in each water column is by-passed}. 515 If \np{ln\_isfcav} ~\forcode{= .true.}, an extra file input file (\ifile{isf\_draft\_meter}) describing517 If \np{ln\_isfcav}\forcode{ = .true.}, an extra file input file (\ifile{isf\_draft\_meter}) describing 516 518 the ice shelf draft (in meters) is needed. 517 519 … … 535 537 %%% 536 538 537 Unless a linear free surface is used (\np{ln\_linssh} ~\forcode{= .false.}),539 Unless a linear free surface is used (\np{ln\_linssh}\forcode{ = .false.}), 538 540 the arrays describing the grid point depths and vertical scale factors are three set of 539 541 three dimensional arrays $(i,j,k)$ defined at \textit{before}, \textit{now} and \textit{after} time step. … … 541 543 They are updated at each model time step using a fixed reference coordinate system which 542 544 computer names have a $\_0$ suffix. 543 When the linear free surface option is used (\np{ln\_linssh} ~\forcode{= .true.}), \textit{before},545 When the linear free surface option is used (\np{ln\_linssh}\forcode{ = .true.}), \textit{before}, 544 546 \textit{now} and \textit{after} arrays are simply set one for all to their reference counterpart. 545 547 … … 553 555 (found in \ngn{namdom} namelist): 554 556 \begin{description} 555 \item[\np{nn\_bathy} ~\forcode{= 0}]:557 \item[\np{nn\_bathy}\forcode{ = 0}]: 556 558 a flat-bottom domain is defined. 557 559 The total depth $z_w (jpk)$ is given by the coordinate transformation. 558 560 The domain can either be a closed basin or a periodic channel depending on the parameter \np{jperio}. 559 \item[\np{nn\_bathy} ~\forcode{= -1}]:561 \item[\np{nn\_bathy}\forcode{ = -1}]: 560 562 a domain with a bump of topography one third of the domain width at the central latitude. 561 563 This is meant for the "EEL-R5" configuration, a periodic or open boundary channel with a seamount. 562 \item[\np{nn\_bathy} ~\forcode{= 1}]:564 \item[\np{nn\_bathy}\forcode{ = 1}]: 563 565 read a bathymetry and ice shelf draft (if needed). 564 566 The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) at … … 571 573 The \ifile{isfdraft\_meter} file (Netcdf format) provides the ice shelf draft (positive, in meters) at 572 574 each grid point of the model grid. 573 This file is only needed if \np{ln\_isfcav} ~\forcode{= .true.}.575 This file is only needed if \np{ln\_isfcav}\forcode{ = .true.}. 574 576 Defining the ice shelf draft will also define the ice shelf edge and the grounding line position. 575 577 \end{description} … … 586 588 % z-coordinate and reference coordinate transformation 587 589 % ------------------------------------------------------------------------------------------------------------- 588 \subsection[$Z$-coordinate (\ protect\np{ln\_zco}~\forcode{= .true.}) and ref. coordinate]589 {$Z$-coordinate (\protect\np{ln\_zco}~\forcode{= .true.}) and reference coordinate}590 \subsection[$Z$-coordinate (\forcode{ln_zco = .true.}) and ref. coordinate] 591 {$Z$-coordinate (\protect\np{ln\_zco}\forcode{ = .true.}) and reference coordinate} 590 592 \label{subsec:DOM_zco} 591 593 … … 593 595 \begin{figure}[!tb] 594 596 \begin{center} 595 \includegraphics[ ]{Fig_zgr}597 \includegraphics[width=\textwidth]{Fig_zgr} 596 598 \caption{ 597 599 \protect\label{fig:zgr} … … 616 618 using parameters provided in the \ngn{namcfg} namelist. 617 619 618 It is possible to define a simple regular vertical grid by giving zero stretching (\np{ppacr} ~\forcode{= 0}).620 It is possible to define a simple regular vertical grid by giving zero stretching (\np{ppacr}\forcode{ = 0}). 619 621 In that case, the parameters \jp{jpk} (number of $w$-levels) and 620 622 \np{pphmax} (total ocean depth in meters) fully define the grid. … … 631 633 a smooth hyperbolic tangent transition in between (\autoref{fig:zgr}). 632 634 633 If the ice shelf cavities are opened (\np{ln\_isfcav} ~\forcode{= .true.}), the definition of $z_0$ is the same.635 If the ice shelf cavities are opened (\np{ln\_isfcav}\forcode{ = .true.}), the definition of $z_0$ is the same. 634 636 However, definition of $e_3^0$ at $t$- and $w$-points is respectively changed to: 635 637 \begin{equation} … … 765 767 % z-coordinate with partial step 766 768 % ------------------------------------------------------------------------------------------------------------- 767 \subsection{$Z$-coordinate with partial step (\protect\np{ln\_zps}~\forcode{= .true.})} 769 \subsection[$Z$-coordinate with partial step (\forcode{ln_zps = .true.})] 770 {$Z$-coordinate with partial step (\protect\np{ln\_zps}\forcode{ = .true.})} 768 771 \label{subsec:DOM_zps} 769 772 %--------------------------------------------namdom------------------------------------------------------- … … 796 799 % s-coordinate 797 800 % ------------------------------------------------------------------------------------------------------------- 798 \subsection{$S$-coordinate (\protect\np{ln\_sco}~\forcode{= .true.})} 801 \subsection[$S$-coordinate (\forcode{ln_sco = .true.})] 802 {$S$-coordinate (\protect\np{ln\_sco}\forcode{ = .true.})} 799 803 \label{subsec:DOM_sco} 800 804 %------------------------------------------nam_zgr_sco--------------------------------------------------- … … 803 807 %-------------------------------------------------------------------------------------------------------------- 804 808 Options are defined in \ngn{namzgr\_sco}. 805 In $s$-coordinate (\np{ln\_sco} ~\forcode{= .true.}), the depth and thickness of the model levels are defined from809 In $s$-coordinate (\np{ln\_sco}\forcode{ = .true.}), the depth and thickness of the model levels are defined from 806 810 the product of a depth field and either a stretching function or its derivative, respectively: 807 811 … … 826 830 827 831 The original default NEMO s-coordinate stretching is available if neither of the other options are specified as true 828 (\np{ln\_s\_SH94} ~\forcode{= .false.} and \np{ln\_s\_SF12}~\forcode{= .false.}).829 This uses a depth independent $\tanh$ function for the stretching \citep{ Madec_al_JPO96}:832 (\np{ln\_s\_SH94}\forcode{ = .false.} and \np{ln\_s\_SF12}\forcode{ = .false.}). 833 This uses a depth independent $\tanh$ function for the stretching \citep{madec.delecluse.ea_JPO96}: 830 834 831 835 \[ … … 846 850 847 851 A stretching function, 848 modified from the commonly used \citet{ Song_Haidvogel_JCP94} stretching (\np{ln\_s\_SH94}~\forcode{= .true.}),852 modified from the commonly used \citet{song.haidvogel_JCP94} stretching (\np{ln\_s\_SH94}\forcode{ = .true.}), 849 853 is also available and is more commonly used for shelf seas modelling: 850 854 … … 859 863 \begin{figure}[!ht] 860 864 \begin{center} 861 \includegraphics[ ]{Fig_sco_function}865 \includegraphics[width=\textwidth]{Fig_sco_function} 862 866 \caption{ 863 867 \protect\label{fig:sco_function} … … 876 880 877 881 Another example has been provided at version 3.5 (\np{ln\_s\_SF12}) that allows a fixed surface resolution in 878 an analytical terrain-following stretching \citet{ Siddorn_Furner_OM12}.882 an analytical terrain-following stretching \citet{siddorn.furner_OM13}. 879 883 In this case the a stretching function $\gamma$ is defined such that: 880 884 … … 911 915 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 912 916 \begin{figure}[!ht] 913 \includegraphics[ ]{Fig_DOM_compare_coordinates_surface}917 \includegraphics[width=\textwidth]{Fig_DOM_compare_coordinates_surface} 914 918 \caption{ 915 A comparison of the \citet{ Song_Haidvogel_JCP94} $S$-coordinate (solid lines),919 A comparison of the \citet{song.haidvogel_JCP94} $S$-coordinate (solid lines), 916 920 a 50 level $Z$-coordinate (contoured surfaces) and 917 the \citet{ Siddorn_Furner_OM12} $S$-coordinate (dashed lines) in the surface $100~m$ for921 the \citet{siddorn.furner_OM13} $S$-coordinate (dashed lines) in the surface $100~m$ for 918 922 a idealised bathymetry that goes from $50~m$ to $5500~m$ depth. 919 923 For clarity every third coordinate surface is shown. … … 929 933 creating a non-analytical vertical coordinate that 930 934 therefore may suffer from large gradients in the vertical resolutions. 931 This stretching is less straightforward to implement than the \citet{ Song_Haidvogel_JCP94} stretching,935 This stretching is less straightforward to implement than the \citet{song.haidvogel_JCP94} stretching, 932 936 but has the advantage of resolving diurnal processes in deep water and has generally flatter slopes. 933 937 934 As with the \citet{ Song_Haidvogel_JCP94} stretching the stretch is only applied at depths greater than938 As with the \citet{song.haidvogel_JCP94} stretching the stretch is only applied at depths greater than 935 939 the critical depth $h_c$. 936 940 In this example two options are available in depths shallower than $h_c$, … … 940 944 Minimising the horizontal slope of the vertical coordinate is important in terrain-following systems as 941 945 large slopes lead to hydrostatic consistency. 942 A hydrostatic consistency parameter diagnostic following \citet{ Haney1991} has been implemented,946 A hydrostatic consistency parameter diagnostic following \citet{haney_JPO91} has been implemented, 943 947 and is output as part of the model mesh file at the start of the run. 944 948 … … 946 950 % z*- or s*-coordinate 947 951 % ------------------------------------------------------------------------------------------------------------- 948 \subsection{\zstar- or \sstar-coordinate (\protect\np{ln\_linssh}~\forcode{= .false.})} 952 \subsection[\zstar- or \sstar-coordinate (\forcode{ln_linssh = .false.})] 953 {\zstar- or \sstar-coordinate (\protect\np{ln\_linssh}\forcode{ = .false.})} 949 954 \label{subsec:DOM_zgr_star} 950 955 … … 960 965 961 966 Whatever the vertical coordinate used, the model offers the possibility of representing the bottom topography with 962 steps that follow the face of the model cells (step like topography) \citep{ Madec_al_JPO96}.967 steps that follow the face of the model cells (step like topography) \citep{madec.delecluse.ea_JPO96}. 963 968 The distribution of the steps in the horizontal is defined in a 2D integer array, mbathy, which 964 969 gives the number of ocean levels (\ie those that are not masked) at each $t$-point. … … 1014 1019 % Domain: Initial State (dtatsd & istate) 1015 1020 % ================================================================ 1016 \section{Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})} 1021 \section[Initial state (\textit{istate.F90} and \textit{dtatsd.F90})] 1022 {Initial state (\protect\mdl{istate} and \protect\mdl{dtatsd})} 1017 1023 \label{sec:DTA_tsd} 1018 1024 %-----------------------------------------namtsd------------------------------------------- … … 1025 1031 salinity fields is controlled through the \np{ln\_tsd\_ini} namelist parameter. 1026 1032 \begin{description} 1027 \item[\np{ln\_tsd\_init} ~\forcode{= .true.}]1033 \item[\np{ln\_tsd\_init}\forcode{ = .true.}] 1028 1034 use a T and S input files that can be given on the model grid itself or on their native input data grid. 1029 1035 In the latter case, … … 1032 1038 The information relative to the input files are given in the \np{sn\_tem} and \np{sn\_sal} structures. 1033 1039 The computation is done in the \mdl{dtatsd} module. 1034 \item[\np{ln\_tsd\_init} ~\forcode{= .false.}]1040 \item[\np{ln\_tsd\_init}\forcode{ = .false.}] 1035 1041 use constant salinity value of $35.5~psu$ and an analytical profile of temperature 1036 1042 (typical of the tropical ocean), see \rou{istate\_t\_s} subroutine called from \mdl{istate} module. -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_DYN.tex
r10499 r11263 65 65 % Horizontal divergence and relative vorticity 66 66 %-------------------------------------------------------------------------------------------------------------- 67 \subsection{Horizontal divergence and relative vorticity (\protect\mdl{divcur})} 67 \subsection[Horizontal divergence and relative vorticity (\textit{divcur.F90})] 68 {Horizontal divergence and relative vorticity (\protect\mdl{divcur})} 68 69 \label{subsec:DYN_divcur} 69 70 … … 101 102 % Sea Surface Height evolution 102 103 %-------------------------------------------------------------------------------------------------------------- 103 \subsection{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})} 104 \subsection[Horizontal divergence and relative vorticity (\textit{sshwzv.F90})] 105 {Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})} 104 106 \label{subsec:DYN_sshwzv} 105 107 … … 127 129 Replacing $T$ by the number $1$ in the tracer equation and summing over the water column must lead to 128 130 the sea surface height equation otherwise tracer content will not be conserved 129 \citep{ Griffies_al_MWR01, Leclair_Madec_OM09}.131 \citep{griffies.pacanowski.ea_MWR01, leclair.madec_OM09}. 130 132 131 133 The vertical velocity is computed by an upward integration of the horizontal divergence starting at the bottom, … … 181 183 % Vorticity term 182 184 % ------------------------------------------------------------------------------------------------------------- 183 \subsection{Vorticity term (\protect\mdl{dynvor})} 185 \subsection[Vorticity term (\textit{dynvor.F90})] 186 {Vorticity term (\protect\mdl{dynvor})} 184 187 \label{subsec:DYN_vor} 185 188 %------------------------------------------nam_dynvor---------------------------------------------------- … … 203 206 % enstrophy conserving scheme 204 207 %------------------------------------------------------------- 205 \subsubsection{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})} 208 \subsubsection[Enstrophy conserving scheme (\forcode{ln_dynvor_ens = .true.})] 209 {Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})} 206 210 \label{subsec:DYN_vor_ens} 207 211 … … 226 230 % energy conserving scheme 227 231 %------------------------------------------------------------- 228 \subsubsection{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})} 232 \subsubsection[Energy conserving scheme (\forcode{ln_dynvor_ene = .true.})] 233 {Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})} 229 234 \label{subsec:DYN_vor_ene} 230 235 … … 246 251 % mix energy/enstrophy conserving scheme 247 252 %------------------------------------------------------------- 248 \subsubsection{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.}) } 253 \subsubsection[Mixed energy/enstrophy conserving scheme (\forcode{ln_dynvor_mix = .true.})] 254 {Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.})} 249 255 \label{subsec:DYN_vor_mix} 250 256 … … 271 277 % energy and enstrophy conserving scheme 272 278 %------------------------------------------------------------- 273 \subsubsection{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.}) } 279 \subsubsection[Energy and enstrophy conserving scheme (\forcode{ln_dynvor_een = .true.})] 280 {Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.})} 274 281 \label{subsec:DYN_vor_een} 275 282 … … 287 294 Nevertheless, this technique strongly distort the phase and group velocity of Rossby waves....} 288 295 289 A very nice solution to the problem of double averaging was proposed by \citet{ Arakawa_Hsu_MWR90}.296 A very nice solution to the problem of double averaging was proposed by \citet{arakawa.hsu_MWR90}. 290 297 The idea is to get rid of the double averaging by considering triad combinations of vorticity. 291 298 It is noteworthy that this solution is conceptually quite similar to the one proposed by 292 \citep{ Griffies_al_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}).293 294 The \citet{ Arakawa_Hsu_MWR90} vorticity advection scheme for a single layer is modified295 for spherical coordinates as described by \citet{ Arakawa_Lamb_MWR81} to obtain the EEN scheme.299 \citep{griffies.gnanadesikan.ea_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}). 300 301 The \citet{arakawa.hsu_MWR90} vorticity advection scheme for a single layer is modified 302 for spherical coordinates as described by \citet{arakawa.lamb_MWR81} to obtain the EEN scheme. 296 303 First consider the discrete expression of the potential vorticity, $q$, defined at an $f$-point: 297 304 \[ … … 309 316 \begin{figure}[!ht] 310 317 \begin{center} 311 \includegraphics[width= 0.70\textwidth]{Fig_DYN_een_triad}318 \includegraphics[width=\textwidth]{Fig_DYN_een_triad} 312 319 \caption{ 313 320 \protect\label{fig:DYN_een_triad} … … 327 334 (with a systematic reduction of $e_{3f}$ when a model level intercept the bathymetry) 328 335 that tends to reinforce the topostrophy of the flow 329 (\ie the tendency of the flow to follow the isobaths) \citep{ Penduff_al_OS07}.336 (\ie the tendency of the flow to follow the isobaths) \citep{penduff.le-sommer.ea_OS07}. 330 337 331 338 Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as … … 356 363 (\ie $\chi$=$0$) (see \autoref{subsec:C_vorEEN}). 357 364 Applied to a realistic ocean configuration, it has been shown that it leads to a significant reduction of 358 the noise in the vertical velocity field \citep{ Le_Sommer_al_OM09}.365 the noise in the vertical velocity field \citep{le-sommer.penduff.ea_OM09}. 359 366 Furthermore, used in combination with a partial steps representation of bottom topography, 360 367 it improves the interaction between current and topography, 361 leading to a larger topostrophy of the flow \citep{ Barnier_al_OD06, Penduff_al_OS07}.368 leading to a larger topostrophy of the flow \citep{barnier.madec.ea_OD06, penduff.le-sommer.ea_OS07}. 362 369 363 370 %-------------------------------------------------------------------------------------------------------------- 364 371 % Kinetic Energy Gradient term 365 372 %-------------------------------------------------------------------------------------------------------------- 366 \subsection{Kinetic energy gradient term (\protect\mdl{dynkeg})} 373 \subsection[Kinetic energy gradient term (\textit{dynkeg.F90})] 374 {Kinetic energy gradient term (\protect\mdl{dynkeg})} 367 375 \label{subsec:DYN_keg} 368 376 … … 384 392 % Vertical advection term 385 393 %-------------------------------------------------------------------------------------------------------------- 386 \subsection{Vertical advection term (\protect\mdl{dynzad}) } 394 \subsection[Vertical advection term (\textit{dynzad.F90})] 395 {Vertical advection term (\protect\mdl{dynzad})} 387 396 \label{subsec:DYN_zad} 388 397 … … 403 412 When \np{ln\_dynzad\_zts}\forcode{ = .true.}, 404 413 a split-explicit time stepping with 5 sub-timesteps is used on the vertical advection term. 405 This option can be useful when the value of the timestep is limited by vertical advection \citep{ Lemarie_OM2015}.414 This option can be useful when the value of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}. 406 415 Note that in this case, 407 416 a similar split-explicit time stepping should be used on vertical advection of tracer to ensure a better stability, … … 430 439 % Coriolis plus curvature metric terms 431 440 %-------------------------------------------------------------------------------------------------------------- 432 \subsection{Coriolis plus curvature metric terms (\protect\mdl{dynvor}) } 441 \subsection[Coriolis plus curvature metric terms (\textit{dynvor.F90})] 442 {Coriolis plus curvature metric terms (\protect\mdl{dynvor})} 433 443 \label{subsec:DYN_cor_flux} 434 444 … … 451 461 % Flux form Advection term 452 462 %-------------------------------------------------------------------------------------------------------------- 453 \subsection{Flux form advection term (\protect\mdl{dynadv}) } 463 \subsection[Flux form advection term (\textit{dynadv.F90})] 464 {Flux form advection term (\protect\mdl{dynadv})} 454 465 \label{subsec:DYN_adv_flux} 455 466 … … 475 486 a $2^{nd}$ order centered finite difference scheme, CEN2, 476 487 or a $3^{rd}$ order upstream biased scheme, UBS. 477 The latter is described in \citet{ Shchepetkin_McWilliams_OM05}.488 The latter is described in \citet{shchepetkin.mcwilliams_OM05}. 478 489 The schemes are selected using the namelist logicals \np{ln\_dynadv\_cen2} and \np{ln\_dynadv\_ubs}. 479 490 In flux form, the schemes differ by the choice of a space and time interpolation to define the value of … … 484 495 % 2nd order centred scheme 485 496 %------------------------------------------------------------- 486 \subsubsection{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})} 497 \subsubsection[CEN2: $2^{nd}$ order centred scheme (\forcode{ln_dynadv_cen2 = .true.})] 498 {CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})} 487 499 \label{subsec:DYN_adv_cen2} 488 500 … … 507 519 % UBS scheme 508 520 %------------------------------------------------------------- 509 \subsubsection{UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})} 521 \subsubsection[UBS: Upstream Biased Scheme (\forcode{ln_dynadv_ubs = .true.})] 522 {UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})} 510 523 \label{subsec:DYN_adv_ubs} 511 524 … … 523 536 where $u"_{i+1/2} =\delta_{i+1/2} \left[ {\delta_i \left[ u \right]} \right]$. 524 537 This results in a dissipatively dominant (\ie hyper-diffusive) truncation error 525 \citep{ Shchepetkin_McWilliams_OM05}.526 The overall performance of the advection scheme is similar to that reported in \citet{ Farrow1995}.538 \citep{shchepetkin.mcwilliams_OM05}. 539 The overall performance of the advection scheme is similar to that reported in \citet{farrow.stevens_JPO95}. 527 540 It is a relatively good compromise between accuracy and smoothness. 528 541 It is not a \emph{positive} scheme, meaning that false extrema are permitted. … … 542 555 while the second term, which is the diffusion part of the scheme, 543 556 is evaluated using the \textit{before} velocity (forward in time). 544 This is discussed by \citet{ Webb_al_JAOT98} in the context of the Quick advection scheme.557 This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme. 545 558 546 559 Note that the UBS and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes only differ by 547 560 one coefficient. 548 Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{ Webb_al_JAOT98}.561 Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 549 562 This option is not available through a namelist parameter, since the $1/6$ coefficient is hard coded. 550 563 Nevertheless it is quite easy to make the substitution in the \mdl{dynadv\_ubs} module and obtain a QUICK scheme. … … 560 573 % Hydrostatic pressure gradient term 561 574 % ================================================================ 562 \section{Hydrostatic pressure gradient (\protect\mdl{dynhpg})} 575 \section[Hydrostatic pressure gradient (\textit{dynhpg.F90})] 576 {Hydrostatic pressure gradient (\protect\mdl{dynhpg})} 563 577 \label{sec:DYN_hpg} 564 578 %------------------------------------------nam_dynhpg--------------------------------------------------- … … 582 596 % z-coordinate with full step 583 597 %-------------------------------------------------------------------------------------------------------------- 584 \subsection{Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})} 598 \subsection[Full step $Z$-coordinate (\forcode{ln_dynhpg_zco = .true.})] 599 {Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})} 585 600 \label{subsec:DYN_hpg_zco} 586 601 … … 627 642 % z-coordinate with partial step 628 643 %-------------------------------------------------------------------------------------------------------------- 629 \subsection{Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})} 644 \subsection[Partial step $Z$-coordinate (\forcode{ln_dynhpg_zps = .true.})] 645 {Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})} 630 646 \label{subsec:DYN_hpg_zps} 631 647 … … 652 668 653 669 Pressure gradient formulations in an $s$-coordinate have been the subject of a vast number of papers 654 (\eg, \citet{ Song1998, Shchepetkin_McWilliams_OM05}).670 (\eg, \citet{song_MWR98, shchepetkin.mcwilliams_OM05}). 655 671 A number of different pressure gradient options are coded but the ROMS-like, 656 672 density Jacobian with cubic polynomial method is currently disabled whilst known bugs are under investigation. 657 673 658 $\bullet$ Traditional coding (see for example \citet{ Madec_al_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.})674 $\bullet$ Traditional coding (see for example \citet{madec.delecluse.ea_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.}) 659 675 \begin{equation} 660 676 \label{eq:dynhpg_sco} … … 679 695 $\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) 680 696 681 $\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{ Shchepetkin_McWilliams_OM05}697 $\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{shchepetkin.mcwilliams_OM05} 682 698 (\np{ln\_dynhpg\_djc}\forcode{ = .true.}) (currently disabled; under development) 683 699 684 700 Note that expression \autoref{eq:dynhpg_sco} is commonly used when the variable volume formulation is activated 685 701 (\key{vvl}) because in that case, even with a flat bottom, 686 the coordinate surfaces are not horizontal but follow the free surface \citep{ Levier2007}.702 the coordinate surfaces are not horizontal but follow the free surface \citep{levier.treguier.ea_rpt07}. 687 703 The pressure jacobian scheme (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) is available as 688 704 an improved option to \np{ln\_dynhpg\_sco}\forcode{ = .true.} when \key{vvl} is active. … … 704 720 corresponds to the water replaced by the ice shelf. 705 721 This top pressure is constant over time. 706 A detailed description of this method is described in \citet{ Losch2008}.\\722 A detailed description of this method is described in \citet{losch_JGR08}.\\ 707 723 708 724 The pressure gradient due to ocean load is computed using the expression \autoref{eq:dynhpg_sco} described in … … 712 728 % Time-scheme 713 729 %-------------------------------------------------------------------------------------------------------------- 714 \subsection{Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .true./.false.})} 730 \subsection[Time-scheme (\forcode{ln_dynhpg_imp = .{true,false}.})] 731 {Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .\{true,false\}}.)} 715 732 \label{subsec:DYN_hpg_imp} 716 733 … … 722 739 the physical phenomenon that controls the time-step is internal gravity waves (IGWs). 723 740 A semi-implicit scheme for doubling the stability limit associated with IGWs can be used 724 \citep{ Brown_Campana_MWR78, Maltrud1998}.741 \citep{brown.campana_MWR78, maltrud.smith.ea_JGR98}. 725 742 It involves the evaluation of the hydrostatic pressure gradient as 726 743 an average over the three time levels $t-\rdt$, $t$, and $t+\rdt$ … … 773 790 % Surface Pressure Gradient 774 791 % ================================================================ 775 \section{Surface pressure gradient (\protect\mdl{dynspg})} 792 \section[Surface pressure gradient (\textit{dynspg.F90})] 793 {Surface pressure gradient (\protect\mdl{dynspg})} 776 794 \label{sec:DYN_spg} 777 795 %-----------------------------------------nam_dynspg---------------------------------------------------- … … 790 808 which imposes a very small time step when an explicit time stepping is used. 791 809 Two methods are proposed to allow a longer time step for the three-dimensional equations: 792 the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt }),810 the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt?}), 793 811 and the split-explicit free surface described below. 794 812 The extra term introduced in the filtered method is calculated implicitly, … … 811 829 % Explicit free surface formulation 812 830 %-------------------------------------------------------------------------------------------------------------- 813 \subsection{Explicit free surface (\protect\key{dynspg\_exp})} 831 \subsection[Explicit free surface (\texttt{\textbf{key\_dynspg\_exp}})] 832 {Explicit free surface (\protect\key{dynspg\_exp})} 814 833 \label{subsec:DYN_spg_exp} 815 834 … … 837 856 % Split-explict free surface formulation 838 857 %-------------------------------------------------------------------------------------------------------------- 839 \subsection{Split-explicit free surface (\protect\key{dynspg\_ts})} 858 \subsection[Split-explicit free surface (\texttt{\textbf{key\_dynspg\_ts}})] 859 {Split-explicit free surface (\protect\key{dynspg\_ts})} 840 860 \label{subsec:DYN_spg_ts} 841 861 %------------------------------------------namsplit----------------------------------------------------------- … … 845 865 846 866 The split-explicit free surface formulation used in \NEMO (\key{dynspg\_ts} defined), 847 also called the time-splitting formulation, follows the one proposed by \citet{ Shchepetkin_McWilliams_OM05}.867 also called the time-splitting formulation, follows the one proposed by \citet{shchepetkin.mcwilliams_OM05}. 848 868 The general idea is to solve the free surface equation and the associated barotropic velocity equations with 849 869 a smaller time step than $\rdt$, the time step used for the three dimensional prognostic variables … … 862 882 \begin{equation} 863 883 \label{eq:BT_dyn} 864 \frac{\partial {\ rm \overline{{\bf U}}_h} }{\partial t}=865 -f\;{\ rm {\bf k}}\times {\rm \overline{{\bf U}}_h}866 -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \ rm {\overline{{\bf U}}_h} + \rm {\overline{\bf G}}884 \frac{\partial {\mathrm \overline{{\mathbf U}}_h} }{\partial t}= 885 -f\;{\mathrm {\mathbf k}}\times {\mathrm \overline{{\mathbf U}}_h} 886 -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \mathrm {\overline{{\mathbf U}}_h} + \mathrm {\overline{\mathbf G}} 867 887 \end{equation} 868 888 \[ 869 889 % \label{eq:BT_ssh} 870 \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\ rm{\bf \overline{U}}}_h \,} \right]+P-E890 \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\mathrm{\mathbf \overline{U}}}_h \,} \right]+P-E 871 891 \] 872 892 % \end{subequations} 873 where $\ rm {\overline{\bf G}}$ is a forcing term held constant, containing coupling term between modes,893 where $\mathrm {\overline{\mathbf G}}$ is a forcing term held constant, containing coupling term between modes, 874 894 surface atmospheric forcing as well as slowly varying barotropic terms not explicitly computed to gain efficiency. 875 895 The third term on the right hand side of \autoref{eq:BT_dyn} represents the bottom stress 876 896 (see section \autoref{sec:ZDF_bfr}), explicitly accounted for at each barotropic iteration. 877 897 Temporal discretization of the system above follows a three-time step Generalized Forward Backward algorithm 878 detailed in \citet{ Shchepetkin_McWilliams_OM05}.898 detailed in \citet{shchepetkin.mcwilliams_OM05}. 879 899 AB3-AM4 coefficients used in \NEMO follow the second-order accurate, 880 "multi-purpose" stability compromise as defined in \citet{ Shchepetkin_McWilliams_Bk08}900 "multi-purpose" stability compromise as defined in \citet{shchepetkin.mcwilliams_ibk09} 881 901 (see their figure 12, lower left). 882 902 … … 884 904 \begin{figure}[!t] 885 905 \begin{center} 886 \includegraphics[width= 0.7\textwidth]{Fig_DYN_dynspg_ts}906 \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts} 887 907 \caption{ 888 908 \protect\label{fig:DYN_dynspg_ts} … … 936 956 and time splitting not compatible. 937 957 Advective barotropic velocities are obtained by using a secondary set of filtering weights, 938 uniquely defined from the filter coefficients used for the time averaging (\citet{ Shchepetkin_McWilliams_OM05}).958 uniquely defined from the filter coefficients used for the time averaging (\citet{shchepetkin.mcwilliams_OM05}). 939 959 Consistency between the time averaged continuity equation and the time stepping of tracers is here the key to 940 960 obtain exact conservation. … … 953 973 external gravity waves in idealized or weakly non-linear cases. 954 974 Although the damping is lower than for the filtered free surface, 955 it is still significant as shown by \citet{ Levier2007} in the case of an analytical barotropic Kelvin wave.975 it is still significant as shown by \citet{levier.treguier.ea_rpt07} in the case of an analytical barotropic Kelvin wave. 956 976 957 977 %>>>>>=============== … … 1051 1071 the leap-frog splitting mode in equation \autoref{eq:DYN_spg_ts_ssh}. 1052 1072 We have tried various forms of such filtering, 1053 with the following method discussed in \cite{ Griffies_al_MWR01} chosen due to1073 with the following method discussed in \cite{griffies.pacanowski.ea_MWR01} chosen due to 1054 1074 its stability and reasonably good maintenance of tracer conservation properties (see ??). 1055 1075 … … 1081 1101 % Filtered free surface formulation 1082 1102 %-------------------------------------------------------------------------------------------------------------- 1083 \subsection{Filtered free surface (\protect\key{dynspg\_flt})} 1103 \subsection[Filtered free surface (\texttt{\textbf{key\_dynspg\_flt}})] 1104 {Filtered free surface (\protect\key{dynspg\_flt})} 1084 1105 \label{subsec:DYN_spg_fltp} 1085 1106 1086 The filtered formulation follows the \citet{ Roullet_Madec_JGR00} implementation.1107 The filtered formulation follows the \citet{roullet.madec_JGR00} implementation. 1087 1108 The extra term introduced in the equations (see \autoref{subsec:PE_free_surface}) is solved implicitly. 1088 1109 The elliptic solvers available in the code are documented in \autoref{chap:MISC}. … … 1092 1113 \[ 1093 1114 % \label{eq:spg_flt} 1094 \frac{\partial {\ rm {\bf U}}_h }{\partial t}= {\rm {\bf M}}1115 \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= {\mathrm {\mathbf M}} 1095 1116 - g \nabla \left( \tilde{\rho} \ \eta \right) 1096 1117 - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right) … … 1098 1119 where $T_c$, is a parameter with dimensions of time which characterizes the force, 1099 1120 $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density, 1100 and $\ rm {\bf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient,1121 and $\mathrm {\mathbf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient, 1101 1122 non-linear and viscous terms in \autoref{eq:PE_dyn}. 1102 1123 } %end gmcomment … … 1109 1130 % Lateral diffusion term 1110 1131 % ================================================================ 1111 \section{Lateral diffusion term and operators (\protect\mdl{dynldf})} 1132 \section[Lateral diffusion term and operators (\textit{dynldf.F90})] 1133 {Lateral diffusion term and operators (\protect\mdl{dynldf})} 1112 1134 \label{sec:DYN_ldf} 1113 1135 %------------------------------------------nam_dynldf---------------------------------------------------- … … 1143 1165 1144 1166 % ================================================================ 1145 \subsection[Iso-level laplacian (\ protect\np{ln\_dynldf\_lap}\forcode{= .true.})]1146 1167 \subsection[Iso-level laplacian (\forcode{ln_dynldf_lap = .true.})] 1168 {Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})} 1147 1169 \label{subsec:DYN_ldf_lap} 1148 1170 … … 1152 1174 \left\{ 1153 1175 \begin{aligned} 1154 D_u^{l{\ rm {\bf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm}1176 D_u^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm} 1155 1177 \;\chi } \right]-\frac{1}{e_{2u} {\kern 1pt}e_{3u} }\delta_j \left[ 1156 1178 {A_f^{lm} \;e_{3f} \zeta } \right] \\ \\ 1157 D_v^{l{\ rm {\bf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm}1179 D_v^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm} 1158 1180 \;\chi } \right]+\frac{1}{e_{1v} {\kern 1pt}e_{3v} }\delta_i \left[ 1159 1181 {A_f^{lm} \;e_{3f} \zeta } \right] … … 1169 1191 % Rotated laplacian operator 1170 1192 %-------------------------------------------------------------------------------------------------------------- 1171 \subsection[Rotated laplacian (\ protect\np{ln\_dynldf\_iso}\forcode{= .true.})]1172 1193 \subsection[Rotated laplacian (\forcode{ln_dynldf_iso = .true.})] 1194 {Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})} 1173 1195 \label{subsec:DYN_ldf_iso} 1174 1196 … … 1228 1250 % Iso-level bilaplacian operator 1229 1251 %-------------------------------------------------------------------------------------------------------------- 1230 \subsection[Iso-level bilaplacian (\ protect\np{ln\_dynldf\_bilap}\forcode{= .true.})]1231 1252 \subsection[Iso-level bilaplacian (\forcode{ln_dynldf_bilap = .true.})] 1253 {Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})} 1232 1254 \label{subsec:DYN_ldf_bilap} 1233 1255 … … 1243 1265 % Vertical diffusion term 1244 1266 % ================================================================ 1245 \section{Vertical diffusion term (\protect\mdl{dynzdf})} 1267 \section[Vertical diffusion term (\textit{dynzdf.F90})] 1268 {Vertical diffusion term (\protect\mdl{dynzdf})} 1246 1269 \label{sec:DYN_zdf} 1247 1270 %----------------------------------------------namzdf------------------------------------------------------ … … 1326 1349 There are two main options for wetting and drying code (wd): 1327 1350 (a) an iterative limiter (il) and (b) a directional limiter (dl). 1328 The directional limiter is based on the scheme developed by \cite{ WarnerEtal13} for RO1351 The directional limiter is based on the scheme developed by \cite{warner.defne.ea_CG13} for RO 1329 1352 MS 1330 which was in turn based on ideas developed for POM by \cite{ Oey06}. The iterative1353 which was in turn based on ideas developed for POM by \cite{oey_OM06}. The iterative 1331 1354 limiter is a new scheme. The iterative limiter is activated by setting $\mathrm{ln\_wd\_il} = \mathrm{.true.}$ 1332 1355 and $\mathrm{ln\_wd\_dl} = \mathrm{.false.}$. The directional limiter is activated … … 1372 1395 % Iterative limiters 1373 1396 %----------------------------------------------------------------------------------------- 1374 \subsection [Directional limiter (\textit{wet\_dry})]1375 1397 \subsection[Directional limiter (\textit{wet\_dry.F90})] 1398 {Directional limiter (\mdl{wet\_dry})} 1376 1399 \label{subsec:DYN_wd_directional_limiter} 1377 1400 The principal idea of the directional limiter is that … … 1400 1423 1401 1424 1402 \cite{ WarnerEtal13} state that in their scheme the velocity masks at the cell faces for the baroclinic1425 \cite{warner.defne.ea_CG13} state that in their scheme the velocity masks at the cell faces for the baroclinic 1403 1426 timesteps are set to 0 or 1 depending on whether the average of the masks over the barotropic sub-steps is respectively less than 1404 1427 or greater than 0.5. That scheme does not conserve tracers in integrations started from constant tracer … … 1412 1435 %----------------------------------------------------------------------------------------- 1413 1436 1414 \subsection [Iterative limiter (\textit{wet\_dry})]1415 1437 \subsection[Iterative limiter (\textit{wet\_dry.F90})] 1438 {Iterative limiter (\mdl{wet\_dry})} 1416 1439 \label{subsec:DYN_wd_iterative_limiter} 1417 1440 1418 \subsubsection [Iterative flux limiter (\textit{wet\_dry})]1419 1441 \subsubsection[Iterative flux limiter (\textit{wet\_dry.F90})] 1442 {Iterative flux limiter (\mdl{wet\_dry})} 1420 1443 \label{subsubsec:DYN_wd_il_spg_limiter} 1421 1444 … … 1494 1517 \end{equation} 1495 1518 1496 Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\it [Q: Why is1519 Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\itshape [Q: Why is 1497 1520 this necessary/desirable?]}. Substituting from (\ref{dyn_wd_continuity_coef}) gives an 1498 1521 expression for the coefficient needed to multiply the outward flux at this cell in order … … 1522 1545 % Surface pressure gradients 1523 1546 %---------------------------------------------------------------------------------------- 1524 \subsubsection [Modification of surface pressure gradients (\textit{dynhpg})]1525 1547 \subsubsection[Modification of surface pressure gradients (\textit{dynhpg.F90})] 1548 {Modification of surface pressure gradients (\mdl{dynhpg})} 1526 1549 \label{subsubsec:DYN_wd_il_spg} 1527 1550 … … 1541 1564 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1542 1565 \begin{figure}[!ht] \begin{center} 1543 \includegraphics[width= 0.8\textwidth]{Fig_WAD_dynhpg}1566 \includegraphics[width=\textwidth]{Fig_WAD_dynhpg} 1544 1567 \caption{ \label{Fig_WAD_dynhpg} 1545 1568 Illustrations of the three possible combinations of the logical variables controlling the … … 1588 1611 conditions. 1589 1612 1590 \subsubsection [Additional considerations (\textit{usrdef\_zgr})]1591 1613 \subsubsection[Additional considerations (\textit{usrdef\_zgr.F90})] 1614 {Additional considerations (\mdl{usrdef\_zgr})} 1592 1615 \label{subsubsec:WAD_additional} 1593 1616 … … 1603 1626 % The WAD test cases 1604 1627 %---------------------------------------------------------------------------------------- 1605 \subsection [The WAD test cases (\textit{usrdef\_zgr})]1606 1628 \subsection[The WAD test cases (\textit{usrdef\_zgr.F90})] 1629 {The WAD test cases (\mdl{usrdef\_zgr})} 1607 1630 \label{WAD_test_cases} 1608 1631 … … 1614 1637 % Time evolution term 1615 1638 % ================================================================ 1616 \section{Time evolution term (\protect\mdl{dynnxt})} 1639 \section[Time evolution term (\textit{dynnxt.F90})] 1640 {Time evolution term (\protect\mdl{dynnxt})} 1617 1641 \label{sec:DYN_nxt} 1618 1642 -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_LBC.tex
