Changeset 7260 for branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles
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- 2016-11-18T09:27:42+01:00 (8 years ago)
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branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Abstracts_Foreword.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 2 4 % ================================================================ … … 13 15 be a flexible tool for studying the ocean and its interactions with the others components of 14 16 the earth climate system over a wide range of space and time scales. 15 Prognostic variables are the three-dimensional velocity field, a linear16 or non-linear sea surface height, the temperature and the salinity. In the horizontal direction,17 the model uses a curvilinear orthogonal grid and in the vertical direction, a full or partial step18 $z$-coordinate, or $s$-coordinate, or a mixture of the two. The distribution of variables is a19 three-dimensional Arakawa C-type grid. Various physical choices are available to describe20 ocean physics, including TKE, GLS and KPP vertical physics. Within NEMO, the ocean is21 interfaced with a sea-ice model (LIM v2 and v3), passive tracer and biogeochemical models (TOP)22 and, via the OASIS coupler, with several atmospheric general circulation models. It also23 support two-way grid embedding via the AGRIF software.17 Prognostic variables are the three-dimensional velocity field, a non-linear sea surface height, 18 the \textit{Conservative} Temperature and the \textit{Absolute} Salinity. 19 In the horizontal direction, the model uses a curvilinear orthogonal grid and in the vertical direction, 20 a full or partial step $z$-coordinate, or $s$-coordinate, or a mixture of the two. 21 The distribution of variables is a three-dimensional Arakawa C-type grid. 22 Various physical choices are available to describe ocean physics, including TKE, and GLS vertical physics. 23 Within NEMO, the ocean is interfaced with a sea-ice model (LIM or CICE), passive tracer and 24 biogeochemical models (TOP) and, via the OASIS coupler, with several atmospheric general circulation models. 25 It also support two-way grid embedding via the AGRIF software. 24 26 25 27 % ================================================================ 26 \vspace{0.5cm}28 % \vspace{0.5cm} 27 29 28 Le moteur oc\'{e}anique de NEMO (Nucleus for European Modelling of the Ocean) est un29 mod\`{e}le aux \'{e}quations primitives de la circulation oc\'{e}anique r\'{e}gionale et globale.30 Il se veut un outil flexible pour \'{e}tudier sur un vaste spectre spatiotemporel l'oc\'{e}an et ses31 interactions avec les autres composantes du syst\`{e}me climatique terrestre.32 Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer33 lin\'{e}aire ou non, la temperature et la salinit\'{e}.34 La distribution des variables se fait sur une grille C d'Arakawa tridimensionnelle utilisant une35 coordonn\'{e}e verticale $z$ \`{a} niveaux entiers ou partiels, ou une coordonn\'{e}e s, ou encore36 une combinaison des deux. Diff\'{e}rents choix sont propos\'{e}s pour d\'{e}crire la physique37 oc\'{e}anique, incluant notamment des physiques verticales TKE, GLS et KPP. A travers l'infrastructure38 NEMO, l'oc\'{e}an est interfac\'{e} avec des mod\`{e}les de glace de mer, de biog\'{e}ochimie39 et de traceurs passifs, et, via le coupleur OASIS, \`{a} plusieurs mod\`{e}les de circulation40 g\'{e}n\'{e}rale atmosph\'{e}rique. Il supporte \'{e}galement l'embo\^{i}tement interactif de41 maillages via le logiciel AGRIF.30 %Le moteur oc\'{e}anique de NEMO (Nucleus for European Modelling of the Ocean) est un 31 %mod\`{e}le aux \'{e}quations primitives de la circulation oc\'{e}anique r\'{e}gionale et globale. 32 %Il se veut un outil flexible pour \'{e}tudier sur un vaste spectre spatiotemporel l'oc\'{e}an et ses 33 %interactions avec les autres composantes du syst\`{e}me climatique terrestre. 34 %Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer 35 %lin\'{e}aire, la Temp\'{e}rature Conservative et la Salinit\'{e} Absolue. 