- Timestamp:
- 2016-04-07T16:32:24+02:00 (8 years ago)
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
branches/UKMO/dev_r5518_GC3p0_package/DOC/TexFiles/Chapters/Chap_ZDF.tex
r5120 r6440 33 33 points, respectively (see \S\ref{TRA_zdf} and \S\ref{DYN_zdf}). These 34 34 coefficients can be assumed to be either constant, or a function of the local 35 Richardson number, or computed from a turbulent closure model (either 36 TKE or KPP formulation). The computation of these coefficients is initialized 37 in the \mdl{zdfini} module and performed in the \mdl{zdfric}, \mdl{zdftke} or 38 \mdl{zdfkpp} modules. The trends due to the vertical momentum and tracer 39 diffusion, including the surface forcing, are computed and added to the 40 general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 35 Richardson number, or computed from a turbulent closure model (TKE, GLS or KPP formulation). 36 The computation of these coefficients is initialized in the \mdl{zdfini} module 37 and performed in the \mdl{zdfric}, \mdl{zdftke}, \mdl{zdfgls} or \mdl{zdfkpp} modules. 38 The trends due to the vertical momentum and tracer diffusion, including the surface forcing, 39 are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 41 40 These trends can be computed using either a forward time stepping scheme 42 41 (namelist parameter \np{ln\_zdfexp}=true) or a backward time stepping … … 262 261 \end{equation} 263 262 264 At the ocean surface, a non zero length scale is set through the \np{rn\_ lmin0} namelist263 At the ocean surface, a non zero length scale is set through the \np{rn\_mxl0} namelist 265 264 parameter. Usually the surface scale is given by $l_o = \kappa \,z_o$ 266 265 where $\kappa = 0.4$ is von Karman's constant and $z_o$ the roughness 267 266 parameter of the surface. Assuming $z_o=0.1$~m \citep{Craig_Banner_JPO94} 268 leads to a 0.04~m, the default value of \np{rn\_ lsurf}. In the ocean interior267 leads to a 0.04~m, the default value of \np{rn\_mxl0}. In the ocean interior 269 268 a minimum length scale is set to recover the molecular viscosity when $\bar{e}$ 270 269 reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). … … 295 294 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 296 295 with $e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}~=~67.83 corresponds 297 to $\alpha_{CB} = 100$. further setting \np{ln\_lsurf} to true applies \eqref{ZDF_Lsbc}298 as surface boundary condition on length scale, with $\beta$ hard coded to the Stace t's value.296 to $\alpha_{CB} = 100$. Further setting \np{ln\_mxl0} to true applies \eqref{ZDF_Lsbc} 297 as surface boundary condition on length scale, with $\beta$ hard coded to the Stacey's value. 299 298 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) 300 299 is applied on surface $\bar{e}$ value. … … 355 354 %--------------------------------------------------------------% 356 355 357 To be add here a description of "penetration of TKE" and the associated namelist parameters 358 \np{nn\_etau}, \np{rn\_efr} and \np{nn\_htau}. 356 Vertical mixing parameterizations commonly used in ocean general circulation models 357 tend to produce mixed-layer depths that are too shallow during summer months and windy conditions. 358 This bias is particularly acute over the Southern Ocean. 359 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}. 360 The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations, 361 but rather is meant to account for observed processes that affect the density structure of 362 the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme 363 ($i.e.$ near-inertial oscillations and ocean swells and waves). 364 365 When using this parameterization ($i.e.$ when \np{nn\_etau}~=~1), the TKE input to the ocean ($S$) 366 imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized 367 by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by: 368 \begin{equation} \label{ZDF_Ehtau} 369 S = (1-f_i) \; f_r \; e_s \; e^{-z / h_\tau} 370 \end{equation} 371 where 372 $z$ is the depth, 373 $e_s$ is TKE surface boundary condition, 374 $f_r$ is the fraction of the surface TKE that penetrate in the ocean, 375 $h_\tau$ is a vertical mixing length scale that controls exponential shape of the penetration, 376 and $f_i$ is the ice concentration (no penetration if $f_i=1$, that is if the ocean is entirely 377 covered by sea-ice). 378 The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter. 379 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}~=~0) 380 or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m 381 at high latitudes (\np{nn\_etau}~=~1). 