r10614 r11263 17 17 % Boundary Condition at the Coast 18 18 % ================================================================ 19 \section{Boundary condition at the coast (\protect\np{rn\_shlat})} 19 \section[Boundary condition at the coast (\texttt{rn\_shlat})] 20 {Boundary condition at the coast (\protect\np{rn\_shlat})} 20 21 \label{sec:LBC_coast} 21 22 %--------------------------------------------nam_lbc------------------------------------------------------- … … 56 57 \begin{figure}[!t] 57 58 \begin{center} 58 \includegraphics[width= 0.90\textwidth]{Fig_LBC_uv}59 \includegraphics[width=\textwidth]{Fig_LBC_uv} 59 60 \caption{ 60 61 \protect\label{fig:LBC_uv} … … 85 86 \begin{figure}[!p] 86 87 \begin{center} 87 \includegraphics[width= 0.90\textwidth]{Fig_LBC_shlat}88 \includegraphics[width=\textwidth]{Fig_LBC_shlat} 88 89 \caption{ 89 90 \protect\label{fig:LBC_shlat} … … 147 148 % Boundary Condition around the Model Domain 148 149 % ================================================================ 149 \section{Model domain boundary condition (\protect\np{jperio})} 150 \section[Model domain boundary condition (\texttt{jperio})] 151 {Model domain boundary condition (\protect\np{jperio})} 150 152 \label{sec:LBC_jperio} 151 153 … … 158 160 % Closed, cyclic (\np{jperio}\forcode{ = 0..2}) 159 161 % ------------------------------------------------------------------------------------------------------------- 160 \subsection{Closed, cyclic (\protect\np{jperio}\forcode{= [0127]})} 162 \subsection[Closed, cyclic (\forcode{jperio = [0127]})] 163 {Closed, cyclic (\protect\np{jperio}\forcode{ = [0127]})} 161 164 \label{subsec:LBC_jperio012} 162 165 … … 194 197 \begin{figure}[!t] 195 198 \begin{center} 196 \includegraphics[width= 1.0\textwidth]{Fig_LBC_jperio}199 \includegraphics[width=\textwidth]{Fig_LBC_jperio} 197 200 \caption{ 198 201 \protect\label{fig:LBC_jperio} … … 206 209 % North fold (\textit{jperio = 3 }to $6)$ 207 210 % ------------------------------------------------------------------------------------------------------------- 208 \subsection{North-fold (\protect\np{jperio}\forcode{ = 3..6})} 211 \subsection[North-fold (\forcode{jperio = [3-6]})] 212 {North-fold (\protect\np{jperio}\forcode{ = [3-6]})} 209 213 \label{subsec:LBC_north_fold} 210 214 … … 218 222 \begin{figure}[!t] 219 223 \begin{center} 220 \includegraphics[width= 0.90\textwidth]{Fig_North_Fold_T}224 \includegraphics[width=\textwidth]{Fig_North_Fold_T} 221 225 \caption{ 222 226 \protect\label{fig:North_Fold_T} … … 232 236 % Exchange with neighbouring processors 233 237 % ==================================================================== 234 \section{Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})} 238 \section[Exchange with neighbouring processors (\textit{lbclnk.F90}, \textit{lib\_mpp.F90})] 239 {Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})} 235 240 \label{sec:LBC_mpp} 236 241 … … 280 285 \begin{figure}[!t] 281 286 \begin{center} 282 \includegraphics[width= 0.90\textwidth]{Fig_mpp}287 \includegraphics[width=\textwidth]{Fig_mpp} 283 288 \caption{ 284 289 \protect\label{fig:mpp} … … 360 365 \begin{figure}[!ht] 361 366 \begin{center} 362 \includegraphics[width= 0.90\textwidth]{Fig_mppini2}367 \includegraphics[width=\textwidth]{Fig_mppini2} 363 368 \caption { 364 369 \protect\label{fig:mppini2} … … 395 400 396 401 The BDY module was modelled on the OBC module (see NEMO 3.4) and shares many features and 397 a similar coding structure \citep{ Chanut2005}.402 a similar coding structure \citep{chanut_rpt05}. 398 403 The specification of the location of the open boundary is completely flexible and 399 404 allows for example the open boundary to follow an isobath or other irregular contour. … … 475 480 \label{subsec:BDY_FRS_scheme} 476 481 477 The Flow Relaxation Scheme (FRS) \citep{ Davies_QJRMS76,Engerdahl_Tel95},482 The Flow Relaxation Scheme (FRS) \citep{davies_QJRMS76,engedahl_T95}, 478 483 applies a simple relaxation of the model fields to externally-specified values over 479 484 a zone next to the edge of the model domain. … … 514 519 \label{subsec:BDY_flather_scheme} 515 520 516 The \citet{ Flather_JPO94} scheme is a radiation condition on the normal,521 The \citet{flather_JPO94} scheme is a radiation condition on the normal, 517 522 depth-mean transport across the open boundary. 518 523 It takes the form … … 535 540 \label{subsec:BDY_orlanski_scheme} 536 541 537 The Orlanski scheme is based on the algorithm described by \citep{ Marchesiello2001}, hereafter MMS.542 The Orlanski scheme is based on the algorithm described by \citep{marchesiello.mcwilliams.ea_OM01}, hereafter MMS. 538 543 539 544 The adaptive Orlanski condition solves a wave plus relaxation equation at the boundary: … … 636 641 \begin{figure}[!t] 637 642 \begin{center} 638 \includegraphics[width= 1.0\textwidth]{Fig_LBC_bdy_geom}643 \includegraphics[width=\textwidth]{Fig_LBC_bdy_geom} 639 644 \caption { 640 645 \protect\label{fig:LBC_bdy_geom} … … 670 675 These restrictions mean that data files used with versions of the 671 676 model prior to Version 3.4 may not work with Version 3.4 onwards. 672 A \fortran utility {\it bdy\_reorder} exists in the TOOLS directory which677 A \fortran utility {\itshape bdy\_reorder} exists in the TOOLS directory which 673 678 will re-order the data in old BDY data files. 674 679 … … 676 681 \begin{figure}[!t] 677 682 \begin{center} 678 \includegraphics[width= 1.0\textwidth]{Fig_LBC_nc_header}683 \includegraphics[width=\textwidth]{Fig_LBC_nc_header} 679 684 \caption { 680 685 \protect\label{fig:LBC_nc_header} -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_LDF.tex
r10442 r11263 38 38 % Direction of lateral Mixing 39 39 % ================================================================ 40 \section{Direction of lateral mixing (\protect\mdl{ldfslp})} 40 \section[Direction of lateral mixing (\textit{ldfslp.F90})] 41 {Direction of lateral mixing (\protect\mdl{ldfslp})} 41 42 \label{sec:LDF_slp} 42 43 … … 44 45 \gmcomment{ 45 46 we should emphasize here that the implementation is a rather old one. 46 Better work can be achieved by using \citet{ Griffies_al_JPO98, Griffies_Bk04} iso-neutral scheme.47 Better work can be achieved by using \citet{griffies.gnanadesikan.ea_JPO98, griffies_bk04} iso-neutral scheme. 47 48 } 48 49 … … 119 120 %In practice, \autoref{eq:ldfslp_iso} is of little help in evaluating the neutral surface slopes. Indeed, for an unsimplified equation of state, the density has a strong dependancy on pressure (here approximated as the depth), therefore applying \autoref{eq:ldfslp_iso} using the $in situ$ density, $\rho$, computed at T-points leads to a flattening of slopes as the depth increases. This is due to the strong increase of the $in situ$ density with depth. 120 121 121 %By definition, neutral surfaces are tangent to the local $in situ$ density \citep{ McDougall1987}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters).122 %By definition, neutral surfaces are tangent to the local $in situ$ density \citep{mcdougall_JPO87}, therefore in \autoref{eq:ldfslp_iso}, all the derivatives have to be evaluated at the same local pressure (which in decibars is approximated by the depth in meters). 122 123 123 124 %In the $z$-coordinate, the derivative of the \autoref{eq:ldfslp_iso} numerator is evaluated at the same depth \nocite{as what?} ($T$-level, which is the same as the $u$- and $v$-levels), so the $in situ$ density can be used for its evaluation. … … 135 136 thus the $in situ$ density can be used. 136 137 This is not the case for the vertical derivatives: $\delta_{k+1/2}[\rho]$ is replaced by $-\rho N^2/g$, 137 where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{ McDougall1987}138 where $N^2$ is the local Brunt-Vais\"{a}l\"{a} frequency evaluated following \citet{mcdougall_JPO87} 138 139 (see \autoref{subsec:TRA_bn2}). 139 140 … … 154 155 Note: The solution for $s$-coordinate passes trough the use of different (and better) expression for 155 156 the constraint on iso-neutral fluxes. 156 Following \citet{ Griffies_Bk04}, instead of specifying directly that there is a zero neutral diffusive flux of157 Following \citet{griffies_bk04}, instead of specifying directly that there is a zero neutral diffusive flux of 157 158 locally referenced potential density, we stay in the $T$-$S$ plane and consider the balance between 158 159 the neutral direction diffusive fluxes of potential temperature and salinity: … … 201 202 a minimum background horizontal diffusion for numerical stability reasons. 202 203 To overcome this problem, several techniques have been proposed in which the numerical schemes of 203 the ocean model are modified \citep{ Weaver_Eby_JPO97, Griffies_al_JPO98}.204 the ocean model are modified \citep{weaver.eby_JPO97, griffies.gnanadesikan.ea_JPO98}. 204 205 Griffies's scheme is now available in \NEMO if \np{traldf\_grif\_iso} is set true; see Appdx \autoref{apdx:triad}. 205 Here, another strategy is presented \citep{ Lazar_PhD97}:206 Here, another strategy is presented \citep{lazar_phd97}: 206 207 a local filtering of the iso-neutral slopes (made on 9 grid-points) prevents the development of 207 208 grid point noise generated by the iso-neutral diffusion operator (\autoref{fig:LDF_ZDF1}). … … 212 213 213 214 Nevertheless, this iso-neutral operator does not ensure that variance cannot increase, 214 contrary to the \citet{ Griffies_al_JPO98} operator which has that property.215 contrary to the \citet{griffies.gnanadesikan.ea_JPO98} operator which has that property. 215 216 216 217 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 217 218 \begin{figure}[!ht] 218 219 \begin{center} 219 \includegraphics[width= 0.70\textwidth]{Fig_LDF_ZDF1}220 \includegraphics[width=\textwidth]{Fig_LDF_ZDF1} 220 221 \caption { 221 222 \protect\label{fig:LDF_ZDF1} … … 235 236 236 237 237 % In addition and also for numerical stability reasons \citep{ Cox1987, Griffies_Bk04},238 % In addition and also for numerical stability reasons \citep{cox_OM87, griffies_bk04}, 238 239 % the slopes are bounded by $1/100$ everywhere. This limit is decreasing linearly 239 240 % to zero fom $70$ meters depth and the surface (the fact that the eddies "feel" the 240 241 % surface motivates this flattening of isopycnals near the surface). 241 242 242 For numerical stability reasons \citep{ Cox1987, Griffies_Bk04}, the slopes must also be bounded by243 For numerical stability reasons \citep{cox_OM87, griffies_bk04}, the slopes must also be bounded by 243 244 $1/100$ everywhere. 244 245 This constraint is applied in a piecewise linear fashion, increasing from zero at the surface to … … 249 250 \begin{figure}[!ht] 250 251 \begin{center} 251 \includegraphics[width= 0.70\textwidth]{Fig_eiv_slp}252 \includegraphics[width=\textwidth]{Fig_eiv_slp} 252 253 \caption{ 253 254 \protect\label{fig:eiv_slp} … … 301 302 % Lateral Mixing Operator 302 303 % ================================================================ 303 \section{Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf}) } 304 \section[Lateral mixing operators (\textit{traldf.F90})] 305 {Lateral mixing operators (\protect\mdl{traldf}, \protect\mdl{traldf})} 304 306 \label{sec:LDF_op} 305 307 … … 309 311 % Lateral Mixing Coefficients 310 312 % ================================================================ 311 \section{Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn}) } 313 \section[Lateral mixing coefficient (\textit{ldftra.F90}, \textit{ldfdyn.F90})] 314 {Lateral mixing coefficient (\protect\mdl{ldftra}, \protect\mdl{ldfdyn})} 312 315 \label{sec:LDF_coef} 313 316 … … 339 342 which is specified through the \np{rn\_ahm0} and \np{rn\_aht0} namelist parameters. 340 343 341 \subsubsection{Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})} 344 \subsubsection[Vertically varying mixing coefficients (\texttt{\textbf{key\_traldf\_c1d}} and \texttt{\textbf{key\_dynldf\_c1d}})] 345 {Vertically varying mixing coefficients (\protect\key{traldf\_c1d} and \key{dynldf\_c1d})} 342 346 The 1D option is only available when using the $z$-coordinate with full step. 343 347 Indeed in all the other types of vertical coordinate, … … 350 354 This profile is hard coded in file \textit{traldf\_c1d.h90}, but can be easily modified by users. 351 355 352 \subsubsection{Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 356 \subsubsection[Horizontally varying mixing coefficients (\texttt{\textbf{key\_traldf\_c2d}} and \texttt{\textbf{key\_dynldf\_c2d}})] 357 {Horizontally varying mixing coefficients (\protect\key{traldf\_c2d} and \protect\key{dynldf\_c2d})} 353 358 By default the horizontal variation of the eddy coefficient depends on the local mesh size and 354 359 the type of operator used: … … 366 371 This variation is intended to reflect the lesser need for subgrid scale eddy mixing where 367 372 the grid size is smaller in the domain. 368 It was introduced in the context of the DYNAMO modelling project \citep{ Willebrand_al_PO01}.373 It was introduced in the context of the DYNAMO modelling project \citep{willebrand.barnier.ea_PO01}. 369 374 Note that such a grid scale dependance of mixing coefficients significantly increase the range of stability of 370 375 model configurations presenting large changes in grid pacing such as global ocean models. … … 376 381 For example, in the ORCA2 global ocean model (see Configurations), 377 382 the laplacian viscosity operator uses \np{rn\_ahm0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$ north and south and 378 decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{ Madec_al_JPO96, Delecluse_Madec_Bk00}.383 decreases linearly to \np{rn\_aht0}~= 2.10$^3$ m$^2$/s at the equator \citep{madec.delecluse.ea_JPO96, delecluse.madec_icol99}. 379 384 This modification can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}. 380 385 Similar modified horizontal variations can be found with the Antarctic or Arctic sub-domain options of 381 386 ORCA2 and ORCA05 (see \&namcfg namelist). 382 387 383 \subsubsection{Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})} 388 \subsubsection[Space varying mixing coefficients (\texttt{\textbf{key\_traldf\_c3d}} and \texttt{\textbf{key\_dynldf\_c3d}})] 389 {Space varying mixing coefficients (\protect\key{traldf\_c3d} and \key{dynldf\_c3d})} 384 390 385 391 The 3D space variation of the mixing coefficient is simply the combination of the 1D and 2D cases, … … 430 436 % Eddy Induced Mixing 431 437 % ================================================================ 432 \section{Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 438 \section[Eddy induced velocity (\textit{traadv\_eiv.F90}, \textit{ldfeiv.F90})] 439 {Eddy induced velocity (\protect\mdl{traadv\_eiv}, \protect\mdl{ldfeiv})} 433 440 \label{sec:LDF_eiv} 434 441 … … 475 482 since it allows us to take advantage of all the advection schemes offered for the tracers 476 483 (see \autoref{sec:TRA_adv}) and not just the $2^{nd}$ order advection scheme as in 477 previous releases of OPA \citep{ Madec1998}.484 previous releases of OPA \citep{madec.delecluse.ea_NPM98}. 478 485 This is particularly useful for passive tracers where \emph{positivity} of the advection scheme is of 479 486 paramount importance. -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_OBS.tex
r10442 r11263 573 573 \subsubsection{Horizontal interpolation} 574 574 575 Consider an observation point ${\ rm P}$ with with longitude and latitude $({\lambda_{}}_{\rm P}, \phi_{\rm P})$ and576 the four nearest neighbouring model grid points ${\ rm A}$, ${\rm B}$, ${\rm C}$ and ${\rm D}$ with577 longitude and latitude ($\lambda_{\ rm A}$, $\phi_{\rm A}$),($\lambda_{\rm B}$, $\phi_{\rm B}$) etc.575 Consider an observation point ${\mathrm P}$ with with longitude and latitude $({\lambda_{}}_{\mathrm P}, \phi_{\mathrm P})$ and 576 the four nearest neighbouring model grid points ${\mathrm A}$, ${\mathrm B}$, ${\mathrm C}$ and ${\mathrm D}$ with 577 longitude and latitude ($\lambda_{\mathrm A}$, $\phi_{\mathrm A}$),($\lambda_{\mathrm B}$, $\phi_{\mathrm B}$) etc. 578 578 All horizontal interpolation methods implemented in NEMO estimate the value of a model variable $x$ at point $P$ as 579 a weighted linear combination of the values of the model variables at the grid points ${\ rm A}$, ${\rm B}$ etc.:579 a weighted linear combination of the values of the model variables at the grid points ${\mathrm A}$, ${\mathrm B}$ etc.: 580 580 \begin{align*} 581 {x_{}}_{\ rm P} & \hspace{-2mm} = \hspace{-2mm} &582 \frac{1}{w} \left( {w_{}}_{\ rm A} {x_{}}_{\rm A} +583 {w_{}}_{\ rm B} {x_{}}_{\rm B} +584 {w_{}}_{\ rm C} {x_{}}_{\rm C} +585 {w_{}}_{\ rm D} {x_{}}_{\rm D} \right)581 {x_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & 582 \frac{1}{w} \left( {w_{}}_{\mathrm A} {x_{}}_{\mathrm A} + 583 {w_{}}_{\mathrm B} {x_{}}_{\mathrm B} + 584 {w_{}}_{\mathrm C} {x_{}}_{\mathrm C} + 585 {w_{}}_{\mathrm D} {x_{}}_{\mathrm D} \right) 586 586 \end{align*} 587 where ${w_{}}_{\ rm A}$, ${w_{}}_{\rm B}$ etc. are the respective weights for the model field at588 points ${\ rm A}$, ${\rm B}$ etc., and $w = {w_{}}_{\rm A} + {w_{}}_{\rm B} + {w_{}}_{\rm C} + {w_{}}_{\rm D}$.587 where ${w_{}}_{\mathrm A}$, ${w_{}}_{\mathrm B}$ etc. are the respective weights for the model field at 588 points ${\mathrm A}$, ${\mathrm B}$ etc., and $w = {w_{}}_{\mathrm A} + {w_{}}_{\mathrm B} + {w_{}}_{\mathrm C} + {w_{}}_{\mathrm D}$. 589 589 590 590 Four different possibilities are available for computing the weights. … … 592 592 \begin{enumerate} 593 593 594 \item[1.] {\bf Great-Circle distance-weighted interpolation.}594 \item[1.] {\bfseries Great-Circle distance-weighted interpolation.} 595 595 The weights are computed as a function of the great-circle distance $s(P, \cdot)$ between $P$ and 596 596 the model grid points $A$, $B$ etc. 597 For example, the weight given to the field ${x_{}}_{\ rm A}$ is specified as the product of the distances598 from ${\ rm P}$ to the other points:597 For example, the weight given to the field ${x_{}}_{\mathrm A}$ is specified as the product of the distances 598 from ${\mathrm P}$ to the other points: 599 599 \begin{align*} 600 {w_{}}_{\ rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D})600 {w_{}}_{\mathrm A} = s({\mathrm P}, {\mathrm B}) \, s({\mathrm P}, {\mathrm C}) \, s({\mathrm P}, {\mathrm D}) 601 601 \end{align*} 602 602 where 603 603 \begin{align*} 604 s\left ({\ rm P}, {\rm M} \right )604 s\left ({\mathrm P}, {\mathrm M} \right ) 605 605 & \hspace{-2mm} = \hspace{-2mm} & 606 606 \cos^{-1} \! \left\{ 607 \sin {\phi_{}}_{\ rm P} \sin {\phi_{}}_{\rm M}608 + \cos {\phi_{}}_{\ rm P} \cos {\phi_{}}_{\rm M}609 \cos ({\lambda_{}}_{\ rm M} - {\lambda_{}}_{\rm P})607 \sin {\phi_{}}_{\mathrm P} \sin {\phi_{}}_{\mathrm M} 608 + \cos {\phi_{}}_{\mathrm P} \cos {\phi_{}}_{\mathrm M} 609 \cos ({\lambda_{}}_{\mathrm M} - {\lambda_{}}_{\mathrm P}) 610 610 \right\} 611 611 \end{align*} 612 612 and $M$ corresponds to $B$, $C$ or $D$. 613 613 A more stable form of the great-circle distance formula for small distances ($x$ near 1) 614 involves the arcsine function (\eg see p.~101 of \citet{ Daley_Barker_Bk01}:614 involves the arcsine function (\eg see p.~101 of \citet{daley.barker_bk01}: 615 615 \begin{align*} 616 s\left( {\ rm P}, {\rm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\}616 s\left( {\mathrm P}, {\mathrm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\} 617 617 \end{align*} 618 618 where 619 619 \begin{align*} 620 620 x & \hspace{-2mm} = \hspace{-2mm} & 621 {a_{}}_{\ rm M} {a_{}}_{\rm P} + {b_{}}_{\rm M} {b_{}}_{\rm P} + {c_{}}_{\rm M} {c_{}}_{\rm P}621 {a_{}}_{\mathrm M} {a_{}}_{\mathrm P} + {b_{}}_{\mathrm M} {b_{}}_{\mathrm P} + {c_{}}_{\mathrm M} {c_{}}_{\mathrm P} 622 622 \end{align*} 623 623 and 624 624 \begin{align*} 625 {a_{}}_{\ rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, \\626 {a_{}}_{\ rm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm P}, \\627 {b_{}}_{\ rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \cos {\phi_{}}_{\rm M}, \\628 {b_{}}_{\ rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm P}, \\629 {c_{}}_{\ rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \sin {\phi_{}}_{\rm M}, \\630 {c_{}}_{\ rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm P}.625 {a_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\mathrm M}, \\ 626 {a_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\mathrm P}, \\ 627 {b_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm M} \cos {\phi_{}}_{\mathrm M}, \\ 628 {b_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm P} \cos {\phi_{}}_{\mathrm P}, \\ 629 {c_{}}_{\mathrm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm M} \sin {\phi_{}}_{\mathrm M}, \\ 630 {c_{}}_{\mathrm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\mathrm P} \sin {\phi_{}}_{\mathrm P}. 631 631 \end{align*} 632 632 633 \item[2.] {\bf Great-Circle distance-weighted interpolation with small angle approximation.}633 \item[2.] {\bfseries Great-Circle distance-weighted interpolation with small angle approximation.} 634 634 Similar to the previous interpolation but with the distance $s$ computed as 635 635 \begin{align*} 636 s\left( {\ rm P}, {\rm M} \right)636 s\left( {\mathrm P}, {\mathrm M} \right) 637 637 & \hspace{-2mm} = \hspace{-2mm} & 638 \sqrt{ \left( {\phi_{}}_{\ rm M} - {\phi_{}}_{\rm P} \right)^{2}639 + \left( {\lambda_{}}_{\ rm M} - {\lambda_{}}_{\rm P} \right)^{2}640 \cos^{2} {\phi_{}}_{\ rm M} }638 \sqrt{ \left( {\phi_{}}_{\mathrm M} - {\phi_{}}_{\mathrm P} \right)^{2} 639 + \left( {\lambda_{}}_{\mathrm M} - {\lambda_{}}_{\mathrm P} \right)^{2} 640 \cos^{2} {\phi_{}}_{\mathrm M} } 641 641 \end{align*} 642 642 where $M$ corresponds to $A$, $B$, $C$ or $D$. 643 643 644 \item[3.] {\bf Bilinear interpolation for a regular spaced grid.}644 \item[3.] {\bfseries Bilinear interpolation for a regular spaced grid.} 645 645 The interpolation is split into two 1D interpolations in the longitude and latitude directions, respectively. 646 646 647 \item[4.] {\bf Bilinear remapping interpolation for a general grid.}647 \item[4.] {\bfseries Bilinear remapping interpolation for a general grid.} 648 648 An iterative scheme that involves first mapping a quadrilateral cell into 649 649 a cell with coordinates (0,0), (1,0), (0,1) and (1,1). 650 This method is based on the SCRIP interpolation package \citep{Jones_1998}.650 This method is based on the \href{https://github.com/SCRIP-Project/SCRIP}{SCRIP interpolation package}. 651 651 652 652 \end{enumerate} … … 678 678 \begin{figure} 679 679 \begin{center} 680 \includegraphics[width= 0.90\textwidth]{Fig_OBS_avg_rec}680 \includegraphics[width=\textwidth]{Fig_OBS_avg_rec} 681 681 \caption{ 682 682 \protect\label{fig:obsavgrec} … … 691 691 \begin{figure} 692 692 \begin{center} 693 \includegraphics[width= 0.90\textwidth]{Fig_OBS_avg_rad}693 \includegraphics[width=\textwidth]{Fig_OBS_avg_rad} 694 694 \caption{ 695 695 \protect\label{fig:obsavgrad} … … 710 710 This is the most difficult and time consuming part of the 2D interpolation procedure. 711 711 A robust test for determining if an observation falls within a given quadrilateral cell is as follows. 712 Let ${\ rm P}({\lambda_{}}_{\rm P} ,{\phi_{}}_{\rm P} )$ denote the observation point,713 and let ${\ rm A}({\lambda_{}}_{\rm A} ,{\phi_{}}_{\rm A} )$, ${\rm B}({\lambda_{}}_{\rm B} ,{\phi_{}}_{\rm B} )$,714 ${\ rm C}({\lambda_{}}_{\rm C} ,{\phi_{}}_{\rm C} )$ and ${\rm D}({\lambda_{}}_{\rm D} ,{\phi_{}}_{\rm D} )$712 Let ${\mathrm P}({\lambda_{}}_{\mathrm P} ,{\phi_{}}_{\mathrm P} )$ denote the observation point, 713 and let ${\mathrm A}({\lambda_{}}_{\mathrm A} ,{\phi_{}}_{\mathrm A} )$, ${\mathrm B}({\lambda_{}}_{\mathrm B} ,{\phi_{}}_{\mathrm B} )$, 714 ${\mathrm C}({\lambda_{}}_{\mathrm C} ,{\phi_{}}_{\mathrm C} )$ and ${\mathrm D}({\lambda_{}}_{\mathrm D} ,{\phi_{}}_{\mathrm D} )$ 715 715 denote the bottom left, bottom right, top left and top right corner points of the cell, respectively. 716 716 To determine if P is inside the cell, we verify that the cross-products 717 717 \begin{align*} 718 718 \begin{array}{lllll} 719 {{\ bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC}720 & = & [({\lambda_{}}_{\ rm A}\; -\; {\lambda_{}}_{\rm P} )721 ({\phi_{}}_{\ rm C} \; -\; {\phi_{}}_{\rm P} )722 - ({\lambda_{}}_{\ rm C}\; -\; {\lambda_{}}_{\rm P} )723 ({\phi_{}}_{\ rm A} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\724 {{\ bf r}_{}}_{\rm PB} \times {{\bf r}_{}}_{\rm PA}725 & = & [({\lambda_{}}_{\ rm B}\; -\; {\lambda_{}}_{\rm P} )726 ({\phi_{}}_{\ rm A} \; -\; {\phi_{}}_{\rm P} )727 - ({\lambda_{}}_{\ rm A}\; -\; {\lambda_{}}_{\rm P} )728 ({\phi_{}}_{\ rm B} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\729 {{\ bf r}_{}}_{\rm PC} \times {{\bf r}_{}}_{\rm PD}730 & = & [({\lambda_{}}_{\ rm C}\; -\; {\lambda_{}}_{\rm P} )731 ({\phi_{}}_{\ rm D} \; -\; {\phi_{}}_{\rm P} )732 - ({\lambda_{}}_{\ rm D}\; -\; {\lambda_{}}_{\rm P} )733 ({\phi_{}}_{\ rm C} \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\734 {{\ bf r}_{}}_{\rm PD} \times {{\bf r}_{}}_{\rm PB}735 & = & [({\lambda_{}}_{\ rm D}\; -\; {\lambda_{}}_{\rm P} )736 ({\phi_{}}_{\ rm B} \; -\; {\phi_{}}_{\rm P} )737 - ({\lambda_{}}_{\ rm B}\; -\; {\lambda_{}}_{\rm P} )738 ({\phi_{}}_{\ rm D} \; - \; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\719 {{\mathbf r}_{}}_{\mathrm PA} \times {{\mathbf r}_{}}_{\mathrm PC} 720 & = & [({\lambda_{}}_{\mathrm A}\; -\; {\lambda_{}}_{\mathrm P} ) 721 ({\phi_{}}_{\mathrm C} \; -\; {\phi_{}}_{\mathrm P} ) 722 - ({\lambda_{}}_{\mathrm C}\; -\; {\lambda_{}}_{\mathrm P} ) 723 ({\phi_{}}_{\mathrm A} \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 724 {{\mathbf r}_{}}_{\mathrm PB} \times {{\mathbf r}_{}}_{\mathrm PA} 725 & = & [({\lambda_{}}_{\mathrm B}\; -\; {\lambda_{}}_{\mathrm P} ) 726 ({\phi_{}}_{\mathrm A} \; -\; {\phi_{}}_{\mathrm P} ) 727 - ({\lambda_{}}_{\mathrm A}\; -\; {\lambda_{}}_{\mathrm P} ) 728 ({\phi_{}}_{\mathrm B} \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 729 {{\mathbf r}_{}}_{\mathrm PC} \times {{\mathbf r}_{}}_{\mathrm PD} 730 & = & [({\lambda_{}}_{\mathrm C}\; -\; {\lambda_{}}_{\mathrm P} ) 731 ({\phi_{}}_{\mathrm D} \; -\; {\phi_{}}_{\mathrm P} ) 732 - ({\lambda_{}}_{\mathrm D}\; -\; {\lambda_{}}_{\mathrm P} ) 733 ({\phi_{}}_{\mathrm C} \; -\; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 734 {{\mathbf r}_{}}_{\mathrm PD} \times {{\mathbf r}_{}}_{\mathrm PB} 735 & = & [({\lambda_{}}_{\mathrm D}\; -\; {\lambda_{}}_{\mathrm P} ) 736 ({\phi_{}}_{\mathrm B} \; -\; {\phi_{}}_{\mathrm P} ) 737 - ({\lambda_{}}_{\mathrm B}\; -\; {\lambda_{}}_{\mathrm P} ) 738 ({\phi_{}}_{\mathrm D} \; - \; {\phi_{}}_{\mathrm P} )] \; \widehat{\mathbf k} \\ 739 739 \end{array} 740 740 % \label{eq:cross} 741 741 \end{align*} 742 point in the opposite direction to the unit normal $\widehat{\ bf k}$743 (\ie that the coefficients of $\widehat{\ bf k}$ are negative),744 where ${{\ bf r}_{}}_{\rm PA}$, ${{\bf r}_{}}_{\rm PB}$, etc. correspond to742 point in the opposite direction to the unit normal $\widehat{\mathbf k}$ 743 (\ie that the coefficients of $\widehat{\mathbf k}$ are negative), 744 where ${{\mathbf r}_{}}_{\mathrm PA}$, ${{\mathbf r}_{}}_{\mathrm PB}$, etc. correspond to 745 745 the vectors between points P and A, P and B, etc.. 746 The method used is similar to the method used in the SCRIP interpolation package \citep{Jones_1998}.746 The method used is similar to the method used in the \href{https://github.com/SCRIP-Project/SCRIP}{SCRIP interpolation package}. 747 747 748 748 In order to speed up the grid search, there is the possibility to construct a lookup table for a user specified resolution. … … 772 772 \begin{figure} 773 773 \begin{center} 774 \includegraphics[width= 10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_local}774 \includegraphics[width=\textwidth]{Fig_ASM_obsdist_local} 775 775 \caption{ 776 776 \protect\label{fig:obslocal} … … 801 801 \begin{figure} 802 802 \begin{center} 803 \includegraphics[width= 10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_global}803 \includegraphics[width=\textwidth]{Fig_ASM_obsdist_global} 804 804 \caption{ 805 805 \protect\label{fig:obsglobal} … … 1370 1370 \begin{figure} 1371 1371 \begin{center} 1372 % \includegraphics[width= 10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_main}1373 \includegraphics[width= 9cm,angle=-90.]{Fig_OBS_dataplot_main}1372 % \includegraphics[width=\textwidth]{Fig_OBS_dataplot_main} 1373 \includegraphics[width=\textwidth]{Fig_OBS_dataplot_main} 1374 1374 \caption{ 1375 1375 \protect\label{fig:obsdataplotmain} … … 1386 1386 \begin{figure} 1387 1387 \begin{center} 1388 % \includegraphics[width= 10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_prof}1389 \includegraphics[width= 7cm,angle=-90.]{Fig_OBS_dataplot_prof}1388 % \includegraphics[width=\textwidth]{Fig_OBS_dataplot_prof} 1389 \includegraphics[width=\textwidth]{Fig_OBS_dataplot_prof} 1390 1390 \caption{ 1391 1391 \protect\label{fig:obsdataplotprofile} -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_SBC.tex
r10614 r11263 5 5 % Chapter —— Surface Boundary Condition (SBC, ISF, ICB) 6 6 % ================================================================ 7 \chapter{Surface Boundary Condition (SBC, ISF, ICB) 7 \chapter{Surface Boundary Condition (SBC, ISF, ICB)} 8 8 \label{chap:SBC} 9 9 \minitoc … … 226 226 % Input Data specification (\mdl{fldread}) 227 227 % ------------------------------------------------------------------------------------------------------------- 228 \subsection{Input data specification (\protect\mdl{fldread})} 228 \subsection[Input data specification (\textit{fldread.F90})] 229 {Input data specification (\protect\mdl{fldread})} 229 230 \label{subsec:SBC_fldread} 230 231 … … 313 314 The only tricky point is therefore to specify the date at which we need to do the interpolation and 314 315 the date of the records read in the input files. 315 Following \citet{ Leclair_Madec_OM09}, the date of a time step is set at the middle of the time step.316 Following \citet{leclair.madec_OM09}, the date of a time step is set at the middle of the time step. 316 317 For example, for an experiment starting at 0h00'00" with a one hour time-step, 317 318 a time interpolation will be performed at the following time: 0h30'00", 1h30'00", 2h30'00", etc. … … 559 560 % Analytical formulation (sbcana module) 560 561 % ================================================================ 561 \section{Analytical formulation (\protect\mdl{sbcana})} 562 \section[Analytical formulation (\textit{sbcana.F90})] 563 {Analytical formulation (\protect\mdl{sbcana})} 562 564 \label{sec:SBC_ana} 563 565 … … 584 586 % Flux formulation 585 587 % ================================================================ 586 \section{Flux formulation (\protect\mdl{sbcflx})} 588 \section[Flux formulation (\textit{sbcflx.F90})] 589 {Flux formulation (\protect\mdl{sbcflx})} 587 590 \label{sec:SBC_flx} 588 591 %------------------------------------------namsbc_flx---------------------------------------------------- … … 606 609 % ================================================================ 607 610 \section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}] 608 611 {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}} 609 612 \label{sec:SBC_blk} 610 613 … … 625 628 % CORE Bulk formulea 626 629 % ------------------------------------------------------------------------------------------------------------- 627 \subsection{CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})} 630 \subsection[CORE formulea (\textit{sbcblk\_core.F90}, \forcode{ln_core = .true.})] 631 {CORE formulea (\protect\mdl{sbcblk\_core}, \protect\np{ln\_core}\forcode{ = .true.})} 628 632 \label{subsec:SBC_blk_core} 629 633 %------------------------------------------namsbc_core---------------------------------------------------- … … 632 636 %------------------------------------------------------------------------------------------------------------- 633 637 634 The CORE bulk formulae have been developed by \citet{ Large_Yeager_Rep04}.638 The CORE bulk formulae have been developed by \citet{large.yeager_rpt04}. 635 639 They have been designed to handle the CORE forcing, a mixture of NCEP reanalysis and satellite data. 636 640 They use an inertial dissipative method to compute the turbulent transfer coefficients 637 641 (momentum, sensible heat and evaporation) from the 10 metre wind speed, air temperature and specific humidity. 638 This \citet{ Large_Yeager_Rep04} dataset is available through642 This \citet{large.yeager_rpt04} dataset is available through 639 643 the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. 640 644 641 645 Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 642 This is the so-called DRAKKAR Forcing Set (DFS) \citep{ Brodeau_al_OM09}.646 This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 643 647 644 648 Options are defined through the \ngn{namsbc\_core} namelist variables. … … 688 692 % CLIO Bulk formulea 689 693 % ------------------------------------------------------------------------------------------------------------- 690 \subsection{CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})} 694 \subsection[CLIO formulea (\textit{sbcblk\_clio.F90}, \forcode{ln_clio = .true.})] 695 {CLIO formulea (\protect\mdl{sbcblk\_clio}, \protect\np{ln\_clio}\forcode{ = .true.})} 691 696 \label{subsec:SBC_blk_clio} 692 697 %------------------------------------------namsbc_clio---------------------------------------------------- … … 696 701 697 702 The CLIO bulk formulae were developed several years ago for the Louvain-la-neuve coupled ice-ocean model 698 (CLIO, \cite{ Goosse_al_JGR99}).703 (CLIO, \cite{goosse.deleersnijder.ea_JGR99}). 699 704 They are simpler bulk formulae. 700 705 They assume the stress to be known and compute the radiative fluxes from a climatological cloud cover. … … 729 734 % Coupled formulation 730 735 % ================================================================ 731 \section{Coupled formulation (\protect\mdl{sbccpl})} 736 \section[Coupled formulation (\textit{sbccpl.F90})] 737 {Coupled formulation (\protect\mdl{sbccpl})} 732 738 \label{sec:SBC_cpl} 733 739 %------------------------------------------namsbc_cpl---------------------------------------------------- … … 770 776 % Atmospheric pressure 771 777 % ================================================================ 772 \section{Atmospheric pressure (\protect\mdl{sbcapr})} 778 \section[Atmospheric pressure (\textit{sbcapr.F90})] 779 {Atmospheric pressure (\protect\mdl{sbcapr})} 773 780 \label{sec:SBC_apr} 774 781 %------------------------------------------namsbc_apr---------------------------------------------------- … … 806 813 % Surface Tides Forcing 807 814 % ================================================================ 808 \section{Surface tides (\protect\mdl{sbctide})} 815 \section[Surface tides (\textit{sbctide.F90})] 816 {Surface tides (\protect\mdl{sbctide})} 809 817 \label{sec:SBC_tide} 810 818 … … 819 827 \[ 820 828 % \label{eq:PE_dyn_tides} 821 \frac{\partial {\ rm {\bf U}}_h }{\partial t}= ...829 \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ... 822 830 +g\nabla (\Pi_{eq} + \Pi_{sal}) 823 831 \] … … 839 847 840 848 The SAL term should in principle be computed online as it depends on 841 the model tidal prediction itself (see \citet{ Arbic2004} for a849 the model tidal prediction itself (see \citet{arbic.garner.ea_DSR04} for a 842 850 discussion about the practical implementation of this term). 843 851 Nevertheless, the complex calculations involved would make this … … 857 865 % River runoffs 858 866 % ================================================================ 859 \section{River runoffs (\protect\mdl{sbcrnf})} 867 \section[River runoffs (\textit{sbcrnf.F90})] 868 {River runoffs (\protect\mdl{sbcrnf})} 860 869 \label{sec:SBC_rnf} 861 870 %------------------------------------------namsbc_rnf---------------------------------------------------- … … 871 880 %coastal modelling and becomes more and more often open ocean and climate modelling 872 881 %\footnote{At least a top cells thickness of 1~meter and a 3 hours forcing frequency are 873 %required to properly represent the diurnal cycle \citep{ Bernie_al_JC05}. see also \autoref{fig:SBC_dcy}.}.882 %required to properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. see also \autoref{fig:SBC_dcy}.}. 874 883 875 884 … … 892 901 \footnote{ 893 902 At least a top cells thickness of 1~meter and a 3 hours forcing frequency are required to 894 properly represent the diurnal cycle \citep{ Bernie_al_JC05}.903 properly represent the diurnal cycle \citep{bernie.woolnough.ea_JC05}. 895 904 see also \autoref{fig:SBC_dcy}.}. 896 905 … … 982 991 % Ice shelf melting 983 992 % ================================================================ 984 \section{Ice shelf melting (\protect\mdl{sbcisf})} 993 \section[Ice shelf melting (\textit{sbcisf.F90})] 994 {Ice shelf melting (\protect\mdl{sbcisf})} 985 995 \label{sec:SBC_isf} 986 996 %------------------------------------------namsbc_isf---------------------------------------------------- … … 989 999 %-------------------------------------------------------------------------------------------------------- 990 1000 The namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation. 991 Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{ Mathiot2017}.1001 Description and result of sensitivity test to \np{nn\_isf} are presented in \citet{mathiot.jenkins.ea_GMD17}. 992 1002 The different options are illustrated in \autoref{fig:SBC_isf}. 993 1003 … … 1001 1011 \item[\np{nn\_isfblk}\forcode{ = 1}]: 1002 1012 The melt rate is based on a balance between the upward ocean heat flux and 1003 the latent heat flux at the ice shelf base. A complete description is available in \citet{ Hunter2006}.1013 the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}. 1004 1014 \item[\np{nn\_isfblk}\forcode{ = 2}]: 1005 1015 The melt rate and the heat flux are based on a 3 equations formulation 1006 1016 (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation). 1007 A complete description is available in \citet{ Jenkins1991}.1017 A complete description is available in \citet{jenkins_JGR91}. 1008 1018 \end{description} 1009 1019 1010 Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{ Losch2008}.1020 Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}. 1011 1021 Its thickness is defined by \np{rn\_hisf\_tbl}. 1012 1022 The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn\_hisf\_tbl} m. … … 1038 1048 \] 1039 1049 where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters). 1040 See \citet{ Jenkins2010} for all the details on this formulation. It is the recommended formulation for realistic application.1050 See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application. 1041 1051 \item[\np{nn\_gammablk}\forcode{ = 2}]: 1042 1052 The salt and heat exchange coefficients are velocity and stability dependent and defined as: … … 1047 1057 $\Gamma_{Turb}$ the contribution of the ocean stability and 1048 1058 $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 1049 See \citet{ Holland1999} for all the details on this formulation.1059 See \citet{holland.jenkins_JPO99} for all the details on this formulation. 1050 1060 This formulation has not been extensively tested in NEMO (not recommended). 1051 1061 \end{description} 1052 1062 \item[\np{nn\_isf}\forcode{ = 2}]: 1053 1063 The ice shelf cavity is not represented. 1054 The fwf and heat flux are computed using the \citet{ Beckmann2003} parameterisation of isf melting.1064 The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting. 1055 1065 The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL) 1056 1066 (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front … … 1089 1099 \begin{figure}[!t] 1090 1100 \begin{center} 1091 \includegraphics[width= 0.8\textwidth]{Fig_SBC_isf}1101 \includegraphics[width=\textwidth]{Fig_SBC_isf} 1092 1102 \caption{ 1093 1103 \protect\label{fig:SBC_isf} … … 1166 1176 %------------------------------------------------------------------------------------------------------------- 1167 1177 1168 Icebergs are modelled as lagrangian particles in NEMO \citep{ Marsh_GMD2015}.1169 Their physical behaviour is controlled by equations as described in \citet{ Martin_Adcroft_OM10} ).1178 Icebergs are modelled as lagrangian particles in NEMO \citep{marsh.ivchenko.ea_GMD15}. 1179 Their physical behaviour is controlled by equations as described in \citet{martin.adcroft_OM10} ). 1170 1180 (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 1171 1181 Icebergs are initially spawned into one of ten classes which have specific mass and thickness as … … 1227 1237 % Interactions with waves (sbcwave.F90, ln_wave) 1228 1238 % ------------------------------------------------------------------------------------------------------------- 1229 \section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 1239 \section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})] 1240 {Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 1230 1241 \label{sec:SBC_wave} 1231 1242 %------------------------------------------namsbc_wave-------------------------------------------------------- … … 1258 1269 1259 1270 % ================================================================ 1260 \subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 1271 \subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})] 1272 {Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 1261 1273 \label{subsec:SBC_wave_cdgw} 1262 1274 … … 1265 1277 Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided, 1266 1278 the drag coefficient is computed according to the stable/unstable conditions of the 1267 air-sea interface following \citet{ Large_Yeager_Rep04}.1279 air-sea interface following \citet{large.yeager_rpt04}. 1268 1280 1269 1281 … … 1271 1283 % 3D Stokes Drift (ln_sdw, nn_sdrift) 1272 1284 % ================================================================ 1273 \subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 1285 \subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})] 1286 {3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 1274 1287 \label{subsec:SBC_wave_sdw} 1275 1288 1276 The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{ Stokes_1847}.1289 The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{stokes_ibk09}. 