Changeset 10377 for NEMO/branches/2018/dev_r10164_HPC09_ESIWACE_PREP_MERGE/doc/latex/NEMO/subfiles/chap_SBC.tex
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NEMO/branches/2018/dev_r10164_HPC09_ESIWACE_PREP_MERGE/doc/latex/NEMO/subfiles/chap_SBC.tex
r10368 r10377 32 32 \end{itemize} 33 33 34 F ivedifferent ways to provide the first six fields to the ocean are available which are controlled by34 Four different ways to provide the first six fields to the ocean are available which are controlled by 35 35 namelist \ngn{namsbc} variables: 36 36 an analytical formulation (\np{ln\_ana}\forcode{ = .true.}), 37 37 a flux formulation (\np{ln\_flx}\forcode{ = .true.}), 38 38 a bulk formulae formulation (CORE (\np{ln\_blk\_core}\forcode{ = .true.}), 39 CLIO (\np{ln\_blk\_clio}\forcode{ = .true.}) or 40 MFS \footnote { Note that MFS bulk formulae compute fluxes only for the ocean component} 41 (\np{ln\_blk\_mfs}\forcode{ = .true.}) bulk formulae) and 39 CLIO (\np{ln\_blk\_clio}\forcode{ = .true.}) bulk formulae) and 42 40 a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler) 43 41 (\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}). … … 76 74 the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle 77 75 (\np{ln\_dm2dc}\forcode{ = .true.}); 78 and a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}\forcode{ = .true.}). 76 \item 77 a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}\forcode{ = .true.}); 78 \item 79 the Stokes drift rom an external wave model can be accounted (\np{ln\_sdw}\forcode{ = .true.}); 80 \item 81 the StokesCoriolis term can be included (\np{ln\_stcor}\forcode{ = .true.}); 82 \item 83 the surface stress felt by the ocean can be modified by surface waves (\np{ln\_tauwoc}\forcode{ = .true.}). 79 84 \end{itemize} 80 The latter option is possible only in case core or mfs bulk formulas are selected.81 85 82 86 In this chapter, we first discuss where the surface boundary condition appears in the model equations. … … 593 597 % Bulk formulation 594 598 % ================================================================ 595 \section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio ,\_mfs\}.F90})}]596 {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio}, \protect\mdl{sbcblk\_mfs})}}599 \section[Bulk formulation {(\textit{sbcblk\{\_core,\_clio\}.F90})}] 600 {Bulk formulation {(\protect\mdl{sbcblk\_core}, \protect\mdl{sbcblk\_clio})}} 597 601 \label{sec:SBC_blk} 598 602 … … 600 604 601 605 The atmospheric fields used depend on the bulk formulae used. 602 T hreebulk formulations are available:603 the CORE , the CLIO and the MFSbulk formulea.606 Two bulk formulations are available: 607 the CORE and the CLIO bulk formulea. 604 608 The choice is made by setting to true one of the following namelist variable: 605 \np{ln\_core} ; \np{ln\_clio} or \np{ln\_mfs}.609 \np{ln\_core} or \np{ln\_clio}. 606 610 607 611 Note: … … 712 716 the namsbc\_blk\_core or namsbc\_blk\_clio namelist (see \autoref{subsec:SBC_fldread}). 713 717 714 % 715 % MFS Bulk formulae716 % 717 \subsection{MFS formulea (\protect\mdl{sbcblk\_mfs}, \protect\np{ln\_mfs}\forcode{ = .true.})}718 \label{subsec:SBC_blk_mfs}719 %namsbc_mfs720 %721 %\nlst{namsbc_mfs}722 %723 724 The MFS (Mediterranean Forecasting System) bulk formulae have been developed by \citet{Castellari_al_JMS1998}.725 They have been designed to handle the ECMWF operational data and are currently in use in726 the MFS operational system \citep{Tonani_al_OS08}, \citep{Oddo_al_OS09}.727 The wind stress computation uses a drag coefficient computed according to \citet{Hellerman_Rosenstein_JPO83}.728 The surface boundary condition for temperature involves the balance between729 surface solar radiation, net longwave radiation, the latent and sensible heat fluxes.730 Solar radiation is dependent on cloud cover and is computed by means of an astronomical formula \citep{Reed_JPO77}.731 Albedo monthly values are from \citet{Payne_JAS72} as means of the values at $40^{o}N$ and $30^{o}N$ for732 the Atlantic Ocean (hence the same latitudinal band of the Mediterranean Sea).733 The net longwave radiation flux \citep{Bignami_al_JGR95} is a function of734 air temperature, seasurface temperature, cloud cover and relative humidity.735 Sensible heat and latent heat fluxes are computed by classical bulk formulae parameterised according to736 \citet{Kondo1975}.737 Details on the bulk formulae used can be found in \citet{Maggiore_al_PCE98} and \citet{Castellari_al_JMS1998}.738 739 Options are defined through the \ngn{namsbc\_mfs} namelist variables.740 The required 7 input fields must be provided on the model GridT and are:741 \begin{itemize}742 \item Zonal Component of the 10m wind ($ms^{1}$) (\np{sn\_windi})743 \item Meridional Component of the 10m wind ($ms^{1}$) (\np{sn\_windj})744 \item Total Claud Cover (\%) (\np{sn\_clc})745 \item 2m Air Temperature ($K$) (\np{sn\_tair})746 \item 2m Dew Point Temperature ($K$) (\np{sn\_rhm})747 \item Total Precipitation ${Kg} m^{2} s^{1}$ (\np{sn\_prec})748 \item Mean Sea Level Pressure (${Pa}$) (\np{sn\_msl})749 \end{itemize}750 % 751 718 % ================================================================ 752 719 % Coupled formulation … … 1203 1170 since its trajectory data may be spread across multiple files. 1204 1171 1172 %  1173 % Interactions with waves (sbcwave.F90, ln_wave) 1174 %  1175 \section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 1176 \label{sec:SBC_wave} 1177 %namsbc_wave 1178 1179 \nlst{namsbc_wave} 1180 % 1181 1182 Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate 1183 physical processes related to ocean surface waves, namely the surface stress modified by growth and 1184 dissipation of the oceanic wave field, the StokesCoriolis force and the Stokes drift impact on mass and 1185 tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate 1186 the wind stress. 1187 1188 Physical processes related to ocean surface waves can be accounted by setting the logical variable 1189 \np{ln\_wave}\forcode{= .true.} in \ngn{namsbc} namelist. In addition, specific flags accounting for 1190 different porcesses should be activated as explained in the following sections. 1191 1192 Wave fields can be provided either in forced or coupled mode: 1193 \begin{description} 1194 \item[forced mode]: wave fields should be defined through the \ngn{namsbc\_wave} namelist 1195 for external data names, locations, frequency, interpolation and all the miscellanous options allowed by 1196 Input Data generic Interface (see \autoref{sec:SBC_input}). 1197 \item[coupled mode]: NEMO and an external wave model can be coupled by setting \np{ln\_cpl} \forcode{= .true.} 1198 in \ngn{namsbc} namelist and filling the \ngn{namsbc\_cpl} namelist. 1199 \end{description} 1200 1201 1202 % ================================================================ 1203 % Neutral drag coefficient from wave model (ln_cdgw) 1204 1205 % ================================================================ 1206 \subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 1207 \label{subsec:SBC_wave_cdgw} 1208 1209 The neutral surface drag coefficient provided from an external data source ($i.e.$ a wave 1210 model), 1211 can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist. 1212 Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided, 1213 the drag coefficient is computed according to the stable/unstable conditions of the 1214 airsea interface following \citet{Large_Yeager_Rep04}. 1215 1216 1217 % ================================================================ 1218 % 3D Stokes Drift (ln_sdw, nn_sdrift) 1219 % ================================================================ 1220 \subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 1221 \label{subsec:SBC_wave_sdw} 1222 1223 The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}. 1224 It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity) 1225 and the current measured at a fixed point (Eulerian velocity). 