Changeset 4644 for branches/2014/dev_r4642_WavesWG/DOC
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- 2014-05-15T15:56:53+02:00 (10 years ago)
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branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Biblio/Biblio.bib
r4560 r4644 514 514 } 515 515 516 @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"} 525 516 526 @ARTICLE{Brown_Campana_MWR78, 517 527 author = {J. A. Brown and K. A. Campana}, … … 651 661 } 652 662 663 @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} 671 653 672 @ARTICLE{Cox1987, 654 673 author = {M. Cox}, … … 742 761 volume = {34}, 743 762 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} 744 777 } 745 778 … … 895 928 url = {http://dx.doi.org/10.1029/2005GL022463} 896 929 } 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"} 897 943 898 944 @ARTICLE{Egbert_Ray_JGR01, … … 1264 1310 } 1265 1311 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 1266 1321 @ARTICLE{Hazeleger_Drijfhout_JPO98, 1267 1322 author = {W. Hazeleger and S. S. Drijfhout}, … … 1381 1436 } 1382 1437 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 1383 1446 @ARTICLE{Hordoir_al_CD08, 1384 1447 author = {R. Hordoir and J. Polcher and J.-C. Brun-Cottan and G. Madec}, … … 1476 1539 pages = {381--389} 1477 1540 } 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"} 1478 1592 1479 1593 @ARTICLE{Jayne_St_Laurent_GRL01, … … 2681 2795 } 2682 2796 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 2683 2805 @ARTICLE{Talagrand_JAS72, 2684 2806 author = {O. Talagrand}, … … 2859 2981 } 2860 2982 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 2861 2991 @ARTICLE{Warner_al_OM05, 2862 2992 author = {J. C. Warner and C. R. Sherwood and H. G. Arango and R. P. Signell}, … … 2956 3086 pages = {593--611} 2957 3087 } 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"} 2958 3097 2959 3098 @ARTICLE{Zalesak_JCP79, -
branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Chapters/Chap_DYN.tex
r4560 r4644 1 1 % ================================================================ 2 % Chapter �Ocean Dynamics (DYN)2 % Chapter Ocean Dynamics (DYN) 3 3 % ================================================================ 4 4 \chapter{Ocean Dynamics (DYN)} … … 795 795 %> > > > > > > > > > > > > > > > > > > > > > > > > > > > 796 796 \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} 798 798 \caption{ \label{Fig_DYN_dynspg_ts} 799 799 Schematic of the split-explicit time stepping scheme for the external … … 1293 1293 1294 1294 % ================================================================ 1295 % Coriolis-Stokes force 1296 % ================================================================ 1297 \section [Coriolis-Stokes Force (\textit{dynstcor})] 1298 {Coriolis-Stokes Force (\mdl{dynstcor})} 1299 \label{DYN_stcor} 1300 Waves set up a Lagrangian drift in the down-wave direction known 1301 as the Stokes drift \citep{Stokes_TCPS47}. Although its drift speed 1302 $\mathbf{v}_\mathrm{s}$ decays rapidly with depth, it can be substantial 1303 near the surface ($v_\mathrm{s} {\sim}0.7\, \mathrm{m/s}$). In combination 1304 with the earth's rotation it adds an additional veering to the upper-ocean 1305 currents 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} 1312 It requires integration of the full two-dimensional spectrum to get the 1313 Stokes 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} 1319 This is computationally demanding and requires access to the full 1320 two-dimensional wave spectra from a numerical wave model (see e.g. the 1321 ECMWF WAM implementation, ECWAM, \citealt{wam38r1}), so 1322 we 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} 1329 The surface velocity vector $\mathbf{v}_0$ is computed by ECWAM and is 1330 available both in ERA-Interim \citep{Dee_QJRMS11} and operationally. 