1277 1290 It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity) 1278 1291 and the current measured at a fixed point (Eulerian velocity). … … 1307 1320 \begin{description} 1308 1321 \item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by 1309 \citet{ Breivik_al_JPO2014}:1322 \citet{breivik.janssen.ea_JPO14}: 1310 1323 1311 1324 \[ … … 1327 1340 \item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a 1328 1341 reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface 1329 \citep{ Breivik_al_OM2016}:1342 \citep{breivik.bidlot.ea_OM16}: 1330 1343 1331 1344 \[ … … 1367 1380 % Stokes-Coriolis term (ln_stcor) 1368 1381 % ================================================================ 1369 \subsection{Stokes-Coriolis term (\protect\np{ln\_stcor})} 1382 \subsection[Stokes-Coriolis term (\texttt{ln\_stcor})] 1383 {Stokes-Coriolis term (\protect\np{ln\_stcor})} 1370 1384 \label{subsec:SBC_wave_stcor} 1371 1385 … … 1381 1395 % Waves modified stress (ln_tauwoc, ln_tauw) 1382 1396 % ================================================================ 1383 \subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 1397 \subsection[Wave modified sress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})] 1398 {Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 1384 1399 \label{subsec:SBC_wave_tauw} 1385 1400 1386 1401 The surface stress felt by the ocean is the atmospheric stress minus the net stress going 1387 into the waves \citep{ Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not1402 into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not 1388 1403 available for forcing the mean circulation, while in the opposite case of a decaying sea 1389 1404 state more momentum is available for forcing the ocean. … … 1428 1443 % Diurnal cycle 1429 1444 % ------------------------------------------------------------------------------------------------------------- 1430 \subsection{Diurnal cycle (\protect\mdl{sbcdcy})} 1445 \subsection[Diurnal cycle (\textit{sbcdcy.F90})] 1446 {Diurnal cycle (\protect\mdl{sbcdcy})} 1431 1447 \label{subsec:SBC_dcy} 1432 1448 %------------------------------------------namsbc_rnf---------------------------------------------------- … … 1438 1454 \begin{figure}[!t] 1439 1455 \begin{center} 1440 \includegraphics[width= 0.8\textwidth]{Fig_SBC_diurnal}1456 \includegraphics[width=\textwidth]{Fig_SBC_diurnal} 1441 1457 \caption{ 1442 1458 \protect\label{fig:SBC_diurnal} … … 1445 1461 the mean value of the analytical cycle (blue line) over a time step, 1446 1462 not as the mid time step value of the analytically cycle (red square). 1447 From \citet{ Bernie_al_CD07}.1463 From \citet{bernie.guilyardi.ea_CD07}. 1448 1464 } 1449 1465 \end{center} … … 1451 1467 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1452 1468 1453 \cite{ Bernie_al_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less.1469 \cite{bernie.woolnough.ea_JC05} have shown that to capture 90$\%$ of the diurnal variability of SST requires a vertical resolution in upper ocean of 1~m or better and a temporal resolution of the surface fluxes of 3~h or less. 1454 1470 Unfortunately high frequency forcing fields are rare, not to say inexistent. 1455 1471 Nevertheless, it is possible to obtain a reasonable diurnal cycle of the SST knowning only short wave flux (SWF) at 1456 high frequency \citep{ Bernie_al_CD07}.1472 high frequency \citep{bernie.guilyardi.ea_CD07}. 1457 1473 Furthermore, only the knowledge of daily mean value of SWF is needed, 1458 1474 as higher frequency variations can be reconstructed from them, 1459 1475 assuming that the diurnal cycle of SWF is a scaling of the top of the atmosphere diurnal cycle of incident SWF. 1460 The \cite{ Bernie_al_CD07} reconstruction algorithm is available in \NEMO by1476 The \cite{bernie.guilyardi.ea_CD07} reconstruction algorithm is available in \NEMO by 1461 1477 setting \np{ln\_dm2dc}\forcode{ = .true.} (a \textit{\ngn{namsbc}} namelist variable) when 1462 1478 using CORE bulk formulea (\np{ln\_blk\_core}\forcode{ = .true.}) or 1463 1479 the flux formulation (\np{ln\_flx}\forcode{ = .true.}). 1464 1480 The reconstruction is performed in the \mdl{sbcdcy} module. 1465 The detail of the algoritm used can be found in the appendix~A of \cite{ Bernie_al_CD07}.1481 The detail of the algoritm used can be found in the appendix~A of \cite{bernie.guilyardi.ea_CD07}. 1466 1482 The algorithm preserve the daily mean incoming SWF as the reconstructed SWF at 1467 1483 a given time step is the mean value of the analytical cycle over this time step (\autoref{fig:SBC_diurnal}). … … 1476 1492 \begin{figure}[!t] 1477 1493 \begin{center} 1478 \includegraphics[width= 0.7\textwidth]{Fig_SBC_dcy}1494 \includegraphics[width=\textwidth]{Fig_SBC_dcy} 1479 1495 \caption{ 1480 1496 \protect\label{fig:SBC_dcy} … … 1514 1530 % Surface restoring to observed SST and/or SSS 1515 1531 % ------------------------------------------------------------------------------------------------------------- 1516 \subsection{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 1532 \subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})] 1533 {Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 1517 1534 \label{subsec:SBC_ssr} 1518 1535 %------------------------------------------namsbc_ssr---------------------------------------------------- … … 1546 1563 (observed, climatological or an atmospheric model product), 1547 1564 \textit{SSS}$_{Obs}$ is a sea surface salinity 1548 (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{ Steele2001}),1565 (usually a time interpolation of the monthly mean Polar Hydrographic Climatology \citep{steele.morley.ea_JC01}), 1549 1566 $\left.S\right|_{k=1}$ is the model surface layer salinity and 1550 1567 $\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter. 1551 1568 Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:sbc_dmp_emp} as 1552 the atmosphere does not care about ocean surface salinity \citep{ Madec1997}.1569 the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}. 1553 1570 The SSS restoring term should be viewed as a flux correction on freshwater fluxes to 1554 1571 reduce the uncertainties we have on the observed freshwater budget. … … 1593 1610 % {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?} 1594 1611 1595 \subsection{Interface to CICE (\protect\mdl{sbcice\_cice})} 1612 \subsection[Interface to CICE (\textit{sbcice\_cice.F90})] 1613 {Interface to CICE (\protect\mdl{sbcice\_cice})} 1596 1614 \label{subsec:SBC_cice} 1597 1615 … … 1626 1644 % Freshwater budget control 1627 1645 % ------------------------------------------------------------------------------------------------------------- 1628 \subsection{Freshwater budget control (\protect\mdl{sbcfwb})} 1646 \subsection[Freshwater budget control (\textit{sbcfwb.F90})] 1647 {Freshwater budget control (\protect\mdl{sbcfwb})} 1629 1648 \label{subsec:SBC_fwb} 1630 1649 -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_STO.tex
r10442 r11263 15 15 16 16 The stochastic parametrization module aims to explicitly simulate uncertainties in the model. 17 More particularly, \cite{ Brankart_OM2013} has shown that,17 More particularly, \cite{brankart_OM13} has shown that, 18 18 because of the nonlinearity of the seawater equation of state, unresolved scales represent a major source of 19 19 uncertainties in the computation of the large scale horizontal density gradient (from T/S large scale fields), … … 46 46 A generic approach is thus to add one single new module in NEMO, 47 47 generating processes with appropriate statistics to simulate each kind of uncertainty in the model 48 (see \cite{ Brankart_al_GMD2015} for more details).48 (see \cite{brankart.candille.ea_GMD15} for more details). 49 49 50 50 In practice, at every model grid point, -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_TRA.tex
r10544 r11263 55 55 56 56 The user has the option of extracting each tendency term on the RHS of the tracer equation for output 57 (\np{ln\_tra\_trd} or \np{ln\_tra\_mxl} ~\forcode{= .true.}), as described in \autoref{chap:DIA}.57 (\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}\forcode{ = .true.}), as described in \autoref{chap:DIA}. 58 58 59 59 % ================================================================ 60 60 % Tracer Advection 61 61 % ================================================================ 62 \section{Tracer advection (\protect\mdl{traadv})} 62 \section[Tracer advection (\textit{traadv.F90})] 63 {Tracer advection (\protect\mdl{traadv})} 63 64 \label{sec:TRA_adv} 64 65 %------------------------------------------namtra_adv----------------------------------------------------- … … 81 82 Indeed, it is obtained by using the following equality: $\nabla \cdot (\vect U \, T) = \vect U \cdot \nabla T$ which 82 83 results from the use of the continuity equation, $\partial_t e_3 + e_3 \; \nabla \cdot \vect U = 0$ 83 (which reduces to $\nabla \cdot \vect U = 0$ in linear free surface, \ie \np{ln\_linssh} ~\forcode{= .true.}).84 (which reduces to $\nabla \cdot \vect U = 0$ in linear free surface, \ie \np{ln\_linssh}\forcode{ = .true.}). 84 85 Therefore it is of paramount importance to design the discrete analogue of the advection tendency so that 85 86 it is consistent with the continuity equation in order to enforce the conservation properties of … … 90 91 \begin{figure}[!t] 91 92 \begin{center} 92 \includegraphics[ ]{Fig_adv_scheme}93 \includegraphics[width=\textwidth]{Fig_adv_scheme} 93 94 \caption{ 94 95 \protect\label{fig:adv_scheme} … … 119 120 \begin{description} 120 121 \item[linear free surface:] 121 (\np{ln\_linssh} ~\forcode{= .true.})122 (\np{ln\_linssh}\forcode{ = .true.}) 122 123 the first level thickness is constant in time: 123 124 the vertical boundary condition is applied at the fixed surface $z = 0$ rather than on … … 127 128 the first level tracer value. 128 129 \item[non-linear free surface:] 129 (\np{ln\_linssh} ~\forcode{= .false.})130 (\np{ln\_linssh}\forcode{ = .false.}) 130 131 convergence/divergence in the first ocean level moves the free surface up/down. 131 132 There is no tracer advection through it so that the advective fluxes through the surface are also zero. … … 136 137 Nevertheless, in the latter case, it is achieved to a good approximation since 137 138 the non-conservative term is the product of the time derivative of the tracer and the free surface height, 138 two quantities that are not correlated \citep{ Roullet_Madec_JGR00, Griffies_al_MWR01, Campin2004}.139 140 The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco }) is139 two quantities that are not correlated \citep{roullet.madec_JGR00, griffies.pacanowski.ea_MWR01, campin.adcroft.ea_OM04}. 140 141 The velocity field that appears in (\autoref{eq:tra_adv} and \autoref{eq:tra_adv_zco?}) is 141 142 the centred (\textit{now}) \textit{effective} ocean velocity, \ie the \textit{eulerian} velocity 142 143 (see \autoref{chap:DYN}) plus the eddy induced velocity (\textit{eiv}) and/or … … 183 184 % 2nd and 4th order centred schemes 184 185 % ------------------------------------------------------------------------------------------------------------- 185 \subsection{CEN: Centred scheme (\protect\np{ln\_traadv\_cen}~\forcode{= .true.})} 186 \subsection[CEN: Centred scheme (\forcode{ln_traadv_cen = .true.})] 187 {CEN: Centred scheme (\protect\np{ln\_traadv\_cen}\forcode{ = .true.})} 186 188 \label{subsec:TRA_adv_cen} 187 189 188 190 % 2nd order centred scheme 189 191 190 The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen} ~\forcode{= .true.}.192 The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}\forcode{ = .true.}. 191 193 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by 192 194 setting \np{nn\_cen\_h} and \np{nn\_cen\_v} to $2$ or $4$. … … 220 222 \tau_u^{cen4} = \overline{T - \frac{1}{6} \, \delta_i \Big[ \delta_{i + 1/2}[T] \, \Big]}^{\,i + 1/2} 221 223 \end{equation} 222 In the vertical direction (\np{nn\_cen\_v} ~\forcode{= 4}),223 a $4^{th}$ COMPACT interpolation has been prefered \citep{ Demange_PhD2014}.224 In the vertical direction (\np{nn\_cen\_v}\forcode{ = 4}), 225 a $4^{th}$ COMPACT interpolation has been prefered \citep{demange_phd14}. 224 226 In the COMPACT scheme, both the field and its derivative are interpolated, which leads, after a matrix inversion, 225 spectral characteristics similar to schemes of higher order \citep{ Lele_JCP1992}.227 spectral characteristics similar to schemes of higher order \citep{lele_JCP92}. 226 228 227 229 Strictly speaking, the CEN4 scheme is not a $4^{th}$ order advection scheme but … … 250 252 % FCT scheme 251 253 % ------------------------------------------------------------------------------------------------------------- 252 \subsection{FCT: Flux Corrected Transport scheme (\protect\np{ln\_traadv\_fct}~\forcode{= .true.})} 254 \subsection[FCT: Flux Corrected Transport scheme (\forcode{ln_traadv_fct = .true.})] 255 {FCT: Flux Corrected Transport scheme (\protect\np{ln\_traadv\_fct}\forcode{ = .true.})} 253 256 \label{subsec:TRA_adv_tvd} 254 257 255 The Flux Corrected Transport schemes (FCT) is used when \np{ln\_traadv\_fct} ~\forcode{= .true.}.258 The Flux Corrected Transport schemes (FCT) is used when \np{ln\_traadv\_fct}\forcode{ = .true.}. 256 259 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by 257 260 setting \np{nn\_fct\_h} and \np{nn\_fct\_v} to $2$ or $4$. … … 277 280 (\ie it depends on the setting of \np{nn\_fct\_h} and \np{nn\_fct\_v}). 278 281 There exist many ways to define $c_u$, each corresponding to a different FCT scheme. 279 The one chosen in \NEMO is described in \citet{ Zalesak_JCP79}.282 The one chosen in \NEMO is described in \citet{zalesak_JCP79}. 280 283 $c_u$ only departs from $1$ when the advective term produces a local extremum in the tracer field. 281 284 The resulting scheme is quite expensive but \textit{positive}. 282 285 It can be used on both active and passive tracers. 283 A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{ Levy_al_GRL01}.286 A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{levy.estublier.ea_GRL01}. 284 287 285 288 An additional option has been added controlled by \np{nn\_fct\_zts}. … … 287 290 a $2^{nd}$ order FCT scheme is used on both horizontal and vertical direction, but on the latter, 288 291 a split-explicit time stepping is used, with a number of sub-timestep equals to \np{nn\_fct\_zts}. 289 This option can be useful when the size of the timestep is limited by vertical advection \citep{ Lemarie_OM2015}.292 This option can be useful when the size of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}. 290 293 Note that in this case, a similar split-explicit time stepping should be used on vertical advection of momentum to 291 294 insure a better stability (see \autoref{subsec:DYN_zad}). … … 300 303 % MUSCL scheme 301 304 % ------------------------------------------------------------------------------------------------------------- 302 \subsection{MUSCL: Monotone Upstream Scheme for Conservative Laws (\protect\np{ln\_traadv\_mus}~\forcode{= .true.})} 305 \subsection[MUSCL: Monotone Upstream Scheme for Conservative Laws (\forcode{ln_traadv_mus = .true.})] 306 {MUSCL: Monotone Upstream Scheme for Conservative Laws (\protect\np{ln\_traadv\_mus}\forcode{ = .true.})} 303 307 \label{subsec:TRA_adv_mus} 304 308 305 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln\_traadv\_mus} ~\forcode{= .true.}.309 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln\_traadv\_mus}\forcode{ = .true.}. 306 310 MUSCL implementation can be found in the \mdl{traadv\_mus} module. 307 311 308 MUSCL has been first implemented in \NEMO by \citet{ Levy_al_GRL01}.312 MUSCL has been first implemented in \NEMO by \citet{levy.estublier.ea_GRL01}. 309 313 In its formulation, the tracer at velocity points is evaluated assuming a linear tracer variation between 310 314 two $T$-points (\autoref{fig:adv_scheme}). … … 331 335 This choice ensure the \textit{positive} character of the scheme. 332 336 In addition, fluxes round a grid-point where a runoff is applied can optionally be computed using upstream fluxes 333 (\np{ln\_mus\_ups} ~\forcode{= .true.}).337 (\np{ln\_mus\_ups}\forcode{ = .true.}). 334 338 335 339 % ------------------------------------------------------------------------------------------------------------- 336 340 % UBS scheme 337 341 % ------------------------------------------------------------------------------------------------------------- 338 \subsection{UBS a.k.a. UP3: Upstream-Biased Scheme (\protect\np{ln\_traadv\_ubs}~\forcode{= .true.})} 342 \subsection[UBS a.k.a. UP3: Upstream-Biased Scheme (\forcode{ln_traadv_ubs = .true.})] 343 {UBS a.k.a. UP3: Upstream-Biased Scheme (\protect\np{ln\_traadv\_ubs}\forcode{ = .true.})} 339 344 \label{subsec:TRA_adv_ubs} 340 345 341 The Upstream-Biased Scheme (UBS) is used when \np{ln\_traadv\_ubs} ~\forcode{= .true.}.346 The Upstream-Biased Scheme (UBS) is used when \np{ln\_traadv\_ubs}\forcode{ = .true.}. 342 347 UBS implementation can be found in the \mdl{traadv\_mus} module. 343 348 … … 358 363 359 364 This results in a dissipatively dominant (i.e. hyper-diffusive) truncation error 360 \citep{ Shchepetkin_McWilliams_OM05}.361 The overall performance of the advection scheme is similar to that reported in \cite{ Farrow1995}.365 \citep{shchepetkin.mcwilliams_OM05}. 366 The overall performance of the advection scheme is similar to that reported in \cite{farrow.stevens_JPO95}. 362 367 It is a relatively good compromise between accuracy and smoothness. 363 368 Nevertheless the scheme is not \textit{positive}, meaning that false extrema are permitted, … … 367 372 The intrinsic diffusion of UBS makes its use risky in the vertical direction where 368 373 the control of artificial diapycnal fluxes is of paramount importance 369 \citep{ Shchepetkin_McWilliams_OM05, Demange_PhD2014}.374 \citep{shchepetkin.mcwilliams_OM05, demange_phd14}. 370 375 Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme or a $4^th$ order COMPACT scheme 371 (\np{nn\_cen\_v} ~\forcode{= 2 or 4}).376 (\np{nn\_cen\_v}\forcode{ = 2 or 4}). 372 377 373 378 For stability reasons (see \autoref{chap:STP}), the first term in \autoref{eq:tra_adv_ubs} … … 376 381 (which is the diffusive part of the scheme), 377 382 is evaluated using the \textit{before} tracer (forward in time). 378 This choice is discussed by \citet{ Webb_al_JAOT98} in the context of the QUICK advection scheme.383 This choice is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the QUICK advection scheme. 379 384 UBS and QUICK schemes only differ by one coefficient. 380 Replacing 1/6 with 1/8 in \autoref{eq:tra_adv_ubs} leads to the QUICK advection scheme \citep{ Webb_al_JAOT98}.385 Replacing 1/6 with 1/8 in \autoref{eq:tra_adv_ubs} leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}. 381 386 This option is not available through a namelist parameter, since the 1/6 coefficient is hard coded. 382 387 Nevertheless it is quite easy to make the substitution in the \mdl{traadv\_ubs} module and obtain a QUICK scheme. … … 408 413 % QCK scheme 409 414 % ------------------------------------------------------------------------------------------------------------- 410 \subsection{QCK: QuiCKest scheme (\protect\np{ln\_traadv\_qck}~\forcode{= .true.})} 415 \subsection[QCK: QuiCKest scheme (\forcode{ln_traadv_qck = .true.})] 416 {QCK: QuiCKest scheme (\protect\np{ln\_traadv\_qck}\forcode{ = .true.})} 411 417 \label{subsec:TRA_adv_qck} 412 418 413 419 The Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms (QUICKEST) scheme 414 proposed by \citet{ Leonard1979} is used when \np{ln\_traadv\_qck}~\forcode{= .true.}.420 proposed by \citet{leonard_CMAME79} is used when \np{ln\_traadv\_qck}\forcode{ = .true.}. 415 421 QUICKEST implementation can be found in the \mdl{traadv\_qck} module. 416 422 417 423 QUICKEST is the third order Godunov scheme which is associated with the ULTIMATE QUICKEST limiter 418 \citep{ Leonard1991}.424 \citep{leonard_CMAME91}. 419 425 It has been implemented in NEMO by G. Reffray (MERCATOR-ocean) and can be found in the \mdl{traadv\_qck} module. 420 426 The resulting scheme is quite expensive but \textit{positive}. … … 431 437 % Tracer Lateral Diffusion 432 438 % ================================================================ 433 \section{Tracer lateral diffusion (\protect\mdl{traldf})} 439 \section[Tracer lateral diffusion (\textit{traldf.F90})] 440 {Tracer lateral diffusion (\protect\mdl{traldf})} 434 441 \label{sec:TRA_ldf} 435 442 %-----------------------------------------nam_traldf------------------------------------------------------ … … 453 460 except for the pure vertical component that appears when a rotation tensor is used. 454 461 This latter component is solved implicitly together with the vertical diffusion term (see \autoref{chap:STP}). 455 When \np{ln\_traldf\_msc} ~\forcode{= .true.}, a Method of Stabilizing Correction is used in which456 the pure vertical component is split into an explicit and an implicit part \citep{ Lemarie_OM2012}.462 When \np{ln\_traldf\_msc}\forcode{ = .true.}, a Method of Stabilizing Correction is used in which 463 the pure vertical component is split into an explicit and an implicit part \citep{lemarie.debreu.ea_OM12}. 457 464 458 465 % ------------------------------------------------------------------------------------------------------------- 459 466 % Type of operator 460 467 % ------------------------------------------------------------------------------------------------------------- 461 \subsection[Type of operator (\protect\np{ln\_traldf}\{\_NONE,\_lap,\_blp\}\})]{Type of operator (\protect\np{ln\_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp}) } 468 \subsection[Type of operator (\texttt{ln\_traldf}\{\texttt{\_NONE,\_lap,\_blp}\})] 469 {Type of operator (\protect\np{ln\_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp}) } 462 470 \label{subsec:TRA_ldf_op} 463 471 … … 465 473 466 474 \begin{description} 467 \item[\np{ln\_traldf\_NONE} ~\forcode{= .true.}:]475 \item[\np{ln\_traldf\_NONE}\forcode{ = .true.}:] 468 476 no operator selected, the lateral diffusive tendency will not be applied to the tracer equation. 469 477 This option can be used when the selected advection scheme is diffusive enough (MUSCL scheme for example). 470 \item[\np{ln\_traldf\_lap} ~\forcode{= .true.}:]478 \item[\np{ln\_traldf\_lap}\forcode{ = .true.}:] 471 479 a laplacian operator is selected. 472 480 This harmonic operator takes the following expression: $\mathpzc{L}(T) = \nabla \cdot A_{ht} \; \nabla T $, 473 481 where the gradient operates along the selected direction (see \autoref{subsec:TRA_ldf_dir}), 474 482 and $A_{ht}$ is the eddy diffusivity coefficient expressed in $m^2/s$ (see \autoref{chap:LDF}). 475 \item[\np{ln\_traldf\_blp} ~\forcode{= .true.}]:483 \item[\np{ln\_traldf\_blp}\forcode{ = .true.}]: 476 484 a bilaplacian operator is selected. 477 485 This biharmonic operator takes the following expression: … … 493 501 % Direction of action 494 502 % ------------------------------------------------------------------------------------------------------------- 495 \subsection[Action direction (\protect\np{ln\_traldf}\{\_lev,\_hor,\_iso,\_triad\})]{Direction of action (\protect\np{ln\_traldf\_lev}, \protect\np{ln\_traldf\_hor}, \protect\np{ln\_traldf\_iso}, or \protect\np{ln\_traldf\_triad}) } 503 \subsection[Action direction (\texttt{ln\_traldf}\{\texttt{\_lev,\_hor,\_iso,\_triad}\})] 504 {Direction of action (\protect\np{ln\_traldf\_lev}, \protect\np{ln\_traldf\_hor}, \protect\np{ln\_traldf\_iso}, or \protect\np{ln\_traldf\_triad}) } 496 505 \label{subsec:TRA_ldf_dir} 497 506 498 507 The choice of a direction of action determines the form of operator used. 499 508 The operator is a simple (re-entrant) laplacian acting in the (\textbf{i},\textbf{j}) plane when 500 iso-level option is used (\np{ln\_traldf\_lev} ~\forcode{= .true.}) or509 iso-level option is used (\np{ln\_traldf\_lev}\forcode{ = .true.}) or 501 510 when a horizontal (\ie geopotential) operator is demanded in \textit{z}-coordinate 502 511 (\np{ln\_traldf\_hor} and \np{ln\_zco} equal \forcode{.true.}). … … 519 528 % iso-level operator 520 529 % ------------------------------------------------------------------------------------------------------------- 521 \subsection{Iso-level (bi -)laplacian operator ( \protect\np{ln\_traldf\_iso}) } 530 \subsection[Iso-level (bi-)laplacian operator (\texttt{ln\_traldf\_iso})] 531 {Iso-level (bi-)laplacian operator ( \protect\np{ln\_traldf\_iso})} 522 532 \label{subsec:TRA_ldf_lev} 523 533 … … 537 547 It is a \textit{horizontal} operator (\ie acting along geopotential surfaces) in 538 548 the $z$-coordinate with or without partial steps, but is simply an iso-level operator in the $s$-coordinate. 539 It is thus used when, in addition to \np{ln\_traldf\_lap} or \np{ln\_traldf\_blp} ~\forcode{= .true.},540 we have \np{ln\_traldf\_lev} ~\forcode{= .true.} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}~\forcode{= .true.}.549 It is thus used when, in addition to \np{ln\_traldf\_lap} or \np{ln\_traldf\_blp}\forcode{ = .true.}, 550 we have \np{ln\_traldf\_lev}\forcode{ = .true.} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}\forcode{ = .true.}. 541 551 In both cases, it significantly contributes to diapycnal mixing. 542 552 It is therefore never recommended, even when using it in the bilaplacian case. 543 553 544 Note that in the partial step $z$-coordinate (\np{ln\_zps} ~\forcode{= .true.}),554 Note that in the partial step $z$-coordinate (\np{ln\_zps}\forcode{ = .true.}), 545 555 tracers in horizontally adjacent cells are located at different depths in the vicinity of the bottom. 546 556 In this case, horizontal derivatives in (\autoref{eq:tra_ldf_lap}) at the bottom level require a specific treatment. … … 550 560 % Rotated laplacian operator 551 561 % ------------------------------------------------------------------------------------------------------------- 552 \subsection{Standard and triad (bi 562 \subsection{Standard and triad (bi-)laplacian operator} 553 563 \label{subsec:TRA_ldf_iso_triad} 554 564 555 %&& Standard rotated (bi 565 %&& Standard rotated (bi-)laplacian operator 556 566 %&& ---------------------------------------------- 557 \subsubsection{Standard rotated (bi -)laplacian operator (\protect\mdl{traldf\_iso})} 567 \subsubsection[Standard rotated (bi-)laplacian operator (\textit{traldf\_iso.F90})] 568 {Standard rotated (bi-)laplacian operator (\protect\mdl{traldf\_iso})} 558 569 \label{subsec:TRA_ldf_iso} 559 570 The general form of the second order lateral tracer subgrid scale physics (\autoref{eq:PE_zdf}) … … 574 585 $r_1$ and $r_2$ are the slopes between the surface of computation ($z$- or $s$-surfaces) and 575 586 the surface along which the diffusion operator acts (\ie horizontal or iso-neutral surfaces). 576 It is thus used when, in addition to \np{ln\_traldf\_lap} ~\forcode{= .true.},577 we have \np{ln\_traldf\_iso} ~\forcode{= .true.},578 or both \np{ln\_traldf\_hor} ~\forcode{= .true.} and \np{ln\_zco}~\forcode{= .true.}.587 It is thus used when, in addition to \np{ln\_traldf\_lap}\forcode{ = .true.}, 588 we have \np{ln\_traldf\_iso}\forcode{ = .true.}, 589 or both \np{ln\_traldf\_hor}\forcode{ = .true.} and \np{ln\_zco}\forcode{ = .true.}. 579 590 The way these slopes are evaluated is given in \autoref{sec:LDF_slp}. 580 591 At the surface, bottom and lateral boundaries, the turbulent fluxes of heat and salt are set to zero using … … 590 601 This formulation conserves the tracer but does not ensure the decrease of the tracer variance. 591 602 Nevertheless the treatment performed on the slopes (see \autoref{chap:LDF}) allows the model to run safely without 592 any additional background horizontal diffusion \citep{ Guilyardi_al_CD01}.593 594 Note that in the partial step $z$-coordinate (\np{ln\_zps} ~\forcode{= .true.}),603 any additional background horizontal diffusion \citep{guilyardi.madec.ea_CD01}. 604 605 Note that in the partial step $z$-coordinate (\np{ln\_zps}\forcode{ = .true.}), 595 606 the horizontal derivatives at the bottom level in \autoref{eq:tra_ldf_iso} require a specific treatment. 596 607 They are calculated in module zpshde, described in \autoref{sec:TRA_zpshde}. 597 608 598 %&& Triad rotated (bi 609 %&& Triad rotated (bi-)laplacian operator 599 610 %&& ------------------------------------------- 600 \subsubsection{Triad rotated (bi -)laplacian operator (\protect\np{ln\_traldf\_triad})} 611 \subsubsection[Triad rotated (bi-)laplacian operator (\textit{ln\_traldf\_triad})] 612 {Triad rotated (bi-)laplacian operator (\protect\np{ln\_traldf\_triad})} 601 613 \label{subsec:TRA_ldf_triad} 602 614 603 If the Griffies triad scheme is employed (\np{ln\_traldf\_triad} ~\forcode{= .true.}; see \autoref{apdx:triad})604 605 An alternative scheme developed by \cite{ Griffies_al_JPO98} which ensures tracer variance decreases606 is also available in \NEMO (\np{ln\_traldf\_grif} ~\forcode{= .true.}).615 If the Griffies triad scheme is employed (\np{ln\_traldf\_triad}\forcode{ = .true.}; see \autoref{apdx:triad}) 616 617 An alternative scheme developed by \cite{griffies.gnanadesikan.ea_JPO98} which ensures tracer variance decreases 618 is also available in \NEMO (\np{ln\_traldf\_grif}\forcode{ = .true.}). 607 619 A complete description of the algorithm is given in \autoref{apdx:triad}. 608 620 … … 632 644 % Tracer Vertical Diffusion 633 645 % ================================================================ 634 \section{Tracer vertical diffusion (\protect\mdl{trazdf})} 646 \section[Tracer vertical diffusion (\textit{trazdf.F90})] 647 {Tracer vertical diffusion (\protect\mdl{trazdf})} 635 648 \label{sec:TRA_zdf} 636 649 %--------------------------------------------namzdf--------------------------------------------------------- … … 663 676 664 677 The large eddy coefficient found in the mixed layer together with high vertical resolution implies that 665 in the case of explicit time stepping (\np{ln\_zdfexp} ~\forcode{= .true.})678 in the case of explicit time stepping (\np{ln\_zdfexp}\forcode{ = .true.}) 666 679 there would be too restrictive a constraint on the time step. 667 680 Therefore, the default implicit time stepping is preferred for the vertical diffusion since 668 681 it overcomes the stability constraint. 669 A forward time differencing scheme (\np{ln\_zdfexp} ~\forcode{= .true.}) using682 A forward time differencing scheme (\np{ln\_zdfexp}\forcode{ = .true.}) using 670 683 a time splitting technique (\np{nn\_zdfexp} $> 1$) is provided as an alternative. 671 684 Namelist variables \np{ln\_zdfexp} and \np{nn\_zdfexp} apply to both tracers and dynamics. … … 680 693 % surface boundary condition 681 694 % ------------------------------------------------------------------------------------------------------------- 682 \subsection{Surface boundary condition (\protect\mdl{trasbc})} 695 \subsection[Surface boundary condition (\textit{trasbc.F90})] 696 {Surface boundary condition (\protect\mdl{trasbc})} 683 697 \label{subsec:TRA_sbc} 684 698 … … 730 744 Such time averaging prevents the divergence of odd and even time step (see \autoref{chap:STP}). 731 745 732 In the linear free surface case (\np{ln\_linssh} ~\forcode{= .true.}), an additional term has to be added on746 In the linear free surface case (\np{ln\_linssh}\forcode{ = .true.}), an additional term has to be added on 733 747 both temperature and salinity. 734 748 On temperature, this term remove the heat content associated with mass exchange that has been added to $Q_{ns}$. … … 747 761 Note that an exact conservation of heat and salt content is only achieved with non-linear free surface. 748 762 In the linear free surface case, there is a small imbalance. 749 The imbalance is larger than the imbalance associated with the Asselin time filter \citep{ Leclair_Madec_OM09}.763 The imbalance is larger than the imbalance associated with the Asselin time filter \citep{leclair.madec_OM09}. 750 764 This is the reason why the modified filter is not applied in the linear free surface case (see \autoref{chap:STP}). 751 765 … … 753 767 % Solar Radiation Penetration 754 768 % ------------------------------------------------------------------------------------------------------------- 755 \subsection{Solar radiation penetration (\protect\mdl{traqsr})} 769 \subsection[Solar radiation penetration (\textit{traqsr.F90})] 770 {Solar radiation penetration (\protect\mdl{traqsr})} 756 771 \label{subsec:TRA_qsr} 757 772 %--------------------------------------------namqsr-------------------------------------------------------- … … 761 776 762 777 Options are defined through the \ngn{namtra\_qsr} namelist variables. 763 When the penetrative solar radiation option is used (\np{ln\_flxqsr} ~\forcode{= .true.}),778 When the penetrative solar radiation option is used (\np{ln\_flxqsr}\forcode{ = .true.}), 764 779 the solar radiation penetrates the top few tens of meters of the ocean. 765 If it is not used (\np{ln\_flxqsr} ~\forcode{= .false.}) all the heat flux is absorbed in the first ocean level.780 If it is not used (\np{ln\_flxqsr}\forcode{ = .false.}) all the heat flux is absorbed in the first ocean level. 766 781 Thus, in the former case a term is added to the time evolution equation of temperature \autoref{eq:PE_tra_T} and 767 782 the surface boundary condition is modified to take into account only the non-penetrative part of the surface … … 792 807 larger depths where it contributes to local heating. 793 808 The way this second part of the solar energy penetrates into the ocean depends on which formulation is chosen. 794 In the simple 2-waveband light penetration scheme (\np{ln\_qsr\_2bd} ~\forcode{= .true.})809 In the simple 2-waveband light penetration scheme (\np{ln\_qsr\_2bd}\forcode{ = .true.}) 795 810 a chlorophyll-independent monochromatic formulation is chosen for the shorter wavelengths, 796 leading to the following expression \citep{ Paulson1977}:811 leading to the following expression \citep{paulson.simpson_JPO77}: 797 812 \[ 798 813 % \label{eq:traqsr_iradiance} … … 805 820 806 821 Such assumptions have been shown to provide a very crude and simplistic representation of 807 observed light penetration profiles (\cite{ Morel_JGR88}, see also \autoref{fig:traqsr_irradiance}).822 observed light penetration profiles (\cite{morel_JGR88}, see also \autoref{fig:traqsr_irradiance}). 808 823 Light absorption in the ocean depends on particle concentration and is spectrally selective. 809 \cite{ Morel_JGR88} has shown that an accurate representation of light penetration can be provided by824 \cite{morel_JGR88} has shown that an accurate representation of light penetration can be provided by 810 825 a 61 waveband formulation. 811 826 Unfortunately, such a model is very computationally expensive. 812 Thus, \cite{ Lengaigne_al_CD07} have constructed a simplified version of this formulation in which827 Thus, \cite{lengaigne.menkes.ea_CD07} have constructed a simplified version of this formulation in which 813 828 visible light is split into three wavebands: blue (400-500 nm), green (500-600 nm) and red (600-700nm). 814 829 For each wave-band, the chlorophyll-dependent attenuation coefficient is fitted to the coefficients computed from 815 the full spectral model of \cite{ Morel_JGR88} (as modified by \cite{Morel_Maritorena_JGR01}),830 the full spectral model of \cite{morel_JGR88} (as modified by \cite{morel.maritorena_JGR01}), 816 831 assuming the same power-law relationship. 817 832 As shown in \autoref{fig:traqsr_irradiance}, this formulation, called RGB (Red-Green-Blue), … … 820 835 The 2-bands formulation does not reproduce the full model very well. 821 836 822 The RGB formulation is used when \np{ln\_qsr\_rgb} ~\forcode{= .true.}.837 The RGB formulation is used when \np{ln\_qsr\_rgb}\forcode{ = .true.}. 823 838 The RGB attenuation coefficients (\ie the inverses of the extinction length scales) are tabulated over 824 839 61 nonuniform chlorophyll classes ranging from 0.01 to 10 g.Chl/L … … 827 842 828 843 \begin{description} 829 \item[\np{nn\_chdta} ~\forcode{= 0}]844 \item[\np{nn\_chdta}\forcode{ = 0}] 830 845 a constant 0.05 g.Chl/L value everywhere ; 831 \item[\np{nn\_chdta} ~\forcode{= 1}]846 \item[\np{nn\_chdta}\forcode{ = 1}] 832 847 an observed time varying chlorophyll deduced from satellite surface ocean color measurement spread uniformly in 833 848 the vertical direction; 834 \item[\np{nn\_chdta} ~\forcode{= 2}]849 \item[\np{nn\_chdta}\forcode{ = 2}] 835 850 same as previous case except that a vertical profile of chlorophyl is used. 836 Following \cite{ Morel_Berthon_LO89}, the profile is computed from the local surface chlorophyll value;837 \item[\np{ln\_qsr\_bio} ~\forcode{= .true.}]851 Following \cite{morel.berthon_LO89}, the profile is computed from the local surface chlorophyll value; 852 \item[\np{ln\_qsr\_bio}\forcode{ = .true.}] 838 853 simulated time varying chlorophyll by TOP biogeochemical model. 839 854 In this case, the RGB formulation is used to calculate both the phytoplankton light limitation in … … 856 871 \begin{figure}[!t] 857 872 \begin{center} 858 \includegraphics[ ]{Fig_TRA_Irradiance}873 \includegraphics[width=\textwidth]{Fig_TRA_Irradiance} 859 874 \caption{ 860 875 \protect\label{fig:traqsr_irradiance} … … 865 880 61 waveband Morel (1988) formulation (black) for a chlorophyll concentration of 866 881 (a) Chl=0.05 mg/m$^3$ and (b) Chl=0.5 mg/m$^3$. 867 From \citet{ Lengaigne_al_CD07}.882 From \citet{lengaigne.menkes.ea_CD07}. 868 883 } 869 884 \end{center} … … 874 889 % Bottom Boundary Condition 875 890 % ------------------------------------------------------------------------------------------------------------- 876 \subsection{Bottom boundary condition (\protect\mdl{trabbc})} 891 \subsection[Bottom boundary condition (\textit{trabbc.F90})] 892 {Bottom boundary condition (\protect\mdl{trabbc})} 877 893 \label{subsec:TRA_bbc} 878 894 %--------------------------------------------nambbc-------------------------------------------------------- … … 883 899 \begin{figure}[!t] 884 900 \begin{center} 885 \includegraphics[ ]{Fig_TRA_geoth}901 \includegraphics[width=\textwidth]{Fig_TRA_geoth} 886 902 \caption{ 887 903 \protect\label{fig:geothermal} 888 Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{ Emile-Geay_Madec_OS09}.889 It is inferred from the age of the sea floor and the formulae of \citet{ Stein_Stein_Nat92}.904 Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{emile-geay.madec_OS09}. 905 It is inferred from the age of the sea floor and the formulae of \citet{stein.stein_N92}. 890 906 } 891 907 \end{center} … … 897 913 This is the default option in \NEMO, and it is implemented using the masking technique. 898 914 However, there is a non-zero heat flux across the seafloor that is associated with solid earth cooling. 899 This flux is weak compared to surface fluxes (a mean global value of $\sim 0.1 \, W/m^2$ \citep{ Stein_Stein_Nat92}),915 This flux is weak compared to surface fluxes (a mean global value of $\sim 0.1 \, W/m^2$ \citep{stein.stein_N92}), 900 916 but it warms systematically the ocean and acts on the densest water masses. 901 917 Taking this flux into account in a global ocean model increases the deepest overturning cell 902 (\ie the one associated with the Antarctic Bottom Water) by a few Sverdrups \citep{ Emile-Geay_Madec_OS09}.918 (\ie the one associated with the Antarctic Bottom Water) by a few Sverdrups \citep{emile-geay.madec_OS09}. 903 919 904 920 Options are defined through the \ngn{namtra\_bbc} namelist variables. … … 907 923 the \np{nn\_geoflx\_cst}, which is also a namelist parameter. 908 924 When \np{nn\_geoflx} is set to 2, a spatially varying geothermal heat flux is introduced which is provided in 909 the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:geothermal}) \citep{ Emile-Geay_Madec_OS09}.925 the \ifile{geothermal\_heating} NetCDF file (\autoref{fig:geothermal}) \citep{emile-geay.madec_OS09}. 910 926 911 927 % ================================================================ 912 928 % Bottom Boundary Layer 913 929 % ================================================================ 914 \section{Bottom boundary layer (\protect\mdl{trabbl} - \protect\key{trabbl})} 930 \section[Bottom boundary layer (\textit{trabbl.F90} - \texttt{\textbf{key\_trabbl}})] 931 {Bottom boundary layer (\protect\mdl{trabbl} - \protect\key{trabbl})} 915 932 \label{sec:TRA_bbl} 916 933 %--------------------------------------------nambbl--------------------------------------------------------- … … 931 948 sometimes over a thickness much larger than the thickness of the observed gravity plume. 932 949 A similar problem occurs in the $s$-coordinate when the thickness of the bottom level varies rapidly downstream of 933 a sill \citep{ Willebrand_al_PO01}, and the thickness of the plume is not resolved.934 935 The idea of the bottom boundary layer (BBL) parameterisation, first introduced by \citet{ Beckmann_Doscher1997},950 a sill \citep{willebrand.barnier.ea_PO01}, and the thickness of the plume is not resolved. 951 952 The idea of the bottom boundary layer (BBL) parameterisation, first introduced by \citet{beckmann.doscher_JPO97}, 936 953 is to allow a direct communication between two adjacent bottom cells at different levels, 937 954 whenever the densest water is located above the less dense water. … … 939 956 In the current implementation of the BBL, only the tracers are modified, not the velocities. 940 957 Furthermore, it only connects ocean bottom cells, and therefore does not include all the improvements introduced by 941 \citet{ Campin_Goosse_Tel99}.958 \citet{campin.goosse_T99}. 