1226 As waves travel, the water particles that make up the waves travel in orbital motions but 1227 without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly 1228 at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift. 1229 An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved 1230 representation of surface physics in ocean general circulation models. 1231 The Stokes drift velocity $\mathbf{U}_{st}$ in deep water can be computed from the wave spectrum and may be written as: 1232 1233 \begin{equation} \label{eq:sbc_wave_sdw} 1234 \mathbf{U}_{st} = \frac{16{\pi^3}} {g} 1235 \int_0^\infty \int_{\pi}^{\pi} (cos{\theta},sin{\theta}) {f^3} 1236 \mathrm{S}(f,\theta) \mathrm{e}^{2kz}\,\mathrm{d}\theta {d}f 1237 \end{equation} 1238 1239 where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency, 1240 $\mathrm{S}($f$,\theta)$ is the 2D frequencydirection spectrum, 1241 $k$ is the mean wavenumber defined as: 1242 $k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\ 1243 1244 In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required 1245 and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level. 1246 To simplify, it is customary to use approximations to the full Stokes profile. 1247 Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile 1248 are included in the code through the \np{nn\_sdrift} parameter once provided the surface Stokes drift 1249 $\mathbf{U}_{st _{z=0}}$ which is evaluated by an external wave model that accurately reproduces the wave spectra 1250 and makes possible the estimation of the surface Stokes drift for random directional waves in 1251 realistic wave conditions: 1252 1253 \begin{description} 1254 \item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by 1255 \citet{Breivik_al_JPO2014}: 1256 1257 \begin{equation} \label{eq:sbc_wave_sdw_0a} 1258 \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \frac{\mathrm{e}^{2k_ez}} {18k_ez} 1259 \end{equation} 1260 1261 where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows: 1262 1263 \begin{equation} \label{eq:sbc_wave_sdw_0b} 1264 k_e = \frac{\mathbf{U}_{\left.st\right_{z=0}}} {T_{st}} 1265 \quad \text{and }\ 1266 T_{st} = \frac{1}{16} \bar{\omega} H_s^2 1267 \end{equation} 1268 1269 where $H_s$ is the significant wave height and $\omega$ is the wave frequency. 1270 1271 \item[\np{nn\_sdrift} = 1]: velocity profile based on the Phillips spectrum which is considered to be a 1272 reasonable estimate of the part of the spectrum most contributing to the Stokes drift velocity near the surface 1273 \citep{Breivik_al_OM2016}: 1274 1275 \begin{equation} \label{eq:sbc_wave_sdw_1} 1276 \mathbf{U}_{st} \cong \mathbf{U}_{st _{z=0}} \Big[exp(2k_pz)\beta \sqrt{2 \pi k_pz} 1277 \textit{ erf } \Big(\sqrt{2 k_pz}\Big)\Big] 1278 \end{equation} 1279 1280 where $erf$ is the complementary error function and $k_p$ is the peak wavenumber. 1281 1282 \item[\np{nn\_sdrift} = 2]: velocity profile based on the Phillips spectrum as for \np{nn\_sdrift} = 1 1283 but using the wave frequency from a wave model. 1284 1285 \end{description} 1286 1287 The Stokes drift enters the waveaveraged momentum equation, as well as the tracer advection equations 1288 and its effect on the evolution of the seasurface height ${\eta}$ is considered as follows: 1289 1290 \begin{equation} \label{eq:sbc_wave_eta_sdw} 1291 \frac{\partial{\eta}}{\partial{t}} = 1292 \nabla_h \int_{H}^{\eta} (\mathbf{U} + \mathbf{U}_{st}) dz 1293 \end{equation} 1294 1295 The tracer advection equation is also modified in order for Eulerian ocean models to properly account 1296 for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection 1297 that is induced by the threedimensional Stokes velocity. 