36 %La distribution des variables se fait sur une grille C d'Arakawa tridimensionnelle utilisant une 37 %coordonn\'{e}e verticale $z$ \`{a} niveaux entiers ou partiels, ou une coordonn\'{e}e s, ou encore 38 %une combinaison des deux. Diff\'{e}rents choix sont propos\'{e}s pour d\'{e}crire la physique 39 %oc\'{e}anique, incluant notamment des physiques verticales TKE et GLS. A travers l'infrastructure 40 %NEMO, l'oc\'{e}an est interfac\'{e} avec des mod\`{e}les de glace de mer (LIM ou CICE), 41 %de biog\'{e}ochimie marine et de traceurs passifs, et, via le coupleur OASIS, \`{a} plusieurs 42 %mod\`{e}les de circulation g\'{e}n\'{e}rale atmosph\'{e}rique. 43 %Il supporte \'{e}galement l'embo\^{i}tement interactif de maillages via le logiciel AGRIF. 42 44 } 43 45 … … 69 71 \vspace{0.5cm} 70 72 73 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_A.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 2 4 % ================================================================ … … 532 534 expression of the 3D divergence in the $s-$coordinates established above. 533 535 536 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_B.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter Ñ Appendix B : Diffusive Operators … … 364 366 \eqref{Apdx_B_Lap_U} is used in both $z$- and $s$-coordinate systems, that is 365 367 a Laplacian diffusion is applied on momentum along the coordinate directions. 368 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_C.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter Ñ Appendix C : Discrete Invariants of the Equations … … 410 412 \end{aligned} } \right. 411 413 \end{equation} 412 where the indices $i_p$ and $ k_p$ take the following value:414 where the indices $i_p$ and $j_p$ take the following value: 413 415 $i_p = -1/2$ or $1/2$ and $j_p = -1/2$ or $1/2$, 414 416 and the vorticity triads, ${^i_j}\mathbb{Q}^{i_p}_{j_p}$, defined at $T$-point, are given by: … … 1103 1105 The discrete formulation of the horizontal diffusion of momentum ensures the 1104 1106 conservation of potential vorticity and the horizontal divergence, and the 1105 dissipation of the square of these quantities ( i.e.enstrophy and the1107 dissipation of the square of these quantities ($i.e.$ enstrophy and the 1106 1108 variance of the horizontal divergence) as well as the dissipation of the 1107 1109 horizontal kinetic energy. In particular, when the eddy coefficients are … … 1127 1129 &\int \limits_D \frac{1} {e_3 } \textbf{k} \cdot \nabla \times 1128 1130 \Bigl[ \nabla_h \left( A^{\,lm}\;\chi \right) 1129 - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right) \Bigr]\;dv = 01130 \end{flalign*}1131 - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right) \Bigr]\;dv \\ 1132 %\end{flalign*} 1131 1133 %%%%%%%%%% recheck here.... (gm) 1132 \begin{flalign*}1133 = \int \limits_D -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times1134 \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right) \Bigr]\;dv &&&\\1135 \end{flalign*}1136 \begin{flalign*}1134 %\begin{flalign*} 1135 =& \int \limits_D -\frac{1} {e_3 } \textbf{k} \cdot \nabla \times 1136 \Bigl[ \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right) \Bigr]\;dv \\ 1137 %\end{flalign*} 1138 %\begin{flalign*} 1137 1139 \equiv& \sum\limits_{i,j} 1138 1140 \left\{ 1139 \delta_{i+1/2} 1140 \left[ 1141 \frac {e_{2v}} {e_{1v}\,e_{3v}} \delta_i 1142 \left[ A_f^{\,lm} e_{3f} \zeta \right] 1143 \right] 1144 + \delta_{j+1/2} 1145 \left[ 1146 \frac {e_{1u}} {e_{2u}\,e_{3u}} \delta_j 1147 \left[ A_f^{\,lm} e_{3f} \zeta \right] 1148 \right] 1149 \right\} 1150 && \\ 1141 \delta_{i+1/2} \left[ \frac {e_{2v}} {e_{1v}\,e_{3v}} \delta_i \left[ A_f^{\,lm} e_{3f} \zeta \right] \right] 1142 + \delta_{j+1/2} \left[ \frac {e_{1u}} {e_{2u}\,e_{3u}} \delta_j \left[ A_f^{\,lm} e_{3f} \zeta \right] \right] 1143 \right\} \\ 1151 1144 % 1152 1145 \intertext{Using \eqref{DOM_di_adj}, it follows:} … … 1154 1147 \equiv& \sum\limits_{i,j,k} 1155 1148 -\,\left\{ 1156 \frac{e_{2v}} {e_{1v}\,e_{3v}} \delta_i 1157 \left[ A_f^{\,lm} e_{3f} \zeta \right]\;\delta_i \left[ 1\right] 1158 + \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j 1159 \left[ A_f^{\,lm} e_{3f} \zeta \right]\;\delta_j \left[ 1\right] 1149 \frac{e_{2v}} {e_{1v}\,e_{3v}} \delta_i \left[ A_f^{\,lm} e_{3f} \zeta \right]\;\delta_i \left[ 1\right] 1150 + \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j \left[ A_f^{\,lm} e_{3f} \zeta \right]\;\delta_j \left[ 1\right] 1160 1151 \right\} \quad \equiv 0 1161 &&\\1152 \\ 1162 1153 \end{flalign*} 1163 1154 … … 1167 1158 \subsection{Dissipation of Horizontal Kinetic Energy} 1168 1159 \label{Apdx_C.3.2} 1169 1170 1160 1171 1161 The lateral momentum diffusion term dissipates the horizontal kinetic energy: … … 1221 1211 \label{Apdx_C.3.3} 1222 1212 1223 1224 1213 The lateral momentum diffusion term dissipates the enstrophy when the eddy 1225 1214 coefficients are horizontally uniform: … … 1228 1217 \left[ \nabla_h \left( A^{\,lm}\;\chi \right) 1229 1218 - \nabla_h \times \left( A^{\,lm}\;\zeta \; \textbf{k} \right) \right]\;dv &&&\\ 1230 & = A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times1219 &\quad = A^{\,lm} \int \limits_D \zeta \textbf{k} \cdot \nabla \times 1231 1220 \left[ \nabla_h \times \left( \zeta \; \textbf{k} \right) \right]\;dv &&&\\ 1232 &\ equiv A^{\,lm} \sum\limits_{i,j,k} \zeta \;e_{3f}1221 &\quad \equiv A^{\,lm} \sum\limits_{i,j,k} \zeta \;e_{3f} 1233 1222 \left\{ \delta_{i+1/2} \left[ \frac{e_{2v}} {e_{1v}\,e_{3v}} \delta_i \left[ e_{3f} \zeta \right] \right] 1234 1223 + \delta_{j+1/2} \left[ \frac{e_{1u}} {e_{2u}\,e_{3u}} \delta_j \left[ e_{3f} \zeta \right] \right] \right\} &&&\\ … … 1236 1225 \intertext{Using \eqref{DOM_di_adj}, it follows:} 1237 1226 % 1238 &\ equiv - A^{\,lm} \sum\limits_{i,j,k}1227 &\quad \equiv - A^{\,lm} \sum\limits_{i,j,k} 1239 1228 \left\{ \left( \frac{1} {e_{1v}\,e_{3v}} \delta_i \left[ e_{3f} \zeta \right] \right)^2 b_v 1240 + \left( \frac{1} {e_{2u}\,e_{3u}} \delta_j \left[ e_{3f} \zeta \right] \right)^2 b_u \right\} &&&\\ 1241 & \leq \;0 &&&\\ 1229 + \left( \frac{1} {e_{2u}\,e_{3u}} \delta_j \left[ e_{3f} \zeta \right] \right)^2 b_u \right\} \quad \leq \;0 &&&\\ 1242 1230 \end{flalign*} 1243 1231 … … 1250 1238 When the horizontal divergence of the horizontal diffusion of momentum 1251 1239 (discrete sense) is taken, the term associated with the vertical curl of the 1252 vorticity is zero locally, due to (!!! II.1.8 !!!!!). The resulting term conserves the1253 $\chi$ and dissipates $\chi^2$ when the eddy coefficients are1254 horizontally uniform.1240 vorticity is zero locally, due to \eqref{Eq_DOM_div_curl}. 1241 The resulting term conserves the $\chi$ and dissipates $\chi^2$ 1242 when the eddy coefficients are horizontally uniform. 1255 1243 \begin{flalign*} 1256 1244 & \int\limits_D \nabla_h \cdot 1257 1245 \Bigl[ \nabla_h \left( A^{\,lm}\;\chi \right) 1258 1246 - \nabla_h \times \left( A^{\,lm}\;\zeta \;\textbf{k} \right) \Bigr] dv 1259 = \int\limits_D \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi \right) dv &&&\\1247 = \int\limits_D \nabla_h \cdot \nabla_h \left( A^{\,lm}\;\chi \right) dv \\ 1260 1248 % 1261 1249 &\equiv \sum\limits_{i,j,k} 1262 1250 \left\{ \delta_i \left[ A_u^{\,lm} \frac{e_{2u}\,e_{3u}} {e_{1u}} \delta_{i+1/2} \left[ \chi \right] \right] 1263 + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}} \delta_{j+1/2} \left[ \chi \right] \right] \right\} &&&\\1251 + \delta_j \left[ A_v^{\,lm} \frac{e_{1v}\,e_{3v}} {e_{2v}} \delta_{j+1/2} \left[ \chi \right] \right] \right\} \\ 1264 1252 % 1265 1253 \intertext{Using \eqref{DOM_di_adj}, it follows:} … … 1267 1255 &\equiv \sum\limits_{i,j,k} 1268 1256 - \left\{ \frac{e_{2u}\,e_{3u}} {e_{1u}} A_u^{\,lm} \delta_{i+1/2} \left[ \chi \right] \delta_{i+1/2} \left[ 1 \right] 1269 + \frac{e_{1v}\,e_{3v}} 1270 \q quad \equiv 0 &&&\\1257 + \frac{e_{1v}\,e_{3v}} {e_{2v}} A_v^{\,lm} \delta_{j+1/2} \left[ \chi \right] \delta_{j+1/2} \left[ 1 \right] \right\} 1258 \quad \equiv 0 \\ 1271 1259 \end{flalign*} 1272 1260 … … 1281 1269 \left[ \nabla_h \left( A^{\,lm}\;\chi \right) 1282 1270 - \nabla_h \times \left( A^{\,lm}\;\zeta \;\textbf{k} \right) \right]\; dv 1283 = A^{\,lm} \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\; dv &&&\\1271 = A^{\,lm} \int\limits_D \chi \;\nabla_h \cdot \nabla_h \left( \chi \right)\; dv \\ 1284 1272 % 1285 1273 &\equiv A^{\,lm} \sum\limits_{i,j,k} \frac{1} {e_{1t}\,e_{2t}\,e_{3t}} \chi … … 1287 1275 \delta_i \left[ \frac{e_{2u}\,e_{3u}} {e_{1u}} \delta_{i+1/2} \left[ \chi \right] \right] 1288 1276 + \delta_j \left[ \frac{e_{1v}\,e_{3v}} {e_{2v}} \delta_{j+1/2} \left[ \chi \right] \right] 1289 \right\} \; e_{1t}\,e_{2t}\,e_{3t} &&&\\1277 \right\} \; e_{1t}\,e_{2t}\,e_{3t} \\ 1290 1278 % 1291 