942 959 943 960 % ------------------------------------------------------------------------------------------------------------- 944 961 % Diffusive BBL 945 962 % ------------------------------------------------------------------------------------------------------------- 946 \subsection{Diffusive bottom boundary layer (\protect\np{nn\_bbl\_ldf}~\forcode{= 1})} 963 \subsection[Diffusive bottom boundary layer (\forcode{nn_bbl_ldf = 1})] 964 {Diffusive bottom boundary layer (\protect\np{nn\_bbl\_ldf}\forcode{ = 1})} 947 965 \label{subsec:TRA_bbl_diff} 948 966 … … 955 973 with $\nabla_\sigma$ the lateral gradient operator taken between bottom cells, and 956 974 $A_l^\sigma$ the lateral diffusivity in the BBL. 957 Following \citet{ Beckmann_Doscher1997}, the latter is prescribed with a spatial dependence,975 Following \citet{beckmann.doscher_JPO97}, the latter is prescribed with a spatial dependence, 958 976 \ie in the conditional form 959 977 \begin{equation} … … 983 1001 % Advective BBL 984 1002 % ------------------------------------------------------------------------------------------------------------- 985 \subsection{Advective bottom boundary layer (\protect\np{nn\_bbl\_adv}~\forcode{= 1..2})} 1003 \subsection[Advective bottom boundary layer (\forcode{nn_bbl_adv = [12]})] 1004 {Advective bottom boundary layer (\protect\np{nn\_bbl\_adv}\forcode{ = [12]})} 986 1005 \label{subsec:TRA_bbl_adv} 987 1006 … … 994 1013 \begin{figure}[!t] 995 1014 \begin{center} 996 \includegraphics[ ]{Fig_BBL_adv}1015 \includegraphics[width=\textwidth]{Fig_BBL_adv} 997 1016 \caption{ 998 1017 \protect\label{fig:bbl} … … 1014 1033 %%%gmcomment : this section has to be really written 1015 1034 1016 When applying an advective BBL (\np{nn\_bbl\_adv} ~\forcode{= 1..2}), an overturning circulation is added which1035 When applying an advective BBL (\np{nn\_bbl\_adv}\forcode{ = 1..2}), an overturning circulation is added which 1017 1036 connects two adjacent bottom grid-points only if dense water overlies less dense water on the slope. 1018 1037 The density difference causes dense water to move down the slope. 1019 1038 1020 \np{nn\_bbl\_adv} ~\forcode{= 1}:1039 \np{nn\_bbl\_adv}\forcode{ = 1}: 1021 1040 the downslope velocity is chosen to be the Eulerian ocean velocity just above the topographic step 1022 (see black arrow in \autoref{fig:bbl}) \citep{ Beckmann_Doscher1997}.1041 (see black arrow in \autoref{fig:bbl}) \citep{beckmann.doscher_JPO97}. 1023 1042 It is a \textit{conditional advection}, that is, advection is allowed only 1024 1043 if dense water overlies less dense water on the slope (\ie $\nabla_\sigma \rho \cdot \nabla H < 0$) and 1025 1044 if the velocity is directed towards greater depth (\ie $\vect U \cdot \nabla H > 0$). 1026 1045 1027 \np{nn\_bbl\_adv} ~\forcode{= 2}:1046 \np{nn\_bbl\_adv}\forcode{ = 2}: 1028 1047 the downslope velocity is chosen to be proportional to $\Delta \rho$, 1029 the density difference between the higher cell and lower cell densities \citep{ Campin_Goosse_Tel99}.1048 the density difference between the higher cell and lower cell densities \citep{campin.goosse_T99}. 1030 1049 The advection is allowed only if dense water overlies less dense water on the slope 1031 1050 (\ie $\nabla_\sigma \rho \cdot \nabla H < 0$). … … 1041 1060 The parameter $\gamma$ should take a different value for each bathymetric step, but for simplicity, 1042 1061 and because no direct estimation of this parameter is available, a uniform value has been assumed. 1043 The possible values for $\gamma$ range between 1 and $10~s$ \citep{ Campin_Goosse_Tel99}.1062 The possible values for $\gamma$ range between 1 and $10~s$ \citep{campin.goosse_T99}. 1044 1063 1045 1064 Scalar properties are advected by this additional transport $(u^{tr}_{bbl},v^{tr}_{bbl})$ using the upwind scheme. … … 1074 1093 % Tracer damping 1075 1094 % ================================================================ 1076 \section{Tracer damping (\protect\mdl{tradmp})} 1095 \section[Tracer damping (\textit{tradmp.F90})] 1096 {Tracer damping (\protect\mdl{tradmp})} 1077 1097 \label{sec:TRA_dmp} 1078 1098 %--------------------------------------------namtra_dmp------------------------------------------------- … … 1109 1129 In the vicinity of these walls, $\gamma$ takes large values (equivalent to a time scale of a few days) whereas 1110 1130 it is zero in the interior of the model domain. 1111 The second case corresponds to the use of the robust diagnostic method \citep{ Sarmiento1982}.1131 The second case corresponds to the use of the robust diagnostic method \citep{sarmiento.bryan_JGR82}. 1112 1132 It allows us to find the velocity field consistent with the model dynamics whilst 1113 1133 having a $T$, $S$ field close to a given climatological field ($T_o$, $S_o$). … … 1121 1141 only below the mixed layer (defined either on a density or $S_o$ criterion). 1122 1142 It is common to set the damping to zero in the mixed layer as the adjustment time scale is short here 1123 \citep{ Madec_al_JPO96}.1143 \citep{madec.delecluse.ea_JPO96}. 1124 1144 1125 1145 For generating \ifile{resto}, see the documentation for the DMP tool provided with the source code under … … 1129 1149 % Tracer time evolution 1130 1150 % ================================================================ 1131 \section{Tracer time evolution (\protect\mdl{tranxt})} 1151 \section[Tracer time evolution (\textit{tranxt.F90})] 1152 {Tracer time evolution (\protect\mdl{tranxt})} 1132 1153 \label{sec:TRA_nxt} 1133 1154 %--------------------------------------------namdom----------------------------------------------------- … … 1137 1158 1138 1159 Options are defined through the \ngn{namdom} namelist variables. 1139 The general framework for tracer time stepping is a modified leap-frog scheme \citep{ Leclair_Madec_OM09},1160 The general framework for tracer time stepping is a modified leap-frog scheme \citep{leclair.madec_OM09}, 1140 1161 \ie a three level centred time scheme associated with a Asselin time filter (cf. \autoref{sec:STP_mLF}): 1141 1162 \begin{equation} … … 1151 1172 (\ie fluxes plus content in mass exchanges). 1152 1173 $\gamma$ is initialized as \np{rn\_atfp} (\textbf{namelist} parameter). 1153 Its default value is \np{rn\_atfp} ~\forcode{= 10.e-3}.1174 Its default value is \np{rn\_atfp}\forcode{ = 10.e-3}. 1154 1175 Note that the forcing correction term in the filter is not applied in linear free surface 1155 (\jp{lk\_vvl} ~\forcode{= .false.}) (see \autoref{subsec:TRA_sbc}).1176 (\jp{lk\_vvl}\forcode{ = .false.}) (see \autoref{subsec:TRA_sbc}). 1156 1177 Not also that in constant volume case, the time stepping is performed on $T$, not on its content, $e_{3t}T$. 1157 1178 … … 1166 1187 % Equation of State (eosbn2) 1167 1188 % ================================================================ 1168 \section{Equation of state (\protect\mdl{eosbn2}) } 1189 \section[Equation of state (\textit{eosbn2.F90})] 1190 {Equation of state (\protect\mdl{eosbn2})} 1169 1191 \label{sec:TRA_eosbn2} 1170 1192 %--------------------------------------------nameos----------------------------------------------------- … … 1176 1198 % Equation of State 1177 1199 % ------------------------------------------------------------------------------------------------------------- 1178 \subsection{Equation of seawater (\protect\np{nn\_eos}~\forcode{= -1..1})} 1200 \subsection[Equation of seawater (\forcode{nn_eos = {-1,1}})] 1201 {Equation of seawater (\protect\np{nn\_eos}\forcode{ = {-1,1}})} 1179 1202 \label{subsec:TRA_eos} 1180 1203 … … 1186 1209 Nonlinearities of the EOS are of major importance, in particular influencing the circulation through 1187 1210 determination of the static stability below the mixed layer, 1188 thus controlling rates of exchange between the atmosphere and the ocean interior \citep{ Roquet_JPO2015}.1189 Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{ UNESCO1983}) or1190 TEOS-10 \citep{ TEOS10} standards should be used anytime a simulation of the real ocean circulation is attempted1191 \citep{ Roquet_JPO2015}.1211 thus controlling rates of exchange between the atmosphere and the ocean interior \citep{roquet.madec.ea_JPO15}. 1212 Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{fofonoff.millard_bk83}) or 1213 TEOS-10 \citep{ioc.iapso_bk10} standards should be used anytime a simulation of the real ocean circulation is attempted 1214 \citep{roquet.madec.ea_JPO15}. 1192 1215 The use of TEOS-10 is highly recommended because 1193 1216 \textit{(i)} it is the new official EOS, … … 1195 1218 \textit{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature and 1196 1219 practical salinity for EOS-980, both variables being more suitable for use as model variables 1197 \citep{ TEOS10, Graham_McDougall_JPO13}.1220 \citep{ioc.iapso_bk10, graham.mcdougall_JPO13}. 1198 1221 EOS-80 is an obsolescent feature of the NEMO system, kept only for backward compatibility. 1199 1222 For process studies, it is often convenient to use an approximation of the EOS. 1200 To that purposed, a simplified EOS (S-EOS) inspired by \citet{ Vallis06} is also available.1223 To that purposed, a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is also available. 1201 1224 1202 1225 In the computer code, a density anomaly, $d_a = \rho / \rho_o - 1$, is computed, with $\rho_o$ a reference density. … … 1204 1227 This is a sensible choice for the reference density used in a Boussinesq ocean climate model, as, 1205 1228 with the exception of only a small percentage of the ocean, 1206 density in the World Ocean varies by no more than 2$\%$ from that value \citep{ Gill1982}.1229 density in the World Ocean varies by no more than 2$\%$ from that value \citep{gill_bk82}. 1207 1230 1208 1231 Options are defined through the \ngn{nameos} namelist variables, and in particular \np{nn\_eos} which … … 1210 1233 1211 1234 \begin{description} 1212 \item[\np{nn\_eos} ~\forcode{= -1}]1213 the polyTEOS10-bsq equation of seawater \citep{ Roquet_OM2015} is used.1235 \item[\np{nn\_eos}\forcode{ = -1}] 1236 the polyTEOS10-bsq equation of seawater \citep{roquet.madec.ea_OM15} is used. 1214 1237 The accuracy of this approximation is comparable to the TEOS-10 rational function approximation, 1215 1238 but it is optimized for a boussinesq fluid and the polynomial expressions have simpler and … … 1217 1240 use in ocean models. 1218 1241 Note that a slightly higher precision polynomial form is now used replacement of 1219 the TEOS-10 rational function approximation for hydrographic data analysis \citep{ TEOS10}.1242 the TEOS-10 rational function approximation for hydrographic data analysis \citep{ioc.iapso_bk10}. 1220 1243 A key point is that conservative state variables are used: 1221 1244 Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \deg{C}, notation: $\Theta$). 1222 1245 The pressure in decibars is approximated by the depth in meters. 1223 1246 With TEOS10, the specific heat capacity of sea water, $C_p$, is a constant. 1224 It is set to $C_p = 3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{ TEOS10}.1247 It is set to $C_p = 3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{ioc.iapso_bk10}. 1225 1248 Choosing polyTEOS10-bsq implies that the state variables used by the model are $\Theta$ and $S_A$. 1226 1249 In particular, the initial state deined by the user have to be given as \textit{Conservative} Temperature and … … 1229 1252 either computing the air-sea and ice-sea fluxes (forced mode) or 1230 1253 sending the SST field to the atmosphere (coupled mode). 1231 \item[\np{nn\_eos} ~\forcode{= 0}]1254 \item[\np{nn\_eos}\forcode{ = 0}] 1232 1255 the polyEOS80-bsq equation of seawater is used. 1233 1256 It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized to … … 1238 1261 The pressure in decibars is approximated by the depth in meters. 1239 1262 With thsi EOS, the specific heat capacity of sea water, $C_p$, is a function of temperature, salinity and 1240 pressure \citep{ UNESCO1983}.1263 pressure \citep{fofonoff.millard_bk83}. 1241 1264 Nevertheless, a severe assumption is made in order to have a heat content ($C_p T_p$) which 1242 1265 is conserved by the model: $C_p$ is set to a constant value, the TEOS10 value. 1243 \item[\np{nn\_eos} ~\forcode{= 1}]1244 a simplified EOS (S-EOS) inspired by \citet{ Vallis06} is chosen,1266 \item[\np{nn\_eos}\forcode{ = 1}] 1267 a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is chosen, 1245 1268 the coefficients of which has been optimized to fit the behavior of TEOS10 1246 (Roquet, personal comm.) (see also \citet{ Roquet_JPO2015}).1269 (Roquet, personal comm.) (see also \citet{roquet.madec.ea_JPO15}). 1247 1270 It provides a simplistic linear representation of both cabbeling and thermobaricity effects which 1248 is enough for a proper treatment of the EOS in theoretical studies \citep{ Roquet_JPO2015}.1271 is enough for a proper treatment of the EOS in theoretical studies \citep{roquet.madec.ea_JPO15}. 1249 1272 With such an equation of state there is no longer a distinction between 1250 1273 \textit{conservative} and \textit{potential} temperature, … … 1303 1326 % Brunt-V\"{a}is\"{a}l\"{a} Frequency 1304 1327 % ------------------------------------------------------------------------------------------------------------- 1305 \subsection{Brunt-V\"{a}is\"{a}l\"{a} frequency (\protect\np{nn\_eos}~\forcode{= 0..2})} 1328 \subsection[Brunt-V\"{a}is\"{a}l\"{a} frequency (\forcode{nn_eos = [0-2]})] 1329 {Brunt-V\"{a}is\"{a}l\"{a} frequency (\protect\np{nn\_eos}\forcode{ = [0-2]})} 1306 1330 \label{subsec:TRA_bn2} 1307 1331 … … 1329 1353 \label{subsec:TRA_fzp} 1330 1354 1331 The freezing point of seawater is a function of salinity and pressure \citep{ UNESCO1983}:1355 The freezing point of seawater is a function of salinity and pressure \citep{fofonoff.millard_bk83}: 1332 1356 \begin{equation} 1333 1357 \label{eq:tra_eos_fzp} … … 1357 1381 % Horizontal Derivative in zps-coordinate 1358 1382 % ================================================================ 1359 \section{Horizontal derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})} 1383 \section[Horizontal derivative in \textit{zps}-coordinate (\textit{zpshde.F90})] 1384 {Horizontal derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})} 1360 1385 \label{sec:TRA_zpshde} 1361 1386 … … 1363 1388 I've changed "derivative" to "difference" and "mean" to "average"} 1364 1389 1365 With partial cells (\np{ln\_zps} ~\forcode{= .true.}) at bottom and top (\np{ln\_isfcav}~\forcode{= .true.}),1390 With partial cells (\np{ln\_zps}\forcode{ = .true.}) at bottom and top (\np{ln\_isfcav}\forcode{ = .true.}), 1366 1391 in general, tracers in horizontally adjacent cells live at different depths. 1367 1392 Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} module) and 1368 1393 the hydrostatic pressure gradient calculations (\mdl{dynhpg} module). 1369 The partial cell properties at the top (\np{ln\_isfcav} ~\forcode{= .true.}) are computed in the same way as1394 The partial cell properties at the top (\np{ln\_isfcav}\forcode{ = .true.}) are computed in the same way as 1370 1395 for the bottom. 1371 1396 So, only the bottom interpolation is explained below. … … 1379 1404 \begin{figure}[!p] 1380 1405 \begin{center} 1381 \includegraphics[ ]{Fig_partial_step_scheme}1406 \includegraphics[width=\textwidth]{Fig_partial_step_scheme} 1382 1407 \caption{ 1383 1408 \protect\label{fig:Partial_step_scheme} 1384 1409 Discretisation of the horizontal difference and average of tracers in the $z$-partial step coordinate 1385 (\protect\np{ln\_zps} ~\forcode{= .true.}) in the case $(e3w_k^{i + 1} - e3w_k^i) > 0$.1410 (\protect\np{ln\_zps}\forcode{ = .true.}) in the case $(e3w_k^{i + 1} - e3w_k^i) > 0$. 1386 1411 A linear interpolation is used to estimate $\widetilde T_k^{i + 1}$, 1387 1412 the tracer value at the depth of the shallower tracer point of the two adjacent bottom $T$-points. -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_ZDF.tex
r10442 r11263 25 25 At the surface they are prescribed from the surface forcing (see \autoref{chap:SBC}), 26 26 while at the bottom they are set to zero for heat and salt, 27 unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \ key{trabbl} defined,27 unless a geothermal flux forcing is prescribed as a bottom boundary condition (\ie \np{ln\_trabbc} defined, 28 28 see \autoref{subsec:TRA_bbc}), and specified through a bottom friction parameterisation for momentum 29 (see \autoref{sec:ZDF_ bfr}).29 (see \autoref{sec:ZDF_drg}). 30 30 31 31 In this section we briefly discuss the various choices offered to compute the vertical eddy viscosity and … … 33 33 respectively (see \autoref{sec:TRA_zdf} and \autoref{sec:DYN_zdf}). 34 34 These coefficients can be assumed to be either constant, or a function of the local Richardson number, 35 or computed from a turbulent closure model (either TKE or GLS formulation).36 The computation of these coefficients is initialized in the \mdl{zdf ini} module and performed in37 the \mdl{zdfric}, \mdl{zdftke} or \mdl{zdfgls} modules.35 or computed from a turbulent closure model (either TKE or GLS or OSMOSIS formulation). 36 The computation of these coefficients is initialized in the \mdl{zdfphy} module and performed in 37 the \mdl{zdfric}, \mdl{zdftke} or \mdl{zdfgls} or \mdl{zdfosm} modules. 38 38 The trends due to the vertical momentum and tracer diffusion, including the surface forcing, 39 39 are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 40 These trends can be computed using either a forward time stepping scheme 41 (namelist parameter \np{ln\_zdfexp}\forcode{ = .true.}) or a backward time stepping scheme 42 (\np{ln\_zdfexp}\forcode{ = .false.}) depending on the magnitude of the mixing coefficients, 43 and thus of the formulation used (see \autoref{chap:STP}). 44 45 % ------------------------------------------------------------------------------------------------------------- 46 % Constant 47 % ------------------------------------------------------------------------------------------------------------- 48 \subsection{Constant (\protect\key{zdfcst})} 49 \label{subsec:ZDF_cst} 50 %--------------------------------------------namzdf--------------------------------------------------------- 40 %These trends can be computed using either a forward time stepping scheme 41 %(namelist parameter \np{ln\_zdfexp}\forcode{ = .true.}) or a backward time stepping scheme 42 %(\np{ln\_zdfexp}\forcode{ = .false.}) depending on the magnitude of the mixing coefficients, 43 %and thus of the formulation used (see \autoref{chap:STP}). 44 45 %--------------------------------------------namzdf-------------------------------------------------------- 51 46 52 47 \nlst{namzdf} 53 48 %-------------------------------------------------------------------------------------------------------------- 54 49 50 % ------------------------------------------------------------------------------------------------------------- 51 % Constant 52 % ------------------------------------------------------------------------------------------------------------- 53 \subsection[Constant (\forcode{ln_zdfcst = .true.})] 54 {Constant (\protect\np{ln\_zdfcst}\forcode{ = .true.})} 55 \label{subsec:ZDF_cst} 56 55 57 Options are defined through the \ngn{namzdf} namelist variables. 56 When \ key{zdfcst} is defined, the momentum and tracer vertical eddy coefficients are set to58 When \np{ln\_zdfcst} is defined, the momentum and tracer vertical eddy coefficients are set to 57 59 constant values over the whole ocean. 58 60 This is the crudest way to define the vertical ocean physics. 59 It is recommended t hat this option is only usedin process studies, not in basin scale simulations.61 It is recommended to use this option only in process studies, not in basin scale simulations. 60 62 Typical values used in this case are: 61 63 \begin{align*} … … 72 74 % Richardson Number Dependent 73 75 % ------------------------------------------------------------------------------------------------------------- 74 \subsection{Richardson number dependent (\protect\key{zdfric})} 76 \subsection[Richardson number dependent (\forcode{ln_zdfric = .true.})] 77 {Richardson number dependent (\protect\np{ln\_zdfric}\forcode{ = .true.})} 75 78 \label{subsec:ZDF_ric} 76 79 … … 80 83 %-------------------------------------------------------------------------------------------------------------- 81 84 82 When \ key{zdfric} is defined, a local Richardson number dependent formulation for the vertical momentum and85 When \np{ln\_zdfric}\forcode{ = .true.}, a local Richardson number dependent formulation for the vertical momentum and 83 86 tracer eddy coefficients is set through the \ngn{namzdf\_ric} namelist variables. 84 87 The vertical mixing coefficients are diagnosed from the large scale variables computed by the model. … … 87 90 a dependency between the vertical eddy coefficients and the local Richardson number 88 91 (\ie the ratio of stratification to vertical shear). 89 Following \citet{ Pacanowski_Philander_JPO81}, the following formulation has been implemented:92 Following \citet{pacanowski.philander_JPO81}, the following formulation has been implemented: 90 93 \[ 91 94 % \label{eq:zdfric} … … 124 127 The final $h_{e}$ is further constrained by the adjustable bounds \np{rn\_mldmin} and \np{rn\_mldmax}. 125 128 Once $h_{e}$ is computed, the vertical eddy coefficients within $h_{e}$ are set to 126 the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{ Lermusiaux2001}.129 the empirical values \np{rn\_wtmix} and \np{rn\_wvmix} \citep{lermusiaux_JMS01}. 127 130 128 131 % ------------------------------------------------------------------------------------------------------------- 129 132 % TKE Turbulent Closure Scheme 130 133 % ------------------------------------------------------------------------------------------------------------- 131 \subsection{TKE turbulent closure scheme (\protect\key{zdftke})} 134 \subsection[TKE turbulent closure scheme (\forcode{ln_zdftke = .true.})] 135 {TKE turbulent closure scheme (\protect\np{ln\_zdftke}\forcode{ = .true.})} 132 136 \label{subsec:ZDF_tke} 133 134 137 %--------------------------------------------namzdf_tke-------------------------------------------------- 135 138 … … 140 143 a prognostic equation for $\bar{e}$, the turbulent kinetic energy, 141 144 and a closure assumption for the turbulent length scales. 142 This turbulent closure model has been developed by \citet{ Bougeault1989} in the atmospheric case,143 adapted by \citet{ Gaspar1990} for the oceanic case, and embedded in OPA, the ancestor of NEMO,144 by \citet{ Blanke1993} for equatorial Atlantic simulations.145 Since then, significant modifications have been introduced by \citet{ Madec1998} in both the implementation and145 This turbulent closure model has been developed by \citet{bougeault.lacarrere_MWR89} in the atmospheric case, 146 adapted by \citet{gaspar.gregoris.ea_JGR90} for the oceanic case, and embedded in OPA, the ancestor of NEMO, 147 by \citet{blanke.delecluse_JPO93} for equatorial Atlantic simulations. 148 Since then, significant modifications have been introduced by \citet{madec.delecluse.ea_NPM98} in both the implementation and 146 149 the formulation of the mixing length scale. 147 150 The time evolution of $\bar{e}$ is the result of the production of $\bar{e}$ through vertical shear, 148 its destruction through stratification, its vertical diffusion, and its dissipation of \citet{ Kolmogorov1942} type:151 its destruction through stratification, its vertical diffusion, and its dissipation of \citet{kolmogorov_IANS42} type: 149 152 \begin{equation} 150 153 \label{eq:zdftke_e} … … 168 171 $P_{rt}$ is the Prandtl number, $K_m$ and $K_\rho$ are the vertical eddy viscosity and diffusivity coefficients. 169 172 The constants $C_k = 0.1$ and $C_\epsilon = \sqrt {2} /2$ $\approx 0.7$ are designed to deal with 170 vertical mixing at any depth \citep{ Gaspar1990}.173 vertical mixing at any depth \citep{gaspar.gregoris.ea_JGR90}. 171 174 They are set through namelist parameters \np{nn\_ediff} and \np{nn\_ediss}. 172 $P_{rt}$ can be set to unity or, following \citet{ Blanke1993}, be a function of the local Richardson number, $R_i$:175 $P_{rt}$ can be set to unity or, following \citet{blanke.delecluse_JPO93}, be a function of the local Richardson number, $R_i$: 173 176 \begin{align*} 174 177 % \label{eq:prt} … … 180 183 \end{cases} 181 184 \end{align*} 182 Options are defined through the \ngn{namzdfy\_tke} namelist variables.183 185 The choice of $P_{rt}$ is controlled by the \np{nn\_pdl} namelist variable. 184 186 185 187 At the sea surface, the value of $\bar{e}$ is prescribed from the wind stress field as 186 188 $\bar{e}_o = e_{bb} |\tau| / \rho_o$, with $e_{bb}$ the \np{rn\_ebb} namelist parameter. 187 The default value of $e_{bb}$ is 3.75. \citep{ Gaspar1990}), however a much larger value can be used when189 The default value of $e_{bb}$ is 3.75. \citep{gaspar.gregoris.ea_JGR90}), however a much larger value can be used when 188 190 taking into account the surface wave breaking (see below Eq. \autoref{eq:ZDF_Esbc}). 189 191 The bottom value of TKE is assumed to be equal to the value of the level just above. … … 191 193 the numerical scheme does not ensure its positivity. 192 194 To overcome this problem, a cut-off in the minimum value of $\bar{e}$ is used (\np{rn\_emin} namelist parameter). 193 Following \citet{ Gaspar1990}, the cut-off value is set to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$.194 This allows the subsequent formulations to match that of \citet{ Gargett1984} for the diffusion in195 Following \citet{gaspar.gregoris.ea_JGR90}, the cut-off value is set to $\sqrt{2}/2~10^{-6}~m^2.s^{-2}$. 196 This allows the subsequent formulations to match that of \citet{gargett_JMR84} for the diffusion in 195 197 the thermocline and deep ocean : $K_\rho = 10^{-3} / N$. 196 198 In addition, a cut-off is applied on $K_m$ and $K_\rho$ to avoid numerical instabilities associated with 197 199 too weak vertical diffusion. 198 200 They must be specified at least larger than the molecular values, and are set through \np{rn\_avm0} and 199 \np{rn\_avt0} ( namzdfnamelist, see \autoref{subsec:ZDF_cst}).201 \np{rn\_avt0} (\ngn{namzdf} namelist, see \autoref{subsec:ZDF_cst}). 200 202 201 203 \subsubsection{Turbulent length scale} 202 204 203 205 For computational efficiency, the original formulation of the turbulent length scales proposed by 204 \citet{ Gaspar1990} has been simplified.206 \citet{gaspar.gregoris.ea_JGR90} has been simplified. 205 207 Four formulations are proposed, the choice of which is controlled by the \np{nn\_mxl} namelist parameter. 206 The first two are based on the following first order approximation \citep{ Blanke1993}:208 The first two are based on the following first order approximation \citep{blanke.delecluse_JPO93}: 207 209 \begin{equation} 208 210 \label{eq:tke_mxl0_1} … … 212 214 The resulting length scale is bounded by the distance to the surface or to the bottom 213 215 (\np{nn\_mxl}\forcode{ = 0}) or by the local vertical scale factor (\np{nn\_mxl}\forcode{ = 1}). 214 \citet{ Blanke1993} notice that this simplification has two major drawbacks:216 \citet{blanke.delecluse_JPO93} notice that this simplification has two major drawbacks: 215 217 it makes no sense for locally unstable stratification and the computation no longer uses all 216 218 the information contained in the vertical density profile. 217 To overcome these drawbacks, \citet{ Madec1998} introduces the \np{nn\_mxl}\forcode{ = 2..3} cases,219 To overcome these drawbacks, \citet{madec.delecluse.ea_NPM98} introduces the \np{nn\_mxl}\forcode{ = 2, 3} cases, 218 220 which add an extra assumption concerning the vertical gradient of the computed length scale. 219 221 So, the length scales are first evaluated as in \autoref{eq:tke_mxl0_1} and then bounded such that: … … 225 227 \autoref{eq:tke_mxl_constraint} means that the vertical variations of the length scale cannot be larger than 226 228 the variations of depth. 227 It provides a better approximation of the \citet{ Gaspar1990} formulation while being much less229 It provides a better approximation of the \citet{gaspar.gregoris.ea_JGR90} formulation while being much less 228 230 time consuming. 229 231 In particular, it allows the length scale to be limited not only by the distance to the surface or … … 237 239 \begin{figure}[!t] 238 240 \begin{center} 239 \includegraphics[width= 1.00\textwidth]{Fig_mixing_length}241 \includegraphics[width=\textwidth]{Fig_mixing_length} 240 242 \caption{ 241 243 \protect\label{fig:mixing_length} … … 258 260 In the \np{nn\_mxl}\forcode{ = 2} case, the dissipation and mixing length scales take the same value: 259 261 $ l_k= l_\epsilon = \min \left(\ l_{up} \;,\; l_{dwn}\ \right)$, while in the \np{nn\_mxl}\forcode{ = 3} case, 260 the dissipation and mixing turbulent length scales are give as in \citet{ Gaspar1990}:262 the dissipation and mixing turbulent length scales are give as in \citet{gaspar.gregoris.ea_JGR90}: 261 263 \[ 262 264 % \label{eq:tke_mxl_gaspar} … … 270 272 Usually the surface scale is given by $l_o = \kappa \,z_o$ where $\kappa = 0.4$ is von Karman's constant and 271 273 $z_o$ the roughness parameter of the surface. 272 Assuming $z_o=0.1$~m \citep{ Craig_Banner_JPO94} leads to a 0.04~m, the default value of \np{rn\_mxl0}.274 Assuming $z_o=0.1$~m \citep{craig.banner_JPO94} leads to a 0.04~m, the default value of \np{rn\_mxl0}. 273 275 In the ocean interior a minimum length scale is set to recover the molecular viscosity when 274 276 $\bar{e}$ reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). … … 277 279 %-----------------------------------------------------------------------% 278 280 279 Following \citet{ Mellor_Blumberg_JPO04}, the TKE turbulence closure model has been modified to281 Following \citet{mellor.blumberg_JPO04}, the TKE turbulence closure model has been modified to 280 282 include the effect of surface wave breaking energetics. 281 283 This results in a reduction of summertime surface temperature when the mixed layer is relatively shallow. 282 The \citet{ Mellor_Blumberg_JPO04} modifications acts on surface length scale and TKE values and284 The \citet{mellor.blumberg_JPO04} modifications acts on surface length scale and TKE values and 283 285 air-sea drag coefficient. 284 The latter concerns the bulk formul eaand is not discussed here.285 286 Following \citet{ Craig_Banner_JPO94}, the boundary condition on surface TKE value is :286 The latter concerns the bulk formulae and is not discussed here. 287 288 Following \citet{craig.banner_JPO94}, the boundary condition on surface TKE value is : 287 289 \begin{equation} 288 290 \label{eq:ZDF_Esbc} 289 291 \bar{e}_o = \frac{1}{2}\,\left( 15.8\,\alpha_{CB} \right)^{2/3} \,\frac{|\tau|}{\rho_o} 290 292 \end{equation} 291 where $\alpha_{CB}$ is the \citet{ Craig_Banner_JPO94} constant of proportionality which depends on the ''wave age'',292 ranging from 57 for mature waves to 146 for younger waves \citep{ Mellor_Blumberg_JPO04}.293 where $\alpha_{CB}$ is the \citet{craig.banner_JPO94} constant of proportionality which depends on the ''wave age'', 294 ranging from 57 for mature waves to 146 for younger waves \citep{mellor.blumberg_JPO04}. 293 295 The boundary condition on the turbulent length scale follows the Charnock's relation: 294 296 \begin{equation} … … 297 299 \end{equation} 298 300 where $\kappa=0.40$ is the von Karman constant, and $\beta$ is the Charnock's constant. 299 \citet{ Mellor_Blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by300 \citet{ Stacey_JPO99} citing observation evidence, and301 \citet{mellor.blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by 302 \citet{stacey_JPO99} citing observation evidence, and 301 303 $\alpha_{CB} = 100$ the Craig and Banner's value. 302 304 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 303 305 with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}\forcode{ = 67.83} corresponds 304 306 to $\alpha_{CB} = 100$. 305 Further setting \np{ln\_mxl0 } to true applies \autoref{eq:ZDF_Lsbc} as surface boundary condition onlength scale,307 Further setting \np{ln\_mxl0=.true.}, applies \autoref{eq:ZDF_Lsbc} as the surface boundary condition on the length scale, 306 308 with $\beta$ hard coded to the Stacey's value. 307 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on 309 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on the 308 310 surface $\bar{e}$ value. 309 311 … … 315 317 Although LC have nothing to do with convection, the circulation pattern is rather similar to 316 318 so-called convective rolls in the atmospheric boundary layer. 317 The detailed physics behind LC is described in, for example, \citet{ Craik_Leibovich_JFM76}.319 The detailed physics behind LC is described in, for example, \citet{craik.leibovich_JFM76}. 318 320 The prevailing explanation is that LC arise from a nonlinear interaction between the Stokes drift and 319 321 wind drift currents. 320 322 321 323 Here we introduced in the TKE turbulent closure the simple parameterization of Langmuir circulations proposed by 322 \citep{ Axell_JGR02} for a $k-\epsilon$ turbulent closure.324 \citep{axell_JGR02} for a $k-\epsilon$ turbulent closure. 323 325 The parameterization, tuned against large-eddy simulation, includes the whole effect of LC in 324 an extra source term sof TKE, $P_{LC}$.326 an extra source term of TKE, $P_{LC}$. 325 327 The presence of $P_{LC}$ in \autoref{eq:zdftke_e}, the TKE equation, is controlled by setting \np{ln\_lc} to 326 \forcode{.true.} in the namtkenamelist.328 \forcode{.true.} in the \ngn{namzdf\_tke} namelist. 327 329 328 By making an analogy with the characteristic convective velocity scale (\eg, \citet{ D'Alessio_al_JPO98}),330 By making an analogy with the characteristic convective velocity scale (\eg, \citet{dalessio.abdella.ea_JPO98}), 329 331 $P_{LC}$ is assumed to be : 330 332 \[ … … 334 336 With no information about the wave field, $w_{LC}$ is assumed to be proportional to 335 337 the Stokes drift $u_s = 0.377\,\,|\tau|^{1/2}$, where $|\tau|$ is the surface wind stress module 336 \footnote{Following \citet{ Li_Garrett_JMR93}, the surface Stoke drift velocity may be expressed as338 \footnote{Following \citet{li.garrett_JMR93}, the surface Stoke drift velocity may be expressed as 337 339 $u_s = 0.016 \,|U_{10m}|$. 338 340 Assuming an air density of $\rho_a=1.22 \,Kg/m^3$ and a drag coefficient of … … 350 352 \end{cases} 351 353 \] 352 where $c_{LC} = 0.15$ has been chosen by \citep{ Axell_JGR02} as a good compromise to fit LES data.354 where $c_{LC} = 0.15$ has been chosen by \citep{axell_JGR02} as a good compromise to fit LES data. 353 355 The chosen value yields maximum vertical velocities $w_{LC}$ of the order of a few centimeters per second. 354 356 The value of $c_{LC}$ is set through the \np{rn\_lc} namelist parameter, 355 having in mind that it should stay between 0.15 and 0.54 \citep{ Axell_JGR02}.357 having in mind that it should stay between 0.15 and 0.54 \citep{axell_JGR02}. 356 358 357 359 The $H_{LC}$ is estimated in a similar way as the turbulent length scale of TKE equations: 358 $H_{LC}$ is depth to which a water parcel with kinetic energy due to Stoke drift can reach on its own by360 $H_{LC}$ is the depth to which a water parcel with kinetic energy due to Stoke drift can reach on its own by 359 361 converting its kinetic energy to potential energy, according to 360 362 \[ … … 368 370 produce mixed-layer depths that are too shallow during summer months and windy conditions. 369 371 This bias is particularly acute over the Southern Ocean. 370 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{ Rodgers_2014}.372 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{rodgers.aumont.ea_B14}. 371 373 The parameterization is an empirical one, \ie not derived from theoretical considerations, 372 374 but rather is meant to account for observed processes that affect the density structure of … … 383 385 \end{equation} 384 386 where $z$ is the depth, $e_s$ is TKE surface boundary condition, $f_r$ is the fraction of the surface TKE that 385 penetrate in the ocean, $h_\tau$ is a vertical mixing length scale that controls exponential shape of387 penetrates in the ocean, $h_\tau$ is a vertical mixing length scale that controls exponential shape of 386 388 the penetration, and $f_i$ is the ice concentration 387 (no penetration if $f_i=1$, that isif the ocean is entirely covered by sea-ice).389 (no penetration if $f_i=1$, \ie if the ocean is entirely covered by sea-ice). 388 390 The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter. 389 391 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}\forcode{ = 0}) or … … 391 393 (\np{nn\_etau}\forcode{ = 1}). 392 394 393 Note that two other option exist e, \np{nn\_etau}\forcode{ = 2..3}.395 Note that two other option exist, \np{nn\_etau}\forcode{ = 2, 3}. 394 396 They correspond to applying \autoref{eq:ZDF_Ehtau} only at the base of the mixed layer, 395 or to using the high frequency part of the stress to evaluate the fraction of TKE that penetrate the ocean.397 or to using the high frequency part of the stress to evaluate the fraction of TKE that penetrates the ocean. 396 398 Those two options are obsolescent features introduced for test purposes. 397 399 They will be removed in the next release. 400 401 % This should be explain better below what this rn_eice parameter is meant for: 402 In presence of Sea Ice, the value of this mixing can be modulated by the \np{rn\_eice} namelist parameter. 403 This parameter varies from \forcode{0} for no effect to \forcode{4} to suppress the TKE input into the ocean when Sea Ice concentration 404 is greater than 25\%. 398 405 399 406 % from Burchard et al OM 2008 : … … 406 413 407 414 % ------------------------------------------------------------------------------------------------------------- 408 % TKE discretization considerations 409 % ------------------------------------------------------------------------------------------------------------- 410 \subsection{TKE discretization considerations (\protect\key{zdftke})} 415 % GLS Generic Length Scale Scheme 416 % ------------------------------------------------------------------------------------------------------------- 417 \subsection[GLS: Generic Length Scale (\forcode{ln_zdfgls = .true.})] 418 {GLS: Generic Length Scale (\protect\np{ln\_zdfgls}\forcode{ = .true.})} 419 \label{subsec:ZDF_gls} 420 421 %--------------------------------------------namzdf_gls--------------------------------------------------------- 422 423 \nlst{namzdf_gls} 424 %-------------------------------------------------------------------------------------------------------------- 425 426 The Generic Length Scale (GLS) scheme is a turbulent closure scheme based on two prognostic equations: 427 one for the turbulent kinetic energy $\bar {e}$, and another for the generic length scale, 428 $\psi$ \citep{umlauf.burchard_JMR03, umlauf.burchard_CSR05}. 429 This later variable is defined as: $\psi = {C_{0\mu}}^{p} \ {\bar{e}}^{m} \ l^{n}$, 430 where the triplet $(p, m, n)$ value given in Tab.\autoref{tab:GLS} allows to recover a number of 431 well-known turbulent closures ($k$-$kl$ \citep{mellor.yamada_RG82}, $k$-$\epsilon$ \citep{rodi_JGR87}, 432 $k$-$\omega$ \citep{wilcox_AJ88} among others \citep{umlauf.burchard_JMR03,kantha.carniel_JMR03}). 433 The GLS scheme is given by the following set of equations: 434 \begin{equation} 435 \label{eq:zdfgls_e} 436 \frac{\partial \bar{e}}{\partial t} = 437 \frac{K_m}{\sigma_e e_3 }\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2 438 +\left( \frac{\partial v}{\partial k} \right)^2} \right] 439 -K_\rho \,N^2 440 +\frac{1}{e_3}\,\frac{\partial}{\partial k} \left[ \frac{K_m}{e_3}\,\frac{\partial \bar{e}}{\partial k} \right] 441 - \epsilon 442 \end{equation} 443 444 \[ 445 % \label{eq:zdfgls_psi} 446 \begin{split} 447 \frac{\partial \psi}{\partial t} =& \frac{\psi}{\bar{e}} \left\{ 448 \frac{C_1\,K_m}{\sigma_{\psi} {e_3}}\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2 449 +\left( \frac{\partial v}{\partial k} \right)^2} \right] 450 - C_3 \,K_\rho\,N^2 - C_2 \,\epsilon \,Fw \right\} \\ 451 &+\frac{1}{e_3} \;\frac{\partial }{\partial k}\left[ {\frac{K_m}{e_3 } 452 \;\frac{\partial \psi}{\partial k}} \right]\; 453 \end{split} 454 \] 455 456 \[ 457 % \label{eq:zdfgls_kz} 458 \begin{split} 459 K_m &= C_{\mu} \ \sqrt {\bar{e}} \ l \\ 460 K_\rho &= C_{\mu'}\ \sqrt {\bar{e}} \ l 461 \end{split} 462 \] 463 464 \[ 465 % \label{eq:zdfgls_eps} 466 {\epsilon} = C_{0\mu} \,\frac{\bar {e}^{3/2}}{l} \; 467 \] 468 where $N$ is the local Brunt-Vais\"{a}l\"{a} frequency (see \autoref{subsec:TRA_bn2}) and 469 $\epsilon$ the dissipation rate. 470 The constants $C_1$, $C_2$, $C_3$, ${\sigma_e}$, ${\sigma_{\psi}}$ and the wall function ($Fw$) depends of 471 the choice of the turbulence model. 472 Four different turbulent models are pre-defined (\autoref{tab:GLS}). 473 They are made available through the \np{nn\_clo} namelist parameter. 474 475 %--------------------------------------------------TABLE-------------------------------------------------- 476 \begin{table}[htbp] 477 \begin{center} 478 % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}c} 479 \begin{tabular}{ccccc} 480 & $k-kl$ & $k-\epsilon$ & $k-\omega$ & generic \\ 481 % & \citep{mellor.yamada_RG82} & \citep{rodi_JGR87} & \citep{wilcox_AJ88} & \\ 482 \hline 483 \hline 484 \np{nn\_clo} & \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} \\ 485 \hline 486 $( p , n , m )$ & ( 0 , 1 , 1 ) & ( 3 , 1.5 , -1 ) & ( -1 , 0.5 , -1 ) & ( 2 , 1 , -0.67 ) \\ 487 $\sigma_k$ & 2.44 & 1. & 2. & 0.8 \\ 488 $\sigma_\psi$ & 2.44 & 1.3 & 2. & 1.07 \\ 489 $C_1$ & 0.9 & 1.44 & 0.555 & 1. \\ 490 $C_2$ & 0.5 & 1.92 & 0.833 & 1.22 \\ 491 $C_3$ & 1. & 1. & 1. & 1. \\ 492 $F_{wall}$ & Yes & -- & -- & -- \\ 493 \hline 494 \hline 495 \end{tabular} 496 \caption{ 497 \protect\label{tab:GLS} 498 Set of predefined GLS parameters, or equivalently predefined turbulence models available with 499 \protect\np{ln\_zdfgls}\forcode{ = .true.} and controlled by the \protect\np{nn\_clos} namelist variable in \protect\ngn{namzdf\_gls}. 500 } 501 \end{center} 502 \end{table} 503 %-------------------------------------------------------------------------------------------------------------- 504 505 In the Mellor-Yamada model, the negativity of $n$ allows to use a wall function to force the convergence of 506 the mixing length towards $\kappa z_b$ ($\kappa$ is the Von Karman constant and $z_b$ the rugosity length scale) value near physical boundaries 507 (logarithmic boundary layer law). 