Changeset 11543 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex
r11537 r11543 109 109 Next, the scheme for interpolation on the fly is described. 110 110 Finally, the different options that further modify the fluxes applied to the ocean are discussed. 111 One of these is modification by icebergs (see \autoref{sec: ICB_icebergs}),111 One of these is modification by icebergs (see \autoref{sec:SBC_ICB_icebergs}), 112 112 which act as drifting sources of fresh water. 113 113 Another example of modification is that due to the ice shelf melting/freezing (see \autoref{sec:SBC_isf}), … … 124 124 The surface ocean stress is the stress exerted by the wind and the sea-ice on the ocean. 125 125 It is applied in \mdl{dynzdf} module as a surface boundary condition of the computation of 126 the momentum vertical mixing trend (see \autoref{eq: dynzdf_sbc} in \autoref{sec:DYN_zdf}).126 the momentum vertical mixing trend (see \autoref{eq:DYN_zdf_sbc} in \autoref{sec:DYN_zdf}). 127 127 As such, it has to be provided as a 2D vector interpolated onto the horizontal velocity ocean mesh, 128 128 \ie\ resolved onto the model (\textbf{i},\textbf{j}) direction at $u$- and $v$-points. … … 135 135 It is applied in \mdl{trasbc} module as a surface boundary condition trend of 136 136 the first level temperature time evolution equation 137 (see \autoref{eq: tra_sbc} and \autoref{eq:tra_sbc_lin} in \autoref{subsec:TRA_sbc}).137 (see \autoref{eq:TRA_sbc} and \autoref{eq:TRA_sbc_lin} in \autoref{subsec:TRA_sbc}). 138 138 The latter is the penetrative part of the heat flux. 139 139 It is applied as a 3D trend of the temperature equation (\mdl{traqsr} module) when … … 177 177 The ocean model provides, at each time step, to the surface module (\mdl{sbcmod}) 178 178 the surface currents, temperature and salinity. 179 These variables are averaged over \np{nn\_fsbc} time-step (\autoref{tab: ssm}), and179 These variables are averaged over \np{nn\_fsbc} time-step (\autoref{tab:SBC_ssm}), and 180 180 these averaged fields are used to compute the surface fluxes at the frequency of \np{nn\_fsbc} time-steps. 181 181 … … 193 193 \end{tabular} 194 194 \caption{ 195 \protect\label{tab: ssm}195 \protect\label{tab:SBC_ssm} 196 196 Ocean variables provided by the ocean to the surface module (SBC). 197 197 The variable are averaged over \np{nn\_fsbc} time-step, … … 264 264 This stem will be completed automatically by the model, with the addition of a '.nc' at its end and 265 265 by date information and possibly a prefix (when using AGRIF). 266 \autoref{tab: fldread} provides the resulting file name in all possible cases according to266 \autoref{tab:SBC_fldread} provides the resulting file name in all possible cases according to 267 267 whether it is a climatological file or not, and to the open/close frequency (see below for definition). 268 268 … … 278 278 \end{center} 279 279 \caption{ 280 \protect\label{tab: fldread}280 \protect\label{tab:SBC_fldread} 281 281 naming nomenclature for climatological or interannual input file(s), as a function of the open/close frequency. 282 282 The stem name is assumed to be 'fn'. … … 515 515 % ------------------------------------------------------------------------------------------------------------- 516 516 \subsection{Standalone surface boundary condition scheme (SAS)} 517 \label{subsec:S AS}517 \label{subsec:SBC_SAS} 518 518 519 519 %---------------------------------------namsbc_sas-------------------------------------------------- … … 649 649 %--------------------------------------------------TABLE-------------------------------------------------- 650 650 \begin{table}[htbp] 651 \label{tab: BULK}651 \label{tab:SBC_BULK} 652 652 \begin{center} 653 653 \begin{tabular}{|l|c|c|c|} … … 852 852 The tidal forcing, generated by the gravity forces of the Earth-Moon and Earth-Sun sytems, 853 853 is activated if \np{ln\_tide} and \np{ln\_tide\_pot} are both set to \forcode{.true.} in \nam{\_tide}. 854 This translates as an additional barotropic force in the momentum equations \ref{eq:PE_dyn} such that:855 \[ 856 % \label{eq: PE_dyn_tides}854 This translates as an additional barotropic force in the momentum \autoref{eq:MB_PE_dyn} such that: 855 \[ 856 % \label{eq:SBC_PE_dyn_tides} 857 857 \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= ... 