382 383 Note that two other option existe, \np{nn\_etau}~=~2, or 3. They correspond to applying 384 \eqref{ZDF_Ehtau} only at the base of the mixed layer, or to using the high frequency part 385 of the stress to evaluate the fraction of TKE that penetrate the ocean. 386 Those two options are obsolescent features introduced for test purposes. 387 They will be removed in the next release. 388 389 359 390 360 391 % from Burchard et al OM 2008 : 361 % the most critical process not reproduced by statistical turbulence models is the activity of internal waves and their interaction with turbulence. After the Reynolds decomposition, internal waves are in principle included in the RANS equations, but later partially excluded by the hydrostatic assumption and the model resolution. Thus far, the representation of internal wave mixing in ocean models has been relatively crude (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 392 % the most critical process not reproduced by statistical turbulence models is the activity of 393 % internal waves and their interaction with turbulence. After the Reynolds decomposition, 394 % internal waves are in principle included in the RANS equations, but later partially 395 % excluded by the hydrostatic assumption and the model resolution. 396 % Thus far, the representation of internal wave mixing in ocean models has been relatively crude 397 % (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 362 398 363 399 … … 586 622 Options are defined through the \ngn{namzdf\_kpp} namelist variables. 587 623 588 \colorbox{yellow}{Add a description of KPP here.} 624 Note that KPP is an obsolescent feature of the \NEMO system. 625 It will be removed in the next release (v3.7 and followings). 589 626 590 627 … … 636 673 637 674 Options are defined through the \ngn{namzdf} namelist variables. 638 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc} =true.675 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}~=~\textit{true}. 639 676 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously 640 677 the statically unstable portion of the water column, but only until the density … … 644 681 (Fig. \ref{Fig_npc}): starting from the top of the ocean, the first instability is 645 682 found. Assume in the following that the instability is located between levels 646 $k$ and $k+1$. The potentialtemperature and salinity in the two levels are683 $k$ and $k+1$. The temperature and salinity in the two levels are 647 684 vertically mixed, conserving the heat and salt contents of the water column. 648 685 The new density is then computed by a linear approximation. If the new … … 664 701 \citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}. 665 702 666 Note that in the current implementation of this algorithm presents several 667 limitations. First, potential density referenced to the sea surface is used to 668 check whether the density profile is stable or not. This is a strong 669 simplification which leads to large errors for realistic ocean simulations. 670 Indeed, many water masses of the world ocean, especially Antarctic Bottom 671 Water, are unstable when represented in surface-referenced potential density. 672 The scheme will erroneously mix them up. Second, the mixing of potential 673 density is assumed to be linear. This assures the convergence of the algorithm 674 even when the equation of state is non-linear. Small static instabilities can thus 675 persist due to cabbeling: they will be treated at the next time step. 676 Third, temperature and salinity, and thus density, are mixed, but the 677 corresponding velocity fields remain unchanged. When using a Richardson 678 Number dependent eddy viscosity, the mixing of momentum is done through 679 the vertical diffusion: after a static adjustment, the Richardson Number is zero 680 and thus the eddy viscosity coefficient is at a maximum. When this convective 681 adjustment algorithm is used with constant vertical eddy viscosity, spurious 682 solutions can occur since the vertical momentum diffusion remains small even 683 after a static adjustment. In that case, we recommend the addition of momentum 684 mixing in a manner that mimics the mixing in temperature and salinity 685 \citep{Speich_PhD92, Speich_al_JPO96}. 703 The current implementation has been modified in order to deal with any non linear 704 equation of seawater (L. Brodeau, personnal communication). 705 Two main differences have been introduced compared to the original algorithm: 706 $(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency 707 (not the the difference in potential density) ; 708 $(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients 709 are vertically mixed in the same way their temperature and salinity has been mixed. 