1298 The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves 1299 can be formulated as follows: 1300 1301 \begin{equation} \label{eq:sbc_wave_tra_sdw} 1302 \frac{\partial{c}}{\partial{t}} = 1303  (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c} 1304 \end{equation} 1305 1306 1307 % ================================================================ 1308 % StokesCoriolis term (ln_stcor) 1309 % ================================================================ 1310 \subsection{StokesCoriolis term (\protect\np{ln\_stcor})} 1311 \label{subsec:SBC_wave_stcor} 1312 1313 In a rotating ocean, waves exert a waveinduced stress on the mean ocean circulation which results 1314 in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter. 1315 This additional force may have impact on the Ekman turning of the surface current. 1316 In order to include this term, once evaluated the Stokes drift (using one of the 3 possible 1317 approximations described in \autoref{subsec:SBC_wave_sdw}), 1318 \np{ln\_stcor}\forcode{ = .true.} has to be set. 1319 1320 1321 % ================================================================ 1322 % Waves modified stress (ln_tauwoc, ln_tauw) 1323 % ================================================================ 1324 \subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})} 1325 \label{subsec:SBC_wave_tauw} 1326 1327 The surface stress felt by the ocean is the atmospheric stress minus the net stress going 1328 into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not 1329 available for forcing the mean circulation, while in the opposite case of a decaying sea 1330 state more momentum is available for forcing the ocean. 1331 Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress, 1332 but in practice an equilibrium sea state is a fairly rare event. 1333 So the atmospheric stress felt by the ocean circulation $\tau_{oc,a}$ can be expressed as: 1334 1335 \begin{equation} \label{eq:sbc_wave_tauoc} 1336 \tau_{oc,a} = \tau_a  \tau_w 1337 \end{equation} 1338 1339 where $\tau_a$ is the atmospheric surface stress; 1340 $\tau_w$ is the atmospheric stress going into the waves defined as: 1341 1342 \begin{equation} \label{eq:sbc_wave_tauw} 1343 \tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})} 1344 \end{equation} 1345 1346 where: $c_p$ is the phase speed of the gravity waves, 1347 $S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent 1348 the physics of ocean waves. The first one, $S_{in}$, describes the generation 1349 of ocean waves by wind and therefore represents the momentum and energy transfer 1350 from air to ocean waves; the second term $S_{nl}$ denotes 1351 the nonlinear transfer by resonant fourwave interactions; while the third term $S_{diss}$ 1352 describes the dissipation of waves by processes such as whitecapping, large scale breaking 1353 eddyinduced damping. 1354 1355 The wave stress derived from an external wave model can be provided either through the normalized 1356 wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and 1357 meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}. 1358 1205 1359 1206 1360 % ================================================================ … … 1421 1575 \end{description} 1422 1576 1423 % 1424 % Neutral Drag Coefficient from external wave model1425 % 1426 \subsection[Neutral drag coeff. from external wave model (\protect\mdl{sbcwave})]1427 {Neutral drag coefficient from external wave model (\protect\mdl{sbcwave})}1428 \label{subsec:SBC_wave}1429 %namwave1430 1431 \nlst{namsbc_wave}1432 %1433 1434 In order to read a neutral drag coefficient, from an external data source ($i.e.$ a wave model),1435 the logical variable \np{ln\_cdgw} in \ngn{namsbc} namelist must be set to \forcode{.true.}.1436 The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the namelist \ngn{namsbc\_wave}1437 (for external data names, locations, frequency, interpolation and all the miscellanous options allowed by1438 Input Data generic Interface see \autoref{sec:SBC_input}) and1439 a 2D field of neutral drag coefficient.1440 Then using the routine TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided,1441 the drag coefficient is computed according to stable/unstable conditions of the airsea interface following1442 \citet{Large_Yeager_Rep04}.1443 1577 1444 1578
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