Changeset 11582 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_TRA.tex
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_TRA.tex
r11578 r11582 1 1 \documentclass[../main/NEMO_manual]{subfiles} 2 3 \onlyinsubfile{\makeindex} 2 4 3 5 \begin{document} … … 55 57 56 58 The user has the option of extracting each tendency term on the RHS of the tracer equation for output 57 (\np{ln_tra_trd}{ln\_tra\_trd} or \np {ln_tra_mxl}{ln\_tra\_mxl}\forcode{=.true.}), as described in \autoref{chap:DIA}.59 (\np{ln_tra_trd}{ln\_tra\_trd} or \np[=.true.]{ln_tra_mxl}{ln\_tra\_mxl}), as described in \autoref{chap:DIA}. 58 60 59 61 % ================================================================ … … 85 87 Indeed, it is obtained by using the following equality: $\nabla \cdot (\vect U \, T) = \vect U \cdot \nabla T$ which 86 88 results from the use of the continuity equation, $\partial_t e_3 + e_3 \; \nabla \cdot \vect U = 0$ 87 (which reduces to $\nabla \cdot \vect U = 0$ in linear free surface, \ie\ \np {ln_linssh}{ln\_linssh}\forcode{=.true.}).89 (which reduces to $\nabla \cdot \vect U = 0$ in linear free surface, \ie\ \np[=.true.]{ln_linssh}{ln\_linssh}). 88 90 Therefore it is of paramount importance to design the discrete analogue of the advection tendency so that 89 91 it is consistent with the continuity equation in order to enforce the conservation properties of … … 121 123 \begin{description} 122 124 \item[linear free surface:] 123 (\np {ln_linssh}{ln\_linssh}\forcode{=.true.})125 (\np[=.true.]{ln_linssh}{ln\_linssh}) 124 126 the first level thickness is constant in time: 125 127 the vertical boundary condition is applied at the fixed surface $z = 0$ rather than on … … 129 131 the first level tracer value. 130 132 \item[non-linear free surface:] 131 (\np {ln_linssh}{ln\_linssh}\forcode{=.false.})133 (\np[=.false.]{ln_linssh}{ln\_linssh}) 132 134 convergence/divergence in the first ocean level moves the free surface up/down. 133 135 There is no tracer advection through it so that the advective fluxes through the surface are also zero. … … 190 192 % 2nd order centred scheme 191 193 192 The centred advection scheme (CEN) is used when \np {ln_traadv_cen}{ln\_traadv\_cen}\forcode{=.true.}.194 The centred advection scheme (CEN) is used when \np[=.true.]{ln_traadv_cen}{ln\_traadv\_cen}. 193 195 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by 194 196 setting \np{nn_cen_h}{nn\_cen\_h} and \np{nn_cen_v}{nn\_cen\_v} to $2$ or $4$. … … 222 224 \tau_u^{cen4} = \overline{T - \frac{1}{6} \, \delta_i \Big[ \delta_{i + 1/2}[T] \, \Big]}^{\,i + 1/2} 223 225 \end{equation} 224 In the vertical direction (\np {nn_cen_v}{nn\_cen\_v}\forcode{=4}),226 In the vertical direction (\np[=4]{nn_cen_v}{nn\_cen\_v}), 225 227 a $4^{th}$ COMPACT interpolation has been prefered \citep{demange_phd14}. 226 228 In the COMPACT scheme, both the field and its derivative are interpolated, which leads, after a matrix inversion, … … 255 257 \label{subsec:TRA_adv_tvd} 256 258 257 The Flux Corrected Transport schemes (FCT) is used when \np {ln_traadv_fct}{ln\_traadv\_fct}\forcode{=.true.}.259 The Flux Corrected Transport schemes (FCT) is used when \np[=.true.]{ln_traadv_fct}{ln\_traadv\_fct}. 258 260 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) and vertical direction by 259 261 setting \np{nn_fct_h}{nn\_fct\_h} and \np{nn_fct_v}{nn\_fct\_v} to $2$ or $4$. … … 298 300 \label{subsec:TRA_adv_mus} 299 301 300 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np {ln_traadv_mus}{ln\_traadv\_mus}\forcode{=.true.