858 858 +g\nabla (\Pi_{eq} + \Pi_{sal}) … … 895 895 % River runoffs 896 896 % ================================================================ 897 \section[River runoffs (\textit{sbcrnf.F90})] 898 {River runoffs (\protect\mdl{sbcrnf})} 897 \section[River runoffs (\textit{sbcrnf.F90})]{River runoffs (\protect\mdl{sbcrnf})} 899 898 \label{sec:SBC_rnf} 900 899 %------------------------------------------namsbc_rnf---------------------------------------------------- … … 1022 1021 % Ice shelf melting 1023 1022 % ================================================================ 1024 \section[Ice shelf melting (\textit{sbcisf.F90})] 1025 {Ice shelf melting (\protect\mdl{sbcisf})} 1023 \section[Ice shelf melting (\textit{sbcisf.F90})]{Ice shelf melting (\protect\mdl{sbcisf})} 1026 1024 \label{sec:SBC_isf} 1027 1025 %------------------------------------------namsbc_isf---------------------------------------------------- … … 1066 1064 The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0}. 1067 1065 \[ 1068 % \label{eq: sbc_isf_gamma_iso}1066 % \label{eq:SBC_isf_gamma_iso} 1069 1067 \gamma^{T} = \np{rn\_gammat0} 1070 1068 \] … … 1213 1211 % ================================================================ 1214 1212 \section{Handling of icebergs (ICB)} 1215 \label{sec: ICB_icebergs}1213 \label{sec:SBC_ICB_icebergs} 1216 1214 %------------------------------------------namberg---------------------------------------------------- 1217 1215 … … 1282 1280 % Interactions with waves (sbcwave.F90, ln_wave) 1283 1281 % ============================================================================================================= 1284 \section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})] 1285 {Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 1282 \section[Interactions with waves (\textit{sbcwave.F90}, \texttt{ln\_wave})]{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 1286 1283 \label{sec:SBC_wave} 1287 1284 %------------------------------------------namsbc_wave-------------------------------------------------------- … … 1314 1311 1315 1312 % ---------------------------------------------------------------- 1316 \subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})] 1317 {Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 1313 \subsection[Neutral drag coefficient from wave model (\texttt{ln\_cdgw})]{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 1318 1314 \label{subsec:SBC_wave_cdgw} 1319 1315 … … 1328 1324 % 3D Stokes Drift (ln_sdw, nn_sdrift) 1329 1325 % ---------------------------------------------------------------- 1330 \subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})] 1331 {3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 1326 \subsection[3D Stokes Drift (\texttt{ln\_sdw}, \texttt{nn\_sdrift})]{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 1332 1327 \label{subsec:SBC_wave_sdw} 1333 1328 … … 1343 1338 1344 1339 \[ 1345 % \label{eq: sbc_wave_sdw}1340 % \label{eq:SBC_wave_sdw} 1346 1341 \mathbf{U}_{st} = \frac{16{\pi^3}} {g} 1347 1342 \int_0^\infty \int_{-\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3} … … 1368 1363 1369 1364 \[ 1370 % \label{eq: sbc_wave_sdw_0a}1365 % \label{eq:SBC_wave_sdw_0a} 1371 1366 \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \frac{\mathrm{e}^{-2k_ez}} {1-8k_ez} 1372 1367 \] … … 1375 1370 1376 1371 \[ 1377 % \label{eq: sbc_wave_sdw_0b}1372 % \label{eq:SBC_wave_sdw_0b} 1378 1373 k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|} 1379 1374 \quad \text{and }\ … … 1388 1383 1389 1384 \[ 1390 % \label{eq: sbc_wave_sdw_1}1385 % \label{eq:SBC_wave_sdw_1} 1391 1386 \mathbf{U}_{st} \cong \mathbf{U}_{st |_{z=0}} \Big[exp(2k_pz)-\beta \sqrt{-2 \pi k_pz} 1392 1387 \textit{ erf } \Big(\sqrt{-2 k_pz}\Big)\Big] … … 1404 1399 1405 1400 \[ 1406 % \label{eq: sbc_wave_eta_sdw}1401 % \label{eq:SBC_wave_eta_sdw} 1407 1402 \frac{\partial{\eta}}{\partial{t}} = 1408 1403 -\nabla_h \int_{-H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz … … 1416 1411 1417 1412 \[ 1418 % \label{eq: sbc_wave_tra_sdw}1413 % \label{eq:SBC_wave_tra_sdw} 1419 1414 \frac{\partial{c}}{\partial{t}} = 1420 1415 - (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c} … … 