1279 \intertext{Using \eqref{DOM_di_adj}, it turns out to be:} … … 1293 1281 &\equiv - A^{\,lm} \sum\limits_{i,j,k} 1294 1282 \left\{ \left( \frac{1} {e_{1u}} \delta_{i+1/2} \left[ \chi \right] \right)^2 b_u 1295 + \left( \frac{1} {e_{2v}} \delta_{j+1/2} \left[ \chi \right] \right)^2 b_v \right\} \; &&&\\ 1296 % 1297 &\leq 0 &&&\\ 1283 + \left( \frac{1} {e_{2v}} \delta_{j+1/2} \left[ \chi \right] \right)^2 b_v \right\} 1284 \quad \leq 0 \\ 1298 1285 \end{flalign*} 1299 1286 … … 1303 1290 \section{Conservation Properties on Vertical Momentum Physics} 1304 1291 \label{Apdx_C_4} 1305 1306 1292 1307 1293 As for the lateral momentum physics, the continuous form of the vertical diffusion … … 1319 1305 \left( \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k} \right)\; dv \quad &\leq 0 \\ 1320 1306 \end{align*} 1307 1321 1308 The first property is obvious. The second results from: 1322 1323 1309 \begin{flalign*} 1324 1310 \int\limits_D … … 1359 1345 e_{1f}\,e_{2f}\,e_{3f} \; \equiv 0 && \\ 1360 1346 \end{flalign*} 1347 1361 1348 If the vertical diffusion coefficient is uniform over the whole domain, the 1362 1349 enstrophy is dissipated, $i.e.$ … … 1366 1353 \left( \frac{A^{\,vm}} {e_3 }\; \frac{\partial \textbf{U}_h } {\partial k} \right) \right)\; dv = 0 &&&\\ 1367 1354 \end{flalign*} 1355 1368 1356 This property is only satisfied in $z$-coordinates: 1369 1370 1357 \begin{flalign*} 1371 1358 \int\limits_D \zeta \, \textbf{k} \cdot \nabla \times … … 1477 1464 1478 1465 The numerical schemes used for tracer subgridscale physics are written such 1479 that the heat and salt contents are conserved (equations in flux form, second 1480 order centered finite differences). Since a flux form is used to compute the 1481 temperature and salinity, the quadratic form of these quantities (i.e. their variance) 1482 globally tends to diminish. As for the advection term, there is generally no strict 1483 conservation of mass, even if in practice the mass is conserved to a very high 1484 accuracy. 1466 that the heat and salt contents are conserved (equations in flux form). 1467 Since a flux form is used to compute the temperature and salinity, 1468 the quadratic form of these quantities ($i.e.$ their variance) globally tends to diminish. 1469 As for the advection term, there is conservation of mass only if the Equation Of Seawater is linear. 1485 1470 1486 1471 % ------------------------------------------------------------------------------------------------------------- … … 1548 1533 %%%% end of appendix in gm comment 1549 1534 %} 1535 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_D.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Appendix D Ñ Coding Rules … … 120 122 \hline 121 123 public \par or \par module variable& 122 \textbf{m n} \par \textit{but not} \par \textbf{nn\_ }&124 \textbf{m n} \par \textit{but not} \par \textbf{nn\_ np\_}& 123 125 \textbf{a b e f g h o q r} \par \textbf{t} \textit{to} \textbf{x} \par but not \par \textbf{fs rn\_}& 124 126 \textbf{l} \par \textit{but not} \par \textbf{lp ld} \par \textbf{ ll ln\_}& … … 156 158 \hline 157 159 parameter& 158 \textbf{jp }&160 \textbf{jp np\_}& 159 161 \textbf{pp}& 160 162 \textbf{lp}& … … 190 192 %-------------------------------------------------------------------------------------------------------------- 191 193 194 N.B. Parameter here, in not only parameter in the \textsc{Fortran} acceptation, it is also used for code variables 195 that are read in namelist and should never been modified during a simulation. 196 It is the case, for example, for the size of a domain (jpi,jpj,jpk). 197 192 198 \newpage 193 199 % ================================================================ … … 198 204 199 205 To be done.... 206 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_E.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Appendix E : Note on some algorithms … … 299 301 \begin{figure}[!ht] \label{Fig_ISO_triad} 300 302 \begin{center} 301 \includegraphics[width=0.70\textwidth]{ ./TexFiles/Figures/Fig_ISO_triad.pdf}303 \includegraphics[width=0.70\textwidth]{Fig_ISO_triad} 302 304 \caption{ \label{Fig_ISO_triad} 303 305 Triads used in the Griffies's like iso-neutral diffision scheme for … … 806 808 tracer is preserved by the discretisation of the skew fluxes. 807 809 810 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Annex_ISO.tex