}.302 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np[=.true.]{ln_traadv_mus}{ln\_traadv\_mus}. 301 303 MUSCL implementation can be found in the \mdl{traadv\_mus} module. 302 304 … … 326 328 This choice ensure the \textit{positive} character of the scheme. 327 329 In addition, fluxes round a grid-point where a runoff is applied can optionally be computed using upstream fluxes 328 (\np {ln_mus_ups}{ln\_mus\_ups}\forcode{=.true.}).330 (\np[=.true.]{ln_mus_ups}{ln\_mus\_ups}). 329 331 330 332 % ------------------------------------------------------------------------------------------------------------- … … 334 336 \label{subsec:TRA_adv_ubs} 335 337 336 The Upstream-Biased Scheme (UBS) is used when \np {ln_traadv_ubs}{ln\_traadv\_ubs}\forcode{=.true.}.338 The Upstream-Biased Scheme (UBS) is used when \np[=.true.]{ln_traadv_ubs}{ln\_traadv\_ubs}. 337 339 UBS implementation can be found in the \mdl{traadv\_mus} module. 338 340 … … 364 366 \citep{shchepetkin.mcwilliams_OM05, demange_phd14}. 365 367 Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme or a $4^th$ order COMPACT scheme 366 (\np {nn_ubs_v}{nn\_ubs\_v}\forcode{=2 or 4}).368 (\np[=2 or 4]{nn_ubs_v}{nn\_ubs\_v}). 367 369 368 370 For stability reasons (see \autoref{chap:TD}), the first term in \autoref{eq:TRA_adv_ubs} … … 407 409 408 410 The Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms (QUICKEST) scheme 409 proposed by \citet{leonard_CMAME79} is used when \np {ln_traadv_qck}{ln\_traadv\_qck}\forcode{=.true.}.411 proposed by \citet{leonard_CMAME79} is used when \np[=.true.]{ln_traadv_qck}{ln\_traadv\_qck}. 410 412 QUICKEST implementation can be found in the \mdl{traadv\_qck} module. 411 413 … … 452 454 except for the pure vertical component that appears when a rotation tensor is used. 453 455 This latter component is solved implicitly together with the vertical diffusion term (see \autoref{chap:TD}). 454 When \np {ln_traldf_msc}{ln\_traldf\_msc}\forcode{=.true.}, a Method of Stabilizing Correction is used in which456 When \np[=.true.]{ln_traldf_msc}{ln\_traldf\_msc}, a Method of Stabilizing Correction is used in which 455 457 the pure vertical component is split into an explicit and an implicit part \citep{lemarie.debreu.ea_OM12}. 456 458 … … 464 466 465 467 \begin{description} 466 \item[ \np{ln_traldf_OFF}{ln\_traldf\_OFF}\forcode{=.true.}:]468 \item[{\np[=.true.]{ln_traldf_OFF}{ln\_traldf\_OFF}}] 467 469 no operator selected, the lateral diffusive tendency will not be applied to the tracer equation. 468 470 This option can be used when the selected advection scheme is diffusive enough (MUSCL scheme for example). 469 \item[ \np{ln_traldf_lap}{ln\_traldf\_lap}\forcode{=.true.}:]471 \item[{\np[=.true.]{ln_traldf_lap}{ln\_traldf\_lap}}] 470 472 a laplacian operator is selected. 471 473 This harmonic operator takes the following expression: $\mathcal{L}(T) = \nabla \cdot A_{ht} \; \nabla T $, 472 474 where the gradient operates along the selected direction (see \autoref{subsec:TRA_ldf_dir}), 473 475 and $A_{ht}$ is the eddy diffusivity coefficient expressed in $m^2/s$ (see \autoref{chap:LDF}). 474 \item[ \np{ln_traldf_blp}{ln\_traldf\_blp}\forcode{=.true.}]:476 \item[{\np[=.true.]