Changeset 10373 for NEMO/trunk/doc/latex


Ignore:
Timestamp:
2018-12-05T10:24:24+01:00 (2 years ago)
Author:
emanuelaclementi
Message:

2179: Update doc chap_SBC including wave interaction

Location:
NEMO/trunk/doc/latex/NEMO
Files:
3 edited

Legend:

Unmodified
Added
Removed
  • NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.bib

    r10124 r10373  
    547547PAGES = {1285--1297}, 
    548548DOI = {10.5194/gmd-8-1285-2015} 
     549} 
     550 
     551@ARTICLE{Breivik_al_JPO2014, 
     552   AUTHOR = {{\O}yvind Breivik and Peter A.E.M. Janssen and Jean-Raymond Bidlot}, 
     553   YEAR = {2014}, 
     554   TITLE = "{Approximate Stokes Drift Profiles in Deep Water}", 
     555   JOURNAL = {JPO}, 
     556   VOLUME = {44}, 
     557   NUMBER = {9}, 
     558   DOI = {10.1175/JPO-D-14-0020.1.}, 
     559   PAGES = {2433--2445, arXiv:1406.5039} 
    549560} 
    550561 
     
    16551666} 
    16561667 
     1668@TECHREPORT{Janssen_al_TM13, 
     1669 author = {P.A.E.M. Janssen and {\O}. Breivik and K. Mogensen  
     1670           and F. Vitart and  M. Balmaseda and J.B. Bidlot and  
     1671           S. Keeley and M. Leut-becher and L. Magnusson and F. Molteni}, 
     1672 title = {Air-Sea Interaction and Surface Waves}, 
     1673 year = {2013}, 
     1674 volume = {712}, 
     1675 institution = {ECMWF}, 
     1676} 
     1677 
    16571678@ARTICLE{Jayne_St_Laurent_GRL01, 
    16581679  author = {S.R. Jayne and L.C. {St. Laurent}}, 
     
    29923013  volume = {359}, 
    29933014  pages = {123--129} 
     3015} 
     3016 
     3017@INCOLLECTION{Stokes_1847, 
     3018  author    = {G.G. Stokes}, 
     3019  title     = {On the theory of oscillatory waves}, 
     3020  booktitle = {Transactions of the Cambridge Philosophy Society}, 
     3021  year      = {1847}, 
     3022  volume    = {8}, 
     3023  Pages     = {441--455} 
    29943024} 
    29953025 
  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex

    r10354 r10373  
    3232\end{itemize} 
    3333 
    34 Five different ways to provide the first six fields to the ocean are available which are controlled by 
     34Four different ways to provide the first six fields to the ocean are available which are controlled by 
    3535namelist \ngn{namsbc} variables: 
    3636an analytical formulation (\np{ln\_ana}\forcode{ = .true.}), 
    3737a flux formulation (\np{ln\_flx}\forcode{ = .true.}), 
    3838a 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 
     39CLIO (\np{ln\_blk\_clio}\forcode{ = .true.}) bulk formulae) and 
    4240a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler) 
    4341(\np{ln\_cpl} or \np{ln\_mixcpl}\forcode{ = .true.}).  
     
    7674  the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle 
    7775  (\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 Stokes-Coriolis 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.}). 
    7984\end{itemize} 
    80 The latter option is possible only in case core or mfs bulk formulas are selected. 
    8185 
    8286In this chapter, we first discuss where the surface boundary condition appears in the model equations. 
     
