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Changeset 4644 for branches/2014/dev_r4642_WavesWG/DOC – NEMO

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Timestamp:
2014-05-15T15:56:53+02:00 (10 years ago)
Author:
acc
Message:

Branch 2014/dev_r4642_WavesWG #1323. Import of surface wave components from the 2013/dev_ECMWF_waves branch + a few compatability changes and some mislaid documentation

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branches/2014/dev_r4642_WavesWG/DOC/TexFiles
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5 edited

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  • branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Biblio/Biblio.bib

    r4560 r4644  
    514514} 
    515515 
     516@TECHREPORT{Breivik_ECMWF13, 
     517      AUTHOR = "{\O} Breivik and PAEM Janssen and JR Bidlot", 
     518      TITLE = "{Approximate Stokes Drift Profiles in Deep Water}", 
     519      YEAR = "2013", 
     520      PAGES = "18", 
     521      NUMBER = "716", 
     522      URL = "http://www.ecmwf.int/publications/library/do/references/list/14", 
     523      TYPE = "ECMWF Technical Memorandum", 
     524      INSTITUTION = "European Centre for Medium-Range Weather Forecasts"} 
     525 
    516526@ARTICLE{Brown_Campana_MWR78, 
    517527  author = {J. A. Brown and K. A. Campana}, 
     
    651661} 
    652662 
     663@article{Charnock_QJRMS55, 
     664  title="{Wind stress on a water surface}", 
     665  author="Charnock, H", 
     666  journal=QJRMS, 
     667  volume="81", 
     668  number="350", 
     669  pages={639--640}, 
     670  year=1955} 
     671 
    653672@ARTICLE{Cox1987, 
    654673  author = {M. Cox}, 
     
    742761  volume = {34}, 
    743762  pages = {8--13} 
     763} 
     764 
     765@article{Dee_QJRMS11, 
     766  title="{The ERA-Interim reanalysis: Configuration and performance of the data assimilation system}", 
     767  author="DP Dee and Uppala, SM and Simmons, AJ and Berrisford, P. and  
     768  Poli, P. and Kobayashi, S. and Andrae, U. and Balmaseda, MA and Balsamo, G. 
     769  and Bauer, P and Bechtold P and Beljaars, ACM and L van de Berg and J Bidlot 
     770  and N Bormann and others", 
     771  journal=QJRMS, 
     772  volume={137}, 
     773  number={656}, 
     774  pages={553--597, doi:10.1002/qj.828}, 
     775  year={2011}, 
     776  publisher={Wiley Online Library} 
    744777} 
    745778 
     
    895928  url = {http://dx.doi.org/10.1029/2005GL022463} 
    896929} 
     930 
     931 
     932@article{Edson_JPO13, 
     933  title="{On the Exchange of Momentum over the Open Ocean}", 
     934  author="Edson, James and Jampana, Venkata and Weller, Robert  
     935          and Bigorre, Sebastien and Plueddemann, Albert and Fairall, Christopher  
     936          and Miller, Scott and Mahrt, Larry and Vickers, Dean and  
     937          Hersbach, Hans", 
     938  journal=JPO, 
     939  volume="43", 
     940  pages = "1589--1610, doi:10.1175/JPO-D-12-0173.1", 
     941  doi = "10.1175/JPO-D-12-0173.1", 
     942  year="2013"} 
    897943 
    898944@ARTICLE{Egbert_Ray_JGR01, 
     
    12641310} 
    12651311 
     1312@article{Hasselmann_GAFD70, 
     1313  title="{Wave-driven inertial oscillations}", 
     1314  author="Hasselmann, K", 
     1315  journal="Geophysical and Astrophysical Fluid Dynamics", 
     1316  volume="1", 
     1317  number="3-4", 
     1318  pages="463--502, doi:10.1080/03091927009365783", 
     1319  year="1970"} 
     1320 
    12661321@ARTICLE{Hazeleger_Drijfhout_JPO98, 
    12671322  author = {W. Hazeleger and S. S. Drijfhout}, 
     
    13811436} 
    13821437 
     1438@book{Holthuijsen07, 
     1439  title="{Waves in Oceanic and Coastal Waters}", 
     1440  author={Holthuijsen, L.H.}, 
     1441  year={2007}, 
     1442  pages={387}, 
     1443  location="Books/holthuisjen07.pdf", 
     1444  publisher={Cambridge University Press} } 
     1445 
    13831446@ARTICLE{Hordoir_al_CD08, 
    13841447  author = {R. Hordoir and J. Polcher and J.-C. Brun-Cottan and G. Madec}, 
     