{ln_traldf_blp}{ln\_traldf\_blp}}]: 475 477 a bilaplacian operator is selected. 476 478 This biharmonic operator takes the following expression: … … 497 499 The choice of a direction of action determines the form of operator used. 498 500 The operator is a simple (re-entrant) laplacian acting in the (\textbf{i},\textbf{j}) plane when 499 iso-level option is used (\np {ln_traldf_lev}{ln\_traldf\_lev}\forcode{=.true.}) or501 iso-level option is used (\np[=.true.]{ln_traldf_lev}{ln\_traldf\_lev}) or 500 502 when a horizontal (\ie\ geopotential) operator is demanded in \textit{z}-coordinate 501 (\np{ln_traldf_hor}{ln\_traldf\_hor} and \np {ln_zco}{ln\_zco}\forcode{=.true.}).503 (\np{ln_traldf_hor}{ln\_traldf\_hor} and \np[=.true.]{ln_zco}{ln\_zco}). 502 504 The associated code can be found in the \mdl{traldf\_lap\_blp} module. 503 505 The operator is a rotated (re-entrant) laplacian when … … 536 538 It is a \textit{horizontal} operator (\ie acting along geopotential surfaces) in 537 539 the $z$-coordinate with or without partial steps, but is simply an iso-level operator in the $s$-coordinate. 538 It is thus used when, in addition to \np{ln_traldf_lap}{ln\_traldf\_lap} or \np {ln_traldf_blp}{ln\_traldf\_blp}\forcode{=.true.},539 we have \np {ln_traldf_lev}{ln\_traldf\_lev}\forcode{=.true.} or \np{ln_traldf_hor}{ln\_traldf\_hor}~=~\np{ln_zco}{ln\_zco}\forcode{=.true.}.540 It is thus used when, in addition to \np{ln_traldf_lap}{ln\_traldf\_lap} or \np[=.true.]{ln_traldf_blp}{ln\_traldf\_blp}, 541 we have \np[=.true.]{ln_traldf_lev}{ln\_traldf\_lev} or \np{ln_traldf_hor}{ln\_traldf\_hor}~=~\np[=.true.]{ln_zco}{ln\_zco}. 540 542 In both cases, it significantly contributes to diapycnal mixing. 541 543 It is therefore never recommended, even when using it in the bilaplacian case. 542 544 543 Note that in the partial step $z$-coordinate (\np {ln_zps}{ln\_zps}\forcode{=.true.}),545 Note that in the partial step $z$-coordinate (\np[=.true.]{ln_zps}{ln\_zps}), 544 546 tracers in horizontally adjacent cells are located at different depths in the vicinity of the bottom. 545 547 In this case, horizontal derivatives in (\autoref{eq:TRA_ldf_lap}) at the bottom level require a specific treatment. … … 573 575 $r_1$ and $r_2$ are the slopes between the surface of computation ($z$- or $s$-surfaces) and 574 576 the surface along which the diffusion operator acts (\ie\ horizontal or iso-neutral surfaces). 575 It is thus used when, in addition to \np {ln_traldf_lap}{ln\_traldf\_lap}\forcode{=.true.},576 we have \np {ln_traldf_iso}{ln\_traldf\_iso}\forcode{=.true.},577 or both \np {ln_traldf_hor}{ln\_traldf\_hor}\forcode{=.true.} and \np{ln_zco}{ln\_zco}\forcode{=.true.}.577 It is thus used when, in addition to \np[=.true.]{ln_traldf_lap}{ln\_traldf\_lap}, 578 we have \np[=.true.]{ln_traldf_iso}{ln\_traldf\_iso}, 579 or both \np[=.true.]{ln_traldf_hor}{ln\_traldf\_hor} and \np[=.true.]{ln_zco}{ln\_zco}. 578 580 The way these slopes are evaluated is given in \autoref{sec:LDF_slp}. 579 581 At the surface, bottom and lateral boundaries, the turbulent fluxes of heat and salt are set to zero using … … 591 593 any additional background horizontal diffusion \citep{guilyardi.madec.ea_CD01}. 592 594 593 Note that in the partial step $z$-coordinate (\np {ln_zps}{ln\_zps}\forcode{=.true.}),595 Note that in the partial step $z$-coordinate (\np[=.true.]