    593597% Bulk formulation 
    594598% ================================================================ 
    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})}} 
    597601\label{sec:SBC_blk} 
    598602 
     
    600604 
    601605The atmospheric fields used depend on the bulk formulae used. 
    602 Three bulk formulations are available: 
    603 the CORE, the CLIO and the MFS bulk formulea. 
     606Two bulk formulations are available: 
     607the CORE and the CLIO bulk formulea. 
    604608The 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}. 
    606610 
    607611Note: 
     
    712716the namsbc\_blk\_core or namsbc\_blk\_clio namelist (see \autoref{subsec:SBC_fldread}).  
    713717 
    714 % ------------------------------------------------------------------------------------------------------------- 
    715 %        MFS Bulk formulae 
    716 % ------------------------------------------------------------------------------------------------------------- 
    717 \subsection{MFS formulea (\protect\mdl{sbcblk\_mfs}, \protect\np{ln\_mfs}\forcode{ = .true.})} 
    718 \label{subsec:SBC_blk_mfs} 
    719 %------------------------------------------namsbc_mfs---------------------------------------------------- 
    720 % 
    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 in 
    726 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 between 
    729 surface solar radiation, net long-wave 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 $30^{o}N$ for 
    732 the Atlantic Ocean (hence the same latitudinal band of the Mediterranean Sea). 
    733 The net long-wave radiation flux \citep{Bignami_al_JGR95} is a function of 
    734 air temperature, sea-surface temperature, cloud cover and relative humidity. 
    735 Sensible heat and latent heat fluxes are computed by classical bulk formulae parameterised according to 
    736 \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 Grid-T 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 % ------------------------------------------------------------------------------------------------------------- 
    751718% ================================================================ 
    752719% Coupled formulation 
     