r4147 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Iso-neutral diffusion : … … 201 203 % >>>>>>>>>>>>>>>>>>>>>>>>>>>> 202 204 \begin{figure}[h] \begin{center} 203 \includegraphics[width=1.05\textwidth]{ ./TexFiles/Figures/Fig_GRIFF_triad_fluxes}205 \includegraphics[width=1.05\textwidth]{Fig_GRIFF_triad_fluxes} 204 206 \caption{ \label{fig:triad:ISO_triad} 205 207 (a) Arrangement of triads $S_i$ and tracer gradients to … … 269 271 % >>>>>>>>>>>>>>>>>>>>>>>>>>>> 270 272 \begin{figure}[h] \begin{center} 271 \includegraphics[width=0.80\textwidth]{ ./TexFiles/Figures/Fig_GRIFF_qcells}273 \includegraphics[width=0.80\textwidth]{Fig_GRIFF_qcells} 272 274 \caption{ \label{fig:triad:qcells} 273 275 Triad notation for quarter cells. $T$-cells are inside … … 676 678 % >>>>>>>>>>>>>>>>>>>>>>>>>>>> 677 679 \begin{figure}[h] \begin{center} 678 \includegraphics[width=0.60\textwidth]{ ./TexFiles/Figures/Fig_GRIFF_bdry_triads}680 \includegraphics[width=0.60\textwidth]{Fig_GRIFF_bdry_triads} 679 681 \caption{ \label{fig:triad:bdry_triads} 680 682 (a) Uppermost model layer $k=1$ with $i,1$ and $i+1,1$ tracer … … 849 851 different $i_p,k_p$, denoted by different colours, (e.g. the green 850 852 triad $i_p=1/2,k_p=-1/2$) are tapered to the appropriate basal triad.}} 851 {\includegraphics[width=0.60\textwidth]{ ./TexFiles/Figures/Fig_GRIFF_MLB_triads}}853 {\includegraphics[width=0.60\textwidth]{Fig_GRIFF_MLB_triads}} 852 854 \end{figure} 853 855 % >>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 1193 1195 \end{split} 1194 1196 \end{equation} 1197 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_ASM.tex
r4147 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter Assimilation increments (ASM) … … 172 174 \end{verbatim} 173 175 \end{alltt} 176 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_CFG.tex
r4147 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter � Configurations … … 88 90 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 89 91 \begin{figure}[!t] \begin{center} 90 \includegraphics[width=0.98\textwidth]{ ./TexFiles/Figures/Fig_ORCA_NH_mesh.pdf}92 \includegraphics[width=0.98\textwidth]{Fig_ORCA_NH_mesh} 91 93 \caption{ \label{Fig_MISC_ORCA_msh} 92 ORCA mesh conception. The departure from an isotropic Mercator grid start poleward of 20\deg 94 ORCA mesh conception. The departure from an isotropic Mercator grid start poleward of 20\degN. 93 95 The two "north pole" are the foci of a series of embedded ellipses (blue curves) 94 96 which are determined analytically and form the i-lines of the ORCA mesh (pseudo latitudes). … … 115 117 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 116 118 \begin{figure}[!tbp] \begin{center} 117 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_ORCA_NH_msh05_e1_e2.pdf}118 \includegraphics[width=0.80\textwidth]{ ./TexFiles/Figures/Fig_ORCA_aniso.pdf}119 \includegraphics[width=1.0\textwidth]{Fig_ORCA_NH_msh05_e1_e2} 120 \includegraphics[width=0.80\textwidth]{Fig_ORCA_aniso} 119 121 \caption { \label{Fig_MISC_ORCA_e1e2} 120 122 \textit{Top}: Horizontal scale factors ($e_1$, $e_2$) and 121 123 \textit{Bottom}: ratio of anisotropy ($e_1 / e_2$) 122 for ORCA 0.5\deg ~mesh. South of 20\deg 123 so that the anisotropy ratio is 1. Poleward of 20\deg 124 for ORCA 0.5\deg ~mesh. South of 20\degN a Mercator grid is used ($e_1 = e_2$) 125 so that the anisotropy ratio is 1. Poleward of 20\degN, the two "north pole" 124 126 introduce a weak anisotropy over the ocean areas ($< 1.2$) except in vicinity of Victoria Island 125 127 (Canadian Arctic Archipelago). } … … 129 131 130 132 The method is applied to Mercator grid ($i.e.$ same zonal and meridional grid spacing) poleward 131 of $20\deg$N, so that the Equator is a mesh line, which provides a better numerical solution133 of 20\degN, so that the Equator is a mesh line, which provides a better numerical solution 132 134 for equatorial dynamics. The choice of the series of embedded ellipses (position of the foci and 133 135 variation of the ellipses) is a compromise between maintaining the ratio of mesh anisotropy … … 178 180 The ORCA\_R2 configuration has the following specificity : starting from a 2\deg~ORCA mesh, 179 181 local mesh refinements were applied to the Mediterranean, Red, Black and Caspian Seas, 180 so that the resolution is $1\deg \time 1\deg$there. A local transformation were also applied182 so that the resolution is 1\deg \time 1\deg there. A local transformation were also applied 181 183 with in the Tropics in order to refine the meridional resolution up to 0.5\deg at the Equator. 