2018-12-10T08:45:39+01:00 (22 months ago)

dev_r10164_HPC09_ESIWACE_PREP_MERGE: merge with trunk@10376, see #2133

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  • NEMO/branches/2018/dev_r10164_HPC09_ESIWACE_PREP_MERGE/doc/latex/NEMO/subfiles/chap_SBC.tex

    r10368 r10377  
    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.}).  
     77  a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}\forcode{ = .true.}); 
     79  the Stokes drift rom an external wave model can be accounted (\np{ln\_sdw}\forcode{ = .true.});  
     81  the Stokes-Coriolis term can be included (\np{ln\_stcor}\forcode{ = .true.}); 
     83  the surface stress felt by the ocean can be modified by surface waves (\np{ln\_tauwoc}\forcode{ = .true.}). 
    80 The latter option is possible only in case core or mfs bulk formulas are selected. 
    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})}} 
    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}. 
    712716the namsbc\_blk\_core or namsbc\_blk\_clio namelist (see \autoref{subsec:SBC_fldread}).  
    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 %---------------------------------------------------------------------------------------------------------- 
    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}. 
    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. 
     1172% ------------------------------------------------------------------------------------------------------------- 
     1173%        Interactions with waves (sbcwave.F90, ln_wave) 
     1174% ------------------------------------------------------------------------------------------------------------- 
     1175\section{Interactions with waves (\protect\mdl{sbcwave}, \protect\np{ln\_wave})} 
     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. 
     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. 
     1192Wave fields can be provided either in forced or coupled mode: 
     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. 
     1202% ================================================================ 
     1203% Neutral drag coefficient from wave model (ln_cdgw) 
     1205% ================================================================ 
     1206\subsection{Neutral drag coefficient from wave model (\protect\np{ln\_cdgw})} 
     1209The neutral surface drag coefficient provided from an external data source ($i.e.$ a wave 
     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}.  
     1217% ================================================================ 
     1218% 3D Stokes Drift (ln_sdw, nn_sdrift) 
     1219% ================================================================ 
     1220\subsection{3D Stokes Drift (\protect\np{ln\_sdw, nn\_sdrift})} 
     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:  
     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 
     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). \\ 
     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: 
     1254\item[\np{nn\_sdrift} = 0]: exponential integral profile parameterization proposed by  
     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}  
     1261where $k_e$ is the effective wave number which depends on the Stokes transport $T_{st}$ defined as follows: 
     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  
     1269where $H_s$ is the significant wave height and $\omega$ is the wave frequency. 
     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 
     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] 
     1280where $erf$ is the complementary error function and $k_p$ is the peak wavenumber. 
     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. 
     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:  
     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  
     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:  
     1301\begin{equation} \label{eq:sbc_wave_tra_sdw} 
     1302\frac{\partial{c}}{\partial{t}} =  
     1303- (\mathbf{U} + \mathbf{U}_{st}) \cdot \nabla{c} 
     1307% ================================================================ 
     1308% Stokes-Coriolis term (ln_stcor) 
     1309% ================================================================ 
     1310\subsection{Stokes-Coriolis term (\protect\np{ln\_stcor})} 
     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. 
     1321% ================================================================ 
     1322% Waves modified stress (ln_tauwoc, ln_tauw) 
     1323% ================================================================ 
     1324\subsection{Wave modified sress (\protect\np{ln\_tauwoc, ln\_tauw})}  
     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:  
     1335\begin{equation} \label{eq:sbc_wave_tauoc} 
     1336\tau_{oc,a} = \tau_a - \tau_w 
     1339where $\tau_a$ is the atmospheric surface stress; 
     1340$\tau_w$ is the atmospheric stress going into the waves defined as: 
     1342\begin{equation} \label{eq:sbc_wave_tauw} 
     1343\tau_w = \rho g \int {\frac{dk}{c_p} (S_{in}+S_{nl}+S_{diss})} 
     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. 
     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.}. 
    12061360% ================================================================ 
    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---------------------------------------------------- 
    1431 \nlst{namsbc_wave} 
    1432 %------------------------------------------------------------------------------------------------------------- 
    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}. 
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