    14761539  pages = {381--389} 
    14771540} 
     1541 
     1542@article{Janssen_JPO89, 
     1543  title="{Wave-induced stress and the drag of air flow over sea waves}", 
     1544  author="Janssen, PAEM", 
     1545  year="1989", 
     1546  journal=JPO, 
     1547  volume={19}, 
     1548  number={6}, 
     1549  pages={745--754, doi:10/fsz7vd} 
     1550} 
     1551 
     1552@inproceedings{Janssen_AH04, 
     1553  title="{Impact of the sea state on the atmosphere and ocean}", 
     1554  author="Janssen, P.A.E.M. and Saetra, O. and Wettre, C. and  
     1555           Hersbach, H. and Bidlot, J.", 
     1556  booktitle="Annales hydrographiques", 
     1557  volume={3-772}, 
     1558  pages={3.1--3.23}, 
     1559  year={2004}, 
     1560  organization={Service hydrographique et oc{\'e}anographique de la marine} 
     1561} 
     1562 
     1563@article{Janssen_Rep08, 
     1564  title="{Progress in ocean wave forecasting}", 
     1565  author="Janssen, PAEM", 
     1566  journal="Journal of Computational Physics", 
     1567  volume="227", 
     1568  number="7", 
     1569  pages="3572--3594, doi:10.1016/j.jcp.2007.04.029", 
     1570  year="2008"} 
     1571 
     1572 
     1573@article{Janssen_JGR12, 
     1574  author="Janssen, PAEM", 
     1575  title="{Ocean Wave Effects on the Daily Cycle in SST}", 
     1576  year="2012", 
     1577  journal=JGR, 
     1578  volume="117", 
     1579  pages="C00J32, 24 pp, doi:10/mth"} 
     1580 
     1581@TECHREPORT{Janssen_ECMWF13, 
     1582      AUTHOR = "PAEM Janssen and {\O} Breivik and K Mogensen and F Vitart and  
     1583                M Balmaseda and JR Bidlot and S Keeley and M Leutbecher and  
     1584                L Magnusson and F Molteni", 
     1585      TITLE = "{Air-Sea Interaction and Surface Waves}", 
     1586      YEAR = "2013", 
     1587      PAGES = "36", 
     1588      NUMBER = "712", 
     1589      URL = "http://www.ecmwf.int/publications/library/do/references/list/14", 
     1590      TYPE = "ECMWF Technical Memorandum", 
     1591      INSTITUTION = "European Centre for Medium-Range Weather Forecasts"} 
    14781592 
    14791593@ARTICLE{Jayne_St_Laurent_GRL01, 
     
    26812795} 
    26822796 
     2797@ARTICLE{Stokes_TCPS47, 
     2798      AUTHOR = "G~G Stokes", 
     2799      YEAR = "1847", 
     2800      TITLE = "{On the theory of oscillatory waves}", 
     2801      JOURNAL = "Trans Cambridge Philos Soc", 
     2802      VOLUME = "8", 
     2803      PAGES = "441--455"} 
     2804 
    26832805@ARTICLE{Talagrand_JAS72, 
    26842806  author = {O. Talagrand}, 
     
    28592981} 
    28602982 
     2983@TECHREPORT{wam38r1, 
     2984      AUTHOR = "ECMWF", 
     2985      TITLE = "{IFS Documentation CY38r1, Part VII: ECMWF Wave Model}", 
     2986      YEAR = "2012", 
     2987      PAGES = "77 pp, available at http://ecmwf.int/research/ifsdocs/CY38r1/", 
     2988      TYPE = "{ECMWF Model Documentation}", 
     2989      INSTITUTION = "European Centre for Medium-Range Weather Forecasts"} 
     2990 
    28612991@ARTICLE{Warner_al_OM05, 
    28622992  author = {J. C. Warner and C. R. Sherwood and H. G. Arango and R. P. Signell}, 
     
    29563086  pages = {593--611} 
    29573087} 
     3088 
     3089@MANUAL{wmo98, 
     3090      AUTHOR = "{World Meteorological Organization}", 
     3091      TITLE = "{Guide to wave analysis and forecasting}", 
     3092      YEAR = "1998", 
     3093      ADDRESS = "Geneva, Switzerland", 
     3094      NUMBER = "702", 
     3095      EDITION = "2", 
     3096      ORGANIZATION = "World Meteorological Organization"} 
    29583097 
    29593098@ARTICLE{Zalesak_JCP79, 
  • branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Chapters/Chap_DYN.tex

    r4560 r4644  
    11% ================================================================ 
    2 % Chapter Ocean Dynamics (DYN) 
     2% Chapter Ocean Dynamics (DYN) 
    33% ================================================================ 
    44\chapter{Ocean Dynamics (DYN)} 
     