1331 1332 The transport under such a profile involves the exponential integral $E_1$ and 1333 can 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} 1338 This 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} 1344 Here $E_1(1/4) \approx 1.34$, 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} 1349 The $n$-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} 1355 The mean frequency is defined as $\overline{f} = m_1/m_0$ 1356 \citep{wmo98,Holthuijsen07} and the significant wave height $H_{m_0} = 1357 4\sqrt{m_0}$. We can derive the first moment from the integrated parameters 1358 of a wave model or from wave observations and find an estimate for the 1359 Stokes 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} 1365 Here $\hat{\mathbf{k}}_\mathrm{s} = (\sin \theta_\mathrm{s}, 1366 \cos \theta_\mathrm{s})$ is the unit vector in the 1367 direction $\theta_\mathrm{s}$ of the Stokes transport. From 1368 Eqs~(\ref{Eq_dynstcor_keapprox})-(\ref{Eq_dynstcor_UVHsf}) it is clear that 1369 in order to compute the Stokes drift velocity profile at the desired vertical 1370 levels we need $H_\mathrm{s}$, $\overline{f}$ and $\mathbf{v}_0$. 1371 1372 The Coriolis-Stokes effect is enabled when \np{ln\_stcor} = true (default = 1373 false). All wave-related switches are found in \ngn{namsbc}. 1374 The surface Stokes drift velocity vectors (east and north components) are 1375 archived in ERA-Interim as GRIB parameters 215 and 216 respectively (table 1376 140). 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 15 15 The ocean needs six fields as surface boundary condition: 16 16 \begin{itemize} 17 18 19 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 $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 20 20 \end{itemize} 21 21 plus an optional field: 22 22 \begin{itemize} 23 23 \item the atmospheric pressure at the ocean surface $\left( p_a \right)$ 24 24 \end{itemize} 25 25 … … 75 75 \begin{equation} \label{Eq_sbc_dynzdf} 76 76 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1} 77 77 = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v } 78 78 \end{equation} 79 79 where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind … … 348 348 horizontal and vertical dimensions of the associated variable and should 349 349 be 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.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. 352 352 353 353 \subsubsection{Bilinear Interpolation} … … 565 565 566 566 The atmospheric fields used depend on the bulk formulae used. Three bulk formulations 567 are available : the CORE, the CLIO and the MFS bulk formul ea. The choice is made by setting to true567 are available : the CORE, the CLIO and the MFS bulk formulae. The choice is made by setting to true 568 568 one of the following namelist variable : \np{ln\_core} ; \np{ln\_clio} or \np{ln\_mfs}. 569 569 570 570 Note : 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) formul eainclude the computation of the fluxes over both571 Therefore the two bulk (CLIO and CORE) formulae include the computation of the fluxes over both 572 572 an ocean and an ice surface. 573 573 574 574 % ------------------------------------------------------------------------------------------------------------- 575 % CORE Bulk formul ea576 % ------------------------------------------------------------------------------------------------------------- 577 \subsection [CORE Bulk formul ea(\np{ln\_core}=true)]578 {CORE Bulk formul ea(\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})} 579 579 \label{SBC_blk_core} 580 580 %------------------------------------------namsbc_core---------------------------------------------------- … … 591 591 592 592 Note that substituting ERA40 to NCEP reanalysis fields 593 does not require changes in the bulk formul eathemself.593 does not require changes in the bulk formulae themself. 594 594 This is the so-called DRAKKAR Forcing Set (DFS) \citep{Brodeau_al_OM09}. 595 595 … … 621 621 or larger than the one of the input atmospheric fields. 622 622 623 % ------------------------------------------------------------------------------------------------------------- 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)} 625 As an alternative to the \citet{Large_Yeager_Rep04} drag law the 626 parameterization used operationally by ECMWF \citep{Janssen_Rep08,Edson_JPO13} is 627 included, 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} 632 The 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)} 637 The atmospheric momentum flux to the ocean is denoted $\tau_\mathrm{a}$. It is 638 customary 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 641 surface to the friction velocity, 642 \begin{equation} 643 z_0 = \alpha_\mathrm{CH} \frac{u_{*}^2}{g}, 644 \end{equation} 645 where $\alpha_\mathrm{CH}$ is known as the Charnock constant. 