1425 1420 % Stokes-Coriolis term (ln_stcor) 1426 1421 % ---------------------------------------------------------------- 1427 \subsection[Stokes-Coriolis term (\texttt{ln\_stcor})] 1428 {Stokes-Coriolis term (\protect\np{ln\_stcor})} 1422 \subsection[Stokes-Coriolis term (\texttt{ln\_stcor})]{Stokes-Coriolis term (\protect\np{ln\_stcor})} 1429 1423 \label{subsec:SBC_wave_stcor} 1430 1424 … … 1440 1434 % Waves modified stress (ln_tauwoc, ln_tauw) 1441 1435 % ---------------------------------------------------------------- 1442 \subsection[Wave modified stress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})] 1443 {Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 1436 \subsection[Wave modified stress (\texttt{ln\_tauwoc}, \texttt{ln\_tauw})]{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 1444 1437 \label{subsec:SBC_wave_tauw} 1445 1438 … … 1453 1446 1454 1447 \[ 1455 % \label{eq: sbc_wave_tauoc}1448 % \label{eq:SBC_wave_tauoc} 1456 1449 \tau_{oc,a} = \tau_a - \tau_w 1457 1450 \] … … 1461 1454 1462 1455 \[ 1463 % \label{eq: sbc_wave_tauw}1456 % \label{eq:SBC_wave_tauw} 1464 1457 \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})} 1465 1458 \] … … 1490 1483 % Diurnal cycle 1491 1484 % ------------------------------------------------------------------------------------------------------------- 1492 \subsection[Diurnal cycle (\textit{sbcdcy.F90})] 1493 {Diurnal cycle (\protect\mdl{sbcdcy})} 1485 \subsection[Diurnal cycle (\textit{sbcdcy.F90})]{Diurnal cycle (\protect\mdl{sbcdcy})} 1494 1486 \label{subsec:SBC_dcy} 1495 1487 %------------------------------------------namsbc------------------------------------------------------------- … … 1577 1569 % Surface restoring to observed SST and/or SSS 1578 1570 % ------------------------------------------------------------------------------------------------------------- 1579 \subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})] 1580 {Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 1571 \subsection[Surface restoring to observed SST and/or SSS (\textit{sbcssr.F90})]{Surface restoring to observed SST and/or SSS (\protect\mdl{sbcssr})} 1581 1572 \label{subsec:SBC_ssr} 1582 1573 %------------------------------------------namsbc_ssr---------------------------------------------------- … … 1589 1580 a feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$: 1590 1581 \[ 1591 % \label{eq: sbc_dmp_q}1582 % \label{eq:SBC_dmp_q} 1592 1583 Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right) 1593 1584 \] … … 1602 1593 1603 1594 \begin{equation} 1604 \label{eq: sbc_dmp_emp}1595 \label{eq:SBC_dmp_emp} 1605 1596 \textit{emp} = \textit{emp}_o + \gamma_s^{-1} e_{3t} \frac{ \left(\left.S\right|_{k=1}-SSS_{Obs}\right)} 1606 1597 {\left.S\right|_{k=1}} … … 1613 1604 $\left.S\right|_{k=1}$ is the model surface layer salinity and 1614 1605 $\gamma_s$ is a negative feedback coefficient which is provided as a namelist parameter. 1615 Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq: sbc_dmp_emp} as1606 Unlike heat flux, there is no physical justification for the feedback term in \autoref{eq:SBC_dmp_emp} as 1616 1607 the atmosphere does not care about ocean surface salinity \citep{madec.delecluse_IWN97}. 1617 1608 The SSS restoring term should be viewed as a flux correction on freshwater fluxes to … … 1663 1654 % CICE-ocean Interface 1664 1655 % ------------------------------------------------------------------------------------------------------------- 1665 \subsection[Interface to CICE (\textit{sbcice\_cice.F90})] 1666 {Interface to CICE (\protect\mdl{sbcice\_cice})} 1656 \subsection[Interface to CICE (\textit{sbcice\_cice.F90})]{Interface to CICE (\protect\mdl{sbcice\_cice})} 1667 1657 \label{subsec:SBC_cice} 1668 1658 … … 1698 1688 % Freshwater budget control 1699 1689 % ------------------------------------------------------------------------------------------------------------- 1700 \subsection[Freshwater budget control (\textit{sbcfwb.F90})] 1701 {Freshwater budget control (\protect\mdl{sbcfwb})} 1690 \subsection[Freshwater budget control (\textit{sbcfwb.F90})]{Freshwater budget control (\protect\mdl{sbcfwb})} 1702 1691 \label{subsec:SBC_fwb} 1703 1692
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