710 These two modifications allow the algorithm to perform properly and accurately 711 with TEOS10 or EOS-80 without having to recompute the expansion coefficients at each 712 mixing iteration. 686 713 687 714 % ------------------------------------------------------------------------------------------------------------- … … 689 716 % ------------------------------------------------------------------------------------------------------------- 690 717 \subsection [Enhanced Vertical Diffusion (\np{ln\_zdfevd})] 691 718 {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 692 719 \label{ZDF_evd} 693 720 … … 830 857 % Bottom Friction 831 858 % ================================================================ 832 \section [Bottom and top Friction (\textit{zdfbfr})] {BottomFriction (\mdl{zdfbfr} module)}859 \section [Bottom and Top Friction (\textit{zdfbfr})] {Bottom and Top Friction (\mdl{zdfbfr} module)} 833 860 \label{ZDF_bfr} 834 861 … … 838 865 839 866 Options to define the top and bottom friction are defined through the \ngn{nambfr} namelist variables. 840 The top friction is activated only if the ice shelf cavities are opened (\np{ln\_isfcav}~=~true). 841 As the friction processes at the top and bottom are the represented similarly, only the bottom friction is described in detail. 867 The bottom friction represents the friction generated by the bathymetry. 868 The top friction represents the friction generated by the ice shelf/ocean interface. 869 As the friction processes at the top and bottom are represented similarly, only the bottom friction is described in detail below.\\ 870 842 871 843 872 Both the surface momentum flux (wind stress) and the bottom momentum … … 912 941 $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$. 913 942 This is the default value used in \NEMO. It corresponds to a decay time scale 914 of 115~days. It can be changed by specifying \np{rn\_bfri c1} (namelist parameter).943 of 115~days. It can be changed by specifying \np{rn\_bfri1} (namelist parameter). 915 944 916 945 For the linear friction case the coefficients defined in the general … … 922 951 \end{split} 923 952 \end{equation} 924 When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri c1}.953 When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri1}. 925 954 Setting \np{nn\_botfr}=0 is equivalent to setting $r=0$ and leads to a free-slip 926 955 bottom boundary condition. These values are assigned in \mdl{zdfbfr}. … … 929 958 in the \ifile{bfr\_coef} input NetCDF file. The mask values should vary from 0 to 1. 930 959 Locations with a non-zero mask value will have the friction coefficient increased 931 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri c1}.960 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri1}. 932 961 933 962 % ------------------------------------------------------------------------------------------------------------- … … 949 978 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992} 950 979 uses $C_D = 1.4\;10^{-3}$ and $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$. 951 The CME choices have been set as default values (\np{rn\_bfri c2} and \np{rn\_bfeb2}980 The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} 952 981 namelist parameters). 953 982 … … 964 993 \end{equation} 965 994 966 The coefficients that control the strength of the non-linear bottom friction are 967 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 968 Note for applications which treat tides explicitly a low or even zero value of 969 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ 970 is possible via an externally defined 2D mask array (\np{ln\_bfr2d}=true). 971 See previous section for details. 995 The coefficients that control the strength of the non-linear bottom friction are 996 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 997 Note for applications which treat tides explicitly a low or even zero value of 998 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ is possible 999 via an externally defined 2D mask array (\np{ln\_bfr2d}=true). This works in the same way 1000 as for the linear bottom friction case with non-zero masked locations increased by 1001 $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}. 1002 1003 % ------------------------------------------------------------------------------------------------------------- 1004 % Bottom Friction Log-layer 1005 % ------------------------------------------------------------------------------------------------------------- 1006 \subsection{Log-layer Bottom Friction enhancement (\np{nn\_botfr} = 2, \np{ln\_loglayer} = .true.)