646 \citet{Janssen_JPO89} showed that $\alpha$ is not constant but varies with 647 the 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} 653 where $\hat{\alpha}_\mathrm{CH} = 0.01$ 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} 661 The wave-modified drag coefficient is then 662 \begin{equation} 663 C_\mathrm{D} = \frac{\kappa^2}{\log^2(10/z_0)}. 664 \end{equation} 665 This parameter is stored as CDWW (GRIB parameter 233, table 140) in ERA-Interim and operationally by ECMWF. 666 Note 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 668 wind vector as before, and only the wind \emph{speed} is changed. Note also 669 that where there is a discrepancy between the ice cover of the wave model 670 and NEMO, a drag parametric drag law should used. Where the wave model 671 has ice (as $C_\mathrm{D} = 0$ under ice), a drag law such as the one put 672 forward by \citet{Large_Yeager_Rep04} or the one used operationally by ECMWF, 673 see 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)} 677 As waves break they feed momentum 678 into the currents. If wind input and dissipation in the wave field were in 679 equilibrium, the air-side stress would be equal to the total water-side 680 stress. However, most of the time waves are not in equilibrium 681 \citep{Janssen_JGR12,Janssen_ECMWF13}, giving 682 differences in air-side and water-side stress of the order of 5-10\%. 683 The water-side stress is the total 684 atmospheric stress minus the momentum absorbed by the wave field (positive) 685 minus 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 688 written \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} 695 This parameter is known as TAUOC (GRIB parameter 214, table 140) is stored in 696 normalized form, $\tilde{\tau} = \tau_\mathrm{oc}/\tau_\mathrm{a}$, in 697 ERA-Interim and operationally by ECMWF. It is controlled by the namelist 698 parameter \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})} 628 706 \label{SBC_blk_clio} 629 707 %------------------------------------------namsbc_clio---------------------------------------------------- … … 665 743 % MFS Bulk formulae 666 744 % ------------------------------------------------------------------------------------------------------------- 667 \subsection [MFS Bulk formul ea(\np{ln\_mfs}=true)]668 {MFS Bulk formul ea(\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})} 669 747 \label{SBC_blk_mfs} 670 748 %------------------------------------------namsbc_mfs---------------------------------------------------- … … 1048 1126 of incident SWF. The \cite{Bernie_al_CD07} reconstruction algorithm is available 1049 1127 in \NEMO by setting \np{ln\_dm2dc}~=~true (a \textit{\ngn{namsbc}} namelist variable) when using 1050 CORE bulk formul ea(\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true).1128 CORE bulk formulae (\np{ln\_blk\_core}~=~true) or the flux formulation (\np{ln\_flx}~=~true). 1051 1129 The reconstruction is performed in the \mdl{sbcdcy} module. The detail of the algoritm used 1052 1130 can 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 197 197 instabilities associated with too weak vertical diffusion. They must be 198 198 specified at least larger than the molecular values, and are set through 199 \np{rn\_avm0} and \np{rn\_avt0} ( namzdfnamelist, see \S\ref{ZDF_cst}).199 \np{rn\_avm0} and \np{rn\_avt0} (\ngn{namzdf} namelist, see \S\ref{ZDF_cst}). 200 200 201 201 \subsubsection{Turbulent length scale} … … 262 262 \end{equation} 263 263 264 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 ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). 264 At the ocean surface, a non zero length scale is set through the 265 \np{rn\_lmin0} namelist parameter. Usually the surface scale is given 266 by $l_o = \kappa \,z_o$ where $\kappa = 0.4$ is von Karman's constant 267 and $z_o$ 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 270 recover the molecular viscosity when $\bar{e}$ reach its minimum value 271 ($1\times 10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$). 