    795795%>   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   >   > 
    796796\begin{figure}[!t]    \begin{center} 
    797 \includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_time_split.pdf} 
     797\includegraphics[width=0.7\textwidth]{./TexFiles/Figures/Fig_DYN_dynspg_ts.pdf} 
    798798\caption{  \label{Fig_DYN_dynspg_ts} 
    799799Schematic of the split-explicit time stepping scheme for the external  
     
    12931293 
    12941294% ================================================================ 
     1295% Coriolis-Stokes force 
     1296% ================================================================ 
     1297\section  [Coriolis-Stokes Force (\textit{dynstcor})] 
     1298                {Coriolis-Stokes Force (\mdl{dynstcor})} 
     1299\label{DYN_stcor} 
     1300Waves set up a Lagrangian drift in the down-wave direction known 
     1301as the Stokes drift \citep{Stokes_TCPS47}. Although its drift speed 
     1302$\mathbf{v}_\mathrm{s}$ decays rapidly with depth, it can be substantial 
     1303near the surface ($v_\mathrm{s} {\sim}0.7\, \mathrm{m/s}$). In combination 
     1304with the earth's rotation it adds an additional veering to the upper-ocean 
     1305currents known as the Coriolis-Stokes force \citep{Hasselmann_GAFD70}, 
     1306\begin{equation} 
     1307   \frac{D\mathbf{u}}{Dt} = -\frac{1}{\rho} \nabla p  
     1308  + (\mathbf{u} + \mathbf{v}_\mathrm{s}) \times f\hat{\mathbf{z}} 
     1309  + \frac{1}{\rho} \frac{\partial \tau}{\partial z}. 
     1310  \label{Eq_dynstcor_stcor} 
     1311\end{equation} 
     1312It requires integration of the full two-dimensional spectrum to get the 
     1313Stokes profile \citep{Janssen_AH04,Janssen_JGR12}, 
     1314\begin{equation} 
     1315   \mathbf{v}_\mathrm{s}(z) = 4\pi \int_0^{2\pi} \int_0^{\infty}  
     1316                              f \mathbf{k} e^{2kz} F(f,\theta) \, df\, d\theta, 
     1317   \label{Eq_dynstcor_uvfth} 
     1318\end{equation} 
     1319This is computationally demanding and requires access to the full 
     1320two-dimensional wave spectra from a numerical wave model (see e.g. the 
     1321ECMWF WAM implementation, ECWAM, \citealt{wam38r1}), so 
     1322we introduce a parameterized Stokes drift velocity profile 
     1323\citep{Janssen_ECMWF13,Breivik_ECMWF13}, 
     1324\begin{equation} 
     1325   \mathbf{v}_\mathrm{e} = \mathbf{v}_0  
     1326   \frac{e^{2k_\mathrm{e}z}}{1-8k_\mathrm{e}z}. 
     1327   \label{Eq_dynstcor_uve1} 
     1328\end{equation} 
     1329The surface velocity vector $\mathbf{v}_0$ is computed by ECWAM and is 
     1330available both in ERA-Interim \citep{Dee_QJRMS11} and operationally. 
     1331 
     1332The transport under such a profile involves the exponential integral $E_1$ and  
     1333can be solved analytically \citep{Breivik_ECMWF13} to yield 
     1334\begin{equation} 
     1335   {T}_\mathrm{s} = \frac{{v}_0 e^{1/4} E_1(1/4)}{8 k_\mathrm{e}}. 
     1336   \label{Eq_dynstcor_UVe}  
     1337\end{equation} 
     1338This imposes the following constraint on the wavenumber, 
     1339\begin{equation} 
     1340   k_\mathrm{e} = \frac{{v}_0 e^{1/4} E_1(1/4)}{8 
     1341   {T}_\mathrm{s}}. 
     1342   \label{Eq_dynstcor_ke}  
     1343\end{equation} 
     1344Here $E_1(1/4) \approx 1.34$, thus 
     1345\begin{equation} 
     1346   k_\mathrm{e} \approx \frac{{v}_0}{5.97{T}_\mathrm{s}}. 
     1347   \label{Eq_dynstcor_keapprox}  
     1348\end{equation} 
     1349The $n$-th order spectral moment is defined as 
     1350\begin{equation} 
     1351   m_{n} = \int_0^{2\pi} \int_0^{\infty}  
     1352           f^{n} F(f,\theta) \, df\, d\theta. 
     1353   \label{Eq_dynstcor_moment} 
     1354\end{equation} 
     1355The mean frequency is defined as $\overline{f} = m_1/m_0$ 
     1356\citep{wmo98,Holthuijsen07} and the significant wave height $H_{m_0} = 
     13574\sqrt{m_0}$.  We can derive the first moment from the integrated parameters 
     1358of a wave model or from wave observations and find an estimate for the 
     1359Stokes transport, 
     1360\begin{equation} 
     1361  \mathbf{T}_\mathrm{s} \approx \frac{2\pi}{16} \overline{f} H_{m_0}^2 
     1362  \hat{\mathbf{k}}_\mathrm{s}. 
     1363  \label{Eq_dynstcor_UVHsf} 
     1364\end{equation} 
     1365Here $\hat{\mathbf{k}}_\mathrm{s} = (\sin \theta_\mathrm{s}, 
     1366\cos \theta_\mathrm{s})$ is the unit vector in the 
     1367direction $\theta_\mathrm{s}$ of the Stokes transport.  From 
     1368Eqs~(\ref{Eq_dynstcor_keapprox})-(\ref{Eq_dynstcor_UVHsf}) it is clear that 
     1369in order to compute the Stokes drift velocity profile at the desired vertical 
     1370levels we need $H_\mathrm{s}$, $\overline{f}$ and $\mathbf{v}_0$. 
     1371 
     1372The Coriolis-Stokes effect is enabled when \np{ln\_stcor} = true (default = 
     1373false). All wave-related switches are found in \ngn{namsbc}. 
     1374The surface Stokes drift velocity vectors (east and north components) are 
     1375archived in ERA-Interim as GRIB parameters 215 and 216 respectively (table 
     1376140). 
     1377%\smallskip 
     1378%%----------------------------------------------namsbc---------------------------------------------------- 
     1379%\namdisplay{namsbc} 
     1380%%-------------------------------------------------------------------------------------------------------- 
     1381%\smallskip 
     1382% 
     1383% ================================================================ 
  • branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Chapters/Chap_SBC.tex