{ln_zps}{ln\_zps}), 594 596 the horizontal derivatives at the bottom level in \autoref{eq:TRA_ldf_iso} require a specific treatment. 595 597 They are calculated in module zpshde, described in \autoref{sec:TRA_zpshde}. … … 601 603 602 604 An alternative scheme developed by \cite{griffies.gnanadesikan.ea_JPO98} which ensures tracer variance decreases 603 is also available in \NEMO\ (\np {ln_traldf_triad}{ln\_traldf\_triad}\forcode{=.true.}).605 is also available in \NEMO\ (\np[=.true.]{ln_traldf_triad}{ln\_traldf\_triad}). 604 606 A complete description of the algorithm is given in \autoref{apdx:TRIADS}. 605 607 … … 647 649 respectively. 648 650 Generally, $A_w^{vT} = A_w^{vS}$ except when double diffusive mixing is parameterised 649 (\ie\ \np {ln_zdfddm}{ln\_zdfddm}\forcode{=.true.},).651 (\ie\ \np[=.true.]{ln_zdfddm}{ln\_zdfddm},). 650 652 The way these coefficients are evaluated is given in \autoref{chap:ZDF} (ZDF). 651 653 Furthermore, when iso-neutral mixing is used, both mixing coefficients are increased by … … 722 724 Such time averaging prevents the divergence of odd and even time step (see \autoref{chap:TD}). 723 725 724 In the linear free surface case (\np {ln_linssh}{ln\_linssh}\forcode{=.true.}), an additional term has to be added on726 In the linear free surface case (\np[=.true.]{ln_linssh}{ln\_linssh}), an additional term has to be added on 725 727 both temperature and salinity. 726 728 On temperature, this term remove the heat content associated with mass exchange that has been added to $Q_{ns}$. … … 757 759 758 760 Options are defined through the \nam{tra_qsr}{tra\_qsr} namelist variables. 759 When the penetrative solar radiation option is used (\np {ln_traqsr}{ln\_traqsr}\forcode{=.true.}),761 When the penetrative solar radiation option is used (\np[=.true.]{ln_traqsr}{ln\_traqsr}), 760 762 the solar radiation penetrates the top few tens of meters of the ocean. 761 If it is not used (\np {ln_traqsr}{ln\_traqsr}\forcode{=.false.}) all the heat flux is absorbed in the first ocean level.763 If it is not used (\np[=.false.]{ln_traqsr}{ln\_traqsr}) all the heat flux is absorbed in the first ocean level. 762 764 Thus, in the former case a term is added to the time evolution equation of temperature \autoref{eq:MB_PE_tra_T} and 763 765 the surface boundary condition is modified to take into account only the non-penetrative part of the surface … … 788 790 larger depths where it contributes to local heating. 789 791 The way this second part of the solar energy penetrates into the ocean depends on which formulation is chosen. 790 In the simple 2-waveband light penetration scheme (\np {ln_qsr_2bd}{ln\_qsr\_2bd}\forcode{=.true.})792 In the simple 2-waveband light penetration scheme (\np[=.true.]{ln_qsr_2bd}{ln\_qsr\_2bd}) 791 793 a chlorophyll-independent monochromatic formulation is chosen for the shorter wavelengths, 792 794 leading to the following expression \citep{paulson.simpson_JPO77}: … … 816 818 The 2-bands formulation does not reproduce the full model very well. 817 819 818 The RGB formulation is used when \np {ln_qsr_rgb}{ln\_qsr\_rgb}\forcode{=.true.}.820 The RGB formulation is used when \np[=.true.]{ln_qsr_rgb}{ln\_qsr\_rgb}. 