182 184 … … 227 229 228 230 The domain geometry is a closed rectangular basin on the $\beta$-plane centred 229 at $\sim 30\deg$N and rotated by 45\deg, 3180~km long, 2120~km wide231 at $\sim$ 30\degN and rotated by 45\deg, 3180~km long, 2120~km wide 230 232 and 4~km deep (Fig.~\ref{Fig_MISC_strait_hand}). 231 233 The domain is bounded by vertical walls and by a flat bottom. The configuration is … … 234 236 The applied forcings vary seasonally in a sinusoidal manner between winter 235 237 and summer extrema \citep{Levy_al_OM10}. 236 The wind stress is zonal and its curl changes sign at 22\deg N and 36\degN.238 The wind stress is zonal and its curl changes sign at 22\degN and 36\degN. 237 239 It forces a subpolar gyre in the north, a subtropical gyre in the wider part of the domain 238 240 and a small recirculation gyre in the southern corner. … … 261 263 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 262 264 \begin{figure}[!t] \begin{center} 263 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_GYRE.pdf}265 \includegraphics[width=1.0\textwidth]{Fig_GYRE} 264 266 \caption{ \label{Fig_GYRE} 265 267 Snapshot of relative vorticity at the surface of the model domain … … 311 313 temperature data. 312 314 315 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_Conservation.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 2 4 % ================================================================ … … 333 335 not been implemented. 334 336 337 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_DIA.tex
r5602 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter I/O & Diagnostics 3 5 % ================================================================ 4 \chapter{Ou put and Diagnostics (IOM, DIA, TRD, FLO)}6 \chapter{Output and Diagnostics (IOM, DIA, TRD, FLO)} 5 7 \label{DIA} 6 8 \minitoc 7 9 8 10 \newpage 9 $\ $\newline % force a new li gne11 $\ $\newline % force a new line 10 12 11 13 % ================================================================ … … 48 50 49 51 50 Since version 3.2, iomput is the NEMO output interface of choice. It has been designed to be simple to use, flexible and efficient. The two main purposes of iomput are: 52 Since version 3.2, iomput is the NEMO output interface of choice. 53 It has been designed to be simple to use, flexible and efficient. 54 The two main purposes of iomput are: 51 55 \begin{enumerate} 52 56 \item The complete and flexible control of the output files through external XML files adapted by the user from standard templates. … … 1116 1120 % ------------------------------------------------------------------------------------------------------------- 1117 1121 \section[Tracer/Dynamics Trends (TRD)] 1118 {Tracer/Dynamics Trends (\key{trdtra}, \key{trddyn}, \\ 1119 \key{trddvor}, \key{trdmld})} 1122 {Tracer/Dynamics Trends (\ngn{namtrd})} 1120 1123 \label{DIA_trd} 1121 1124 … … 1124 1127 %------------------------------------------------------------------------------------------------------------- 1125 1128 1126 When \key{trddyn} and/or \key{trddyn} CPP variables are defined, each 1127 trend of the dynamics and/or temperature and salinity time evolution equations 1128 is stored in three-dimensional arrays just after their computation ($i.e.$ at the end 1129 of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). Options are defined by 1130 \ngn{namtrd} namelist variables. These trends are then 1131 used in \mdl{trdmod} (see TRD directory) every \textit{nn\_trd } time-steps. 1132 1133 What is done depends on the CPP keys defined: 1129 Each trend of the dynamics and/or temperature and salinity time evolution equations 1130 can be send to \mdl{trddyn} and/or \mdl{trdtra} modules (see TRD directory) just after their computation 1131 ($i.e.$ at the end of each $dyn\cdots.F90$ and/or $tra\cdots.F90$ routines). 1132 This capability is controlled by options offered in \ngn{namtrd} namelist. 