508 $C_{\mu}$ and $C_{\mu'}$ are calculated from stability function proposed by \citet{galperin.kantha.ea_JAS88}, 509 or by \citet{kantha.clayson_JGR94} or one of the two functions suggested by \citet{canuto.howard.ea_JPO01} 510 (\np{nn\_stab\_func}\forcode{ = 0, 3}, resp.). 511 The value of $C_{0\mu}$ depends on the choice of the stability function. 512 513 The surface and bottom boundary condition on both $\bar{e}$ and $\psi$ can be calculated thanks to Dirichlet or 514 Neumann condition through \np{nn\_bc\_surf} and \np{nn\_bc\_bot}, resp. 515 As for TKE closure, the wave effect on the mixing is considered when 516 \np{rn\_crban}\forcode{ > 0.} \citep{craig.banner_JPO94, mellor.blumberg_JPO04}. 517 The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and 518 \np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}. 519 520 The $\psi$ equation is known to fail in stably stratified flows, and for this reason 521 almost all authors apply a clipping of the length scale as an \textit{ad hoc} remedy. 522 With this clipping, the maximum permissible length scale is determined by $l_{max} = c_{lim} \sqrt{2\bar{e}}/ N$. 523 A value of $c_{lim} = 0.53$ is often used \citep{galperin.kantha.ea_JAS88}. 524 \cite{umlauf.burchard_CSR05} show that the value of the clipping factor is of crucial importance for 525 the entrainment depth predicted in stably stratified situations, 526 and that its value has to be chosen in accordance with the algebraic model for the turbulent fluxes. 527 The clipping is only activated if \np{ln\_length\_lim}\forcode{ = .true.}, 528 and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value. 529 530 The time and space discretization of the GLS equations follows the same energetic consideration as for 531 the TKE case described in \autoref{subsec:ZDF_tke_ene} \citep{burchard_OM02}. 532 Evaluation of the 4 GLS turbulent closure schemes can be found in \citet{warner.sherwood.ea_OM05} in ROMS model and 533 in \citet{reffray.guillaume.ea_GMD15} for the \NEMO model. 534 535 536 % ------------------------------------------------------------------------------------------------------------- 537 % OSM OSMOSIS BL Scheme 538 % ------------------------------------------------------------------------------------------------------------- 539 \subsection[OSM: OSMosis boundary layer scheme (\forcode{ln_zdfosm = .true.})] 540 {OSM: OSMosis boundary layer scheme (\protect\np{ln\_zdfosm}\forcode{ = .true.})} 541 \label{subsec:ZDF_osm} 542 %--------------------------------------------namzdf_osm--------------------------------------------------------- 543 544 \nlst{namzdf_osm} 545 %-------------------------------------------------------------------------------------------------------------- 546 547 The OSMOSIS turbulent closure scheme is based on...... TBC 548 549 % ------------------------------------------------------------------------------------------------------------- 550 % TKE and GLS discretization considerations 551 % ------------------------------------------------------------------------------------------------------------- 552 \subsection[ Discrete energy conservation for TKE and GLS schemes] 553 {Discrete energy conservation for TKE and GLS schemes} 411 554 \label{subsec:ZDF_tke_ene} 412 555 … … 414 557 \begin{figure}[!t] 415 558 \begin{center} 416 \includegraphics[width= 1.00\textwidth]{Fig_ZDF_TKE_time_scheme}559 \includegraphics[width=\textwidth]{Fig_ZDF_TKE_time_scheme} 417 560 \caption{ 418 561 \protect\label{fig:TKE_time_scheme} 419 Illustration of the TKE time integrationand its links to the momentum and tracer time integration.562 Illustration of the subgrid kinetic energy integration in GLS and TKE schemes and its links to the momentum and tracer time integration. 420 563 } 421 564 \end{center} … … 424 567 425 568 The production of turbulence by vertical shear (the first term of the right hand side of 426 \autoref{eq:zdftke_e}) should balance the loss of kinetic energy associated with the vertical momentum diffusion569 \autoref{eq:zdftke_e}) and \autoref{eq:zdfgls_e}) should balance the loss of kinetic energy associated with the vertical momentum diffusion 427 570 (first line in \autoref{eq:PE_zdf}). 428 To do so a special care ha veto be taken for both the time and space discretization of429 the TKE equation \citep{Burchard_OM02,Marsaleix_al_OM08}.571 To do so a special care has to be taken for both the time and space discretization of 572 the kinetic energy equation \citep{burchard_OM02,marsaleix.auclair.ea_OM08}. 430 573 431 574 Let us first address the time stepping issue. \autoref{fig:TKE_time_scheme} shows how 432 575 the two-level Leap-Frog time stepping of the momentum and tracer equations interplays with 433 the one-level forward time stepping of TKE equation.576 the one-level forward time stepping of the equation for $\bar{e}$. 434 577 With this framework, the total loss of kinetic energy (in 1D for the demonstration) due to 435 578 the vertical momentum diffusion is obtained by multiplying this quantity by $u^t$ and … … 456 599 457 600 A similar consideration applies on the destruction rate of $\bar{e}$ due to stratification 458 (second term of the right hand side of \autoref{eq:zdftke_e} ).601 (second term of the right hand side of \autoref{eq:zdftke_e} and \autoref{eq:zdfgls_e}). 459 602 This term must balance the input of potential energy resulting from vertical mixing. 460 The rate of change of potential energy (in 1D for the demonstration) due vertical mixing is obtained by461 multiplying vertical density diffusion tendency by $g\,z$ and and summing the result vertically:603 The rate of change of potential energy (in 1D for the demonstration) due to vertical mixing is obtained by 604 multiplying the vertical density diffusion tendency by $g\,z$ and and summing the result vertically: 462 605 \begin{equation} 463 606 \label{eq:energ2} … … 475 618 The second term is minus the destruction rate of $\bar{e}$ due to stratification. 476 619 Therefore \autoref{eq:energ1} implies that, to be energetically consistent, 477 the product ${K_\rho}^{t-\rdt}\,(N^2)^t$ should be used in \autoref{eq:zdftke_e} , the TKE equation.620 the product ${K_\rho}^{t-\rdt}\,(N^2)^t$ should be used in \autoref{eq:zdftke_e} and \autoref{eq:zdfgls_e}. 478 621 479 622 Let us now address the space discretization issue. … … 483 626 By redoing the \autoref{eq:energ1} in the 3D case, it can be shown that the product of eddy coefficient by 484 627 the shear at $t$ and $t-\rdt$ must be performed prior to the averaging. 485 Furthermore, the possible time variation of $e_3$ (\key{vvl} case) have tobe taken into account.628 Furthermore, the time variation of $e_3$ has be taken into account. 486 629 487 630 The above energetic considerations leads to the following final discrete form for the TKE equation: … … 507 650 are time stepped using a backward scheme (see\autoref{sec:STP_forward_imp}). 508 651 Note that the Kolmogorov term has been linearized in time in order to render the implicit computation possible. 509 The restart of the TKE scheme requires the storage of $\bar {e}$, $K_m$, $K_\rho$ and $l_\epsilon$ as 510 they all appear in the right hand side of \autoref{eq:zdftke_ene}. 511 For the latter, it is in fact the ratio $\sqrt{\bar{e}}/l_\epsilon$ which is stored. 512 513 % ------------------------------------------------------------------------------------------------------------- 514 % GLS Generic Length Scale Scheme 515 % ------------------------------------------------------------------------------------------------------------- 516 \subsection{GLS: Generic Length Scale (\protect\key{zdfgls})} 517 \label{subsec:ZDF_gls} 518 519 %--------------------------------------------namzdf_gls--------------------------------------------------------- 520 521 \nlst{namzdf_gls} 522 %-------------------------------------------------------------------------------------------------------------- 523 524 The Generic Length Scale (GLS) scheme is a turbulent closure scheme based on two prognostic equations: 525 one for the turbulent kinetic energy $\bar {e}$, and another for the generic length scale, 526 $\psi$ \citep{Umlauf_Burchard_JMS03, Umlauf_Burchard_CSR05}. 527 This later variable is defined as: $\psi = {C_{0\mu}}^{p} \ {\bar{e}}^{m} \ l^{n}$, 528 where the triplet $(p, m, n)$ value given in Tab.\autoref{tab:GLS} allows to recover a number of 529 well-known turbulent closures ($k$-$kl$ \citep{Mellor_Yamada_1982}, $k$-$\epsilon$ \citep{Rodi_1987}, 530 $k$-$\omega$ \citep{Wilcox_1988} among others \citep{Umlauf_Burchard_JMS03,Kantha_Carniel_CSR05}). 531 The GLS scheme is given by the following set of equations: 532 \begin{equation} 533 \label{eq:zdfgls_e} 534 \frac{\partial \bar{e}}{\partial t} = 535 \frac{K_m}{\sigma_e e_3 }\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2 536 +\left( \frac{\partial v}{\partial k} \right)^2} \right] 537 -K_\rho \,N^2 538 +\frac{1}{e_3}\,\frac{\partial}{\partial k} \left[ \frac{K_m}{e_3}\,\frac{\partial \bar{e}}{\partial k} \right] 539 - \epsilon 540 \end{equation} 541 542 \[ 543 % \label{eq:zdfgls_psi} 544 \begin{split} 545 \frac{\partial \psi}{\partial t} =& \frac{\psi}{\bar{e}} \left\{ 546 \frac{C_1\,K_m}{\sigma_{\psi} {e_3}}\;\left[ {\left( \frac{\partial u}{\partial k} \right)^2 547 +\left( \frac{\partial v}{\partial k} \right)^2} \right] 548 - C_3 \,K_\rho\,N^2 - C_2 \,\epsilon \,Fw \right\} \\ 549 &+\frac{1}{e_3} \;\frac{\partial }{\partial k}\left[ {\frac{K_m}{e_3 } 550 \;\frac{\partial \psi}{\partial k}} \right]\; 551 \end{split} 552 \] 553 554 \[ 555 % \label{eq:zdfgls_kz} 556 \begin{split} 557 K_m &= C_{\mu} \ \sqrt {\bar{e}} \ l \\ 558 K_\rho &= C_{\mu'}\ \sqrt {\bar{e}} \ l 559 \end{split} 560 \] 561 562 \[ 563 % \label{eq:zdfgls_eps} 564 {\epsilon} = C_{0\mu} \,\frac{\bar {e}^{3/2}}{l} \; 565 \] 566 where $N$ is the local Brunt-Vais\"{a}l\"{a} frequency (see \autoref{subsec:TRA_bn2}) and 567 $\epsilon$ the dissipation rate. 568 The constants $C_1$, $C_2$, $C_3$, ${\sigma_e}$, ${\sigma_{\psi}}$ and the wall function ($Fw$) depends of 569 the choice of the turbulence model. 570 Four different turbulent models are pre-defined (Tab.\autoref{tab:GLS}). 571 They are made available through the \np{nn\_clo} namelist parameter. 572 573 %--------------------------------------------------TABLE-------------------------------------------------- 574 \begin{table}[htbp] 575 \begin{center} 576 % \begin{tabular}{cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}cp{70pt}c} 577 \begin{tabular}{ccccc} 578 & $k-kl$ & $k-\epsilon$ & $k-\omega$ & generic \\ 579 % & \citep{Mellor_Yamada_1982} & \citep{Rodi_1987} & \citep{Wilcox_1988} & \\ 580 \hline 581 \hline 582 \np{nn\_clo} & \textbf{0} & \textbf{1} & \textbf{2} & \textbf{3} \\ 583 \hline 584 $( p , n , m )$ & ( 0 , 1 , 1 ) & ( 3 , 1.5 , -1 ) & ( -1 , 0.5 , -1 ) & ( 2 , 1 , -0.67 ) \\ 585 $\sigma_k$ & 2.44 & 1. & 2. & 0.8 \\ 586 $\sigma_\psi$ & 2.44 & 1.3 & 2. & 1.07 \\ 587 $C_1$ & 0.9 & 1.44 & 0.555 & 1. \\ 588 $C_2$ & 0.5 & 1.92 & 0.833 & 1.22 \\ 589 $C_3$ & 1. & 1. & 1. & 1. \\ 590 $F_{wall}$ & Yes & -- & -- & -- \\ 591 \hline 592 \hline 593 \end{tabular} 594 \caption{ 595 \protect\label{tab:GLS} 596 Set of predefined GLS parameters, or equivalently predefined turbulence models available with 597 \protect\key{zdfgls} and controlled by the \protect\np{nn\_clos} namelist variable in \protect\ngn{namzdf\_gls}. 598 } 599 \end{center} 600 \end{table} 601 %-------------------------------------------------------------------------------------------------------------- 602 603 In the Mellor-Yamada model, the negativity of $n$ allows to use a wall function to force the convergence of 604 the mixing length towards $K z_b$ ($K$: Kappa and $z_b$: rugosity length) value near physical boundaries 605 (logarithmic boundary layer law). 606 $C_{\mu}$ and $C_{\mu'}$ are calculated from stability function proposed by \citet{Galperin_al_JAS88}, 607 or by \citet{Kantha_Clayson_1994} or one of the two functions suggested by \citet{Canuto_2001} 608 (\np{nn\_stab\_func}\forcode{ = 0..3}, resp.). 609 The value of $C_{0\mu}$ depends of the choice of the stability function. 610 611 The surface and bottom boundary condition on both $\bar{e}$ and $\psi$ can be calculated thanks to Dirichlet or 612 Neumann condition through \np{nn\_tkebc\_surf} and \np{nn\_tkebc\_bot}, resp. 613 As for TKE closure, the wave effect on the mixing is considered when 614 \np{ln\_crban}\forcode{ = .true.} \citep{Craig_Banner_JPO94, Mellor_Blumberg_JPO04}. 615 The \np{rn\_crban} namelist parameter is $\alpha_{CB}$ in \autoref{eq:ZDF_Esbc} and 616 \np{rn\_charn} provides the value of $\beta$ in \autoref{eq:ZDF_Lsbc}. 617 618 The $\psi$ equation is known to fail in stably stratified flows, and for this reason 619 almost all authors apply a clipping of the length scale as an \textit{ad hoc} remedy. 620 With this clipping, the maximum permissible length scale is determined by $l_{max} = c_{lim} \sqrt{2\bar{e}}/ N$. 621 A value of $c_{lim} = 0.53$ is often used \citep{Galperin_al_JAS88}. 622 \cite{Umlauf_Burchard_CSR05} show that the value of the clipping factor is of crucial importance for 623 the entrainment depth predicted in stably stratified situations, 624 and that its value has to be chosen in accordance with the algebraic model for the turbulent fluxes. 625 The clipping is only activated if \np{ln\_length\_lim}\forcode{ = .true.}, 626 and the $c_{lim}$ is set to the \np{rn\_clim\_galp} value. 627 628 The time and space discretization of the GLS equations follows the same energetic consideration as for 629 the TKE case described in \autoref{subsec:ZDF_tke_ene} \citep{Burchard_OM02}. 630 Examples of performance of the 4 turbulent closure scheme can be found in \citet{Warner_al_OM05}. 631 632 % ------------------------------------------------------------------------------------------------------------- 633 % OSM OSMOSIS BL Scheme 634 % ------------------------------------------------------------------------------------------------------------- 635 \subsection{OSM: OSMOSIS boundary layer scheme (\protect\key{zdfosm})} 636 \label{subsec:ZDF_osm} 637 638 %--------------------------------------------namzdf_osm--------------------------------------------------------- 639 640 \nlst{namzdf_osm} 641 %-------------------------------------------------------------------------------------------------------------- 642 643 The OSMOSIS turbulent closure scheme is based on...... TBC 652 %The restart of the TKE scheme requires the storage of $\bar {e}$, $K_m$, $K_\rho$ and $l_\epsilon$ as 653 %they all appear in the right hand side of \autoref{eq:zdftke_ene}. 654 %For the latter, it is in fact the ratio $\sqrt{\bar{e}}/l_\epsilon$ which is stored. 644 655 645 656 % ================================================================ … … 648 659 \section{Convection} 649 660 \label{sec:ZDF_conv} 650 651 %--------------------------------------------namzdf--------------------------------------------------------652 653 \nlst{namzdf}654 %--------------------------------------------------------------------------------------------------------------655 661 656 662 Static instabilities (\ie light potential densities under heavy ones) may occur at particular ocean grid points. … … 664 670 % Non-Penetrative Convective Adjustment 665 671 % ------------------------------------------------------------------------------------------------------------- 666 \subsection[Non-penetrative convective adj mt (\protect\np{ln\_tranpc}\forcode{= .true.})]667 672 \subsection[Non-penetrative convective adjustment (\forcode{ln_tranpc = .true.})] 673 {Non-penetrative convective adjustment (\protect\np{ln\_tranpc}\forcode{ = .true.})} 668 674 \label{subsec:ZDF_npc} 669 670 %--------------------------------------------namzdf--------------------------------------------------------671 672 \nlst{namzdf}673 %--------------------------------------------------------------------------------------------------------------674 675 675 676 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 676 677 \begin{figure}[!htb] 677 678 \begin{center} 678 \includegraphics[width= 0.90\textwidth]{Fig_npc}679 \includegraphics[width=\textwidth]{Fig_npc} 679 680 \caption{ 680 681 \protect\label{fig:npc} … … 700 701 the water column, but only until the density structure becomes neutrally stable 701 702 (\ie until the mixed portion of the water column has \textit{exactly} the density of the water just below) 702 \citep{ Madec_al_JPO91}.703 \citep{madec.delecluse.ea_JPO91}. 703 704 The associated algorithm is an iterative process used in the following way (\autoref{fig:npc}): 704 705 starting from the top of the ocean, the first instability is found. … … 718 719 the algorithm used in \NEMO converges for any profile in a number of iterations which is less than 719 720 the number of vertical levels. 720 This property is of paramount importance as pointed out by \citet{ Killworth1989}:721 This property is of paramount importance as pointed out by \citet{killworth_iprc89}: 721 722 it avoids the existence of permanent and unrealistic static instabilities at the sea surface. 722 723 This non-penetrative convective algorithm has been proved successful in studies of the deep water formation in 723 the north-western Mediterranean Sea \citep{ Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}.724 the north-western Mediterranean Sea \citep{madec.delecluse.ea_JPO91, madec.chartier.ea_DAO91, madec.crepon_iprc91}. 724 725 725 726 The current implementation has been modified in order to deal with any non linear equation of seawater … … 727 728 Two main differences have been introduced compared to the original algorithm: 728 729 $(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency 729 (not the thedifference in potential density);730 (not the difference in potential density); 730 731 $(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients are vertically mixed in 731 732 the same way their temperature and salinity has been mixed. … … 736 737 % Enhanced Vertical Diffusion 737 738 % ------------------------------------------------------------------------------------------------------------- 738 \subsection{Enhanced vertical diffusion (\protect\np{ln\_zdfevd}\forcode{ = .true.})} 739 \subsection[Enhanced vertical diffusion (\forcode{ln_zdfevd = .true.})] 740 {Enhanced vertical diffusion (\protect\np{ln\_zdfevd}\forcode{ = .true.})} 739 741 \label{subsec:ZDF_evd} 740 741 %--------------------------------------------namzdf--------------------------------------------------------742 743 \nlst{namzdf}744 %--------------------------------------------------------------------------------------------------------------745 742 746 743 Options are defined through the \ngn{namzdf} namelist variables. 747 744 The enhanced vertical diffusion parameterisation is used when \np{ln\_zdfevd}\forcode{ = .true.}. 748 In this case, the vertical eddy mixing coefficients are assigned very large values 749 (a typical value is $10\;m^2s^{-1})$in regions where the stratification is unstable750 (\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{ Lazar_PhD97, Lazar_al_JPO99}.745 In this case, the vertical eddy mixing coefficients are assigned very large values 746 in regions where the stratification is unstable 747 (\ie when $N^2$ the Brunt-Vais\"{a}l\"{a} frequency is negative) \citep{lazar_phd97, lazar.madec.ea_JPO99}. 751 748 This is done either on tracers only (\np{nn\_evdm}\forcode{ = 0}) or 752 749 on both momentum and tracers (\np{nn\_evdm}\forcode{ = 1}). … … 759 756 the convective adjustment algorithm presented above when mixing both tracers and 760 757 momentum in the case of static instabilities. 761 It requires the use of an implicit time stepping on vertical diffusion terms762 (\ie np{ln\_zdfexp}\forcode{ = .false.}).763 758 764 759 Note that the stability test is performed on both \textit{before} and \textit{now} values of $N^2$. 765 760 This removes a potential source of divergence of odd and even time step in 766 a leapfrog environment \citep{ Leclair_PhD2010} (see \autoref{sec:STP_mLF}).761 a leapfrog environment \citep{leclair_phd10} (see \autoref{sec:STP_mLF}). 767 762 768 763 % ------------------------------------------------------------------------------------------------------------- 769 764 % Turbulent Closure Scheme 770 765 % ------------------------------------------------------------------------------------------------------------- 771 \subsection[Turbulent closure scheme (\protect\key{zdf}\{tke,gls,osm\})]{Turbulent Closure Scheme (\protect\key{zdftke}, \protect\key{zdfgls} or \protect\key{zdfosm})} 766 \subsection[Handling convection with turbulent closure schemes (\forcode{ln_zdf/tke/gls/osm = .true.})] 767 {Handling convection with turbulent closure schemes (\protect\np{ln\_zdf/tke/gls/osm}\forcode{ = .true.})} 772 768 \label{subsec:ZDF_tcs} 773 769 774 The turbulent closure scheme presented in \autoref{subsec:ZDF_tke} and \autoref{subsec:ZDF_gls} 775 (\key{zdftke} or \key{zdftke} is defined) in theory solves the problem of statically unstable density profiles. 770 771 The turbulent closure schemes presented in \autoref{subsec:ZDF_tke}, \autoref{subsec:ZDF_gls} and 772 \autoref{subsec:ZDF_osm} (\ie \np{ln\_zdftke} or \np{ln\_zdfgls} or \np{ln\_zdfosm} defined) deal, in theory, 773 with statically unstable density profiles. 776 774 In such a case, the term corresponding to the destruction of turbulent kinetic energy through stratification in 777 775 \autoref{eq:zdftke_e} or \autoref{eq:zdfgls_e} becomes a source term, since $N^2$ is negative. 778 It results in large values of $A_T^{vT}$ and $A_T^{vT}$, and also the four neighbouring $A_u^{vm} {and}\;A_v^{vm}$779 (up to $1\;m^2s^{-1}$).776 It results in large values of $A_T^{vT}$ and $A_T^{vT}$, and also of the four neighboring values at 777 velocity points $A_u^{vm} {and}\;A_v^{vm}$ (up to $1\;m^2s^{-1}$). 780 778 These large values restore the static stability of the water column in a way similar to that of 781 779 the enhanced vertical diffusion parameterisation (\autoref{subsec:ZDF_evd}). … … 785 783 It can thus be useful to combine the enhanced vertical diffusion with the turbulent closure scheme, 786 784 \ie setting the \np{ln\_zdfnpc} namelist parameter to true and 787 defining the turbulent closure CPP keyall together.788 789 The KPPturbulent closure scheme already includes enhanced vertical diffusion in the case of convection,790 as governed by the variables $bvsqcon$ and $difcon$ found in \mdl{zdfkpp},791 therefore \np{ln\_zdfevd}\forcode{ = .false.} should be used with the KPPscheme.785 defining the turbulent closure (\np{ln\_zdftke} or \np{ln\_zdfgls} = \forcode{.true.}) all together. 786 787 The OSMOSIS turbulent closure scheme already includes enhanced vertical diffusion in the case of convection, 788 %as governed by the variables $bvsqcon$ and $difcon$ found in \mdl{zdfkpp}, 789 therefore \np{ln\_zdfevd}\forcode{ = .false.} should be used with the OSMOSIS scheme. 792 790 % gm% + one word on non local flux with KPP scheme trakpp.F90 module... 793 791 … … 795 793 % Double Diffusion Mixing 796 794 % ================================================================ 797 \section{Double diffusion mixing (\protect\key{zdfddm})} 798 \label{sec:ZDF_ddm} 795 \section[Double diffusion mixing (\forcode{ln_zdfddm = .true.})] 796 {Double diffusion mixing (\protect\np{ln\_zdfddm}\forcode{ = .true.})} 797 \label{subsec:ZDF_ddm} 798 799 799 800 800 %-------------------------------------------namzdf_ddm------------------------------------------------- … … 803 803 %-------------------------------------------------------------------------------------------------------------- 804 804 805 Options are defined through the \ngn{namzdf\_ddm} namelist variables. 805 This parameterisation has been introduced in \mdl{zdfddm} module and is controlled by the namelist parameter 806 \np{ln\_zdfddm} in \ngn{namzdf}. 806 807 Double diffusion occurs when relatively warm, salty water overlies cooler, fresher water, or vice versa. 807 808 The former condition leads to salt fingering and the latter to diffusive convection. 808 809 Double-diffusive phenomena contribute to diapycnal mixing in extensive regions of the ocean. 809 \citet{ Merryfield1999} include a parameterisation of such phenomena in a global ocean model and show that810 \citet{merryfield.holloway.ea_JPO99} include a parameterisation of such phenomena in a global ocean model and show that 810 811 it leads to relatively minor changes in circulation but exerts significant regional influences on 811 812 temperature and salinity. 812 This parameterisation has been introduced in \mdl{zdfddm} module and is controlled by the \key{zdfddm} CPP key. 813 813 814 814 815 Diapycnal mixing of S and T are described by diapycnal diffusion coefficients … … 839 840 \begin{figure}[!t] 840 841 \begin{center} 841 \includegraphics[width= 0.99\textwidth]{Fig_zdfddm}842 \includegraphics[width=\textwidth]{Fig_zdfddm} 842 843 \caption{ 843 844 \protect\label{fig:zdfddm} 844 From \citet{ Merryfield1999} :845 From \citet{merryfield.holloway.ea_JPO99} : 845 846 (a) Diapycnal diffusivities $A_f^{vT}$ and $A_f^{vS}$ for temperature and salt in regions of salt fingering. 846 847 Heavy curves denote $A^{\ast v} = 10^{-3}~m^2.s^{-1}$ and thin curves $A^{\ast v} = 10^{-4}~m^2.s^{-1}$; … … 855 856 856 857 The factor 0.7 in \autoref{eq:zdfddm_f_T} reflects the measured ratio $\alpha F_T /\beta F_S \approx 0.7$ of 857 buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{ McDougall_Taylor_JMR84}).858 Following \citet{ Merryfield1999}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$.858 buoyancy flux of heat to buoyancy flux of salt (\eg, \citet{mcdougall.taylor_JMR84}). 859 Following \citet{merryfield.holloway.ea_JPO99}, we adopt $R_c = 1.6$, $n = 6$, and $A^{\ast v} = 10^{-4}~m^2.s^{-1}$. 859 860 860 861 To represent mixing of S and T by diffusive layering, the diapycnal diffusivities suggested by … … 887 888 % Bottom Friction 888 889 % ================================================================ 889 \section{Bottom and top friction (\protect\mdl{zdfbfr})} 890 \label{sec:ZDF_bfr} 890 \section[Bottom and top friction (\textit{zdfdrg.F90})] 891 {Bottom and top friction (\protect\mdl{zdfdrg})} 892 \label{sec:ZDF_drg} 891 893 892 894 %--------------------------------------------nambfr-------------------------------------------------------- 893 895 % 894 %\nlst{nambfr} 896 \nlst{namdrg} 897 \nlst{namdrg_top} 898 \nlst{namdrg_bot} 899 895 900 %-------------------------------------------------------------------------------------------------------------- 896 901 897 Options to define the top and bottom friction are defined through the \ngn{nam bfr} namelist variables.902 Options to define the top and bottom friction are defined through the \ngn{namdrg} namelist variables. 898 903 The bottom friction represents the friction generated by the bathymetry. 899 904 The top friction represents the friction generated by the ice shelf/ocean interface. 900 As the friction processes at the top and bottom are treated in similar way,901 only the bottom friction is described in detail below.905 As the friction processes at the top and the bottom are treated in and identical way, 906 the description below considers mostly the bottom friction case, if not stated otherwise. 902 907 903 908 … … 905 910 a condition on the vertical diffusive flux. 906 911 For the bottom boundary layer, one has: 907 \[908 % \label{eq:zdfbfr_flux}909 A^{vm} \left( \partial {\textbf U}_h / \partial z \right) = {{\cal F}}_h^{\textbf U}910 \]912 \[ 913 % \label{eq:zdfbfr_flux} 914 A^{vm} \left( \partial {\textbf U}_h / \partial z \right) = {{\cal F}}_h^{\textbf U} 915 \] 911 916 where ${\cal F}_h^{\textbf U}$ is represents the downward flux of horizontal momentum outside 912 917 the logarithmic turbulent boundary layer (thickness of the order of 1~m in the ocean). … … 922 927 To illustrate this, consider the equation for $u$ at $k$, the last ocean level: 923 928 \begin{equation} 924 \label{eq:zdf bfr_flux2}929 \label{eq:zdfdrg_flux2} 925 930 \frac{\partial u_k}{\partial t} = \frac{1}{e_{3u}} \left[ \frac{A_{uw}^{vm}}{e_{3uw}} \delta_{k+1/2}\;[u] - {\cal F}^u_h \right] \approx - \frac{{\cal F}^u_{h}}{e_{3u}} 926 931 \end{equation} … … 935 940 936 941 In the code, the bottom friction is imposed by adding the trend due to the bottom friction to 937 the general momentum trend in \mdl{dynbfr}.942 the general momentum trend in \mdl{dynzdf}. 938 943 For the time-split surface pressure gradient algorithm, the momentum trend due to 939 944 the barotropic component needs to be handled separately. 940 945 For this purpose it is convenient to compute and store coefficients which can be simply combined with 941 946 bottom velocities and geometric values to provide the momentum trend due to bottom friction. 942 These coefficients are computed in \mdl{zdfbfr} and generally take the form $c_b^{\textbf U}$ where:947 These coefficients are computed in \mdl{zdfdrg} and generally take the form $c_b^{\textbf U}$ where: 943 948 \begin{equation} 944 949 \label{eq:zdfbfr_bdef} … … 946 951 - \frac{{\cal F}^{\textbf U}_{h}}{e_{3u}} = \frac{c_b^{\textbf U}}{e_{3u}} \;{\textbf U}_h^b 947 952 \end{equation} 948 where $\textbf{U}_h^b = (u_b\;,\;v_b)$ is the near-bottom, horizontal, ocean velocity. 953 where $\textbf{U}_h^b = (u_b\;,\;v_b)$ is the near-bottom, horizontal, ocean velocity. 954 Note than from \NEMO 4.0, drag coefficients are only computed at cell centers (\ie at T-points) and refer to as $c_b^T$ in the following. These are then linearly interpolated in space to get $c_b^\textbf{U}$ at velocity points. 949 955 950 956 % ------------------------------------------------------------------------------------------------------------- 951 957 % Linear Bottom Friction 952 958 % ------------------------------------------------------------------------------------------------------------- 953 \subsection{Linear bottom friction (\protect\np{nn\_botfr}\forcode{ = 0..1})} 954 \label{subsec:ZDF_bfr_linear} 955 956 The linear bottom friction parameterisation (including the special case of a free-slip condition) assumes that 957 the bottom friction is proportional to the interior velocity (\ie the velocity of the last model level): 959 \subsection[Linear top/bottom friction (\forcode{ln_lin = .true.})] 960 {Linear top/bottom friction (\protect\np{ln\_lin}\forcode{ = .true.)}} 961 \label{subsec:ZDF_drg_linear} 962 963 The linear friction parameterisation (including the special case of a free-slip condition) assumes that 964 the friction is proportional to the interior velocity (\ie the velocity of the first/last model level): 958 965 \[ 959 966 % \label{eq:zdfbfr_linear} 960 967 {\cal F}_h^\textbf{U} = \frac{A^{vm}}{e_3} \; \frac{\partial \textbf{U}_h}{\partial k} = r \; \textbf{U}_h^b 961 968 \] 962 where $r$ is a friction coefficient expressed in ms$^{-1}$.969 where $r$ is a friction coefficient expressed in $m s^{-1}$. 963 970 This coefficient is generally estimated by setting a typical decay time $\tau$ in the deep ocean, 964 971 and setting $r = H / \tau$, where $H$ is the ocean depth. 965 Commonly accepted values of $\tau$ are of the order of 100 to 200 days \citep{ Weatherly_JMR84}.972 Commonly accepted values of $\tau$ are of the order of 100 to 200 days \citep{weatherly_JMR84}. 966 973 A value $\tau^{-1} = 10^{-7}$~s$^{-1}$ equivalent to 115 days, is usually used in quasi-geostrophic models. 967 974 One may consider the linear friction as an approximation of quadratic friction, $r \approx 2\;C_D\;U_{av}$ 968 (\citet{ Gill1982}, Eq. 9.6.6).975 (\citet{gill_bk82}, Eq. 9.6.6). 969 976 For example, with a drag coefficient $C_D = 0.002$, a typical speed of tidal currents of $U_{av} =0.1$~m\;s$^{-1}$, 970 977 and assuming an ocean depth $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$. 971 978 This is the default value used in \NEMO. It corresponds to a decay time scale of 115~days. 972 It can be changed by specifying \np{rn\_ bfri1} (namelist parameter).973 974 For the linear friction case the coefficients defined in the general expression \autoref{eq:zdfbfr_bdef} are:979 It can be changed by specifying \np{rn\_Uc0} (namelist parameter). 980 981 For the linear friction case the drag coefficient used in the general expression \autoref{eq:zdfbfr_bdef} is: 975 982 \[ 976 983 % \label{eq:zdfbfr_linbfr_b} 977 \begin{split} 978 c_b^u &= - r\\ 979 c_b^v &= - r\\ 980 \end{split} 981 \] 982 When \np{nn\_botfr}\forcode{ = 1}, the value of $r$ used is \np{rn\_bfri1}. 983 Setting \np{nn\_botfr}\forcode{ = 0} is equivalent to setting $r=0$ and 984 leads to a free-slip bottom boundary condition. 985 These values are assigned in \mdl{zdfbfr}. 986 From v3.2 onwards there is support for local enhancement of these values via an externally defined 2D mask array 987 (\np{ln\_bfr2d}\forcode{ = .true.}) given in the \ifile{bfr\_coef} input NetCDF file. 984 c_b^T = - r 985 \] 986 When \np{ln\_lin} \forcode{= .true.}, the value of $r$ used is \np{rn\_Uc0}*\np{rn\_Cd0}. 987 Setting \np{ln\_OFF} \forcode{= .true.} (and \forcode{ln_lin = .true.}) is equivalent to setting $r=0$ and leads to a free-slip boundary condition. 988 989 These values are assigned in \mdl{zdfdrg}. 990 Note that there is support for local enhancement of these values via an externally defined 2D mask array 991 (\np{ln\_boost}\forcode{ = .true.}) given in the \ifile{bfr\_coef} input NetCDF file. 988 992 The mask values should vary from 0 to 1. 989 993 Locations with a non-zero mask value will have the friction coefficient increased by 990 $mask\_value$ *\np{rn\_bfrien}*\np{rn\_bfri1}.994 $mask\_value$ * \np{rn\_boost} * \np{rn\_Cd0}. 991 995 992 996 % ------------------------------------------------------------------------------------------------------------- 993 997 % Non-Linear Bottom Friction 994 998 % ------------------------------------------------------------------------------------------------------------- 995 \subsection{Non-linear bottom friction (\protect\np{nn\_botfr}\forcode{ = 2})} 996 \label{subsec:ZDF_bfr_nonlinear} 997 998 The non-linear bottom friction parameterisation assumes that the bottom friction is quadratic: 999 \[ 1000 % \label{eq:zdfbfr_nonlinear} 999 \subsection[Non-linear top/bottom friction (\forcode{ln_no_lin = .true.})] 1000 {Non-linear top/bottom friction (\protect\np{ln\_no\_lin}\forcode{ = .true.})} 1001 \label{subsec:ZDF_drg_nonlinear} 1002 1003 The non-linear bottom friction parameterisation assumes that the top/bottom friction is quadratic: 1004 \[ 1005 % \label{eq:zdfdrg_nonlinear} 1001 1006 {\cal F}_h^\textbf{U} = \frac{A^{vm}}{e_3 }\frac{\partial \textbf {U}_h 1002 1007 }{\partial k}=C_D \;\sqrt {u_b ^2+v_b ^2+e_b } \;\; \textbf {U}_h^b 1003 1008 \] 1004 where $C_D$ is a drag coefficient, and $e_b $ a bottom turbulent kinetic energy due to tides,1009 where $C_D$ is a drag coefficient, and $e_b $ a top/bottom turbulent kinetic energy due to tides, 1005 1010 internal waves breaking and other short time scale currents. 1006 1011 A typical value of the drag coefficient is $C_D = 10^{-3} $. 1007 As an example, the CME experiment \citep{ Treguier_JGR92} uses $C_D = 10^{-3}$ and1008 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{ Killworth1992} uses $C_D = 1.4\;10^{-3}$ and1012 As an example, the CME experiment \citep{treguier_JGR92} uses $C_D = 10^{-3}$ and 1013 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{killworth_JPO92} uses $C_D = 1.4\;10^{-3}$ and 1009 1014 $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$. 1010 The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} namelist parameters). 1011 1012 As for the linear case, the bottom friction is imposed in the code by adding the trend due to 1013 the bottom friction to the general momentum trend in \mdl{dynbfr}. 1014 For the non-linear friction case the terms computed in \mdl{zdfbfr} are: 1015 \[ 1016 % \label{eq:zdfbfr_nonlinbfr} 1017 \begin{split} 1018 c_b^u &= - \; C_D\;\left[ u^2 + \left(\bar{\bar{v}}^{i+1,j}\right)^2 + e_b \right]^{1/2}\\ 1019 c_b^v &= - \; C_D\;\left[ \left(\bar{\bar{u}}^{i,j+1}\right)^2 + v^2 + e_b \right]^{1/2}\\ 1020 \end{split} 1021 \] 1022 1023 The coefficients that control the strength of the non-linear bottom friction are initialised as namelist parameters: 1024 $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 1025 Note for applications which treat tides explicitly a low or even zero value of \np{rn\_bfeb2} is recommended. 1026 From v3.2 onwards a local enhancement of $C_D$ is possible via an externally defined 2D mask array 1027 (\np{ln\_bfr2d}\forcode{ = .true.}). 1028 This works in the same way as for the linear bottom friction case with non-zero masked locations increased by 1029 $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}. 1015 The CME choices have been set as default values (\np{rn\_Cd0} and \np{rn\_ke0} namelist parameters). 1016 1017 As for the linear case, the friction is imposed in the code by adding the trend due to 1018 the friction to the general momentum trend in \mdl{dynzdf}. 1019 For the non-linear friction case the term computed in \mdl{zdfdrg} is: 1020 \[ 1021 % \label{eq:zdfdrg_nonlinbfr} 1022 c_b^T = - \; C_D\;\left[ \left(\bar{u_b}^{i}\right)^2 + \left(\bar{v_b}^{j}\right)^2 + e_b \right]^{1/2} 1023 \] 1024 1025 The coefficients that control the strength of the non-linear friction are initialised as namelist parameters: 1026 $C_D$= \np{rn\_Cd0}, and $e_b$ =\np{rn\_bfeb2}. 1027 Note that for applications which consider tides explicitly, a low or even zero value of \np{rn\_bfeb2} is recommended. A local enhancement of $C_D$ is again possible via an externally defined 2D mask array 1028 (\np{ln\_boost}\forcode{ = .true.}). 1029 This works in the same way as for the linear friction case with non-zero masked locations increased by 1030 $mask\_value$ * \np{rn\_boost} * \np{rn\_Cd0}. 1030 1031 1031 1032 % ------------------------------------------------------------------------------------------------------------- 1032 1033 % Bottom Friction Log-layer 1033 1034 % ------------------------------------------------------------------------------------------------------------- 1034 \subsection[Log-layer btm frict enhncmnt (\protect\np{nn\_botfr}\forcode{ = 2}, \protect\np{ln\_loglayer}\forcode{ = .true.})] 1035 {Log-layer bottom friction enhancement (\protect\np{nn\_botfr}\forcode{ = 2}, \protect\np{ln\_loglayer}\forcode{ = .true.})} 1036 \label{subsec:ZDF_bfr_loglayer} 1037 1038 In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally enhanced using 1039 a "law of the wall" scaling. 1040 If \np{ln\_loglayer} = .true., $C_D$ is no longer constant but is related to the thickness of 1041 the last wet layer in each column by: 1042 \[ 1043 C_D = \left ( {\kappa \over {\rm log}\left ( 0.5e_{3t}/rn\_bfrz0 \right ) } \right )^2 1044 \] 1045 1046 \noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness length provided via 1047 the namelist. 1048 1049 For stability, the drag coefficient is bounded such that it is kept greater or equal to 1050 the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional namelist parameter: 1051 \np{rn\_bfri2\_max}, \ie 1052 \[ 1053 rn\_bfri2 \leq C_D \leq rn\_bfri2\_max 1054 \] 1055 1056 \noindent Note also that a log-layer enhancement can also be applied to the top boundary friction if 1057 under ice-shelf cavities are in use (\np{ln\_isfcav}\forcode{ = .true.}). 1058 In this case, the relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} and \np{rn\_tfri2\_max}. 1059 1060 % ------------------------------------------------------------------------------------------------------------- 1061 % Bottom Friction stability 1062 % ------------------------------------------------------------------------------------------------------------- 1063 \subsection{Bottom friction stability considerations} 1064 \label{subsec:ZDF_bfr_stability} 1065 1066 Some care needs to exercised over the choice of parameters to ensure that the implementation of 1067 bottom friction does not induce numerical instability. 1068 For the purposes of stability analysis, an approximation to \autoref{eq:zdfbfr_flux2} is: 1035 \subsection[Log-layer top/bottom friction (\forcode{ln_loglayer = .true.})] 1036 {Log-layer top/bottom friction (\protect\np{ln\_loglayer}\forcode{ = .true.})} 1037 \label{subsec:ZDF_drg_loglayer} 1038 1039 In the non-linear friction case, the drag coefficient, $C_D$, can be optionally enhanced using 1040 a "law of the wall" scaling. This assumes that the model vertical resolution can capture the logarithmic layer which typically occur for layers thinner than 1 m or so. 1041 If \np{ln\_loglayer} \forcode{= .true.}, $C_D$ is no longer constant but is related to the distance to the wall (or equivalently to the half of the top/bottom layer thickness): 1042 \[ 1043 C_D = \left ( {\kappa \over {\mathrm log}\left ( 0.5 \; e_{3b} / rn\_{z0} \right ) } \right )^2 1044 \] 1045 1046 \noindent where $\kappa$ is the von-Karman constant and \np{rn\_z0} is a roughness length provided via the namelist. 1047 1048 The drag coefficient is bounded such that it is kept greater or equal to 1049 the base \np{rn\_Cd0} value which occurs where layer thicknesses become large and presumably logarithmic layers are not resolved at all. For stability reason, it is also not allowed to exceed the value of an additional namelist parameter: 1050 \np{rn\_Cdmax}, \ie 1051 \[ 1052 rn\_Cd0 \leq C_D \leq rn\_Cdmax 1053 \] 1054 1055 \noindent The log-layer enhancement can also be applied to the top boundary friction if 1056 under ice-shelf cavities are activated (\np{ln\_isfcav}\forcode{ = .true.}). 1057 %In this case, the relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} and \np{rn\_tfri2\_max}. 1058 1059 % ------------------------------------------------------------------------------------------------------------- 1060 % Explicit bottom Friction 1061 % ------------------------------------------------------------------------------------------------------------- 1062 \subsection{Explicit top/bottom friction (\forcode{ln_drgimp = .false.