    r4230 r4644  
    1515The ocean needs six fields as surface boundary condition: 
    1616\begin{itemize} 
    17    \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 
    18    \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 
    19    \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 
     17    \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 
     18    \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 
     19    \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 
    2020\end{itemize} 
    2121plus an optional field: 
    2222\begin{itemize} 
    23    \item the atmospheric pressure at the ocean surface $\left( p_a \right)$ 
     23    \item the atmospheric pressure at the ocean surface $\left( p_a \right)$ 
    2424\end{itemize} 
    2525 
     
    7575\begin{equation} \label{Eq_sbc_dynzdf} 
    7676\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1} 
    77     = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v } 
     77    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v } 
    7878\end{equation} 
    7979where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind  
     
    348348horizontal and vertical dimensions of the associated variable and should  
    349349be equal to 1 over land and 0 elsewhere. 
    350 The procedure can be recursively applied setting nn_lsm > 1 in namsbc namelist.  
    351 Note that nn_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied. 
     350The procedure can be recursively applied setting nn\_lsm > 1 in namsbc namelist.  
     351Note that nn\_lsm=0 forces the code to not apply the procedure even if a file for land/sea mask is supplied. 
    352352 
    353353\subsubsection{Bilinear Interpolation} 
     
    565565 
    566566The atmospheric fields used depend on the bulk formulae used. Three bulk formulations  
    567 are available : the CORE, the CLIO and the MFS bulk formulea. The choice is made by setting to true 
     567are available : the CORE, the CLIO and the MFS bulk formulae. The choice is made by setting to true 
    568568one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or  \np{ln\_mfs}. 
    569569 
    570570Note : in forced mode, when a sea-ice model is used, a bulk formulation (CLIO or CORE) have to be used.  
    571 Therefore the two bulk (CLIO and CORE) formulea include the computation of the fluxes over both  
     571Therefore the two bulk (CLIO and CORE) formulae include the computation of the fluxes over both  
    572572an ocean and an ice surface.  
    573573 
    574574% ------------------------------------------------------------------------------------------------------------- 
    575 %        CORE Bulk formulea 
    576 % ------------------------------------------------------------------------------------------------------------- 
    577 \subsection    [CORE Bulk formulea (\np{ln\_core}=true)] 
    578             {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})} 
     575%        CORE Bulk formulae 
     576% ------------------------------------------------------------------------------------------------------------- 
     577\subsection    [CORE Bulk formulae (\np{ln\_core}=true)] 
     578            {CORE Bulk formulae (\np{ln\_core}=true, \mdl{sbcblk\_core})} 
    579579\label{SBC_blk_core} 
    580580%------------------------------------------namsbc_core---------------------------------------------------- 
     