271 272 272 273 … … 283 284 \bar{e}_o = \frac{1}{2}\,\left( 15.8\,\alpha_{CB} \right)^{2/3} \,\frac{|\tau|}{\rho_o} 284 285 \end{equation} 285 where $\alpha_{CB}$ is the \citet{Craig_Banner_JPO94} constant of proportionality286 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 theCharnock's relation:286 where $\alpha_{CB}$ is the \citet{Craig_Banner_JPO94} constant of 287 proportionality which depends on the ''wave age'', ranging from 57 for mature 288 waves to 146 for younger waves \citep{Mellor_Blumberg_JPO04}. The boundary 289 condition on the turbulent length scale follows Charnock's relation: 289 290 \begin{equation} \label{ZDF_Lsbc} 290 291 l_o = \kappa \beta \,\frac{|\tau|}{g\,\rho_o} 291 292 \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. 293 where $\kappa=0.40$ is the von Karman constant, and $\beta$ is Charnock's 294 constant. \citet{Mellor_Blumberg_JPO04} suggest $\beta = 2\times10^{5}$ the value 295 chosen by \citet{Stacey_JPO99} citing observation evidence, and $\alpha_{CB} 296 = 100$ the Craig and Banner's value. As the surface boundary condition 297 on 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}~=~67.83 299 corresponds to $\alpha_{CB} = 100$. further setting \np{ln\_lsurf} to true 300 applies \eqref{ZDF_Lsbc} as surface boundary condition on length scale, with 301 $\beta$ hard coded to Stacey's value. Note that a minimal threshold 302 of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) is applied on 303 surface $\bar{e}$ value. 304 305 \subsubsection{Surface wave breaking flux from a wave model \np{ln\_wavetke}} 306 %-----------------------------------------------------------------------% 307 The constant of proportionality $\alpha_{CB}$ in Eq~\eqref{ZDF_Esbc} relates 308 the 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} 313 The default option in NEMO \eqref{ZDF_Esbc} is to assume $\alpha_{CB} 314 = 100$ as explained in the previous section. 315 However, the energy flux can be computed from the dissipation source term 316 of 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} 323 Assuming high-frequency equilibrium and ignoring the direct turbulent energy 324 flux 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} 331 Here, $m \approx -\sqrt{\rho_\mathrm{a}/\rho_\mathrm{w}} \alpha_\mathrm{CB}$ 332 is the energy flux \emph{from} the waves (thus always negative) normalized by 333 the air friction velocity $u_*$. It 334 is archived as PHIOC (GRIB parameter 212, table 140) in ERA-Interim and also 335 operationally by ECMWF. The namelist parameter \np{ln\_wavetke} controls 336 the wave TKE flux. We assume that the flux has been converted to physical 337 units following \eqref{Eq_ZDF_m} before ingested by NEMO. 338 339 NEMO computes the upper boundary condition following 340 \citet{Mellor_Blumberg_JPO04}, see \eqref{ZDF_Esbc}. Since $e$ varies 341 rapidly with depth, we want to weight the surface value $\overline{e}_o$ 342 by the thickness of the uppermost level to attain a value representative 343 for 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} 348 Here $L = \Delta z_1/2$ is the depth of the $T$-point of the uppermost level. 349 This adjustment is crucial with model configurations with a thick uppermost 350 level, e.g. ORCA1L42. If we assume, as \citet{Mellor_Blumberg_JPO04} do, that in the 351 wave-affected layer the roughness length can be set to a constant which we 352 choose to be $z_\mathrm{w} = 0.5H_\mathrm{s}$ and that in this near-surface 353 region diffusion balances dissipation, the TKE equation attains the simple 354 exponential 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} 359 Here, 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} 365 We have assumed $S_q=0.2$ and $B=16.6$ \citep{Mellor_Yamada_1982}, as 366 used in NEMO. For a wave height of 2.5 m, which is close to the global 367 mean, $\lambda^{-1} \approx 0.5\, \mathrm{m}$. Integrating \eqref{Eq_ZDF_phimb} 368 is 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} 373 The wave model energy flux is controlled by \np{ln\_wavetke} in namelist 374 \ngn{namsbc}. 301 375 302 376 … … 318 392 319 393 By 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: 321 395 \begin{equation} 322 396 P_{LC}(z) = \frac{w_{LC}^3(z)}{H_{LC}} -
branches/2014/dev_r4642_WavesWG/DOC/TexFiles/Namelist/namsbc
r4230 r4644 30 30 ! is left empty in namelist) , 31 31 ! =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 32 35 /
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