})} 1063 \label{subsec:ZDF_drg_stability} 1064 1065 Setting \np{ln\_drgimp} \forcode{= .false.} means that bottom friction is treated explicitly in time, which has the advantage of simplifying the interaction with the split-explicit free surface (see \autoref{subsec:ZDF_drg_ts}). The latter does indeed require the knowledge of bottom stresses in the course of the barotropic sub-iteration, which becomes less straightforward in the implicit case. In the explicit case, top/bottom stresses can be computed using \textit{before} velocities and inserted in the overall momentum tendency budget. This reads: 1066 1067 At the top (below an ice shelf cavity): 1068 \[ 1069 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{t} 1070 = c_{t}^{\textbf{U}}\textbf{u}^{n-1}_{t} 1071 \] 1072 1073 At the bottom (above the sea floor): 1074 \[ 1075 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{b} 1076 = c_{b}^{\textbf{U}}\textbf{u}^{n-1}_{b} 1077 \] 1078 1079 Since this is conditionally stable, some care needs to exercised over the choice of parameters to ensure that the implementation of explicit top/bottom friction does not induce numerical instability. 1080 For the purposes of stability analysis, an approximation to \autoref{eq:zdfdrg_flux2} is: 1069 1081 \begin{equation} 1070 \label{eq:Eqn_ bfrstab}1082 \label{eq:Eqn_drgstab} 1071 1083 \begin{split} 1072 1084 \Delta u &= -\frac{{{\cal F}_h}^u}{e_{3u}}\;2 \rdt \\ … … 1074 1086 \end{split} 1075 1087 \end{equation} 1076 \noindent where linear bottomfriction and a leapfrog timestep have been assumed.1077 To ensure that the bottomfriction cannot reverse the direction of flow it is necessary to have:1088 \noindent where linear friction and a leapfrog timestep have been assumed. 1089 To ensure that the friction cannot reverse the direction of flow it is necessary to have: 1078 1090 \[ 1079 1091 |\Delta u| < \;|u| 1080 1092 \] 1081 \noindent which, using \autoref{eq:Eqn_ bfrstab}, gives:1093 \noindent which, using \autoref{eq:Eqn_drgstab}, gives: 1082 1094 \[ 1083 1095 r\frac{2\rdt}{e_{3u}} < 1 \qquad \Rightarrow \qquad r < \frac{e_{3u}}{2\rdt}\\ … … 1093 1105 For most applications, with physically sensible parameters these restrictions should not be of concern. 1094 1106 But caution may be necessary if attempts are made to locally enhance the bottom friction parameters. 1095 To ensure stability limits are imposed on the bottom friction coefficients both1107 To ensure stability limits are imposed on the top/bottom friction coefficients both 1096 1108 during initialisation and at each time step. 1097 Checks at initialisation are made in \mdl{zdf bfr} (assuming a 1 m.s$^{-1}$ velocity in the non-linear case).1109 Checks at initialisation are made in \mdl{zdfdrg} (assuming a 1 m.s$^{-1}$ velocity in the non-linear case). 1098 1110 The number of breaches of the stability criterion are reported as well as 1099 1111 the minimum and maximum values that have been set. 1100 The criterion is also checked at each time step, using the actual velocity, in \mdl{dyn bfr}.1101 Values of the bottomfriction coefficient are reduced as necessary to ensure stability;1112 The criterion is also checked at each time step, using the actual velocity, in \mdl{dynzdf}. 1113 Values of the friction coefficient are reduced as necessary to ensure stability; 1102 1114 these changes are not reported. 1103 1115 1104 Limits on the bottom friction coefficient are not imposed if the user has elected to1105 handle the bottom friction implicitly (see \autoref{subsec:ZDF_bfr_imp}).1116 Limits on the top/bottom friction coefficient are not imposed if the user has elected to 1117 handle the friction implicitly (see \autoref{subsec:ZDF_drg_imp}). 1106 1118 The number of potential breaches of the explicit stability criterion are still reported for information purposes. 1107 1119 … … 1109 1121 % Implicit Bottom Friction 1110 1122 % ------------------------------------------------------------------------------------------------------------- 1111 \subsection{Implicit bottom friction (\protect\np{ln\_bfrimp}\forcode{ = .true.})} 1112 \label{subsec:ZDF_bfr_imp} 1123 \subsection[Implicit top/bottom friction (\forcode{ln_drgimp = .true.})] 1124 {Implicit top/bottom friction (\protect\np{ln\_drgimp}\forcode{ = .true.})} 1125 \label{subsec:ZDF_drg_imp} 1113 1126 1114 1127 An optional implicit form of bottom friction has been implemented to improve model stability. 1115 We recommend this option for shelf sea and coastal ocean applications, especially for split-explicit time splitting. 1116 This option can be invoked by setting \np{ln\_bfrimp} to \forcode{.true.} in the \textit{nambfr} namelist. 1117 This option requires \np{ln\_zdfexp} to be \forcode{.false.} in the \textit{namzdf} namelist. 1118 1119 This implementation is realised in \mdl{dynzdf\_imp} and \mdl{dynspg\_ts}. In \mdl{dynzdf\_imp}, 1120 the bottom boundary condition is implemented implicitly. 1121 1122 \[ 1123 % \label{eq:dynzdf_bfr} 1124 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{mbk} 1125 = \binom{c_{b}^{u}u^{n+1}_{mbk}}{c_{b}^{v}v^{n+1}_{mbk}} 1126 \] 1127 1128 where $mbk$ is the layer number of the bottom wet layer. 1129 Superscript $n+1$ means the velocity used in the friction formula is to be calculated, so, it is implicit. 1130 1131 If split-explicit time splitting is used, care must be taken to avoid the double counting of the bottom friction in 1132 the 2-D barotropic momentum equations. 1133 As NEMO only updates the barotropic pressure gradient and Coriolis' forcing terms in the 2-D barotropic calculation, 1134 we need to remove the bottom friction induced by these two terms which has been included in the 3-D momentum trend 1135 and update it with the latest value. 1136 On the other hand, the bottom friction contributed by the other terms 1137 (\eg the advection term, viscosity term) has been included in the 3-D momentum equations and 1138 should not be added in the 2-D barotropic mode. 1139 1140 The implementation of the implicit bottom friction in \mdl{dynspg\_ts} is done in two steps as the following: 1141 1142 \[ 1143 % \label{eq:dynspg_ts_bfr1} 1144 \frac{\textbf{U}_{med}-\textbf{U}^{m-1}}{2\Delta t}=-g\nabla\eta-f\textbf{k}\times\textbf{U}^{m}+c_{b} 1145 \left(\textbf{U}_{med}-\textbf{U}^{m-1}\right) 1146 \] 1147 \[ 1148 \frac{\textbf{U}^{m+1}-\textbf{U}_{med}}{2\Delta t}=\textbf{T}+ 1149 \left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{U}^{'}\right)- 1150 2\Delta t_{bc}c_{b}\left(g\nabla\eta^{'}+f\textbf{k}\times\textbf{u}_{b}\right) 1151 \] 1152 1153 where $\textbf{T}$ is the vertical integrated 3-D momentum trend. 1154 We assume the leap-frog time-stepping is used here. 1155 $\Delta t$ is the barotropic mode time step and $\Delta t_{bc}$ is the baroclinic mode time step. 1156 $c_{b}$ is the friction coefficient. 1157 $\eta$ is the sea surface level calculated in the barotropic loops while $\eta^{'}$ is the sea surface level used in 1158 the 3-D baroclinic mode. 1159 $\textbf{u}_{b}$ is the bottom layer horizontal velocity. 1160 1161 % ------------------------------------------------------------------------------------------------------------- 1162 % Bottom Friction with split-explicit time splitting 1163 % ------------------------------------------------------------------------------------------------------------- 1164 \subsection[Bottom friction w/ split-explicit time splitting (\protect\np{ln\_bfrimp})] 1165 {Bottom friction with split-explicit time splitting (\protect\np{ln\_bfrimp})} 1166 \label{subsec:ZDF_bfr_ts} 1167 1168 When calculating the momentum trend due to bottom friction in \mdl{dynbfr}, 1169 the bottom velocity at the before time step is used. 1170 This velocity includes both the baroclinic and barotropic components which is appropriate when 1171 using either the explicit or filtered surface pressure gradient algorithms 1172 (\key{dynspg\_exp} or \key{dynspg\_flt}). 1173 Extra attention is required, however, when using split-explicit time stepping (\key{dynspg\_ts}). 1174 In this case the free surface equation is solved with a small time step \np{rn\_rdt}/\np{nn\_baro}, 1175 while the three dimensional prognostic variables are solved with the longer time step of \np{rn\_rdt} seconds. 1176 The trend in the barotropic momentum due to bottom friction appropriate to this method is that given by 1177 the selected parameterisation (\ie linear or non-linear bottom friction) computed with 1178 the evolving velocities at each barotropic timestep. 1179 1180 In the case of non-linear bottom friction, we have elected to partially linearise the problem by 1181 keeping the coefficients fixed throughout the barotropic time-stepping to those computed in 1182 \mdl{zdfbfr} using the now timestep. 1183 This decision allows an efficient use of the $c_b^{\vect{U}}$ coefficients to: 1184 1128 We recommend this option for shelf sea and coastal ocean applications. %, especially for split-explicit time splitting. 1129 This option can be invoked by setting \np{ln\_drgimp} to \forcode{.true.} in the \textit{namdrg} namelist. 1130 %This option requires \np{ln\_zdfexp} to be \forcode{.false.} in the \textit{namzdf} namelist. 1131 1132 This implementation is performed in \mdl{dynzdf} where the following boundary conditions are set while solving the fully implicit diffusion step: 1133 1134 At the top (below an ice shelf cavity): 1135 \[ 1136 % \label{eq:dynzdf_drg_top} 1137 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{t} 1138 = c_{t}^{\textbf{U}}\textbf{u}^{n+1}_{t} 1139 \] 1140 1141 At the bottom (above the sea floor): 1142 \[ 1143 % \label{eq:dynzdf_drg_bot} 1144 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{b} 1145 = c_{b}^{\textbf{U}}\textbf{u}^{n+1}_{b} 1146 \] 1147 1148 where $t$ and $b$ refers to top and bottom layers respectively. 1149 Superscript $n+1$ means the velocity used in the friction formula is to be calculated, so it is implicit. 1150 1151 % ------------------------------------------------------------------------------------------------------------- 1152 % Bottom Friction with split-explicit free surface 1153 % ------------------------------------------------------------------------------------------------------------- 1154 \subsection[Bottom friction with split-explicit free surface] 1155 {Bottom friction with split-explicit free surface} 1156 \label{subsec:ZDF_drg_ts} 1157 1158 With split-explicit free surface, the sub-stepping of barotropic equations needs the knowledge of top/bottom stresses. An obvious way to satisfy this is to take them as constant over the course of the barotropic integration and equal to the value used to update the baroclinic momentum trend. Provided \np{ln\_drgimp}\forcode{= .false.} and a centred or \textit{leap-frog} like integration of barotropic equations is used (\ie \forcode{ln_bt_fw = .false.}, cf \autoref{subsec:DYN_spg_ts}), this does ensure that barotropic and baroclinic dynamics feel the same stresses during one leapfrog time step. However, if \np{ln\_drgimp}\forcode{= .true.}, stresses depend on the \textit{after} value of the velocities which themselves depend on the barotropic iteration result. This cyclic dependency makes difficult obtaining consistent stresses in 2d and 3d dynamics. Part of this mismatch is then removed when setting the final barotropic component of 3d velocities to the time splitting estimate. This last step can be seen as a necessary evil but should be minimized since it interferes with the adjustment to the boundary conditions. 1159 1160 The strategy to handle top/bottom stresses with split-explicit free surface in \NEMO is as follows: 1185 1161 \begin{enumerate} 1186 \item On entry to \rou{dyn\_spg\_ts}, remove the contribution of the before barotropic velocity to 1187 the bottom friction component of the vertically integrated momentum trend. 1188 Note the same stability check that is carried out on the bottom friction coefficient in \mdl{dynbfr} has to 1189 be applied here to ensure that the trend removed matches that which was added in \mdl{dynbfr}. 1190 \item At each barotropic step, compute the contribution of the current barotropic velocity to 1191 the trend due to bottom friction. 1192 Add this contribution to the vertically integrated momentum trend. 1193 This contribution is handled implicitly which eliminates the need to impose a stability criteria on 1194 the values of the bottom friction coefficient within the barotropic loop. 1195 \end{enumerate} 1196 1197 Note that the use of an implicit formulation within the barotropic loop for the bottom friction trend means that 1198 any limiting of the bottom friction coefficient in \mdl{dynbfr} does not adversely affect the solution when 1199 using split-explicit time splitting. 1200 This is because the major contribution to bottom friction is likely to come from the barotropic component which 1201 uses the unrestricted value of the coefficient. 1202 However, if the limiting is thought to be having a major effect 1203 (a more likely prospect in coastal and shelf seas applications) then 1204 the fully implicit form of the bottom friction should be used (see \autoref{subsec:ZDF_bfr_imp}) 1205 which can be selected by setting \np{ln\_bfrimp} $=$ \forcode{.true.}. 1206 1207 Otherwise, the implicit formulation takes the form: 1208 \[ 1209 % \label{eq:zdfbfr_implicitts} 1210 \bar{U}^{t+ \rdt} = \; \left [ \bar{U}^{t-\rdt}\; + 2 \rdt\;RHS \right ] / \left [ 1 - 2 \rdt \;c_b^{u} / H_e \right ] 1211 \] 1212 where $\bar U$ is the barotropic velocity, $H_e$ is the full depth (including sea surface height), 1213 $c_b^u$ is the bottom friction coefficient as calculated in \rou{zdf\_bfr} and 1214 $RHS$ represents all the components to the vertically integrated momentum trend except for 1215 that due to bottom friction. 1216 1217 % ================================================================ 1218 % Tidal Mixing 1219 % ================================================================ 1220 \section{Tidal mixing (\protect\key{zdftmx})} 1221 \label{sec:ZDF_tmx} 1222 1223 %--------------------------------------------namzdf_tmx-------------------------------------------------- 1162 \item To extend the stability of the barotropic sub-stepping, bottom stresses are refreshed at each sub-iteration. The baroclinic part of the flow entering the stresses is frozen at the initial time of the barotropic iteration. In case of non-linear friction, the drag coefficient is also constant. 1163 \item In case of an implicit drag, specific computations are performed in \mdl{dynzdf} which renders the overall scheme mixed explicit/implicit: the barotropic components of 3d velocities are removed before seeking for the implicit vertical diffusion result. Top/bottom stresses due to the barotropic components are explicitly accounted for thanks to the updated values of barotropic velocities. Then the implicit solution of 3d velocities is obtained. Lastly, the residual barotropic component is replaced by the time split estimate. 1164 \end{enumerate} 1165 1166 Note that other strategies are possible, like considering vertical diffusion step in advance, \ie prior barotropic integration. 1167 1168 1169 % ================================================================ 1170 % Internal wave-driven mixing 1171 % ================================================================ 1172 \section[Internal wave-driven mixing (\forcode{ln_zdfiwm = .true.})] 1173 {Internal wave-driven mixing (\protect\np{ln\_zdfiwm}\forcode{ = .true.})} 1174 \label{subsec:ZDF_tmx_new} 1175 1176 %--------------------------------------------namzdf_iwm------------------------------------------ 1224 1177 % 1225 %\nlst{namzdf_tmx}1178 \nlst{namzdf_iwm} 1226 1179 %-------------------------------------------------------------------------------------------------------------- 1227 1180 1228 1229 % -------------------------------------------------------------------------------------------------------------1230 % Bottom intensified tidal mixing1231 % -------------------------------------------------------------------------------------------------------------1232 \subsection{Bottom intensified tidal mixing}1233 \label{subsec:ZDF_tmx_bottom}1234 1235 Options are defined through the \ngn{namzdf\_tmx} namelist variables.1236 The parameterization of tidal mixing follows the general formulation for the vertical eddy diffusivity proposed by1237 \citet{St_Laurent_al_GRL02} and first introduced in an OGCM by \citep{Simmons_al_OM04}.1238 In this formulation an additional vertical diffusivity resulting from internal tide breaking,1239 $A^{vT}_{tides}$ is expressed as a function of $E(x,y)$,1240 the energy transfer from barotropic tides to baroclinic tides:1241 \begin{equation}1242 \label{eq:Ktides}1243 A^{vT}_{tides} = q \,\Gamma \,\frac{ E(x,y) \, F(z) }{ \rho \, N^2 }1244 \end{equation}1245 where $\Gamma$ is the mixing efficiency, $N$ the Brunt-Vais\"{a}l\"{a} frequency (see \autoref{subsec:TRA_bn2}),1246 $\rho$ the density, $q$ the tidal dissipation efficiency, and $F(z)$ the vertical structure function.1247 1248 The mixing efficiency of turbulence is set by $\Gamma$ (\np{rn\_me} namelist parameter) and1249 is usually taken to be the canonical value of $\Gamma = 0.2$ (Osborn 1980).1250 The tidal dissipation efficiency is given by the parameter $q$ (\np{rn\_tfe} namelist parameter)1251 represents the part of the internal wave energy flux $E(x, y)$ that is dissipated locally,1252 with the remaining $1-q$ radiating away as low mode internal waves and1253 contributing to the background internal wave field.1254 A value of $q=1/3$ is typically used \citet{St_Laurent_al_GRL02}.1255 The vertical structure function $F(z)$ models the distribution of the turbulent mixing in the vertical.1256 It is implemented as a simple exponential decaying upward away from the bottom,1257 with a vertical scale of $h_o$ (\np{rn\_htmx} namelist parameter,1258 with a typical value of $500\,m$) \citep{St_Laurent_Nash_DSR04},1259 \[1260 % \label{eq:Fz}1261 F(i,j,k) = \frac{ e^{ -\frac{H+z}{h_o} } }{ h_o \left( 1- e^{ -\frac{H}{h_o} } \right) }1262 \]1263 and is normalized so that vertical integral over the water column is unity.1264 1265 The associated vertical viscosity is calculated from the vertical diffusivity assuming a Prandtl number of 1,1266 \ie $A^{vm}_{tides}=A^{vT}_{tides}$.1267 In the limit of $N \rightarrow 0$ (or becoming negative), the vertical diffusivity is capped at $300\,cm^2/s$ and1268 impose a lower limit on $N^2$ of \np{rn\_n2min} usually set to $10^{-8} s^{-2}$.1269 These bounds are usually rarely encountered.1270 1271 The internal wave energy map, $E(x, y)$ in \autoref{eq:Ktides}, is derived from a barotropic model of1272 the tides utilizing a parameterization of the conversion of barotropic tidal energy into internal waves.1273 The essential goal of the parameterization is to represent the momentum exchange between the barotropic tides and1274 the unrepresented internal waves induced by the tidal flow over rough topography in a stratified ocean.1275 In the current version of \NEMO, the map is built from the output of1276 the barotropic global ocean tide model MOG2D-G \citep{Carrere_Lyard_GRL03}.1277 This model provides the dissipation associated with internal wave energy for the M2 and K1 tides component1278 (\autoref{fig:ZDF_M2_K1_tmx}).1279 The S2 dissipation is simply approximated as being $1/4$ of the M2 one.1280 The internal wave energy is thus : $E(x, y) = 1.25 E_{M2} + E_{K1}$.1281 Its global mean value is $1.1$ TW,1282 in agreement with independent estimates \citep{Egbert_Ray_Nat00, Egbert_Ray_JGR01}.1283 1284 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>1285 \begin{figure}[!t]1286 \begin{center}1287 \includegraphics[width=0.90\textwidth]{Fig_ZDF_M2_K1_tmx}1288 \caption{1289 \protect\label{fig:ZDF_M2_K1_tmx}1290 (a) M2 and (b) K1 internal wave drag energy from \citet{Carrere_Lyard_GRL03} ($W/m^2$).1291 }1292 \end{center}1293 \end{figure}1294 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>1295 1296 % -------------------------------------------------------------------------------------------------------------1297 % Indonesian area specific treatment1298 % -------------------------------------------------------------------------------------------------------------1299 \subsection{Indonesian area specific treatment (\protect\np{ln\_zdftmx\_itf})}1300 \label{subsec:ZDF_tmx_itf}1301 1302 When the Indonesian Through Flow (ITF) area is included in the model domain,1303 a specific treatment of tidal induced mixing in this area can be used.1304 It is activated through the namelist logical \np{ln\_tmx\_itf}, and the user must provide an input NetCDF file,1305 \ifile{mask\_itf}, which contains a mask array defining the ITF area where the specific treatment is applied.1306 1307 When \np{ln\_tmx\_itf}\forcode{ = .true.}, the two key parameters $q$ and $F(z)$ are adjusted following1308 the parameterisation developed by \citet{Koch-Larrouy_al_GRL07}:1309 1310 First, the Indonesian archipelago is a complex geographic region with a series of1311 large, deep, semi-enclosed basins connected via numerous narrow straits.1312 Once generated, internal tides remain confined within this semi-enclosed area and hardly radiate away.1313 Therefore all the internal tides energy is consumed within this area.1314 So it is assumed that $q = 1$, \ie all the energy generated is available for mixing.1315 Note that for test purposed, the ITF tidal dissipation efficiency is a namelist parameter (\np{rn\_tfe\_itf}).1316 A value of $1$ or close to is this recommended for this parameter.1317 1318 Second, the vertical structure function, $F(z)$, is no more associated with a bottom intensification of the mixing,1319 but with a maximum of energy available within the thermocline.1320 \citet{Koch-Larrouy_al_GRL07} have suggested that the vertical distribution of1321 the energy dissipation proportional to $N^2$ below the core of the thermocline and to $N$ above.1322 The resulting $F(z)$ is:1323 \[1324 % \label{eq:Fz_itf}1325 F(i,j,k) \sim \left\{1326 \begin{aligned}1327 \frac{q\,\Gamma E(i,j) } {\rho N \, \int N dz} \qquad \text{when $\partial_z N < 0$} \\1328 \frac{q\,\Gamma E(i,j) } {\rho \, \int N^2 dz} \qquad \text{when $\partial_z N > 0$}1329 \end{aligned}1330 \right.1331 \]1332 1333 Averaged over the ITF area, the resulting tidal mixing coefficient is $1.5\,cm^2/s$,1334 which agrees with the independent estimates inferred from observations.1335 Introduced in a regional OGCM, the parameterization improves the water mass characteristics in1336 the different Indonesian seas, suggesting that the horizontal and vertical distributions of1337 the mixing are adequately prescribed \citep{Koch-Larrouy_al_GRL07, Koch-Larrouy_al_OD08a, Koch-Larrouy_al_OD08b}.1338 Note also that such a parameterisation has a significant impact on the behaviour of1339 global coupled GCMs \citep{Koch-Larrouy_al_CD10}.1340 1341 % ================================================================1342 % Internal wave-driven mixing1343 % ================================================================1344 \section{Internal wave-driven mixing (\protect\key{zdftmx\_new})}1345 \label{sec:ZDF_tmx_new}1346 1347 %--------------------------------------------namzdf_tmx_new------------------------------------------1348 %1349 %\nlst{namzdf_tmx_new}1350 %--------------------------------------------------------------------------------------------------------------1351 1352 1181 The parameterization of mixing induced by breaking internal waves is a generalization of 1353 the approach originally proposed by \citet{ St_Laurent_al_GRL02}.1182 the approach originally proposed by \citet{st-laurent.simmons.ea_GRL02}. 1354 1183 A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed, 1355 1184 and the resulting diffusivity is obtained as … … 1360 1189 where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution of 1361 1190 the energy available for mixing. 1362 If the \np{ln\_mevar} namelist parameter is set to false, the mixing efficiency is taken as constant and1363 equal to 1/6 \citep{ Osborn_JPO80}.1191 If the \np{ln\_mevar} namelist parameter is set to \forcode{.false.}, the mixing efficiency is taken as constant and 1192 equal to 1/6 \citep{osborn_JPO80}. 1364 1193 In the opposite (recommended) case, $R_f$ is instead a function of 1365 1194 the turbulence intensity parameter $Re_b = \frac{ \epsilon}{\nu \, N^2}$, 1366 with $\nu$ the molecular viscosity of seawater, following the model of \cite{ Bouffard_Boegman_DAO2013} and1367 the implementation of \cite{de _lavergne_JPO2016_efficiency}.1195 with $\nu$ the molecular viscosity of seawater, following the model of \cite{bouffard.boegman_DAO13} and 1196 the implementation of \cite{de-lavergne.madec.ea_JPO16}. 1368 1197 Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when 1369 1198 the mixing efficiency is constant. 1370 1199 1371 1200 In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary 1372 as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice.1373 This parameterization of differential mixing, due to \cite{ Jackson_Rehmann_JPO2014},1374 is implemented as in \cite{de _lavergne_JPO2016_efficiency}.1201 as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to \forcode{.true.}, a recommended choice. 1202 This parameterization of differential mixing, due to \cite{jackson.rehmann_JPO14}, 1203 is implemented as in \cite{de-lavergne.madec.ea_JPO16}. 1375 1204 1376 1205 The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, 1377 1206 is constructed from three static maps of column-integrated internal wave energy dissipation, 1378 $E_{cri}(i,j)$, $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures 1379 (de Lavergne et al., in prep): 1207 $E_{cri}(i,j)$, $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures: 1208 1380 1209 \begin{align*} 1381 1210 F_{cri}(i,j,k) &\propto e^{-h_{ab} / h_{cri} }\\ 1382 F_{pyc}(i,j,k) &\propto N^{n \_p}\\1211 F_{pyc}(i,j,k) &\propto N^{n_p}\\ 1383 1212 F_{bot}(i,j,k) &\propto N^2 \, e^{- h_{wkb} / h_{bot} } 1384 1213 \end{align*} … … 1388 1217 h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz' } \; , 1389 1218 \] 1390 The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_ tmx\_new} namelist)1219 The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_iwm} namelist) 1391 1220 controls the stratification-dependence of the pycnocline-intensified dissipation. 1392 It can take values of 1 (recommended) or 2.1221 It can take values of $1$ (recommended) or $2$. 1393 1222 Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of 1394 1223 the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps. 1395 1224 $h_{cri}$ is related to the large-scale topography of the ocean (etopo2) and 1396 1225 $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of 1397 the abyssal hill topography \citep{Goff_JGR2010} and the latitude. 1226 the abyssal hill topography \citep{goff_JGR10} and the latitude. 1227 % 1228 % Jc: input files names ? 1229 1230 % ================================================================ 1231 % surface wave-induced mixing 1232 % ================================================================ 1233 \section[Surface wave-induced mixing (\forcode{ln_zdfswm = .true.})] 1234 {Surface wave-induced mixing (\protect\np{ln\_zdfswm}\forcode{ = .true.})} 1235 \label{subsec:ZDF_swm} 1236 1237 TBC ... 1238 1239 % ================================================================ 1240 % Adaptive-implicit vertical advection 1241 % ================================================================ 1242 \section[Adaptive-implicit vertical advection (\forcode{ln_zad_Aimp = .true.})] 1243 {Adaptive-implicit vertical advection(\protect\np{ln\_zad\_Aimp}\forcode{ = .true.})} 1244 \label{subsec:ZDF_aimp} 1245 1246 This refers to \citep{shchepetkin_OM15}. 1247 1248 TBC ... 1249 1250 1398 1251 1399 1252 % ================================================================ -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_conservation.tex
r10442 r11263 21 21 horizontal kinetic energy and/or potential enstrophy of horizontally non-divergent flow, 22 22 and variance of temperature and salinity will be conserved in the absence of dissipative effects and forcing. 23 \citet{ Arakawa1966} has first pointed out the advantage of this approach.23 \citet{arakawa_JCP66} has first pointed out the advantage of this approach. 24 24 He showed that if integral constraints on energy are maintained, 25 25 the computation will be free of the troublesome "non linear" instability originally pointed out by 26 \citet{ Phillips1959}.26 \citet{phillips_TAMS59}. 27 27 A consistent formulation of the energetic properties is also extremely important in carrying out 28 28 long-term numerical simulations for an oceanographic model. 29 Such a formulation avoids systematic errors that accumulate with time \citep{ Bryan1997}.29 Such a formulation avoids systematic errors that accumulate with time \citep{bryan_JCP97}. 30 30 31 31 The general philosophy of OPA which has led to the discrete formulation presented in {\S}II.2 and II.3 is to … … 39 39 Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required. 40 40 In that case, and in that case only, the advective scheme used for passive tracer is a flux correction scheme 41 \citep{Marti1992 , Levy1996, Levy1998}.41 \citep{Marti1992?, Levy1996?, Levy1998?}. 42 42 43 43 % ------------------------------------------------------------------------------------------------------------- … … 65 65 % \label{eq:vor_vorticity} 66 66 \int_D {{\textbf {k}}\cdot \frac{1}{e_3 }\nabla \times \left( {\varsigma 67 \;{\ rm {\bf k}}\times {\textbf {U}}_h } \right)\;dv} =067 \;{\mathrm {\mathbf k}}\times {\textbf {U}}_h } \right)\;dv} =0 68 68 \] 69 69 … … 189 189 \[ 190 190 % \label{eq:dynldf_dyn} 191 \int\limits_D {\frac{1}{e_3 }{\ rm {\bf k}}\cdot \nabla \times \left[ {\nabla191 \int\limits_D {\frac{1}{e_3 }{\mathrm {\mathbf k}}\cdot \nabla \times \left[ {\nabla 192 192 _h \left( {A^{lm}\;\chi } \right)-\nabla _h \times \left( {A^{lm}\;\zeta 193 \;{\ rm {\bf k}}} \right)} \right]\;dv} =0193 \;{\mathrm {\mathbf k}}} \right)} \right]\;dv} =0 194 194 \] 195 195 … … 197 197 % \label{eq:dynldf_div} 198 198 \int\limits_D {\nabla _h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi } 199 \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\ rm {\bf k}}} \right)}199 \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} 200 200 \right]\;dv} =0 201 201 \] … … 203 203 \[ 204 204 % \label{eq:dynldf_curl} 205 \int_D {{\ rm {\bf U}}_h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi }206 \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\ rm {\bf k}}} \right)}205 \int_D {{\mathrm {\mathbf U}}_h \cdot \left[ {\nabla _h \left( {A^{lm}\;\chi } 206 \right)-\nabla _h \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} 207 207 \right]\;dv} \leqslant 0 208 208 \] … … 210 210 \[ 211 211 % \label{eq:dynldf_curl2} 212 \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\zeta \;{\ rm {\bf k}}\cdot212 \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\zeta \;{\mathrm {\mathbf k}}\cdot 213 213 \nabla \times \left[ {\nabla _h \left( {A^{lm}\;\chi } \right)-\nabla _h 214 \times \left( {A^{lm}\;\zeta \;{\ rm {\bf k}}} \right)} \right]\;dv}214 \times \left( {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} \right]\;dv} 215 215 \leqslant 0 216 216 \] … … 220 220 \mbox{if}\quad A^{lm}=cste\quad \quad \int_D {\chi \;\nabla _h \cdot \left[ 221 221 {\nabla _h \left( {A^{lm}\;\chi } \right)-\nabla _h \times \left( 222 {A^{lm}\;\zeta \;{\ rm {\bf k}}} \right)} \right]\;dv} \leqslant 0222 {A^{lm}\;\zeta \;{\mathrm {\mathbf k}}} \right)} \right]\;dv} \leqslant 0 223 223 \] 224 224 … … 260 260 % \label{eq:dynzdf_vor} 261 261 \begin{aligned} 262 & \int_D {\frac{1}{e_3 }{\ rm {\bf k}}\cdot \nabla \times \left( {\frac{1}{e_3263 }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\ rm264 {\ bf U}}_h }{\partial k}} \right)} \right)\;dv} =0 \\265 & \int_D {\zeta \,{\ rm {\bf k}}\cdot \nabla \times \left( {\frac{1}{e_3266 }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\ rm267 {\ bf U}}_h }{\partial k}} \right)} \right)\;dv} \leq 0 \\262 & \int_D {\frac{1}{e_3 }{\mathrm {\mathbf k}}\cdot \nabla \times \left( {\frac{1}{e_3 263 }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm 264 {\mathbf U}}_h }{\partial k}} \right)} \right)\;dv} =0 \\ 265 & \int_D {\zeta \,{\mathrm {\mathbf k}}\cdot \nabla \times \left( {\frac{1}{e_3 266 }\frac{\partial }{\partial k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm 267 {\mathbf U}}_h }{\partial k}} \right)} \right)\;dv} \leq 0 \\ 268 268 \end{aligned} 269 269 \] … … 273 273 \begin{aligned} 274 274 &\int_D {\nabla \cdot \left( {\frac{1}{e_3 }\frac{\partial }{\partial 275 k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\ rm {\bf U}}_h }{\partial k}}275 k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}} 276 276 \right)} \right)\;dv} =0 \\ 277 277 & \int_D {\chi \;\nabla \cdot \left( {\frac{1}{e_3 }\frac{\partial }{\partial 278 k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\ rm {\bf U}}_h }{\partial k}}278 k}\left( {\frac{A^{vm}}{e_3 }\frac{\partial {\mathrm {\mathbf U}}_h }{\partial k}} 279 279 \right)} \right)\;dv} \leq 0 \\ 280 280 \end{aligned} -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_misc.tex
r10601 r11263 63 63 \begin{figure}[!tbp] 64 64 \begin{center} 65 \includegraphics[width= 0.80\textwidth]{Fig_Gibraltar}66 \includegraphics[width= 0.80\textwidth]{Fig_Gibraltar2}65 \includegraphics[width=\textwidth]{Fig_Gibraltar} 66 \includegraphics[width=\textwidth]{Fig_Gibraltar2} 67 67 \caption{ 68 68 \protect\label{fig:MISC_strait_hand} … … 84 84 \begin{figure}[!tbp] 85 85 \begin{center} 86 \includegraphics[width= 1.0\textwidth]{Fig_closea_mask_example}86 \includegraphics[width=\textwidth]{Fig_closea_mask_example} 87 87 \caption{ 88 88 \protect\label{fig:closea_mask_example} … … 102 102 % Closed seas 103 103 % ================================================================ 104 \section{Closed seas (\protect\mdl{closea})} 104 \section[Closed seas (\textit{closea.F90})] 105 {Closed seas (\protect\mdl{closea})} 105 106 \label{sec:MISC_closea} 106 107 … … 122 123 123 124 \begin{enumerate} 124 \item{{\bf No ``closea\_mask'' field is included in domain configuration125 \item{{\bfseries No ``closea\_mask'' field is included in domain configuration 125 126 file.} In this case the closea module does nothing.} 126 127 127 \item{{\bf A field called closea\_mask is included in the domain128 \item{{\bfseries A field called closea\_mask is included in the domain 128 129 configuration file and ln\_closea=.false. in namelist namcfg.} In this 129 130 case the inland seas defined by the closea\_mask field are filled in … … 131 132 closea\_mask that is nonzero is set to be a land point.} 132 133 133 \item{{\bf A field called closea\_mask is included in the domain134 \item{{\bfseries A field called closea\_mask is included in the domain 134 135 configuration file and ln\_closea=.true. in namelist namcfg.} Each 135 136 inland sea or group of inland seas is set to a positive integer value … … 140 141 closea\_mask is zero).} 141 142 142 \item{{\bf Fields called closea\_mask and closea\_mask\_rnf are143 \item{{\bfseries Fields called closea\_mask and closea\_mask\_rnf are 143 144 included in the domain configuration file and ln\_closea=.true. in 144 145 namelist namcfg.} This option works as for option 3, except that if … … 154 155 ocean.} 155 156 156 \item{{\bf Fields called closea\_mask and closea\_mask\_emp are157 \item{{\bfseries Fields called closea\_mask and closea\_mask\_emp are 157 158 included in the domain configuration file and ln\_closea=.true. in 158 159 namelist namcfg.} This option works the same as option 4 except that … … 223 224 \begin{figure}[!ht] 224 225 \begin{center} 225 \includegraphics[width= 0.90\textwidth]{Fig_LBC_zoom}226 \includegraphics[width=\textwidth]{Fig_LBC_zoom} 226 227 \caption{ 227 228 \protect\label{fig:LBC_zoom} … … 236 237 % Accuracy and Reproducibility 237 238 % ================================================================ 238 \section{Accuracy and reproducibility (\protect\mdl{lib\_fortran})} 239 \section[Accuracy and reproducibility (\textit{lib\_fortran.F90})] 240 {Accuracy and reproducibility (\protect\mdl{lib\_fortran})} 239 241 \label{sec:MISC_fortran} 240 242 241 \subsection{Issues with intrinsinc SIGN function (\protect\key{nosignedzero})} 243 \subsection[Issues with intrinsinc SIGN function (\texttt{\textbf{key\_nosignedzero}})] 244 {Issues with intrinsinc SIGN function (\protect\key{nosignedzero})} 242 245 \label{subsec:MISC_sign} 243 246 … … 272 275 and their propagation and accumulation cause uncertainty in final simulation reproducibility on 273 276 different numbers of processors. 274 To avoid so, based on \citet{ He_Ding_JSC01} review of different technics,277 To avoid so, based on \citet{he.ding_JS01} review of different technics, 275 278 we use a so called self-compensated summation method. 276 279 The idea is to estimate the roundoff error, store it in a buffer, and then add it back in the next addition. … … 314 317 This alternative method should give identical results to the default \textsc{ALLGATHER} method and 315 318 is recommended for large values of \np{jpni}. 316 The new method is activated by setting \np{ln\_nnogather} to be true ( {\bfnammpp}).319 The new method is activated by setting \np{ln\_nnogather} to be true (\ngn{nammpp}). 317 320 The reproducibility of results using the two methods should be confirmed for each new, 318 321 non-reference configuration. -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_model_basics.tex