1133 Note that the output are done with xIOS, and therefore the \key{IOM} is required. 1134 1135 What is done depends on the \ngn{namtrd} logical set to \textit{true}: 1134 1136 \begin{description} 1135 \item[\key{trddyn}, \key{trdtra}] : a check of the basin averaged properties of the momentum 1136 and/or tracer equations is performed ; 1137 \item[\key{trdvor}] : a vertical summation of the moment tendencies is performed, 1138 then the curl is computed to obtain the barotropic vorticity tendencies which are output ; 1139 \item[\key{trdmld}] : output of the tracer tendencies averaged vertically 1140 either over the mixed layer (\np{nn\_ctls}=0), 1141 or over a fixed number of model levels (\np{nn\_ctls}$>$1 provides the number of level), 1142 or over a spatially varying but temporally fixed number of levels (typically the base 1143 of the winter mixed layer) read in \ifile{ctlsurf\_idx} (\np{nn\_ctls}=1) ; 1137 \item[\np{ln\_glo\_trd}] : at each \np{nn\_trd} time-step a check of the basin averaged properties 1138 of the momentum and tracer equations is performed. This also includes a check of $T^2$, $S^2$, 1139 $\tfrac{1}{2} (u^2+v2)$, and potential energy time evolution equations properties ; 1140 \item[\np{ln\_dyn\_trd}] : each 3D trend of the evolution of the two momentum components is output ; 1141 \item[\np{ln\_dyn\_mxl}] : each 3D trend of the evolution of the two momentum components averaged 1142 over the mixed layer is output ; 1143 \item[\np{ln\_vor\_trd}] : a vertical summation of the moment tendencies is performed, 1144 then the curl is computed to obtain the barotropic vorticity tendencies which are output ; 1145 \item[\np{ln\_KE\_trd}] : each 3D trend of the Kinetic Energy equation is output ; 1146 \item[\np{ln\_tra\_trd}] : each 3D trend of the evolution of temperature and salinity is output ; 1147 \item[\np{ln\_tra\_mxl}] : each 2D trend of the evolution of temperature and salinity averaged 1148 over the mixed layer is output ; 1144 1149 \end{description} 1145 1146 The units in the output file can be changed using the \np{nn\_ucf} namelist parameter.1147 For example, in case of salinity tendency the units are given by PSU/s/\np{nn\_ucf}.1148 Setting \np{nn\_ucf}=86400 ($i.e.$ the number of second in a day) provides the tendencies in PSU/d.1149 1150 When \key{trdmld} is defined, two time averaging procedure are proposed.1151 Setting \np{ln\_trdmld\_instant} to \textit{true}, a simple time averaging is performed,1152 so that the resulting tendency is the contribution to the change of a quantity between1153 the two instantaneous values taken at the extremities of the time averaging period.1154 Setting \np{ln\_trdmld\_instant} to \textit{false}, a double time averaging is performed,1155 so that the resulting tendency is the contribution to the change of a quantity between1156 two \textit{time mean} values. The later option requires the use of an extra file, \ifile{restart\_mld}1157 (\np{ln\_trdmld\_restart}=true), to restart a run.1158 1159 1150 1160 1151 Note that the mixed layer tendency diagnostic can also be used on biogeochemical models 1161 1152 via the \key{trdtrc} and \key{trdmld\_trc} CPP keys. 1153 1154 \textbf{Note that} in the current version (v3.6), many changes has been introduced but not fully tested. 1155 In particular, options associated with \np{ln\_dyn\_mxl}, \np{ln\_vor\_trd}, and \np{ln\_tra\_mxl} 1156 are not working, and none of the option have been tested with variable volume ($i.e.$ \key{vvl} defined). 1157 1162 1158 1163 1159 % ------------------------------------------------------------------------------------------------------------- … … 1280 1276 \label{DIA_diag_harm} 1281 1277 1282 A module is available to compute the amplitude and phase for tidal waves.1283 This diagnostic is actived with \key{diaharm}.1284 1285 1278 %------------------------------------------namdia_harm---------------------------------------------------- 1286 1279 \namdisplay{namdia_harm} 1287 1280 %---------------------------------------------------------------------------------------------------------- 1288 1281 1289 Concerning the on-line Harmonic analysis, some parameters are available in namelist 1290 \ngn{namdia\_harm} : 1291 1292 - \texttt{nit000\_han} is the first time step used for harmonic analysis 1293 1294 - \texttt{nitend\_han} is the last time step used for harmonic analysis 1295 1296 - \texttt{nstep\_han} is the time step frequency for harmonic analysis 1297 1298 - \texttt{nb\_ana} is the number of harmonics to analyse 1299 1300 - \texttt{tname} is an array with names of tidal constituents to analyse 1301 1302 \texttt{nit000\_han} and \texttt{nitend\_han} must be between \texttt{nit000} and \texttt{nitend} of the simulation. 