819 821 The RGB attenuation coefficients (\ie\ the inverses of the extinction length scales) are tabulated over 820 822 61 nonuniform chlorophyll classes ranging from 0.01 to 10 g.Chl/L … … 823 825 824 826 \begin{description} 825 \item[ \np{nn_chldta}{nn\_chldta}\forcode{=0}]827 \item[{\np[=0]{nn_chldta}{nn\_chldta}}] 826 828 a constant 0.05 g.Chl/L value everywhere ; 827 \item[ \np{nn_chldta}{nn\_chldta}\forcode{=1}]829 \item[{\np[=1]{nn_chldta}{nn\_chldta}}] 828 830 an observed time varying chlorophyll deduced from satellite surface ocean color measurement spread uniformly in 829 831 the vertical direction; 830 \item[ \np{nn_chldta}{nn\_chldta}\forcode{=2}]832 \item[{\np[=2]{nn_chldta}{nn\_chldta}}] 831 833 same as previous case except that a vertical profile of chlorophyl is used. 832 834 Following \cite{morel.berthon_LO89}, the profile is computed from the local surface chlorophyll value; 833 \item[ \np{ln_qsr_bio}{ln\_qsr\_bio}\forcode{=.true.}]835 \item[{\np[=.true.]{ln_qsr_bio}{ln\_qsr\_bio}}] 834 836 simulated time varying chlorophyll by TOP biogeochemical model. 835 837 In this case, the RGB formulation is used to calculate both the phytoplankton light limitation in … … 944 946 % Diffusive BBL 945 947 % ------------------------------------------------------------------------------------------------------------- 946 \subsection[Diffusive bottom boundary layer (\forcode{nn_bbl_ldf=1})]{Diffusive bottom boundary layer (\protect\np {nn_bbl_ldf}{nn\_bbl\_ldf}\forcode{=1})}948 \subsection[Diffusive bottom boundary layer (\forcode{nn_bbl_ldf=1})]{Diffusive bottom boundary layer (\protect\np[=1]{nn_bbl_ldf}{nn\_bbl\_ldf})} 947 949 \label{subsec:TRA_bbl_diff} 948 950 949 When applying sigma-diffusion (\np {ln_trabbl}{ln\_trabbl}\forcode{=.true.} and \np{nn_bbl_ldf}{nn\_bbl\_ldf} set to 1),951 When applying sigma-diffusion (\np[=.true.]{ln_trabbl}{ln\_trabbl} and \np{nn_bbl_ldf}{nn\_bbl\_ldf} set to 1), 950 952 the diffusive flux between two adjacent cells at the ocean floor is given by 951 953 \[ … … 983 985 % Advective BBL 984 986 % ------------------------------------------------------------------------------------------------------------- 985 \subsection[Advective bottom boundary layer (\forcode{nn_bbl_adv=1,2})]{Advective bottom boundary layer (\protect\np {nn_bbl_adv}{nn\_bbl\_adv}\forcode{=1,2})}987 \subsection[Advective bottom boundary layer (\forcode{nn_bbl_adv=1,2})]{Advective bottom boundary layer (\protect\np[=1,2]{nn_bbl_adv}{nn\_bbl\_adv})} 986 988 \label{subsec:TRA_bbl_adv} 987 989 … … 1014 1016 %%%gmcomment : this section has to be really written 1015 1017 1016 When applying an advective BBL (\np {nn_bbl_adv}{nn\_bbl\_adv}\forcode{=1..2}), an overturning circulation is added which1018 When applying an advective BBL (\np[=1..2]{nn_bbl_adv}{nn\_bbl\_adv}), an overturning circulation is added which 1017 1019 connects two adjacent bottom grid-points only if dense water overlies less dense water on the slope. 1018 1020 The density difference causes dense water to move down the slope. 1019 1021 1020 \np {nn_bbl_adv}{nn\_bbl\_adv}\forcode{=1}:1022 \np[=1]{nn_bbl_adv}{nn\_bbl\_adv}: 1021 1023 the downslope velocity is chosen to be the Eulerian ocean velocity just above the topographic step 1022 1024 (see black arrow in \autoref{fig:TRA_bbl}) \citep{beckmann.doscher_JPO97}. … … 1025 1027 if the velocity is directed towards greater depth (\ie\ $\vect U \cdot \nabla H > 0$). 