    12031170since its trajectory data may be spread across multiple files. 
    12041171 
     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 
     1182Ocean waves represent the interface between the ocean and the atmosphere, so NEMO is extended to incorporate  
     1183physical processes related to ocean surface waves, namely the surface stress modified by growth and  
     1184dissipation of the oceanic wave field, the Stokes-Coriolis force and the Stokes drift impact on mass and  
     1185tracer advection; moreover the neutral surface drag coefficient from a wave model can be used to evaluate  
     1186the wind stress. 
     1187 
     1188Physical 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  
     1190different porcesses should be activated as explained in the following sections. 
     1191 
     1192Wave 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  
     1195for external data names, locations, frequency, interpolation and all the miscellanous options allowed by  
     1196Input 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.}  
     1198in \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 
     1209The neutral surface drag coefficient provided from an external data source ($i.e.$ a wave 
     1210model),  
     1211can be used by setting the logical variable \np{ln\_cdgw} \forcode{= .true.} in \ngn{namsbc} namelist.  
     1212Then using the routine \rou{turb\_ncar} and starting from the neutral drag coefficent provided,  
     1213the drag coefficient is computed according to the stable/unstable conditions of the  
     1214air-sea 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 
     1223The Stokes drift is a wave driven mechanism of mass and momentum transport \citep{Stokes_1847}.  
     1224It is defined as the difference between the average velocity of a fluid parcel (Lagrangian velocity)  
     1225and the current measured at a fixed point (Eulerian velocity).  
     1226As waves travel, the water particles that make up the waves travel in orbital motions but  
     1227without a closed path. Their movement is enhanced at the top of the orbit and slowed slightly  
     1228at the bottom so the result is a net forward motion of water particles, referred to as the Stokes drift.  
     1229An accurate evaluation of the Stokes drift and the inclusion of related processes may lead to improved  
     1230representation of surface physics in ocean general circulation models. 
     1231The 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 
     1239where: ${\theta}$ is the wave direction, $f$ is the wave intrinsic frequency,  
     1240$\mathrm{S}($f$,\theta)$ is the 2D frequency-direction spectrum,  
     1241$k$ is the mean wavenumber defined as:  
     1242$k=\frac{2\pi}{\lambda}$ (being $\lambda$ the wavelength). \\ 
     1243 
     1244In order to evaluate the Stokes drift in a realistic ocean wave field the wave spectral shape is required  
     1245and its computation quickly becomes expensive as the 2D spectrum must be integrated for each vertical level.  
     1246To simplify, it is customary to use approximations to the full Stokes profile. 
     1247Three possible parameterizations for the calculation for the approximate Stokes drift velocity profile  
     1248are 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  
     1250and makes possible the estimation of the surface Stokes drift for random directional waves in  
     1251realistic 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}} {1-8k_ez}  
     1259\end{equation} 
     1260 
     1261where $k_e$ 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} 
     1264k_e = \frac{|\mathbf{U}_{\left.st\right|_{z=0}}|} {|T_{st}|}  
     1265\quad \text{and }\ 
     1266T_{st} = \frac{1}{16} \bar{\omega} H_s^2  
     1267\end{equation} 
     1268 
     1269where $H_s$ 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  
     1272reasonable 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 
     1280where $erf$ 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  
     1283but using the wave frequency from a wave model. 
     1284 
     1285\end{description} 
     1286 
     1287The Stokes drift enters the wave-averaged momentum equation, as well as the tracer advection equations  
     1288and its effect on the evolution of the sea-surface 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 
     1295The tracer advection equation is also modified in order for Eulerian ocean models to properly account  
     1296for unresolved wave effect. The divergence of the wave tracer flux equals the mean tracer advection  
     1297that is induced by the three-dimensional Stokes velocity.  
     1298The advective equation for a tracer $c$ combining the effects of the mean current and sea surface waves  
     1299can 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% Stokes-Coriolis term (ln_stcor) 
     1309% ================================================================ 
     1310\subsection{Stokes-Coriolis term (\protect\np{ln\_stcor})} 
     1311\label{subsec:SBC_wave_stcor} 
     1312 
     1313In a rotating ocean, waves exert a wave-induced stress on the mean ocean circulation which results  
     1314in a force equal to $\mathbf{U}_{st}$×$f$, where $f$ is the Coriolis parameter.  
     1315This additional force may have impact on the Ekman turning of the surface current.  
     1316In order to include this term, once evaluated the Stokes drift (using one of the 3 possible  
     1317approximations 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 
     1327The surface stress felt by the ocean is the atmospheric stress minus the net stress going  
     1328into the waves \citep{Janssen_al_TM13}. Therefore, when waves are growing, momentum and energy is spent and is not  
     1329available for forcing the mean circulation, while in the opposite case of a decaying sea  
     1330state more momentum is available for forcing the ocean.  
     1331Only when the sea state is in equilibrium the ocean is forced by the atmospheric stress,  
     1332but in practice an equilibrium sea state is a fairly rare event.  
     1333So 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 
     1339where $\tau_a$ 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 
     1346where: $c_p$ is the phase speed of the gravity waves, 
     1347$S_{in}$, $S_{nl}$ and $S_{diss}$ are three source terms that represent  
     1348the physics of ocean waves. The first one, $S_{in}$, describes the generation  
     1349of ocean waves by wind and therefore represents the momentum and energy transfer  
     1350from air to ocean waves; the second term $S_{nl}$ denotes  
     1351the nonlinear transfer by resonant four-wave interactions; while the third term $S_{diss}$  
     1352describes the dissipation of waves by processes such as white-capping, large scale breaking  
     1353eddy-induced damping. 
     1354 
     1355The wave stress derived from an external wave model can be provided either through the normalized  
     1356wave stress into the ocean by setting \np{ln\_tauwoc}\forcode{ = .true.}, or through the zonal and  
     1357meridional stress components by setting \np{ln\_tauw}\forcode{ = .true.}. 
     1358 
    12051359 
    12061360% ================================================================ 
     
    14211575\end{description} 
    14221576 
    1423 % ------------------------------------------------------------------------------------------------------------- 
    1424 %        Neutral Drag Coefficient from external wave model 
    1425 % ------------------------------------------------------------------------------------------------------------- 
    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 %------------------------------------------namwave---------------------------------------------------- 
    1430  
    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 by 
    1438 Input Data generic Interface see \autoref{sec:SBC_input}) and 
    1439 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 air-sea interface following 
    1442 \citet{Large_Yeager_Rep04}. 
    14431577 
    14441578 
  • NEMO/trunk/doc/latex/NEMO/subfiles/introduction.tex

    r10354 r10373  
    311311\item new definition of configurations ; 
    312312\item bulk formulation ; 
     313\item NEMO-wave large scale interactions ; 
    313314\item ... ;  
    314315\end{enumerate} 
Note: See TracChangeset for help on using the changeset viewer.