r10544 r11263 120 120 \begin{figure}[!ht] 121 121 \begin{center} 122 \includegraphics[ ]{Fig_I_ocean_bc}122 \includegraphics[width=\textwidth]{Fig_I_ocean_bc} 123 123 \caption{ 124 124 \protect\label{fig:ocean_bc} … … 258 258 If further, an approximative conservation of heat and salt contents is sufficient for the problem solved, 259 259 then it is sufficient to solve a linearized version of \autoref{eq:PE_ssh}, 260 which still allows to take into account freshwater fluxes applied at the ocean surface \citep{ Roullet_Madec_JGR00}.260 which still allows to take into account freshwater fluxes applied at the ocean surface \citep{roullet.madec_JGR00}. 261 261 Nevertheless, with the linearization, an exact conservation of heat and salt contents is lost. 262 262 263 263 The filtering of EGWs in models with a free surface is usually a matter of discretisation of 264 264 the temporal derivatives, 265 using a split-explicit method \citep{ Killworth_al_JPO91, Zhang_Endoh_JGR92} or266 the implicit scheme \citep{ Dukowicz1994} or267 the addition of a filtering force in the momentum equation \citep{ Roullet_Madec_JGR00}.265 using a split-explicit method \citep{killworth.webb.ea_JPO91, zhang.endoh_JGR92} or 266 the implicit scheme \citep{dukowicz.smith_JGR94} or 267 the addition of a filtering force in the momentum equation \citep{roullet.madec_JGR00}. 268 268 With the present release, \NEMO offers the choice between 269 269 an explicit free surface (see \autoref{subsec:DYN_spg_exp}) or 270 a split-explicit scheme strongly inspired the one proposed by \citet{ Shchepetkin_McWilliams_OM05}270 a split-explicit scheme strongly inspired the one proposed by \citet{shchepetkin.mcwilliams_OM05} 271 271 (see \autoref{subsec:DYN_spg_ts}). 272 272 … … 292 292 cannot be easily treated in a global model without filtering. 293 293 A solution consists of introducing an appropriate coordinate transformation that 294 shifts the singular point onto land \citep{ Madec_Imbard_CD96, Murray_JCP96}.294 shifts the singular point onto land \citep{madec.imbard_CD96, murray_JCP96}. 295 295 As a consequence, it is important to solve the primitive equations in various curvilinear coordinate systems. 296 296 An efficient way of introducing an appropriate coordinate transform can be found when using a tensorial formalism. … … 298 298 Ocean modellers mainly use three-dimensional orthogonal grids on the sphere (spherical earth approximation), 299 299 with preservation of the local vertical. Here we give the simplified equations for this particular case. 300 The general case is detailed by \citet{ Eiseman1980} in their survey of the conservation laws of fluid dynamics.300 The general case is detailed by \citet{eiseman.stone_SR80} in their survey of the conservation laws of fluid dynamics. 301 301 302 302 Let $(i,j,k)$ be a set of orthogonal curvilinear coordinates on … … 323 323 \begin{figure}[!tb] 324 324 \begin{center} 325 \includegraphics[ ]{Fig_I_earth_referential}325 \includegraphics[width=\textwidth]{Fig_I_earth_referential} 326 326 \caption{ 327 327 \protect\label{fig:referential} … … 577 577 In order to satisfy two or more constrains one can even be tempted to mixed these coordinate systems, as in 578 578 HYCOM (mixture of $z$-coordinate at the surface, isopycnic coordinate in the ocean interior and $\sigma$ at 579 the ocean bottom) \citep{ Chassignet_al_JPO03} or579 the ocean bottom) \citep{chassignet.smith.ea_JPO03} or 580 580 OPA (mixture of $z$-coordinate in vicinity the surface and steep topography areas and $\sigma$-coordinate elsewhere) 581 \citep{ Madec_al_JPO96} among others.581 \citep{madec.delecluse.ea_JPO96} among others. 582 582 583 583 In fact one is totally free to choose any space and time vertical coordinate by … … 592 592 the $(i,j,s,t)$ generalised coordinate system with $s$ depending on the other three variables through 593 593 \autoref{eq:PE_s}. 594 This so-called \textit{generalised vertical coordinate} \citep{ Kasahara_MWR74} is in fact594 This so-called \textit{generalised vertical coordinate} \citep{kasahara_MWR74} is in fact 595 595 an Arbitrary Lagrangian--Eulerian (ALE) coordinate. 596 596 Indeed, choosing an expression for $s$ is an arbitrary choice that determines 597 597 which part of the vertical velocity (defined from a fixed referential) will cross the levels (Eulerian part) and 598 598 which part will be used to move them (Lagrangian part). 599 The coordinate is also sometime referenced as an adaptive coordinate \citep{ Hofmeister_al_OM09},599 The coordinate is also sometime referenced as an adaptive coordinate \citep{hofmeister.burchard.ea_OM10}, 600 600 since the coordinate system is adapted in the course of the simulation. 601 601 Its most often used implementation is via an ALE algorithm, 602 602 in which a pure lagrangian step is followed by regridding and remapping steps, 603 603 the later step implicitly embedding the vertical advection 604 \citep{ Hirt_al_JCP74, Chassignet_al_JPO03, White_al_JCP09}.605 Here we follow the \citep{ Kasahara_MWR74} strategy:604 \citep{hirt.amsden.ea_JCP74, chassignet.smith.ea_JPO03, white.adcroft.ea_JCP09}. 605 Here we follow the \citep{kasahara_MWR74} strategy: 606 606 a regridding step (an update of the vertical coordinate) followed by an eulerian step with 607 607 an explicit computation of vertical advection relative to the moving s-surfaces. … … 738 738 \begin{figure}[!b] 739 739 \begin{center} 740 \includegraphics[ ]{Fig_z_zstar}740 \includegraphics[width=\textwidth]{Fig_z_zstar} 741 741 \caption{ 742 742 \protect\label{fig:z_zstar} … … 744 744 (b) $z$-coordinate in non-linear free surface case ; 745 745 (c) re-scaled height coordinate 746 (become popular as the \zstar-coordinate \citep{ Adcroft_Campin_OM04}).746 (become popular as the \zstar-coordinate \citep{adcroft.campin_OM04}). 747 747 } 748 748 \end{center} … … 751 751 752 752 In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account. 753 These coordinates systems is presented in a report \citep{ Levier2007} available on the \NEMO web site.753 These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site. 754 754 755 755 The \zstar coordinate approach is an unapproximated, non-linear free surface implementation which allows one to 756 deal with large amplitude free-surface variations relative to the vertical resolution \citep{ Adcroft_Campin_OM04}.756 deal with large amplitude free-surface variations relative to the vertical resolution \citep{adcroft.campin_OM04}. 757 757 In the \zstar formulation, 758 758 the variation of the column thickness due to sea-surface undulations is not concentrated in the surface level, … … 805 805 The quasi -horizontal nature of the coordinate surfaces also facilitates the implementation of 806 806 neutral physics parameterizations in \zstar models using the same techniques as in $z$-models 807 (see Chapters 13-16 of \cite{ Griffies_Bk04}) for a discussion of neutral physics in $z$-models,807 (see Chapters 13-16 of \cite{griffies_bk04}) for a discussion of neutral physics in $z$-models, 808 808 as well as \autoref{sec:LDF_slp} in this document for treatment in \NEMO). 809 809 … … 849 849 The response to such a velocity field often leads to numerical dispersion effects. 850 850 One solution to strongly reduce this error is to use a partial step representation of bottom topography instead of 851 a full step one \cite{ Pacanowski_Gnanadesikan_MWR98}.851 a full step one \cite{pacanowski.gnanadesikan_MWR98}. 852 852 Another solution is to introduce a terrain-following coordinate system (hereafter $s$-coordinate). 853 853 … … 876 876 introduces a truncation error that is not present in a $z$-model. 877 877 In the special case of a $\sigma$-coordinate (i.e. a depth-normalised coordinate system $\sigma = z/H$), 878 \citet{ Haney1991} and \citet{Beckmann1993} have given estimates of the magnitude of this truncation error.878 \citet{haney_JPO91} and \citet{beckmann.haidvogel_JPO93} have given estimates of the magnitude of this truncation error. 879 879 It depends on topographic slope, stratification, horizontal and vertical resolution, the equation of state, 880 880 and the finite difference scheme. … … 884 884 The large-scale slopes require high horizontal resolution, and the computational cost becomes prohibitive. 885 885 This problem can be at least partially overcome by mixing $s$-coordinate and 886 step-like representation of bottom topography \citep{ Gerdes1993a,Gerdes1993b,Madec_al_JPO96}.886 step-like representation of bottom topography \citep{gerdes_JGR93*a,gerdes_JGR93*b,madec.delecluse.ea_JPO96}. 887 887 However, the definition of the model domain vertical coordinate becomes then a non-trivial thing for 888 888 a realistic bottom topography: … … 904 904 In contrast, the ocean will stay at rest in a $z$-model. 905 905 As for the truncation error, the problem can be reduced by introducing the terrain-following coordinate below 906 the strongly stratified portion of the water column (\ie the main thermocline) \citep{ Madec_al_JPO96}.906 the strongly stratified portion of the water column (\ie the main thermocline) \citep{madec.delecluse.ea_JPO96}. 907 907 An alternate solution consists of rotating the lateral diffusive tensor to geopotential or to isoneutral surfaces 908 908 (see \autoref{subsec:PE_ldf}). … … 910 910 strongly exceeding the stability limit of such a operator when it is discretized (see \autoref{chap:LDF}). 911 911 912 The $s$-coordinates introduced here \citep{ Lott_al_OM90,Madec_al_JPO96} differ mainly in two aspects from912 The $s$-coordinates introduced here \citep{lott.madec.ea_OM90,madec.delecluse.ea_JPO96} differ mainly in two aspects from 913 913 similar models: 914 914 it allows a representation of bottom topography with mixed full or partial step-like/terrain following topography; … … 921 921 \label{subsec:PE_zco_tilde} 922 922 923 The \ztilde -coordinate has been developed by \citet{ Leclair_Madec_OM11}.923 The \ztilde -coordinate has been developed by \citet{leclair.madec_OM11}. 924 924 It is available in \NEMO since the version 3.4. 925 925 Nevertheless, it is currently not robust enough to be used in all possible configurations. … … 1005 1005 The resulting lateral diffusive and dissipative operators are of second order. 1006 1006 Observations show that lateral mixing induced by mesoscale turbulence tends to be along isopycnal surfaces 1007 (or more precisely neutral surfaces \cite{ McDougall1987}) rather than across them.1007 (or more precisely neutral surfaces \cite{mcdougall_JPO87}) rather than across them. 1008 1008 As the slope of neutral surfaces is small in the ocean, a common approximation is to assume that 1009 1009 the `lateral' direction is the horizontal, \ie the lateral mixing is performed along geopotential surfaces. … … 1016 1016 both horizontal and isoneutral operators have no effect on mean (\ie large scale) potential energy whereas 1017 1017 potential energy is a main source of turbulence (through baroclinic instabilities). 1018 \citet{ Gent1990} have proposed a parameterisation of mesoscale eddy-induced turbulence which1018 \citet{gent.mcwilliams_JPO90} have proposed a parameterisation of mesoscale eddy-induced turbulence which 1019 1019 associates an eddy-induced velocity to the isoneutral diffusion. 1020 1020 Its mean effect is to reduce the mean potential energy of the ocean. … … 1040 1040 There are not all available in \NEMO. For active tracers (temperature and salinity) the main ones are: 1041 1041 Laplacian and bilaplacian operators acting along geopotential or iso-neutral surfaces, 1042 \citet{ Gent1990} parameterisation, and various slightly diffusive advection schemes.1042 \citet{gent.mcwilliams_JPO90} parameterisation, and various slightly diffusive advection schemes. 1043 1043 For momentum, the main ones are: Laplacian and bilaplacian operators acting along geopotential surfaces, 1044 1044 and UBS advection schemes when flux form is chosen for the momentum advection. … … 1062 1062 the rotation between geopotential and $s$-surfaces, 1063 1063 while it is only an approximation for the rotation between isoneutral and $z$- or $s$-surfaces. 1064 Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{ Cox1987}.1064 Indeed, in the latter case, two assumptions are made to simplify \autoref{eq:PE_iso_tensor} \citep{cox_OM87}. 1065 1065 First, the horizontal contribution of the dianeutral mixing is neglected since the ratio between iso and 1066 1066 dia-neutral diffusive coefficients is known to be several orders of magnitude smaller than unity. … … 1087 1087 \subsubsection{Eddy induced velocity} 1088 1088 1089 When the \textit{eddy induced velocity} parametrisation (eiv) \citep{ Gent1990} is used,1089 When the \textit{eddy induced velocity} parametrisation (eiv) \citep{gent.mcwilliams_JPO90} is used, 1090 1090 an additional tracer advection is introduced in combination with the isoneutral diffusion of tracers: 1091 1091 \[ … … 1162 1162 \ie on a $f$- or $\beta$-plane, not on the sphere. 1163 1163 It is also a very good approximation in vicinity of the Equator in 1164 a geographical coordinate system \citep{ Lengaigne_al_JGR03}.1164 a geographical coordinate system \citep{lengaigne.madec.ea_JGR03}. 1165 1165 1166 1166 \subsubsection{lateral bilaplacian momentum diffusive operator} -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_model_basics_zstar.tex
r10544 r11263 18 18 19 19 In that case, the free surface equation is nonlinear, and the variations of volume are fully taken into account. 20 These coordinates systems is presented in a report \citep{ Levier2007} available on the \NEMO web site.20 These coordinates systems is presented in a report \citep{levier.treguier.ea_rpt07} available on the \NEMO web site. 21 21 22 22 \colorbox{yellow}{ end of to be updated} … … 73 73 % Surface Pressure Gradient and Sea Surface Height 74 74 % ================================================================ 75 \section{Surface pressure gradient and sea surface heigth (\protect\mdl{dynspg})} 75 \section[Surface pressure gradient and sea surface heigth (\textit{dynspg.F90})] 76 {Surface pressure gradient and sea surface heigth (\protect\mdl{dynspg})} 76 77 \label{sec:DYN_hpg_spg} 77 78 %-----------------------------------------nam_dynspg---------------------------------------------------- … … 89 90 which imposes a very small time step when an explicit time stepping is used. 90 91 Two methods are proposed to allow a longer time step for the three-dimensional equations: 91 the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt }),92 the filtered free surface, which is a modification of the continuous equations %(see \autoref{eq:PE_flt?}), 92 93 and the split-explicit free surface described below. 93 94 The extra term introduced in the filtered method is calculated implicitly, … … 97 98 % Explicit 98 99 %------------------------------------------------------------- 99 \subsubsection{Explicit (\protect\key{dynspg\_exp})} 100 \subsubsection[Explicit (\texttt{\textbf{key\_dynspg\_exp}})] 101 {Explicit (\protect\key{dynspg\_exp})} 100 102 \label{subsec:DYN_spg_exp} 101 103 … … 133 135 % Split-explicit time-stepping 134 136 %------------------------------------------------------------- 135 \subsubsection{Split-explicit time-stepping (\protect\key{dynspg\_ts})} 137 \subsubsection[Split-explicit time-stepping (\texttt{\textbf{key\_dynspg\_ts}})] 138 {Split-explicit time-stepping (\protect\key{dynspg\_ts})} 136 139 \label{subsec:DYN_spg_ts} 137 140 %--------------------------------------------namdom---------------------------------------------------- … … 139 142 \nlst{namdom} 140 143 %-------------------------------------------------------------------------------------------------------------- 141 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004 }.144 The split-explicit free surface formulation used in OPA follows the one proposed by \citet{Griffies2004?}. 142 145 The general idea is to solve the free surface equation with a small time step, 143 146 while the three dimensional prognostic variables are solved with a longer time step that … … 147 150 \begin{figure}[!t] 148 151 \begin{center} 149 \includegraphics[width= 0.90\textwidth]{Fig_DYN_dynspg_ts}152 \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts} 150 153 \caption{ 151 154 \protect\label{fig:DYN_dynspg_ts} 152 155 Schematic of the split-explicit time stepping scheme for the barotropic and baroclinic modes, 153 after \citet{Griffies2004 }.156 after \citet{Griffies2004?}. 154 157 Time increases to the right. 155 158 Baroclinic time steps are denoted by $t-\Delta t$, $t, t+\Delta t$, and $t+2\Delta t$. … … 171 174 172 175 The split-explicit formulation has a damping effect on external gravity waves, 173 which is weaker than the filtered free surface but still significant as shown by \citet{ Levier2007} in176 which is weaker than the filtered free surface but still significant as shown by \citet{levier.treguier.ea_rpt07} in 174 177 the case of an analytical barotropic Kelvin wave. 175 178 … … 291 294 % Filtered formulation 292 295 %------------------------------------------------------------- 293 \subsubsection{Filtered formulation (\protect\key{dynspg\_flt})} 296 \subsubsection[Filtered formulation (\texttt{\textbf{key\_dynspg\_flt}})] 297 {Filtered formulation (\protect\key{dynspg\_flt})} 294 298 \label{subsec:DYN_spg_flt} 295 299 296 The filtered formulation follows the \citet{Roullet2000 } implementation.300 The filtered formulation follows the \citet{Roullet2000?} implementation. 297 301 The extra term introduced in the equations (see {\S}I.2.2) is solved implicitly. 298 302 The elliptic solvers available in the code are documented in \autoref{chap:MISC}. 299 303 The amplitude of the extra term is given by the namelist variable \np{rnu}. 300 The default value is 1, as recommended by \citet{Roullet2000 }304 The default value is 1, as recommended by \citet{Roullet2000?} 301 305 302 306 \colorbox{red}{\np{rnu}\forcode{ = 1} to be suppressed from namelist !} … … 305 309 % Non-linear free surface formulation 306 310 %------------------------------------------------------------- 307 \subsection{Non-linear free surface formulation (\protect\key{vvl})} 311 \subsection[Non-linear free surface formulation (\texttt{\textbf{key\_vvl}})] 312 {Non-linear free surface formulation (\protect\key{vvl})} 308 313 \label{subsec:DYN_spg_vvl} 309 314 310 315 In the non-linear free surface formulation, the variations of volume are fully taken into account. 311 This option is presented in a report \citep{ Levier2007} available on the NEMO web site.316 This option is presented in a report \citep{levier.treguier.ea_rpt07} available on the NEMO web site. 312 317 The three time-stepping methods (explicit, split-explicit and filtered) are the same as in 313 318 \autoref{DYN_spg_linear} except that the ocean depth is now time-dependent. -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_time_domain.tex
r10501 r11263 11 11 12 12 % Missing things: 13 % - daymod: definition of the time domain (nit000, nitend and dthe calendar)13 % - daymod: definition of the time domain (nit000, nitend and the calendar) 14 14 15 15 \gmcomment{STEVEN :maybe a picture of the directory structure in the introduction which could be referred to here, … … 22 22 a key feature of an ocean model as it exerts a strong influence on the structure of the computer code 23 23 (\ie on its flowchart). 24 In the present chapter, we provide a general description of the \NEMO time stepping strategy and24 In the present chapter, we provide a general description of the \NEMO time stepping strategy and 25 25 the consequences for the order in which the equations are solved. 26 26 … … 40 40 $\rdt$ is the time step; 41 41 and the superscripts indicate the time at which a quantity is evaluated. 42 Each term of the RHS is evaluated at a specific time step depending on the physics with which it is associated.43 44 The choice of the time step used for this evaluation is discussed below as well as42 Each term of the RHS is evaluated at a specific time stepping depending on the physics with which it is associated. 43 44 The choice of the time stepping used for this evaluation is discussed below as well as 45 45 the implications for starting or restarting a model simulation. 46 46 Note that the time stepping calculation is generally performed in a single operation. … … 53 53 is usually not the variable at the after time step; 54 54 but rather it is used to store the time derivative (RHS in \autoref{eq:STP}) prior to time-stepping the equation. 55 Generally, the time stepping is performed once at each time step in the \mdl{tranxt} and \mdl{dynnxt} modules, 56 except when using implicit vertical diffusion or calculating sea surface height in which 57 case time-splitting options are used. 55 The time stepping itself is performed once at each time step where implicit vertical diffusion is computed, \ie in the \mdl{trazdf} and \mdl{dynzdf} modules. 58 56 59 57 % ------------------------------------------------------------------------------------------------------------- … … 64 62 65 63 The time stepping used for processes other than diffusion is the well-known leapfrog scheme 66 \citep{ Mesinger_Arakawa_Bk76}.64 \citep{mesinger.arakawa_bk76}. 67 65 This scheme is widely used for advection processes in low-viscosity fluids. 68 66 It is a time centred scheme, \ie the RHS in \autoref{eq:STP} is evaluated at time step $t$, the now time step. … … 80 78 To prevent it, the leapfrog scheme is often used in association with a Robert-Asselin time filter 81 79 (hereafter the LF-RA scheme). 82 This filter, first designed by \citet{ Robert_JMSJ66} and more comprehensively studied by \citet{Asselin_MWR72},80 This filter, first designed by \citet{robert_JMSJ66} and more comprehensively studied by \citet{asselin_MWR72}, 83 81 is a kind of laplacian diffusion in time that mixes odd and even time steps: 84 82 \begin{equation} … … 88 86 where the subscript $F$ denotes filtered values and $\gamma$ is the Asselin coefficient. 89 87 $\gamma$ is initialized as \np{rn\_atfp} (namelist parameter). 90 Its default value is \np{rn\_atfp} ~\forcode{= 10.e-3} (see \autoref{sec:STP_mLF}),91 causing only a weak dissipation of high frequency motions (\citep{ Farge1987}).88 Its default value is \np{rn\_atfp}\forcode{ = 10.e-3} (see \autoref{sec:STP_mLF}), 89 causing only a weak dissipation of high frequency motions (\citep{farge-coulombier_phd87}). 92 90 The addition of a time filter degrades the accuracy of the calculation from second to first order. 93 91 However, the second order truncation error is proportional to $\gamma$, which is small compared to 1. 94 92 Therefore, the LF-RA is a quasi second order accurate scheme. 95 93 The LF-RA scheme is preferred to other time differencing schemes such as predictor corrector or trapezoidal schemes, 96 because the user has an explicit and simple control of the magnitude of the time diffusion of the scheme. 94 because the user has an explicit and simple control of the magnitude of the time diffusion of the scheme. 97 95 When used with the 2nd order space centred discretisation of the advection terms in 98 96 the momentum and tracer equations, LF-RA avoids implicit numerical diffusion: … … 107 105 108 106 The leapfrog differencing scheme is unsuitable for the representation of diffusion and damping processes. 109 For a tend ancy $D_x$, representing a diffusion term or a restoring term to a tracer climatology107 For a tendency $D_x$, representing a diffusion term or a restoring term to a tracer climatology 110 108 (when present, see \autoref{sec:TRA_dmp}), a forward time differencing scheme is used : 111 109 \[ … … 115 113 116 114 This is diffusive in time and conditionally stable. 117 The conditions for stability of second and fourth order horizontal diffusion schemes are \citep{ Griffies_Bk04}:115 The conditions for stability of second and fourth order horizontal diffusion schemes are \citep{griffies_bk04}: 118 116 \begin{equation} 119 117 \label{eq:STP_euler_stability} … … 130 128 131 129 For the vertical diffusion terms, a forward time differencing scheme can be used, 132 but usually the numerical stability condition imposes a strong constraint on the time step. 133 Two solutions are available in \NEMO to overcome the stability constraint: 134 $(a)$ a forward time differencing scheme using a time splitting technique (\np{ln\_zdfexp}~\forcode{= .true.}) or 135 $(b)$ a backward (or implicit) time differencing scheme (\np{ln\_zdfexp}~\forcode{= .false.}). 136 In $(a)$, the master time step $\Delta$t is cut into $N$ fractional time steps so that 137 the stability criterion is reduced by a factor of $N$. 138 The computation is performed as follows: 139 \begin{alignat*}{2} 140 % \label{eq:STP_ts} 141 &x_\ast^{t - \rdt} &= &x^{t - \rdt} \\ 142 &x_\ast^{t - \rdt + L \frac{2 \rdt}{N}} &= &x_\ast ^{t - \rdt + (L - 1) \frac{2 \rdt}{N}} 143 + \frac{2 \rdt}{N} \; DF^{t - \rdt + (L - 1) \frac{2 \rdt}{N}} 144 \quad \text{for $L = 1$ to $N$} \\ 145 &x^{t + \rdt} &= &x_\ast^{t + \rdt} 146 \end{alignat*} 147 with DF a vertical diffusion term. 148 The number of fractional time steps, $N$, is given by setting \np{nn\_zdfexp}, (namelist parameter). 149 The scheme $(b)$ is unconditionally stable but diffusive. It can be written as follows: 130 but usually the numerical stability condition imposes a strong constraint on the time step. To overcome the stability constraint, a 131 backward (or implicit) time differencing scheme is used. This scheme is unconditionally stable but diffusive and can be written as follows: 150 132 \begin{equation} 151 133 \label{eq:STP_imp} … … 157 139 %%gm 158 140 159 This scheme is rather time consuming since it requires a matrix inversion, 160 but it becomes attractive since a value of 3 or more is needed for N in the forward time differencing scheme. 161 For example, the finite difference approximation of the temperature equation is: 141 This scheme is rather time consuming since it requires a matrix inversion. For example, the finite difference approximation of the temperature equation is: 162 142 \[ 163 143 % \label{eq:STP_imp_zdf} … … 183 163 $c(k)$ and $d(k)$ are positive and the diagonal term is greater than the sum of the two extra-diagonal terms, 184 164 therefore a special adaptation of the Gauss elimination procedure is used to find the solution 185 (see for example \citet{ Richtmyer1967}).165 (see for example \citet{richtmyer.morton_bk67}). 186 166 187 167 % ------------------------------------------------------------------------------------------------------------- … … 191 171 \label{sec:STP_spg_ts} 192 172 193 ===>>>> TO BE written.... :-) 173 The leapfrog environment supports a centred in time computation of the surface pressure, \ie evaluated 174 at \textit{now} time step. This refers to as the explicit free surface case in the code (\np{ln\_dynspg\_exp}\forcode{ = .true.}). 175 This choice however imposes a strong constraint on the time step which should be small enough to resolve the propagation 176 of external gravity waves. As a matter of fact, one rather use in a realistic setup, a split-explicit free surface 177 (\np{ln\_dynspg\_ts}\forcode{ = .true.}) in which barotropic and baroclinic dynamical equations are solved separately with ad-hoc 178 time steps. The use of the time-splitting (in combination with non-linear free surface) imposes some constraints on the design of 179 the overall flowchart, in particular to ensure exact tracer conservation (see \autoref{fig:TimeStep_flowchart}). 180 181 Compared to the former use of the filtered free surface in \NEMO v3.6 (\citet{roullet.madec_JGR00}), the use of a split-explicit free surface is advantageous 182 on massively parallel computers. Indeed, no global computations are anymore required by the elliptic solver which saves a substantial amount of communication 183 time. Fast barotropic motions (such as tides) are also simulated with a better accuracy. 194 184 195 185 %\gmcomment{ … … 197 187 \begin{figure}[!t] 198 188 \begin{center} 199 \includegraphics[ ]{Fig_TimeStepping_flowchart}189 \includegraphics[width=\textwidth]{Fig_TimeStepping_flowchart_v4} 200 190 \caption{ 201 191 \protect\label{fig:TimeStep_flowchart} 202 Sketch of the leapfrog time stepping sequence in \NEMO from \citet{Leclair_Madec_OM09}. 203 The use of a semi -implicit computation of the hydrostatic pressure gradient requires the tracer equation to 204 be stepped forward prior to the momentum equation. 205 The need for knowledge of the vertical scale factor (here denoted as $h$) requires the sea surface height and 206 the continuity equation to be stepped forward prior to the computation of the tracer equation. 207 Note that the method for the evaluation of the surface pressure gradient $\nabla p_s$ is not presented here 208 (see \autoref{sec:DYN_spg}). 192 Sketch of the leapfrog time stepping sequence in \NEMO with split-explicit free surface. The latter combined 193 with non-linear free surface requires the dynamical tendency being updated prior tracers tendency to ensure 194 conservation. Note the use of time integrated fluxes issued from the barotropic loop in subsequent calculations 195 of tracer advection and in the continuity equation. Details about the time-splitting scheme can be found 196 in \autoref{subsec:DYN_spg_ts}. 209 197 } 210 198 \end{center} … … 219 207 \label{sec:STP_mLF} 220 208 221 Significant changes have been introduced by \cite{ Leclair_Madec_OM09} in the LF-RA scheme in order to209 Significant changes have been introduced by \cite{leclair.madec_OM09} in the LF-RA scheme in order to 222 210 ensure tracer conservation and to allow the use of a much smaller value of the Asselin filter parameter. 223 211 The modifications affect both the forcing and filtering treatments in the LF-RA scheme. … … 237 225 The change in the forcing formulation given by \autoref{eq:STP_forcing} (see \autoref{fig:MLF_forcing}) 238 226 has a significant effect: 239 the forcing term no longer excites the divergence of odd and even time steps \citep{ Leclair_Madec_OM09}.227 the forcing term no longer excites the divergence of odd and even time steps \citep{leclair.madec_OM09}. 240 228 % forcing seen by the model.... 241 This property improves the LF-RA scheme in two respects.229 This property improves the LF-RA scheme in two aspects. 242 230 First, the LF-RA can now ensure the local and global conservation of tracers. 243 231 Indeed, time filtering is no longer required on the forcing part. 244 The influence of the Asselin filter on the forcing is beremoved by adding a new term in the filter232 The influence of the Asselin filter on the forcing is explicitly removed by adding a new term in the filter 245 233 (last term in \autoref{eq:STP_RA} compared to \autoref{eq:STP_asselin}). 246 234 Since the filtering of the forcing was the source of non-conservation in the classical LF-RA scheme, 247 the modified formulation becomes conservative \citep{ Leclair_Madec_OM09}.235 the modified formulation becomes conservative \citep{leclair.madec_OM09}. 248 236 Second, the LF-RA becomes a truly quasi -second order scheme. 249 237 Indeed, \autoref{eq:STP_forcing} used in combination with a careful treatment of static instability 250 (\autoref{subsec:ZDF_evd}) and of the TKE physics (\autoref{subsec:ZDF_tke_ene}) ,251 the two other main sources of time step divergence,238 (\autoref{subsec:ZDF_evd}) and of the TKE physics (\autoref{subsec:ZDF_tke_ene}) 239 (the two other main sources of time step divergence), 252 240 allows a reduction by two orders of magnitude of the Asselin filter parameter. 253 241 … … 255 243 $Q^{t + \rdt / 2}$ is the forcing applied over the $[t,t + \rdt]$ time interval. 256 244 This and the change in the time filter, \autoref{eq:STP_RA}, 257 allows an exact evaluation of the contribution due to the forcing term between any two time steps,245 allows for an exact evaluation of the contribution due to the forcing term between any two time steps, 258 246 even if separated by only $\rdt$ since the time filter is no longer applied to the forcing term. 259 247 … … 261 249 \begin{figure}[!t] 262 250 \begin{center} 263 \includegraphics[ ]{Fig_MLF_forcing}251 \includegraphics[width=\textwidth]{Fig_MLF_forcing} 264 252 \caption{ 265 253 \protect\label{fig:MLF_forcing} … … 294 282 This is done simply by keeping the leapfrog environment (\ie the \autoref{eq:STP} three level time stepping) but 295 283 setting all $x^0$ (\textit{before}) and $x^1$ (\textit{now}) fields equal at the first time step and 296 using half the value of $\rdt$.284 using half the value of a leapfrog time step ($2 \rdt$). 297 285 298 286 It is also possible to restart from a previous computation, by using a restart file. … … 303 291 This requires saving two time levels and many auxiliary data in the restart files in machine precision. 304 292 305 Note that when a semi -implicit scheme is used to evaluate the hydrostatic pressure gradient 306 (see \autoref{subsec:DYN_hpg_imp}), an extra three-dimensional field has to 307 be added to the restart file to ensure an exact restartability. 308 This is done optionally via the \np{nn\_dynhpg\_rst} namelist parameter, 309 so that the size of the restart file can be reduced when restartability is not a key issue 310 (operational oceanography or in ensemble simulations for seasonal forecasting). 311 312 Note the size of the time step used, $\rdt$, is also saved in the restart file. 313 When restarting, if the the time step has been changed, a restart using an Euler time stepping scheme is imposed. 314 Options are defined through the \ngn{namrun} namelist variables. 293 Note that the time step $\rdt$, is also saved in the restart file. 294 When restarting, if the time step has been changed, or one of the prognostic variables at \textit{before} time step 295 is missing, an Euler time stepping scheme is imposed. A forward initial step can still be enforced by the user by setting 296 the namelist variable \np{nn\_euler}\forcode{=0}. Other options to control the time integration of the model 297 are defined through the \ngn{namrun} namelist variables. 315 298 %%% 316 299 \gmcomment{ -
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r10544 r11263 27 27 28 28 The ocean component of \NEMO has been developed from the legacy of the OPA model, release 8.2, 29 described in \citet{ Madec1998}.29 described in \citet{madec.delecluse.ea_NPM98}. 30 30 This model has been used for a wide range of applications, both regional or global, as a forced ocean model and 31 31 as a model coupled with the sea-ice and/or the atmosphere. … … 67 67 Within the \NEMO system the ocean model is interactively coupled with a sea ice model (SI$^3$) and 68 68 a biogeochemistry model (PISCES). 69 Interactive coupling to Atmospheric models is possible via the OASIS coupler \citep{OASIS2006}.69 Interactive coupling to Atmospheric models is possible via the \href{https://portal.enes.org/oasis}{OASIS coupler}. 70 70 Two-way nesting is also available through an interface to the AGRIF package 71 (Adaptative Grid Refinement in \fortran) \citep{ Debreu_al_CG2008}.71 (Adaptative Grid Refinement in \fortran) \citep{debreu.vouland.ea_CG08}. 72 72 % Needs to be reviewed 73 73 %The interface code for coupling to an alternative sea ice model (CICE, \citet{Hunke2008}) has now been upgraded so … … 83 83 The lateral Laplacian and biharmonic viscosity and diffusion can be rotated following 84 84 a geopotential or neutral direction. 85 There is an optional eddy induced velocity \citep{ Gent1990} with a space and time variable coefficient86 \citet{ Treguier1997}.85 There is an optional eddy induced velocity \citep{gent.mcwilliams_JPO90} with a space and time variable coefficient 86 \citet{treguier.held.ea_JPO97}. 87 87 The model has vertical harmonic viscosity and diffusion with a space and time variable coefficient, 88 with options to compute the coefficients with \citet{ Blanke1993}, \citet{Pacanowski_Philander_JPO81}, or89 \citet{ Umlauf_Burchard_JMS03} mixing schemes.88 with options to compute the coefficients with \citet{blanke.delecluse_JPO93}, \citet{pacanowski.philander_JPO81}, or 89 \citet{umlauf.burchard_JMR03} mixing schemes. 90 90 91 91 %%gm To be put somewhere else .... … … 213 213 NEMO/OPA, like all research tools, is in perpetual evolution. 214 214 The present document describes the OPA version include in the release 3.4 of NEMO. 215 This release differs significantly from version 8, documented in \citet{ Madec1998}. \\215 This release differs significantly from version 8, documented in \citet{madec.delecluse.ea_NPM98}. \\ 216 216 217 217 The main modifications from OPA v8 and NEMO/OPA v3.2 are : … … 222 222 \item 223 223 introduction of partial step representation of bottom topography 224 \citep{ Barnier_al_OD06, Le_Sommer_al_OM09, Penduff_al_OS07};224 \citep{barnier.madec.ea_OD06, le-sommer.penduff.ea_OM09, penduff.le-sommer.ea_OS07}; 225 225 \item 226 226 partial reactivation of a terrain-following vertical coordinate ($s$- and hybrid $s$-$z$) with … … 242 242 additional advection schemes for tracers; 243 243 \item 244 implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{ Debreu_al_CG2008};244 implementation of the AGRIF package (Adaptative Grid Refinement in \fortran) \citep{debreu.vouland.ea_CG08}; 245 245 \item 246 246 online diagnostics : tracers trend in the mixed layer and vorticity balance; … … 255 255 RGB light penetration and optional use of ocean color 256 256 \item 257 major changes in the TKE schemes: it now includes a Langmuir cell parameterization \citep{ Axell_JGR02},258 the \citet{ Mellor_Blumberg_JPO04} surface wave breaking parameterization, and has a time discretization which259 is energetically consistent with the ocean model equations \citep{ Burchard_OM02, Marsaleix_al_OM08};257 major changes in the TKE schemes: it now includes a Langmuir cell parameterization \citep{axell_JGR02}, 258 the \citet{mellor.blumberg_JPO04} surface wave breaking parameterization, and has a time discretization which 259 is energetically consistent with the ocean model equations \citep{burchard_OM02, marsaleix.auclair.ea_OM08}; 260 260 \item 261 261 tidal mixing parametrisation (bottom intensification) + Indonesian specific tidal mixing 262 \citep{ Koch-Larrouy_al_GRL07};262 \citep{koch-larrouy.madec.ea_GRL07}; 263 263 \item 264 264 introduction of LIM-3, the new Louvain-la-Neuve sea-ice model 265 265 (C-grid rheology and new thermodynamics including bulk ice salinity) 266 \citep{ Vancoppenolle_al_OM09a, Vancoppenolle_al_OM09b}266 \citep{vancoppenolle.fichefet.ea_OM09*a, vancoppenolle.fichefet.ea_OM09*b} 267 267 \end{itemize} 268 268 … … 272 272 \item 273 273 introduction of a modified leapfrog-Asselin filter time stepping scheme 274 \citep{ Leclair_Madec_OM09};275 \item 276 additional scheme for iso-neutral mixing \citep{ Griffies_al_JPO98}, although it is still a "work in progress";277 \item 278 a rewriting of the bottom boundary layer scheme, following \citet{ Campin_Goosse_Tel99};279 \item 280 addition of a Generic Length Scale vertical mixing scheme, following \citet{ Umlauf_Burchard_JMS03};274 \citep{leclair.madec_OM09}; 275 \item 276 additional scheme for iso-neutral mixing \citep{griffies.gnanadesikan.ea_JPO98}, although it is still a "work in progress"; 277 \item 278 a rewriting of the bottom boundary layer scheme, following \citet{campin.goosse_T99}; 279 \item 280 addition of a Generic Length Scale vertical mixing scheme, following \citet{umlauf.burchard_JMR03}; 281 281 \item 282 282 addition of the atmospheric pressure as an external forcing on both ocean and sea-ice dynamics; 283 283 \item 284 addition of a diurnal cycle on solar radiation \citep{ Bernie_al_CD07};284 addition of a diurnal cycle on solar radiation \citep{bernie.guilyardi.ea_CD07}; 285 285 \item 286 286 river runoffs added through a non-zero depth, and having its own temperature and salinity; … … 296 296 coupling interface adjusted for WRF atmospheric model; 297 297 \item 298 C-grid ice rheology now available fro both LIM-2 and LIM-3 \citep{ Bouillon_al_OM09};298 C-grid ice rheology now available fro both LIM-2 and LIM-3 \citep{bouillon.maqueda.ea_OM09}; 299 299 \item 300 300 LIM-3 ice-ocean momentum coupling applied to LIM-2; … … 318 318 319 319 \begin{itemize} 320 \item finalisation of above iso-neutral mixing \citep{ Griffies_al_JPO98}";320 \item finalisation of above iso-neutral mixing \citep{griffies.gnanadesikan.ea_JPO98}"; 321 321 \item "Neptune effect" parametrisation; 322 322 \item horizontal pressure gradient suitable for s-coordinate; -
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r11031 r11263 28 28 29 29 \subsection{Scales, thermodynamics and dynamics} 30 Because sea ice is much wider -- $\mathcal{O}$(100-1000 km) -- than thick -- $\mathcal{O}$(1 m) -- ice drift can be considered as purely horizontal: vertical motions around the hydrostatic equilibrium position are negligible. The same scaling argument justifies the assumption that heat exchanges are purely vertical\footnote{The latter assumption is probably less valid, because the horizontal scales of temperature variations are $\mathcal{O}$(10-100 m)}. It is on this basis that thermodynamics and dynamics are separated and rely upon different frameworks and sets of hypotheses: thermodynamics use the ice thickness distribution \citep{thorndike_1975} and the mushy-layer \citep{worster_1992} frameworks, whereas dynamics assume continuum mechanics \citep[e.g.,][]{lepp _ranta_2011}. Thermodynamics and dynamics interact by two means: first, advection impacts state variables; second, the horizontal momentum equation depends, among other things, on the ice state.30 Because sea ice is much wider -- $\mathcal{O}$(100-1000 km) -- than thick -- $\mathcal{O}$(1 m) -- ice drift can be considered as purely horizontal: vertical motions around the hydrostatic equilibrium position are negligible. The same scaling argument justifies the assumption that heat exchanges are purely vertical\footnote{The latter assumption is probably less valid, because the horizontal scales of temperature variations are $\mathcal{O}$(10-100 m)}. It is on this basis that thermodynamics and dynamics are separated and rely upon different frameworks and sets of hypotheses: thermodynamics use the ice thickness distribution \citep{thorndike_1975} and the mushy-layer \citep{worster_1992} frameworks, whereas dynamics assume continuum mechanics \citep[e.g.,][]{lepparanta_2011}. Thermodynamics and dynamics interact by two means: first, advection impacts state variables; second, the horizontal momentum equation depends, among other things, on the ice state. 31 31 32 32 \subsection{Subgrid scale variations} … … 70 70 & Description & Value & Units & Ref \\ \hline 71 71 $c_i$ (cpic) & Pure ice specific heat & 2067 & J/kg/K & ? \\ 72 $c_w$ (rcp) & Seawater specific heat & 3991 & J/kg/K & \cite{ TEOS_2010} \\72 $c_w$ (rcp) & Seawater specific heat & 3991 & J/kg/K & \cite{teos-10_2010} \\ 73 73 $L$ (lfus) & Latent heat of fusion (0$^\circ$C) & 334000 & J/kg/K & \cite{bitz_1999} \\ 74 74 $\rho_i$ (rhoic) & Sea ice density & 917 & kg/m$^3$ & \cite{bitz_1999} \\ … … 154 154 \subsection{Dynamic formulation} 155 155 156 The formulation of ice dynamics is based on the continuum approach. The latter holds provided the drift ice particles are much larger than single ice floes, and much smaller than typical gradient scales. This compromise is rarely achieved in practice \citep{lepp _ranta_2011}. Yet the continuum approach generates a convenient momentum equation for the horizontal ice velocity vector $\mathbf{u}=(u,v)$, which can be solved with classical numerical methods (here, finite differences on the NEMO C-grid). The most important term in the momentum equation is internal stress. We follow the viscous-plastic (VP) rheological framework \citep{hibler_1979}, assuming that sea ice has no tensile strength but responds to compressive and shear deformations in a plastic way. In practice, the elastic-viscous-plastic (EVP) technique of \citep{bouillon_2013} is used, more convient numerically than VP. It is well accepted that the VP rheology and its relatives are the minimum complexity to get reasonable ice drift patterns \citep{kreyscher_2000}, but fail at generating the observed deformation patterns \citep{girard_2009}. This is a long-lasting problem: what is the ideal rheological model for sea ice and how it should be applied are still being debated \citep[see, e.g.][]{weiss_2013}.156 The formulation of ice dynamics is based on the continuum approach. The latter holds provided the drift ice particles are much larger than single ice floes, and much smaller than typical gradient scales. This compromise is rarely achieved in practice \citep{lepparanta_2011}. Yet the continuum approach generates a convenient momentum equation for the horizontal ice velocity vector $\mathbf{u}=(u,v)$, which can be solved with classical numerical methods (here, finite differences on the NEMO C-grid). The most important term in the momentum equation is internal stress. We follow the viscous-plastic (VP) rheological framework \citep{hibler_1979}, assuming that sea ice has no tensile strength but responds to compressive and shear deformations in a plastic way. In practice, the elastic-viscous-plastic (EVP) technique of \citep{bouillon_2013} is used, more convient numerically than VP. It is well accepted that the VP rheology and its relatives are the minimum complexity to get reasonable ice drift patterns \citep{kreyscher_2000}, but fail at generating the observed deformation patterns \citep{girard_2009}. This is a long-lasting problem: what is the ideal rheological model for sea ice and how it should be applied are still being debated \citep[see, e.g.][]{weiss_2013}. 157 157 158 158 %------------------------------------------------------------------------------------------------------------------------- … … 296 296 $C$ (rn\_crhg) & ice strength concentration param. & 20 & - & \citep{hibler_1979} \\ 297 297 $H^*$ (rn\_hstar) & maximum ridged ice thickness param. & 25 & m & \citep{lipscomb_2007} \\ 298 $p$ (rn\_por\_rdg) & porosity of new ridges & 0.3 & - & \citep{lepp _ranta_1995} \\298 $p$ (rn\_por\_rdg) & porosity of new ridges & 0.3 & - & \citep{lepparanta_1995} \\ 299 299 $amax$ (rn\_amax) & maximum ice concentration & 0.999 & - & -\\ 300 300 $h_0$ (rn\_hnewice) & thickness of newly formed ice & 0.1 & m & - \\ … … 313 313 Transport connects the horizontal velocity fields and the rest of the ice properties. LIM assumes that the ice properties in the different thickness categories are transported at the same velocity. The scheme of \cite{prather_1986}, based on the conservation of 0, 1$^{st}$ and 2$^{nd}$ order moments in $x-$ and $y-$directions, is used, with some numerical diffusion if desired. Whereas this scheme is accurate, nearly conservative, it is also quite expensive since, for each advected field, five moments need to be advected, which proves CPU consuming, in particular when multiple categories are used. Other solutions are currently explored. 314 314 315 The dissipation of energy associated with plastic failure under convergence and shear is accomplished by rafting (overriding of two ice plates) and ridging (breaking of an ice plate and subsequent piling of the broken ice blocks into pressure ridges). Thin ice preferentially rafts whereas thick ice preferentially ridges \citep{tuhkuri_2002}. Because observations of these processes are limited, their representation in LIM is rather heuristic. The amount of ice that rafts/ridges depends on the strain rate tensor invariants (shear and divergence) as in \citep{flato_1995}, while the ice categories involved are determined by a participation function favouring thin ice \citep{lipscomb_2007}. The thickness of ice being deformed ($h'$) determines whether ice rafts ($h'<$ 0.75 m) or ridges ($h'>$ 0.75 m), following \cite{haapala_2000}. The deformed ice thickness is $2h'$ after rafting, and is distributed between $2h'$ and $2 \sqrt{H^*h'}$ after ridging, where $H^* = 25$ m \citep{lipscomb_2007}. Newly ridged ice is highly porous, effectively trapping seawater. To represent this, a prescribed volume fraction (30\%) of newly ridged ice \citep{lepp _ranta_1995} incorporates mass, salt and heat are extracted from the ocean. Hence, in contrast with other models, the net thermodynamic ice production during convergence is not zero in LIM, since mass is added to sea ice during ridging. Consequently, simulated new ridges have high temperature and salinity as observed \citep{h_yland_2002}. A fraction of snow (50 \%) falls into the ocean during deformation.315 The dissipation of energy associated with plastic failure under convergence and shear is accomplished by rafting (overriding of two ice plates) and ridging (breaking of an ice plate and subsequent piling of the broken ice blocks into pressure ridges). Thin ice preferentially rafts whereas thick ice preferentially ridges \citep{tuhkuri_2002}. Because observations of these processes are limited, their representation in LIM is rather heuristic. The amount of ice that rafts/ridges depends on the strain rate tensor invariants (shear and divergence) as in \citep{flato_1995}, while the ice categories involved are determined by a participation function favouring thin ice \citep{lipscomb_2007}. The thickness of ice being deformed ($h'$) determines whether ice rafts ($h'<$ 0.75 m) or ridges ($h'>$ 0.75 m), following \cite{haapala_2000}. The deformed ice thickness is $2h'$ after rafting, and is distributed between $2h'$ and $2 \sqrt{H^*h'}$ after ridging, where $H^* = 25$ m \citep{lipscomb_2007}. Newly ridged ice is highly porous, effectively trapping seawater. To represent this, a prescribed volume fraction (30\%) of newly ridged ice \citep{lepparanta_1995} incorporates mass, salt and heat are extracted from the ocean. Hence, in contrast with other models, the net thermodynamic ice production during convergence is not zero in LIM, since mass is added to sea ice during ridging. Consequently, simulated new ridges have high temperature and salinity as observed \citep{hoyland_2002}. A fraction of snow (50 \%) falls into the ocean during deformation. 316 316 317 317 \section{Ice thermodynamics} -