1026 1028 1027 \np {nn_bbl_adv}{nn\_bbl\_adv}\forcode{=2}:1029 \np[=2]{nn_bbl_adv}{nn\_bbl\_adv}: 1028 1030 the downslope velocity is chosen to be proportional to $\Delta \rho$, 1029 1031 the density difference between the higher cell and lower cell densities \citep{campin.goosse_T99}. … … 1153 1155 (\ie\ fluxes plus content in mass exchanges). 1154 1156 $\gamma$ is initialized as \np{rn_atfp}{rn\_atfp} (\textbf{namelist} parameter). 1155 Its default value is \np {rn_atfp}{rn\_atfp}\forcode{=10.e-3}.1157 Its default value is \np[=10.e-3]{rn_atfp}{rn\_atfp}. 1156 1158 Note that the forcing correction term in the filter is not applied in linear free surface 1157 1159 (\jp{ln\_linssh}\forcode{=.true.}) (see \autoref{subsec:TRA_sbc}). … … 1216 1218 1217 1219 \begin{description} 1218 \item[ \np{ln_teos10}{ln\_teos10}\forcode{=.true.}]1220 \item[{\np[=.true.]{ln_teos10}{ln\_teos10}}] 1219 1221 the polyTEOS10-bsq equation of seawater \citep{roquet.madec.ea_OM15} is used. 1220 1222 The accuracy of this approximation is comparable to the TEOS-10 rational function approximation, … … 1235 1237 either computing the air-sea and ice-sea fluxes (forced mode) or 1236 1238 sending the SST field to the atmosphere (coupled mode). 1237 \item[ \np{ln_eos80}{ln\_eos80}\forcode{=.true.}]1239 \item[{\np[=.true.]{ln_eos80}{ln\_eos80}}] 1238 1240 the polyEOS80-bsq equation of seawater is used. 1239 1241 It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized to … … 1247 1249 Nevertheless, a severe assumption is made in order to have a heat content ($C_p T_p$) which 1248 1250 is conserved by the model: $C_p$ is set to a constant value, the TEOS10 value. 1249 \item[ \np{ln_seos}{ln\_seos}\forcode{=.true.}]1251 \item[{\np[=.true.]{ln_seos}{ln\_seos}}] 1250 1252 a simplified EOS (S-EOS) inspired by \citet{vallis_bk06} is chosen, 1251 1253 the coefficients of which has been optimized to fit the behavior of TEOS10 … … 1367 1369 I've changed "derivative" to "difference" and "mean" to "average"} 1368 1370 1369 With partial cells (\np {ln_zps}{ln\_zps}\forcode{=.true.}) at bottom and top (\np{ln_isfcav}{ln\_isfcav}\forcode{=.true.}),1371 With partial cells (\np[=.true.]{ln_zps}{ln\_zps}) at bottom and top (\np[=.true.]{ln_isfcav}{ln\_isfcav}), 1370 1372 in general, tracers in horizontally adjacent cells live at different depths. 1371 1373 Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} module) and 1372 1374 the hydrostatic pressure gradient calculations (\mdl{dynhpg} module). 1373 The partial cell properties at the top (\np {ln_isfcav}{ln\_isfcav}\forcode{=.true.}) are computed in the same way as1375 The partial cell properties at the top (\np[=.true.]{ln_isfcav}{ln\_isfcav}) are computed in the same way as 1374 1376 for the bottom. 1375 1377 So, only the bottom interpolation is explained below. … … 1387 1389 the $z$-partial step coordinate]{ 1388 1390 Discretisation of the horizontal difference and average of tracers in 1389 the $z$-partial step coordinate (\protect\np {ln_zps}{ln\_zps}\forcode{=.true.}) in1391 the $z$-partial step coordinate (\protect\np[=.true.]{ln_zps}{ln\_zps}) in 1390 1392 the case $(e3w_k^{i + 1} - e3w_k^i) > 0$. 1391 1393 A linear interpolation is used to estimate $\widetilde T_k^{i + 1}$, … … 1459 1461 %%% 1460 1462 1461 \ biblio1462 1463 \ pindex1463 \onlyinsubfile{\bibliography{../main/bibliography}} 1464 1465 \onlyinsubfile{\printindex} 1464 1466 1465 1467 \end{document}
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