    591591 
    592592Note that substituting ERA40 to NCEP reanalysis fields  
    593 does not require changes in the bulk formulea themself.  
     593does not require changes in the bulk formulae themself.  
    594594This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}.  
    595595 
     
    621621or larger than the one of the input atmospheric fields. 
    622622 
    623 % ------------------------------------------------------------------------------------------------------------- 
    624 %        CLIO Bulk formulea 
    625 % ------------------------------------------------------------------------------------------------------------- 
    626 \subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)] 
    627             {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})} 
     623\subsubsection    [The ECMWF parametric drag law (\np{ln\_cdec}=true)] 
     624                  {The ECMWF parametric drag law (\np{ln\_cdec}=true)} 
     625As an alternative to the \citet{Large_Yeager_Rep04} drag law the 
     626parameterization used operationally by ECMWF \citep{Janssen_Rep08,Edson_JPO13} is 
     627included, 
     628\begin{equation} 
     629   C_\mathrm{D}(z=10 \, \mathrm{m}) = \left(a + bU_{10}^{p_1}\right)/U_{10}^{p_2}. 
     630   \label{Eq_blk_core_cdec} 
     631\end{equation} 
     632The coefficients are $a = 1.03 \times 10^{-3}$, $b = 0.04\times 10^{-3}$, 
     633$p_1 = 1.48$ and $p_2 = 0.21$.  
     634 
     635\subsubsection    [Wave-modified air-side stress (\np{ln\_cdgw}=true)] 
     636                  {Wave-modified air-side stress (\np{ln\_cdgw}=true)} 
     637The atmospheric momentum flux to the ocean is denoted $\tau_\mathrm{a}$. It is 
     638customary to define an air-side friction velocity as $u_*^2 =  
     639\tau_\mathrm{a}/\rho_\mathrm{a}$. 
     640\citet{Charnock_QJRMS55} was the first to relate the roughness of the sea 
     641surface to the friction velocity, 
     642\begin{equation} 
     643   z_0 = \alpha_\mathrm{CH} \frac{u_{*}^2}{g}, 
     644\end{equation} 
     645where $\alpha_\mathrm{CH}$ is known as the Charnock constant. 
     646\citet{Janssen_JPO89} showed that $\alpha$ is not constant but varies with 
     647the sea state, 
     648\begin{equation} 
     649   \alpha_\mathrm{CH} = 
     650   \frac{\hat{\alpha}_\mathrm{CH}} 
     651        {\sqrt{1-\tau_\mathrm{w}/\tau_\mathrm{a}}}, 
     652\end{equation} 
     653where $\hat{\alpha}_\mathrm{CH} = 0.01$ and the wave-induced stress, 
     654$\tau_\mathrm{in}$, is related to the wind input as 
     655\begin{equation} 
     656   \boldsymbol{\tau}_\mathrm{in} = \rho_\mathrm{w}g \int_0^{2\pi}  
     657      \int_0^{\infty} \frac{\mathbf{k}}{\omega} S_\mathrm{in} \,  
     658      d\omega \, d\theta. 
     659   \label{Eq_blk_core_tauin} 
     660\end{equation} 
     661The wave-modified drag coefficient is then 
     662\begin{equation} 
     663   C_\mathrm{D} = \frac{\kappa^2}{\log^2(10/z_0)}. 
     664\end{equation} 
     665This parameter is stored as CDWW (GRIB parameter 233, table 140) in ERA-Interim and operationally by ECMWF. 
     666Note that it is used in conjunction with the 10-m \emph{neutral} wind speed, 
     667$U_\mathrm{10N}$, also archived. The wind direction is taken from the 10-m 
     668wind vector as before, and only the wind \emph{speed} is changed.  Note also 
     669that where there is a discrepancy between the ice cover of the wave model 
     670and NEMO, a drag parametric drag law should used.  Where the wave model 
     671has ice (as $C_\mathrm{D} = 0$ under ice), a drag law such as the one put 
     672forward by \citet{Large_Yeager_Rep04} or the one used operationally by ECMWF, 
     673see Eq~(\ref{Eq_blk_core_cdec}), must be used to pad the fields. 
     674 
     675\subsubsection    [Wave-modified water-side stress (\np{ln\_tauoc}=true)] 
     676                  {Wave-modified water-side stress (\np{ln\_tauoc}=true)} 
     677As waves break they feed momentum 
     678into the currents. If wind input and dissipation in the wave field were in 
     679equilibrium, the air-side stress would be equal to the total water-side 
     680stress. However, most of the time waves are not in equilibrium 
     681\citep{Janssen_JGR12,Janssen_ECMWF13}, giving 
     682differences in air-side and water-side stress of the order of 5-10\%. 
     683The water-side stress is the total 
     684atmospheric stress minus the momentum absorbed by the wave field (positive) 
     685minus the momentum injected from breaking waves to the ocean (negative),  
     686$\boldsymbol{\tau}_\mathrm{oc} = \boldsymbol{\tau}_\mathrm{a} - 
     687\boldsymbol{\tau}_\mathrm{in} - \boldsymbol{\tau}_\mathrm{ds}$. This can be 
     688written \citep{wam38r1} 
     689\begin{equation} 
     690   \boldsymbol{\tau}_\mathrm{oc} = \boldsymbol{\tau}_\mathrm{a} - 
     691   \rho_\mathrm{w}g \int_0^{2\pi} \int_0^{\infty}  
     692   \frac{\mathbf{k}}{\omega}(S_\mathrm{in} + S_\mathrm{ds})\, d\omega d\theta. 
     693   \label{eq:tauoc} 
     694\end{equation} 
     695This parameter is known as TAUOC (GRIB parameter 214, table 140) is stored in 
     696normalized form, $\tilde{\tau} = \tau_\mathrm{oc}/\tau_\mathrm{a}$, in 
     697ERA-Interim and operationally by ECMWF.  It is controlled by the namelist 
     698parameter \np{ln\_tauoc} in namelist \ngn{namsbc}. 
     699 
     700 
     701% ------------------------------------------------------------------------------------------------------------- 
     702%        CLIO Bulk formulae 
     703% ------------------------------------------------------------------------------------------------------------- 
     704\subsection    [CLIO Bulk formulae (\np{ln\_clio}=true)] 
     705            {CLIO Bulk formulae (\np{ln\_clio}=true, \mdl{sbcblk\_clio})} 
    628706\label{SBC_blk_clio} 
    629707%------------------------------------------namsbc_clio---------------------------------------------------- 
     