} 1007 \label{ZDF_bfr_loglayer} 1008 1009 In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally 1010 enhanced using a "law of the wall" scaling. If \np{ln\_loglayer} = .true., $C_D$ is no 1011 longer constant but is related to the thickness of the last wet layer in each column by: 1012 1013 \begin{equation} 1014 C_D = \left ( {\kappa \over {\rm log}\left ( 0.5e_{3t}/rn\_bfrz0 \right ) } \right )^2 1015 \end{equation} 1016 1017 \noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness 1018 length provided via the namelist. 1019 1020 For stability, the drag coefficient is bounded such that it is kept greater or equal to 1021 the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional 1022 namelist parameter: \np{rn\_bfri2\_max}, i.e.: 1023 1024 \begin{equation} 1025 rn\_bfri2 \leq C_D \leq rn\_bfri2\_max 1026 \end{equation} 1027 1028 \noindent Note also that a log-layer enhancement can also be applied to the top boundary 1029 friction if under ice-shelf cavities are in use (\np{ln\_isfcav}=.true.). In this case, the 1030 relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} 1031 and \np{rn\_tfri2\_max}. 972 1032 973 1033 % ------------------------------------------------------------------------------------------------------------- … … 1253 1313 1254 1314 % ================================================================ 1315 % Internal wave-driven mixing 1316 % ================================================================ 1317 \section{Internal wave-driven mixing (\key{zdftmx\_new})} 1318 \label{ZDF_tmx_new} 1319 1320 %--------------------------------------------namzdf_tmx_new------------------------------------------ 1321 \namdisplay{namzdf_tmx_new} 1322 %-------------------------------------------------------------------------------------------------------------- 1323 1324 The parameterization of mixing induced by breaking internal waves is a generalization 1325 of the approach originally proposed by \citet{St_Laurent_al_GRL02}. 1326 A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed, 1327 and the resulting diffusivity is obtained as 1328 \begin{equation} \label{Eq_Kwave} 1329 A^{vT}_{wave} = R_f \,\frac{ \epsilon }{ \rho \, N^2 } 1330 \end{equation} 1331 where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution 1332 of the energy available for mixing. If the \np{ln\_mevar} namelist parameter is set to false, 1333 the mixing efficiency is taken as constant and equal to 1/6 \citep{Osborn_JPO80}. 1334 In the opposite (recommended) case, $R_f$ is instead a function of the turbulence intensity parameter 1335 $Re_b = \frac{ \epsilon}{\nu \, N^2}$, with $\nu$ the molecular viscosity of seawater, 1336 following the model of \cite{Bouffard_Boegman_DAO2013} 1337 and the implementation of \cite{de_lavergne_JPO2016_efficiency}. 1338 Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when the mixing efficiency is constant. 1339 1340 In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary 1341 as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice). 1342 This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014}, 1343 is implemented as in \cite{de_lavergne_JPO2016_efficiency}. 1344 1345 The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, is constructed 1346 from three static maps of column-integrated internal wave energy dissipation, $E_{cri}(i,j)$, 1347 $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures 1348 (de Lavergne et al., in prep): 1349 \begin{align*} 1350 F_{cri}(i,j,k) &\propto e^{-h_{ab} / h_{cri} }\\ 1351 F_{pyc}(i,j,k) &\propto N^{n\_p}\\ 1352 F_{bot}(i,j,k) &\propto N^2 \, e^{- h_{wkb} / h_{bot} } 1353 \end{align*} 1354 In the above formula, $h_{ab}$ denotes the height above bottom, 1355 $h_{wkb}$ denotes the WKB-stretched height above bottom, defined by 1356 \begin{equation*} 1357 h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz' } \; , 1358 \end{equation*} 1359 The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_tmx\_new} namelist) controls the stratification-dependence of the pycnocline-intensified dissipation. 1360 It can take values of 1 (recommended) or 2. 1361 Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of 1362 the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps. 1363 $h_{cri}$ is related to the large-scale topography of the ocean (etopo2) 1364 and $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of 1365 the abyssal hill topography \citep{Goff_JGR2010} and the latitude. 1366 1367 % ================================================================ 1368 1369 1370
Note: See TracChangeset
for help on using the changeset viewer.