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r11031 r11263 70 70 \textbf{Rafting} is the piling of two ice sheets on top of each other. Rafting doubles the participating ice thickness and is a volume-conserving process. \cite{babko_2002} concluded that rafting plays a significant role during initial ice growth in fall, therefore we included it into the model. 71 71 72 \textbf{Ridging} is the piling of a series of broken ice blocks into pressure ridges. Ridging redistributes participating ice on a various range of thicknesses. Ridging does not conserve ice volume, as pressure ridges are porous. Therefore, the volume of ridged ice is larger than the volume of new ice being ridged. In the model, newly ridged is has a prescribed porosity $p=30\%$ (\textit{ridge\_por} in \textit{namelist\_ice}), following observations \citep{lepp _ranta_1995,h_yland_2002}. The importance of ridging is now since the early works of \citep{thorndike_1975}.72 \textbf{Ridging} is the piling of a series of broken ice blocks into pressure ridges. Ridging redistributes participating ice on a various range of thicknesses. Ridging does not conserve ice volume, as pressure ridges are porous. Therefore, the volume of ridged ice is larger than the volume of new ice being ridged. In the model, newly ridged is has a prescribed porosity $p=30\%$ (\textit{ridge\_por} in \textit{namelist\_ice}), following observations \citep{lepparanta_1995,hoyland_2002}. The importance of ridging is now since the early works of \citep{thorndike_1975}. 73 73 74 74 The deformation modes are formulated using \textbf{participation} and \textbf{transfer} functions with specific contributions from ridging and rafting: … … 115 115 \label{eq:nri} 116 116 \end{equation} 117 The redistributor $\gamma(h',h)$ specifies how area of thickness $h'$ is redistributed on area of thickness $h$. We follow \citep{hibler_1980} who constructed a rule, based on observations, that forces all ice participating in ridging with thickness $h'$ to be linearly distributed between ice that is between $2h'$ and $2\sqrt{H^*h'}$ thick, where $H^\star=100$ m (\textit{Hstar} in \textit{namelist\_ice}). This in turn determines how to construct the ice volume redistribution function $\Psi^v$. Volumes equal to participating area times thickness are removed from thin ice. They are redistributed following Hibler's rule. The factor $(1+p)$ accounts for initial ridge porosity $p$ (\textit{ridge\_por} in \textit{namelist\_ice}, defined as the fractional volume of seawater initially included into ridges. In many previous models, the initial ridge porosity has been assumed to be 0, which is not the case in reality since newly formed ridges are porous, as indicated by in-situ observations \citep{lepp _ranta_1995,h_yland_2002}. In other words, LIM3 creates a higher volume of ridged ice with the same participating ice.117 The redistributor $\gamma(h',h)$ specifies how area of thickness $h'$ is redistributed on area of thickness $h$. We follow \citep{hibler_1980} who constructed a rule, based on observations, that forces all ice participating in ridging with thickness $h'$ to be linearly distributed between ice that is between $2h'$ and $2\sqrt{H^*h'}$ thick, where $H^\star=100$ m (\textit{Hstar} in \textit{namelist\_ice}). This in turn determines how to construct the ice volume redistribution function $\Psi^v$. Volumes equal to participating area times thickness are removed from thin ice. They are redistributed following Hibler's rule. The factor $(1+p)$ accounts for initial ridge porosity $p$ (\textit{ridge\_por} in \textit{namelist\_ice}, defined as the fractional volume of seawater initially included into ridges. In many previous models, the initial ridge porosity has been assumed to be 0, which is not the case in reality since newly formed ridges are porous, as indicated by in-situ observations \citep{lepparanta_1995,hoyland_2002}. In other words, LIM3 creates a higher volume of ridged ice with the same participating ice. 118 118 119 119 For the numerical computation of the integrals, we have to compute several temporary values: … … 152 152 \section{Mechanical redistribution for other global ice variables} 153 153 154 The other global ice state variables redistribution functions $\Psi^X$ are computed based on $\Psi^g$ for the ice age content and on $\Psi^{v^i}$ for the remainder (ice enthalpy and salt content, snow volume and enthalpy). The general principles behind this derivation are described in Appendix A of \cite{bitz_2001}. A fraction $f_s=0.5$ (\textit{fsnowrdg} and \textit{fsnowrft} in \textit{namelist\_ice}) of the snow volume and enthalpy is assumed to be lost during ridging and rafting and transferred to the ocean. The contribution of the seawater trapped into the porous ridges is included in the computation of the redistribution of ice enthalpy and salt content (i.e., $\Psi^{e^i}$ and $\Psi^{M^s}$). During this computation, seawater is supposed to be in thermal equilibrium with the surrounding ice blocks. Ridged ice desalination induces an implicit decrease in internal brine volume, and heat supply to the ocean, which accounts for ridge consolidation as described by \cite{h _yland_2002}. The inclusion of seawater in ridges does not imply any net change in ocean salinity. The energy used to cool down the seawater trapped in porous ridges until the seawater freezing point is rejected into the ocean.154 The other global ice state variables redistribution functions $\Psi^X$ are computed based on $\Psi^g$ for the ice age content and on $\Psi^{v^i}$ for the remainder (ice enthalpy and salt content, snow volume and enthalpy). The general principles behind this derivation are described in Appendix A of \cite{bitz_2001}. A fraction $f_s=0.5$ (\textit{fsnowrdg} and \textit{fsnowrft} in \textit{namelist\_ice}) of the snow volume and enthalpy is assumed to be lost during ridging and rafting and transferred to the ocean. The contribution of the seawater trapped into the porous ridges is included in the computation of the redistribution of ice enthalpy and salt content (i.e., $\Psi^{e^i}$ and $\Psi^{M^s}$). During this computation, seawater is supposed to be in thermal equilibrium with the surrounding ice blocks. Ridged ice desalination induces an implicit decrease in internal brine volume, and heat supply to the ocean, which accounts for ridge consolidation as described by \cite{hoyland_2002}. The inclusion of seawater in ridges does not imply any net change in ocean salinity. The energy used to cool down the seawater trapped in porous ridges until the seawater freezing point is rejected into the ocean. 155 155 156 156 \end{document} -
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r11031 r11263 15 15 16 16 % Limitations & scope 17 %There are limitations to the applicability of models such as SI$^3$. The continuum approach is not invalid for grid cell size above at least 1 km, below which sea ice particles may include just a few floes, which is not sufficient \citep{lepp _ranta_2011}. Second, one must remember that our current knowledge of sea ice is not as complete as for the ocean: there are no fundamental equations such as Navier Stokes equations for sea ice. Besides, important features and processes span widely different scales, such as brine inclusions (1 $\mu$m-1 mm) \citep{perovich_1996}, horizontal thickness variations (1 m-100 km) \citep{percival_2008}, deformation and fracturing (10 m-1000 km) \citep{marsan_2004}. These impose complicated and often subjective subgrid-scale treatments. All in all, there is more empirism in sea ice models than in ocean models.17 %There are limitations to the applicability of models such as SI$^3$. The continuum approach is not invalid for grid cell size above at least 1 km, below which sea ice particles may include just a few floes, which is not sufficient \citep{lepparanta_2011}. Second, one must remember that our current knowledge of sea ice is not as complete as for the ocean: there are no fundamental equations such as Navier Stokes equations for sea ice. Besides, important features and processes span widely different scales, such as brine inclusions (1 $\mu$m-1 mm) \citep{perovich_1996}, horizontal thickness variations (1 m-100 km) \citep{percival_2008}, deformation and fracturing (10 m-1000 km) \citep{marsan_2004}. These impose complicated and often subjective subgrid-scale treatments. All in all, there is more empirism in sea ice models than in ocean models. 18 18 19 19 In order to handle all the subsequent required subjective choices, we applied the following guidelines or principles: -
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r11032 r11263 26 26 \end{equation} 27 27 28 where expressions of $D^{lC}$ and $D^{vC}$ depend on the choice for the lateral and vertical subgrid scale parameterizations, see equations 5.10 and 5.11 in \citep{ Madec_Bk2008}28 where expressions of $D^{lC}$ and $D^{vC}$ depend on the choice for the lateral and vertical subgrid scale parameterizations, see equations 5.10 and 5.11 in \citep{nemo_manual} 29 29 30 30 {S(C)} , the first term on the right hand side of \ref{Eq_tracer}; is the SMS - Source Minus Sink - inherent to the tracer. In the case of biological tracer such as phytoplankton, {S(C)} is the balance between phytoplankton growth and its decay through mortality and grazing. In the case of a tracer comprising carbon, {S(C)} accounts for gas exchange, river discharge, flux to the sediments, gravitational sinking and other biological processes. In the case of a radioactive tracer, {S(C)} is simply loss due to radioactive decay. … … 61 61 \item \textbf{AGE} : Water age tracking 62 62 \item \textbf{MY\_TRC} : Template for creation of new modules and external BGC models coupling 63 \item \textbf{PISCES} : Built in BGC model. See \citep{ Aumont_al_2015} for a throughout description.63 \item \textbf{PISCES} : Built in BGC model. See \citep{aumont_2015} for a throughout description. 64 64 \end{itemize} 65 65 % ---------------------------------------------------------- … … 73 73 \nlst{namtrc_adv} 74 74 %------------------------------------------------------------------------------------------------------------- 75 The advection schemes used for the passive tracers are the same than the ones for $T$ and $S$ and described in section 5.1 of \citep{ Madec_Bk2008}. The choice of an advection scheme can be selected independently and can differ from the ones used for active tracers. This choice is made in the \textit{namtrc\_adv} namelist, by setting to \textit{true} one and only one of the logicals \textit{ln\_trcadv\_xxx}, the same way of what is done for dynamics.75 The advection schemes used for the passive tracers are the same than the ones for $T$ and $S$ and described in section 5.1 of \citep{nemo_manual}. The choice of an advection scheme can be selected independently and can differ from the ones used for active tracers. This choice is made in the \textit{namtrc\_adv} namelist, by setting to \textit{true} one and only one of the logicals \textit{ln\_trcadv\_xxx}, the same way of what is done for dynamics. 76 76 cen2, MUSCL2, and UBS are not \textit{positive} schemes meaning that negative values can appear in an initially strictly positive tracer field which is advected, implying that false extrema are permitted. Their use is not recommended on passive tracers 77 77 … … 80 80 \nlst{namtrc_ldf} 81 81 %------------------------------------------------------------------------------------------------------------- 82 In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set in the \ngn{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{ Madec_Bk2008}.82 In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set in the \ngn{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{nemo_manual}. 83 83 84 84 … … 145 145 146 146 147 This implementation was first used in the CORE-II intercomparison runs described e.g.\ in \citet{ Danabasoglu_al_2014}.147 This implementation was first used in the CORE-II intercomparison runs described e.g.\ in \citet{danabasoglu_2014}. 148 148 149 149 \subsection{Inert carbons tracer} … … 178 178 Measuring the dissolved concentrations of the gases -- as well as the mixing ratios between them -- shows circulation pathways within the ocean as well as water mass ages (i.e. the time since last contact with the 179 179 atmosphere). This feature of the gases has made them valuable across a wide range of oceanographic problems. One use lies in ocean modelling, where they can be used to evaluate the realism of the circulation and 180 ventilation of models, key for understanding the behaviour of wider modelled marine biogeochemistry (e.g. \citep{ Dutay_al_2002,Palmieri_2015}). \\180 ventilation of models, key for understanding the behaviour of wider modelled marine biogeochemistry (e.g. \citep{dutay_2002,palmieri_2015}). \\ 181 181 182 182 Modelling these gases (henceforth CFCs) in NEMO is done within the passive tracer transport module, TOP, using the conservation state equation \ref{Eq_tracer} … … 187 187 stable within the ocean, we assume that there are no sinks (i.e. no loss processes) within the ocean interior. 188 188 Consequently, the sinks-minus-sources term for CFCs consists only of their air-sea fluxes, $F_{cfc}$, as 189 described in the Ocean Model Inter-comparison Project (OMIP) protocol \citep{ Orr_al_2017}:189 described in the Ocean Model Inter-comparison Project (OMIP) protocol \citep{orr_2017}: 190 190 191 191 % Because CFCs being stable in the ocean, we consider that there is no CFCs sink. … … 213 213 Where $Sol$ is the gas solubility in mol~m$^{-3}$~pptv$^{-1}$, as defined in Equation \ref{equ_Sol_CFC}; 214 214 and $P_{cfc}$ is the atmosphere concentration of the CFC (in parts per trillion by volume, pptv). 215 This latter concentration is provided to the model by the historical time-series of \citet{ Bullister_2015}.215 This latter concentration is provided to the model by the historical time-series of \citet{bullister_2017}. 216 216 This includes bulk atmospheric concentrations of the CFCs for both hemispheres -- this is necessary because of 217 217 the geographical asymmetry in the production and release of CFCs to the atmosphere. … … 220 220 221 221 The piston velocity $K_{w}$ is a function of 10~m wind speed (in m~s$^{-1}$) and sea surface temperature, 222 $T$ (in $^{\circ}$C), and is calculated here following \citet{ Wanninkhof_1992}:222 $T$ (in $^{\circ}$C), and is calculated here following \citet{wanninkhof_1992}: 223 223 224 224 \begin{eqnarray} … … 229 229 Where $X_{conv}$ = $\frac{0.01}{3600}$, a conversion factor that changes the piston velocity 230 230 from cm~h$^{-1}$ to m~s$^{-1}$; 231 $a$ is a constant re-estimated by \citet{ Wanninkhof_2014} to 0.251 (in $\frac{cm~h^{-1}}{(m~s^{-1})^{2}}$);231 $a$ is a constant re-estimated by \citet{wanninkhof_2014} to 0.251 (in $\frac{cm~h^{-1}}{(m~s^{-1})^{2}}$); 232 232 and $u$ is the 10~m wind speed in m~s$^{-1}$ from either an atmosphere model or reanalysis atmospheric forcing. 233 $Sc$ is the Schmidt number, and is calculated as follow, using coefficients from \citet{ Wanninkhof_2014} (see Table \ref{tab_Sc}).233 $Sc$ is the Schmidt number, and is calculated as follow, using coefficients from \citet{wanninkhof_2014} (see Table \ref{tab_Sc}). 234 234 235 235 \begin{eqnarray} … … 240 240 The solubility, $Sol$, used in Equation \ref{equ_C_sat} is calculated in mol~l$^{-1}$~atm$^{-1}$, 241 241 and is specific for each gas. 242 It has been experimentally estimated by \citet{ Warner_Weiss_1985} as a function of temperature242 It has been experimentally estimated by \citet{warner_1985} as a function of temperature 243 243 and salinity: 244 244 … … 363 363 where $\Rq_{\textrm{ref}}$ is a reference ratio. For the purpose of ocean ventilation studies $\Rq_{\textrm{ref}}$ is set to one. 364 364 365 Here we adopt the approach of \cite{ Fiadeiro_1982} and \cite{Toggweiler_al_1989a,Toggweiler_al_1989b} in which the ratio $\Rq$ is transported rather than the individual concentrations C and $\cq$.366 This approach calls for a strong assumption, i.e., that of a homogeneous and constant dissolved inorganic carbon (DIC) field \citep{ Toggweiler_al_1989a,Mouchet_2013}. While in terms of367 oceanic $\Dcq$, it yields similar results to approaches involving carbonate chemistry, it underestimates the bomb radiocarbon inventory because it assumes a constant air-sea $\cd$ disequilibrium (Mouchet, 2013). Yet, field reconstructions of the ocean bomb $\cq$ inventory are also biased low \citep{ Naegler_2009} since they assume that the anthropogenic perturbation did not affect ocean DIC since the pre-bomb epoch. For these reasons, bomb $\cq$ inventories obtained with the present method are directly comparable to reconstructions based on field measurements.368 369 This simplified approach also neglects the effects of fractionation (e.g., air-sea exchange) and of biological processes. Previous studies by \cite{ Bacastow_MaierReimer_1990} and \cite{Joos_al_1997} resulted in nearly identical $\Dcq$ distributions among experiments considering biology or not.370 Since observed $\Rq$ ratios are corrected for the isotopic fractionation when converted to the standard $\Dcq$ notation \citep{ Stuiver_Polach_1977} the model results are directly comparable to observations.365 Here we adopt the approach of \cite{fiadeiro_1982} and \cite{toggweiler_1989a,toggweiler_1989b} in which the ratio $\Rq$ is transported rather than the individual concentrations C and $\cq$. 366 This approach calls for a strong assumption, i.e., that of a homogeneous and constant dissolved inorganic carbon (DIC) field \citep{toggweiler_1989a,mouchet_2013}. While in terms of 367 oceanic $\Dcq$, it yields similar results to approaches involving carbonate chemistry, it underestimates the bomb radiocarbon inventory because it assumes a constant air-sea $\cd$ disequilibrium (Mouchet, 2013). Yet, field reconstructions of the ocean bomb $\cq$ inventory are also biased low \citep{naegler_2009} since they assume that the anthropogenic perturbation did not affect ocean DIC since the pre-bomb epoch. For these reasons, bomb $\cq$ inventories obtained with the present method are directly comparable to reconstructions based on field measurements. 368 369 This simplified approach also neglects the effects of fractionation (e.g., air-sea exchange) and of biological processes. Previous studies by \cite{bacastow_1990} and \cite{joos_1997} resulted in nearly identical $\Dcq$ distributions among experiments considering biology or not. 370 Since observed $\Rq$ ratios are corrected for the isotopic fractionation when converted to the standard $\Dcq$ notation \citep{stuiver_1977} the model results are directly comparable to observations. 371 371 372 372 Therefore the simplified approach is justified for the purpose of assessing the circulation and ventilation of OGCMs. … … 378 378 where $\lambda$ is the radiocarbon decay rate, ${\mathbf{u}}$ the 3-D velocity field, and $\mathbf{K}$ the diffusivity tensor. 379 379 380 At the air-sea interface a Robin boundary condition \citep{ Haine_2006} is applied to \eqref{eq:quick}, i.e., the flux380 At the air-sea interface a Robin boundary condition \citep{haine_2006} is applied to \eqref{eq:quick}, i.e., the flux 381 381 through the interface is proportional to the difference in the ratios between 382 382 the ocean and the atmosphere … … 391 391 392 392 393 The $\cd$ transfer velocity is based on the empirical formulation of \cite{ Wanninkhof_1992} with chemical enhancement \citep{Wanninkhof_Knox_1996,Wanninkhof_2014}. The original formulation is modified to account for the reduction of the air-sea exchange rate in the presence of sea ice. Hence393 The $\cd$ transfer velocity is based on the empirical formulation of \cite{wanninkhof_1992} with chemical enhancement \citep{wanninkhof_1996,wanninkhof_2014}. The original formulation is modified to account for the reduction of the air-sea exchange rate in the presence of sea ice. Hence 394 394 \begin{equation} 395 395 \kappa_\cd=\left( K_W\,\mathrm{w}^2 + b \right)\, (1-f_\mathrm{ice})\,\sqrt{660/Sc}, \label{eq:wanc14} … … 397 397 with $\mathrm{w}$ the wind magnitude, $f_\mathrm{ice}$ the fractional ice cover, and $Sc$ the Schmidt number. 398 398 $K_W$ in \eqref{eq:wanc14} is an empirical coefficient with dimension of an inverse velocity. 399 The chemical enhancement term $b$ is represented as a function of temperature $T$ \citep{ Wanninkhof_1992}399 The chemical enhancement term $b$ is represented as a function of temperature $T$ \citep{wanninkhof_1992} 400 400 \begin{equation} 401 401 b=2.5 ( 0.5246 + 0.016256 T+ 0.00049946 * T^2 ). \label{eq:wanchem} … … 413 413 \label{sec:param} 414 414 % 415 The radiocarbon decay rate (\CODE{rlam14}; in \texttt{trcnam\_c14} module) is set to $\lambda=(1/8267)$ yr$^{-1}$ \citep{ Stuiver_Polach_1977}, which corresponds to a half-life of 5730 yr.\\[1pt]416 % 417 The Schmidt number $Sc$, Eq. \eqref{eq:wanc14}, is calculated with the help of the formulation of \cite{ Wanninkhof_2014}. The $\cd$ solubility $K_0$ in \eqref{eq:Rspeed} is taken from \cite{Weiss_1974}. $K_0$ and $Sc$ are computed with the OGCM temperature and salinity fields (\texttt{trcsms\_c14} module).\\[1pt]415 The radiocarbon decay rate (\CODE{rlam14}; in \texttt{trcnam\_c14} module) is set to $\lambda=(1/8267)$ yr$^{-1}$ \citep{stuiver_1977}, which corresponds to a half-life of 5730 yr.\\[1pt] 416 % 417 The Schmidt number $Sc$, Eq. \eqref{eq:wanc14}, is calculated with the help of the formulation of \cite{wanninkhof_2014}. The $\cd$ solubility $K_0$ in \eqref{eq:Rspeed} is taken from \cite{weiss_1974}. $K_0$ and $Sc$ are computed with the OGCM temperature and salinity fields (\texttt{trcsms\_c14} module).\\[1pt] 418 418 % 419 419 The following parameters intervening in the air-sea exchange rate are set in \texttt{namelist\_c14}: 420 420 \begin{itemize} 421 \item The reference DIC concentration $\overline{\Ct}$ (\CODE{xdicsur}) intervening in \eqref{eq:Rspeed} is classically set to 2 mol m$^{-3}$ \citep{ Toggweiler_al_1989a,Orr_al_2001,Butzin_al_2005}.422 % 423 \item The value of the empirical coefficient $K_W$ (\CODE{xkwind}) in \eqref{eq:wanc14} depends on the wind field and on the model upper ocean mixing rate \citep{ Toggweiler_al_1989a,Wanninkhof_1992,Naegler_2009,Wanninkhof_2014}.424 It should be adjusted so that the globally averaged $\cd$ piston velocity is $\kappa_\cd = 16.5\pm 3.2$ cm/h \citep{ Naegler_2009}.421 \item The reference DIC concentration $\overline{\Ct}$ (\CODE{xdicsur}) intervening in \eqref{eq:Rspeed} is classically set to 2 mol m$^{-3}$ \citep{toggweiler_1989a,orr_2001,butzin_2005}. 422 % 423 \item The value of the empirical coefficient $K_W$ (\CODE{xkwind}) in \eqref{eq:wanc14} depends on the wind field and on the model upper ocean mixing rate \citep{toggweiler_1989a,wanninkhof_1992,naegler_2009,wanninkhof_2014}. 424 It should be adjusted so that the globally averaged $\cd$ piston velocity is $\kappa_\cd = 16.5\pm 3.2$ cm/h \citep{naegler_2009}. 425 425 %The sensitivity to this parametrization is discussed in section \ref{sec:result}. 426 426 % … … 440 440 \CODE{kc14typ}=0 441 441 442 Unless otherwise specified in \texttt{namelist\_c14}, the atmospheric $\Rq_a$ (\CODE{rc14at}) is set to one, the atmospheric $\cd$ (\CODE{pco2at}) to 280 ppm, and the ocean $\Rq$ is initialized with \CODE{rc14init=0.85}, i.e., $\Dcq=$-150\textperthousand \cite[typical for deep-ocean, Fig 6 in][]{ Key_al_2004}.443 444 Equilibrium experiment should last until 98\% of the ocean volume exhibit a drift of less than 0.001\textperthousand/year \citep{ Orr_al_2000}; this is usually achieved after few kyr (Fig. \ref{fig:drift}).442 Unless otherwise specified in \texttt{namelist\_c14}, the atmospheric $\Rq_a$ (\CODE{rc14at}) is set to one, the atmospheric $\cd$ (\CODE{pco2at}) to 280 ppm, and the ocean $\Rq$ is initialized with \CODE{rc14init=0.85}, i.e., $\Dcq=$-150\textperthousand \cite[typical for deep-ocean, Fig 6 in][]{key_2004}. 443 444 Equilibrium experiment should last until 98\% of the ocean volume exhibit a drift of less than 0.001\textperthousand/year \citep{orr_2000}; this is usually achieved after few kyr (Fig. \ref{fig:drift}). 445 445 % 446 446 \begin{figure}[!h] … … 469 469 470 470 The model is integrated from a given initial date following the observed records provided from 1765 AD on ( Fig. \ref{fig:bomb}). 471 The file \texttt{atmc14.dat} \cite[][\& I. Levin, personal comm.]{ Enting_al_1994} provides atmospheric $\Dcq$ for three latitudinal bands: 90S-20S, 20S-20N \& 20N-90N.472 Atmospheric $\cd$ in the file \texttt{splco2.dat} is obtained from a spline fit through ice core data and direct atmospheric measurements \cite[][\& J. Orr, personal comm.]{ Orr_al_2000}.471 The file \texttt{atmc14.dat} \cite[][\& I. Levin, personal comm.]{enting_1994} provides atmospheric $\Dcq$ for three latitudinal bands: 90S-20S, 20S-20N \& 20N-90N. 472 Atmospheric $\cd$ in the file \texttt{splco2.dat} is obtained from a spline fit through ice core data and direct atmospheric measurements \cite[][\& J. Orr, personal comm.]{orr_2000}. 473 473 Dates in these forcing files are expressed as yr AD. 474 474 … … 496 496 Atmospheric $\Rq_a$ and $\cd$ are prescribed from forcing files. The ocean $\Rq$ is initialized with the value attributed to \CODE{rc14init} in \texttt{namelist\_c14}. 497 497 498 The file \texttt{intcal13.14c} \citep{ Reimer_al_2013} contains atmospheric $\Dcq$ from 0 to 50 kyr cal BP\footnote{cal BP: number of years before 1950 AD}.499 The $\cd$ forcing is provided in file \texttt{ByrdEdcCO2.txt}. The content of this file is based on the high resolution record from EPICA Dome C \citep{ Monnin_al_2004} for the Holocene and the Transition, and on Byrd Ice Core CO2 Data for 20--90 kyr BP \citep{Ahn_Brook_2008}. These atmospheric values are reproduced in Fig. \ref{fig:paleo}. Dates in these files are expressed as yr BP.498 The file \texttt{intcal13.14c} \citep{reimer_2013} contains atmospheric $\Dcq$ from 0 to 50 kyr cal BP\footnote{cal BP: number of years before 1950 AD}. 499 The $\cd$ forcing is provided in file \texttt{ByrdEdcCO2.txt}. The content of this file is based on the high resolution record from EPICA Dome C \citep{monnin_2004} for the Holocene and the Transition, and on Byrd Ice Core CO2 Data for 20--90 kyr BP \citep{ahn_2008}. These atmospheric values are reproduced in Fig. \ref{fig:paleo}. Dates in these files are expressed as yr BP. 500 500 501 501 To ensure that the atmospheric forcing is applied properly as well as that output files contain consistent dates and inventories the experiment should be set up carefully. … … 539 539 The radiocarbon age is computed as $(-1/\lambda) \ln{ \left( \Rq \right)}$, with zero age corresponding to $\Rq=1$. 540 540 541 The reservoir age is the age difference between the ocean uppermost layer and the atmosphere. It is usually reported as conventional radiocarbon age; i.e., computed by means of the Libby radiocarbon mean life \cite[8033 yr;][]{ Stuiver_Polach_1977}541 The reservoir age is the age difference between the ocean uppermost layer and the atmosphere. It is usually reported as conventional radiocarbon age; i.e., computed by means of the Libby radiocarbon mean life \cite[8033 yr;][]{stuiver_1977} 542 542 \begin{align} 543 543 {^{14}\tau_\mathrm{c}}= -8033 \; \ln \left(1 + \frac{\Dcq}{10^3}\right), \label{eq:convage} … … 549 549 N_A \Rq_\mathrm{oxa} \overline{\Ct} \left( \int_\Omega \Rq d\Omega \right) /10^{26}, \label{eq:inv} 550 550 \end{equation} 551 where $N_A$ is the Avogadro's number ($N_A=6.022\times10^{23}$ at/mol), $\Rq_\mathrm{oxa}$ is the oxalic acid radiocarbon standard \cite[$\Rq_\mathrm{oxa}=1.176\times10^{-12}$;][]{ Stuiver_Polach_1977}, and $\Omega$ is the ocean volume. Bomb $\cq$ inventories are traditionally reported in units of $10^{26}$ atoms, hence the denominator in \eqref{eq:inv}.551 where $N_A$ is the Avogadro's number ($N_A=6.022\times10^{23}$ at/mol), $\Rq_\mathrm{oxa}$ is the oxalic acid radiocarbon standard \cite[$\Rq_\mathrm{oxa}=1.176\times10^{-12}$;][]{stuiver_1977}, and $\Omega$ is the ocean volume. Bomb $\cq$ inventories are traditionally reported in units of $10^{26}$ atoms, hence the denominator in \eqref{eq:inv}. 552 552 553 553 All transformations from second to year, and inversely, are performed with the help of the physical constant \CODE{rsiyea} the sideral year length expressed in seconds\footnote{The variable (\CODE{nyear\_len}) which reports the length in days of the previous/current/future year (see \textrm{oce\_trc.F90}) is not a constant. }. … … 564 564 Two versions of PISCES are available in NEMO v4.0 : 565 565 566 PISCES-v2, by setting in namelist\_pisces\_ref \np{ln\_p4z} to true, can be seen as one of the many Monod models \citep{ Monod_1942}. It assumes a constant Redfield ratio and phytoplankton growth depends on the external concentration in nutrients. There are twenty-four prognostic variables (tracers) including two phytoplankton compartments (diatoms and nanophytoplankton), two zooplankton size-classes (microzooplankton and mesozooplankton) and a description of the carbonate chemistry. Formulations in PISCES-v2 are based on a mixed Monod/Quota formalism: On one hand, stoichiometry of C/N/P is fixed and growth rate of phytoplankton is limited by the external availability in N, P and Si. On the other hand, the iron and silicium quotas are variable and growth rate of phytoplankton is limited by the internal availability in Fe. Various parameterizations can be activated in PISCES-v2, setting for instance the complexity of iron chemistry or the description of particulate organic materials.567 568 PISCES-QUOTA has been built on the PISCES-v2 model described in \citet{ Aumont_al_2015}. PISCES-QUOTA has thirty-nine prognostic compartments. Phytoplankton growth can be controlled by five modeled limiting nutrients: Nitrate and Ammonium, Phosphate, Silicate and Iron. Five living compartments are represented: Three phytoplankton size classes/groups corresponding to picophytoplankton, nanophytoplankton and diatoms, and two zooplankton size classes which are microzooplankton and mesozooplankton. For phytoplankton, the prognostic variables are the carbon, nitrogen, phosphorus, iron, chlorophyll and silicon biomasses (the latter only for diatoms). This means that the N/C, P/C, Fe/C and Chl/C ratios of both phytoplankton groups as well as the Si/C ratio of diatoms are prognostically predicted by the model. Zooplankton are assumed to be strictly homeostatic \citep[e.g.,][]{Sterner_2002,Woods_Wilson_2013,Meunier_al_2014}. As a consequence, the C/N/P/Fe ratios of these groups are maintained constant and are not allowed to vary. In PISCES, the Redfield ratios C/N/P are set to 122/16/1 \citep{Takahashi_al_1985} and the -O/C ratio is set to 1.34 \citep{Kortzinger_al_2001}. No silicified zooplankton is assumed. The bacterial pool is not yet explicitly modeled.569 570 There are three non-living compartments: Semi-labile dissolved organic matter, small sinking particles, and large sinking particles. As a consequence of the variable stoichiometric ratios of phytoplankton and of the stoichiometric regulation of zooplankton, elemental ratios in organic matter cannot be supposed constant anymore as that was the case in PISCES-v2. Indeed, the nitrogen, phosphorus, iron, silicon and calcite pools of the particles are now all explicitly modeled. The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (''The ballast effect'', \citep{ Honjo_1996,Armstrong_al_2002}). The latter particles are assumed to sink at the same speed as the large organic matter particles. All the non-living compartments experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM.566 PISCES-v2, by setting in namelist\_pisces\_ref \np{ln\_p4z} to true, can be seen as one of the many Monod models \citep{monod_1958}. It assumes a constant Redfield ratio and phytoplankton growth depends on the external concentration in nutrients. There are twenty-four prognostic variables (tracers) including two phytoplankton compartments (diatoms and nanophytoplankton), two zooplankton size-classes (microzooplankton and mesozooplankton) and a description of the carbonate chemistry. Formulations in PISCES-v2 are based on a mixed Monod/Quota formalism: On one hand, stoichiometry of C/N/P is fixed and growth rate of phytoplankton is limited by the external availability in N, P and Si. On the other hand, the iron and silicium quotas are variable and growth rate of phytoplankton is limited by the internal availability in Fe. Various parameterizations can be activated in PISCES-v2, setting for instance the complexity of iron chemistry or the description of particulate organic materials. 567 568 PISCES-QUOTA has been built on the PISCES-v2 model described in \citet{aumont_2015}. PISCES-QUOTA has thirty-nine prognostic compartments. Phytoplankton growth can be controlled by five modeled limiting nutrients: Nitrate and Ammonium, Phosphate, Silicate and Iron. Five living compartments are represented: Three phytoplankton size classes/groups corresponding to picophytoplankton, nanophytoplankton and diatoms, and two zooplankton size classes which are microzooplankton and mesozooplankton. For phytoplankton, the prognostic variables are the carbon, nitrogen, phosphorus, iron, chlorophyll and silicon biomasses (the latter only for diatoms). This means that the N/C, P/C, Fe/C and Chl/C ratios of both phytoplankton groups as well as the Si/C ratio of diatoms are prognostically predicted by the model. Zooplankton are assumed to be strictly homeostatic \citep[e.g.,][]{sterner_2003,woods_2013,meunier_2014}. As a consequence, the C/N/P/Fe ratios of these groups are maintained constant and are not allowed to vary. In PISCES, the Redfield ratios C/N/P are set to 122/16/1 \citep{takahashi_1985} and the -O/C ratio is set to 1.34 \citep{kortzinger_2001}. No silicified zooplankton is assumed. The bacterial pool is not yet explicitly modeled. 569 570 There are three non-living compartments: Semi-labile dissolved organic matter, small sinking particles, and large sinking particles. As a consequence of the variable stoichiometric ratios of phytoplankton and of the stoichiometric regulation of zooplankton, elemental ratios in organic matter cannot be supposed constant anymore as that was the case in PISCES-v2. Indeed, the nitrogen, phosphorus, iron, silicon and calcite pools of the particles are now all explicitly modeled. The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (''The ballast effect'', \citep{honjo_1996,armstrong_2001}). The latter particles are assumed to sink at the same speed as the large organic matter particles. All the non-living compartments experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM. 571 571 572 572 -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/manual_build.sh
r11042 r11263 4 4 ##--------------- 5 5 6 ## latekmk options7 opts='-shell-escape -quiet -pdf'8 9 6 ## Default selection for models 10 7 if [ "$1" = 'all' ]; then 11 8 models='NEMO SI3 TOP' 12 9 elif [ "$1" = '' ]; then 13 10 models='NEMO' 14 11 else 15 12 models=$* 16 13 fi 17 14 … … 24 21 25 22 ## LaTeX installation, find latexmk should be enough 26 [ -z $( which latexmk ) ] && { echo 'latexmk binary is not present => QUIT'; exit 2; } 23 [ -z $( which latexmk ) ] && { echo 'latexmk not installed => QUIT'; exit 2; } 24 25 ## Pygments package for syntax highlighting of source code (namelists & snippets) 26 [ -n "$( ./tools/check_pkg.py pygments )" ] && { echo 'Python pygments is missing => QUIT'; exit 2; } 27 27 28 28 ## Retrieve figures if not already there 29 29 if [ ! -d latex/figures ]; then 30 31 30 printf "Downloading of shared figures and logos\n\n" 31 svn co https://forge.ipsl.jussieu.fr/nemo/svn/utils/figures latex/figures > /dev/null 32 32 fi 33 34 ## Pygments package for syntax highlighting of source code (namelists & snippets)35 [ -n "$( ./tools/check_pkg.py pygments )" ] && { exit 2; }36 33 37 34 … … 40 37 41 38 for model in $models; do 42 43 clean $model; build$model44 printf "\t¤ End of building run\n" 45 printf "\t The export should be available at root\n"46 printf "\t If not check LaTeX log in ./latex/$model/main/${model}_manual.log\n" 39 echo $model 40 clean $model 41 build $model 42 printf "\t¤ End of building run\n" 43 echo 47 44 done 48 45 49 46 exit 0 47 -
NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/tools/shr_func.sh
r11033 r11263 1 1 #!/bin/sh 2 3 4 ## Default options for GNU find (Linux OS)5 find_pre=''; find_suf='-regextype posix-extended'6 7 ## Test OS to tweak the options in find command for working in extended mode everywhere8 [ '$( uname )' = 'Darwin' ] && { find_pre='-E'; find_suf=''; }9 2 10 3 clean() { 11 4 ## Not sure if this step is needed, guess latexmk should be able to detect a change 12 printf "\t¤ Clean previous build\n" 13 14 ## Delete temp files from previous build 15 printf "\t - delete all temporary files (.aux, .bbl, ...)\n" 16 find ${find_pre} latex/$1 ${find_suf} \ 17 -regex ".*\.(aux|bbl|blg|dvi|fdb|fls|idx|ilg|ind|log|maf|mtc|out|pdf|toc)" \ 18 -exec rm {} \; 19 20 ## Remove minted folders 21 printf "\t - remove pygments input hash files (\"_minted\" folders)\n" 22 find latex/$1 -type d -name '_minted*' -exec rm -r {} \; 2> /dev/null 5 printf "\t¤ Clean previous build" 6 find latex/$1/build -mindepth 1 -prune -not -name $1_manual.pyg -exec rm -rf {} \; 23 7 24 8 ## HTML exports … … 31 15 build() { 32 16 printf "\t¤ Generation of the PDF format\n" 33 cd latex/$1/main34 latexmk $opts $1'_manual' 1> /dev/null 35 [ -f $1'_manual'.pdf ] && mv $1'_manual'.pdf ../../.. 36 cd - > /dev/null17 latexmk -r ./latex/global/latexmkrc \ 18 -cd ./latex/$1/main/$1_manual \ 19 1> /dev/null 20 [ -f ./latex/$1/build/$1_manual.pdf ] && mv ./latex/$1/build/$1_manual.pdf . 37 21 echo 38 22 } 23
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