    665743%        MFS Bulk formulae 
    666744% ------------------------------------------------------------------------------------------------------------- 
    667 \subsection    [MFS Bulk formulea (\np{ln\_mfs}=true)] 
    668             {MFS Bulk formulea (\np{ln\_mfs}=true, \mdl{sbcblk\_mfs})} 
     745\subsection    [MFS Bulk formulae (\np{ln\_mfs}=true)] 
     746            {MFS Bulk formulae (\np{ln\_mfs}=true, \mdl{sbcblk\_mfs})} 
    669747\label{SBC_blk_mfs} 
    670748%------------------------------------------namsbc_mfs---------------------------------------------------- 
     
    10481126of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available 
    10491127in \NEMO by setting \np{ln\_dm2dc}~=~true (a \textit{\ngn{namsbc}} namelist variable) when using  
    1050 CORE bulk formulea (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).  
     1128CORE bulk formulae (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).  
    10511129The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used  
    10521130can be found in the appendix~A of \cite{Bernie_al_CD07}. The algorithm preserve the daily  
  • branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Chapters/Chap_ZDF.tex

    r4147 r4644  
    197197instabilities associated with too weak vertical diffusion. They must be  
    198198specified at least larger than the molecular values, and are set through  
    199 \np{rn\_avm0} and \np{rn\_avt0} (namzdf namelist, see \S\ref{ZDF_cst}). 
     199\np{rn\_avm0} and \np{rn\_avt0} (\ngn{namzdf} namelist, see \S\ref{ZDF_cst}). 
    200200 
    201201\subsubsection{Turbulent length scale} 
     
    262262\end{equation} 
    263263 
    264 At the ocean surface, a non zero length scale is set through the  \np{rn\_lmin0} namelist  
    265 parameter. Usually the surface scale is given by $l_o = \kappa \,z_o$  
    266 where $\kappa = 0.4$ is von Karman's constant and $z_o$ the roughness  
    267 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 interior  
    269 a minimum length scale is set to recover the molecular viscosity when $\bar{e}$  
    270 reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). 
     264At the ocean surface, a non zero length scale is set through the 
     265\np{rn\_lmin0} namelist parameter. Usually the surface scale is given 
     266by $l_o = \kappa \,z_o$ where $\kappa = 0.4$ is von Karman's constant 
     267and $z_o$ the roughness parameter of the surface. Assuming $z_o=0.1$~m 
     268\citep{Craig_Banner_JPO94} leads to a 0.04~m, the default value of 
     269\np{rn\_lsurf}. In the ocean interior a minimum length scale is set to 
     270recover the molecular viscosity when $\bar{e}$ reach its minimum value 
     271($1\times 10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$). 
    271272 
    272273 
     
    283284\bar{e}_o = \frac{1}{2}\,\left(  15.8\,\alpha_{CB} \right)^{2/3} \,\frac{|\tau|}{\rho_o} 
    284285\end{equation} 
    285 where $\alpha_{CB}$ is the \citet{Craig_Banner_JPO94} constant of proportionality  
    286 which depends on the ''wave age'', ranging from 57 for mature waves to 146 for  
    287 younger waves \citep{Mellor_Blumberg_JPO04}.  
    288 The boundary condition on the turbulent length scale follows the Charnock's relation: 
     286where $\alpha_{CB}$ is the \citet{Craig_Banner_JPO94} constant of 
     287proportionality which depends on the ''wave age'', ranging from 57 for mature 
     288waves to 146 for younger waves \citep{Mellor_Blumberg_JPO04}.  The boundary 
     289condition on the turbulent length scale follows Charnock's relation: 
    289290\begin{equation} \label{ZDF_Lsbc} 
    290291l_o = \kappa \beta \,\frac{|\tau|}{g\,\rho_o} 
    291292\end{equation} 
    292 where $\kappa=0.40$ is the von Karman constant, and $\beta$ is the Charnock's constant. 
    293 \citet{Mellor_Blumberg_JPO04} suggest $\beta = 2.10^{5}$ the value chosen by \citet{Stacey_JPO99} 
    294 citing observation evidence, and $\alpha_{CB} = 100$ the Craig and Banner's value. 
    295 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$,  
    296 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 Stacet's value. 
    299 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters)  
    300 is applied on surface $\bar{e}$ value. 
     293where $\kappa=0.40$ is the von Karman constant, and $\beta$ is Charnock's 
     294constant.  \citet{Mellor_Blumberg_JPO04} suggest $\beta = 2\times10^{5}$ the value 
     295chosen by \citet{Stacey_JPO99} citing observation evidence, and $\alpha_{CB} 
     296= 100$ the Craig and Banner's value.  As the surface boundary condition 
     297on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, with 
     298$e_{bb}$ the \np{rn\_ebb} namelist parameter, setting \np{rn\_ebb}~=~67.83 
     299corresponds to $\alpha_{CB} = 100$. further setting  \np{ln\_lsurf} to true 
     300applies \eqref{ZDF_Lsbc} as surface boundary condition on length scale, with 
     301$\beta$ hard coded to Stacey's value.  Note that a minimal threshold 
     302of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on 
     303surface $\bar{e}$ value. 
     304 
     305\subsubsection{Surface wave breaking flux from a wave model \np{ln\_wavetke}} 
     306%-----------------------------------------------------------------------% 
     307The constant of proportionality $\alpha_{CB}$ in Eq~\eqref{ZDF_Esbc} relates 
     308the water-side friction velocity $w_*$ to the turbulent energy flux as follows, 
     309\begin{equation} 
     310   \Phi_\mathrm{oc} = \rho_\mathrm{w} \alpha_\mathrm{CB} w_*^3. 
     311   \label{Eq_ZDF_alpha} 
     312\end{equation} 
     313The default option in NEMO \eqref{ZDF_Esbc} is to assume $\alpha_{CB} 
     314= 100$ as explained in the previous section. 
     315However, the energy flux can be computed from the dissipation source term 
     316of a wave model \citep{Janssen_AH04,Janssen_JGR12,Janssen_ECMWF13}, 
     317\begin{equation} 
     318   \Phi_\mathrm{oc} = \Phi_\mathrm{in} - \rho_\mathrm{w}g \int_0^{2\pi}  
     319                      \int_0^{\infty} (S_\mathrm{in} + S_\mathrm{ds})\,  
     320                        d\omega d\theta. 
     321   \label{Eq_ZDF_phioc} 
     322\end{equation} 
     323Assuming high-frequency equilibrium and ignoring the direct turbulent energy 
     324flux from the atmosphere to the ocean we get 
     325\begin{equation} 
     326   \Phi_\mathrm{oc} = -\rho_\mathrm{w}g \int_0^{2\pi}  
     327                      \int_0^{\omega_\mathrm{c}} S_\mathrm{ds}\,  
     328                        d\omega d\theta = -\rho_\mathrm{a} m u_*^3. 
     329   \label{Eq_ZDF_m} 
     330\end{equation} 
     331Here, $m \approx -\sqrt{\rho_\mathrm{a}/\rho_\mathrm{w}} \alpha_\mathrm{CB}$ 
     332is the energy flux \emph{from} the waves (thus always negative) normalized by 
     333the air friction velocity $u_*$. It 
     334is archived as PHIOC (GRIB parameter 212, table 140) in ERA-Interim and also 
     335operationally by ECMWF.  The namelist parameter \np{ln\_wavetke} controls 
     336the wave TKE flux.  We assume that the flux has been converted to physical 
     337units following \eqref{Eq_ZDF_m} before ingested by NEMO. 
     338 
     339NEMO computes the upper boundary condition following 
     340\citet{Mellor_Blumberg_JPO04}, see \eqref{ZDF_Esbc}.  Since $e$ varies 
     341rapidly with depth, we want to weight the surface value $\overline{e}_o$ 
     342by the thickness of the uppermost level to attain a value representative 
     343for the turbulence level of the uppermost level, 
     344\begin{equation} 
     345   \overline{e}_1 = \frac{\overline{e}_o}{L} \int_{-L}^{0} e(z) \,dz. 
     346   \label{Eq_ZDF_eavg} 
     347\end{equation} 
     348Here $L = \Delta z_1/2$ is the depth of the $T$-point of the uppermost level. 
     349This adjustment is crucial with model configurations with a thick uppermost 
     350level, e.g. ORCA1L42.  If we assume, as \citet{Mellor_Blumberg_JPO04} do, that in the 
     351wave-affected layer the roughness length can be set to a constant which we 
     352choose to be $z_\mathrm{w} = 0.5H_\mathrm{s}$ and that in this near-surface 
     353region diffusion balances dissipation, the TKE equation attains the simple 
     354exponential solution \citep{Mellor_Blumberg_JPO04} 
     355\begin{equation} 
     356  e(z) = \overline{e}_o \exp(2\lambda z/3). 
     357   \label{Eq_ZDF_phimb} 
     358\end{equation} 
     359Here, the length scale $\lambda^{-1}$ is sea-state dependent, see Eq (10) by 
     360\citet{Mellor_Blumberg_JPO04}, 
     361\begin{equation} 
     362   \lambda = [3/(S_q B_1 \kappa^2)]^{1/2}z_\mathrm{w}^{-1} \approx 
     363   \frac{2.38}{z_\mathrm{w}}. 
     364\end{equation} 
     365We have assumed $S_q=0.2$ and $B=16.6$ \citep{Mellor_Yamada_1982}, as 
     366used in NEMO.  For a wave height of 2.5 m, which is close to the global 
     367mean, $\lambda^{-1} \approx 0.5\, \mathrm{m}$.  Integrating \eqref{Eq_ZDF_phimb} 
     368is straightforward, and the average TKE in \eqref{Eq_ZDF_eavg} becomes 
     369\begin{equation} 
     370  \overline{e}_1 = \overline{e}_o \frac{3}{2\lambda L} \left[1 - 
     371  \exp(-2\lambda L/3)\right]. 
     372\end{equation} 
     373The wave model energy flux is controlled by \np{ln\_wavetke} in namelist 
     374\ngn{namsbc}. 
    301375 
    302376 
     
    318392  
    319393By making an analogy with the characteristic convective velocity scale  
    320 ($e.g.$, \citet{D'Alessio_al_JPO98}), $P_{LC}$ is assumed to be :  
     394($e.g.$, \citet{D'Alessio_al_JPO98}), $P_{LC}$ is assumed to be:  
    321395\begin{equation} 
    322396P_{LC}(z) = \frac{w_{LC}^3(z)}{H_{LC}} 
  • branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Namelist/namsbc

    r4230 r4644  
    3030                           !       is left empty in namelist)  , 
    3131                           !  =1:n number of iterations of land/sea mask application for input fields 
     32   ln_stcor    = .false.   !   Stokes drift read from wave model 
     33   ln_wavetke  = .false.   !   Wave parameters from wave model for the TKE BC 
     34   ln_tauoc    = .false.   !   Wave-modified stress from wave model 
    3235/ 
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