1282 A module is available to compute the amplitude and phase of tidal waves. 1283 This on-line Harmonic analysis is actived with \key{diaharm}. 1284 Some parameters are available in namelist \ngn{namdia\_harm} : 1285 1286 - \np{nit000\_han} is the first time step used for harmonic analysis 1287 1288 - \np{nitend\_han} is the last time step used for harmonic analysis 1289 1290 - \np{nstep\_han} is the time step frequency for harmonic analysis 1291 1292 - \np{nb\_ana} is the number of harmonics to analyse 1293 1294 - \np{tname} is an array with names of tidal constituents to analyse 1295 1296 \np{nit000\_han} and \np{nitend\_han} must be between \np{nit000} and \np{nitend} of the simulation. 1303 1297 The restart capability is not implemented. 1304 1298 1305 The Harmonic analysis solve th isequation:1299 The Harmonic analysis solve the following equation: 1306 1300 \begin{equation} 1307 1301 h_{i} - A_{0} + \sum^{nb\_ana}_{j=1}[A_{j}cos(\nu_{j}t_{j}-\phi_{j})] = e_{i} … … 1324 1318 \label{DIA_diag_dct} 1325 1319 1326 A module is available to compute the transport of volume, heat and salt through sections. This diagnostic1327 is actived with \key{diadct}.1320 A module is available to compute the transport of volume, heat and salt through sections. 1321 This diagnostic is actived with \key{diadct}. 1328 1322 1329 1323 Each section is defined by the coordinates of its 2 extremities. The pathways between them are contructed … … 1347 1341 %------------------------------------------------------------------------------------------------------------- 1348 1342 1349 \ texttt{nn\_dct}: frequency of instantaneous transports computing1350 1351 \ texttt{nn\_dctwri}: frequency of writing ( mean of instantaneous transports )1352 1353 \ texttt{nn\_debug}: debugging of the section1343 \np{nn\_dct}: frequency of instantaneous transports computing 1344 1345 \np{nn\_dctwri}: frequency of writing ( mean of instantaneous transports ) 1346 1347 \np{nn\_debug}: debugging of the section 1354 1348 1355 1349 \subsubsection{ To create a binary file containing the pathway of each section } … … 1482 1476 the \key{diahth} CPP key: 1483 1477 1484 - the mixed layer depth (based on a density criterion , \citet{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth})1478 - the mixed layer depth (based on a density criterion \citep{de_Boyer_Montegut_al_JGR04}) (\mdl{diahth}) 1485 1479 1486 1480 - the turbocline depth (based on a turbulent mixing coefficient criterion) (\mdl{diahth}) 1487 1481 1488 - the depth of the 20\deg 1482 - the depth of the 20\degC isotherm (\mdl{diahth}) 1489 1483 1490 1484 - the depth of the thermocline (maximum of the vertical temperature gradient) (\mdl{diahth}) … … 1494 1488 \np{ln\_diaptr} to true (see the \textit{\ngn{namptr} } namelist below). 1495 1489 When \np{ln\_subbas}~=~true, transports and stream function are computed 1496 for the Atlantic, Indian, Pacific and Indo-Pacific Oceans (defined north of 30\deg 1490 for the Atlantic, Indian, Pacific and Indo-Pacific Oceans (defined north of 30\degS) 1497 1491 as well as for the World Ocean. The sub-basin decomposition requires an input file 1498 1492 (\ifile{subbasins}) which contains three 2D mask arrays, the Indo-Pacific mask … … 1504 1498 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1505 1499 \begin{figure}[!t] \begin{center} 1506 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_mask_subasins.pdf}1500 \includegraphics[width=1.0\textwidth]{Fig_mask_subasins} 1507 1501 \caption{ \label{Fig_mask_subasins} 1508 1502 Decomposition of the World Ocean (here ORCA2) into sub-basin used in to compute … … 1690 1684 1691 1685 1686 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_DOM.tex
r5602 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 % Chapter 2 �Space and Time Domain (DOM)4 % Chapter 2 ——— Space and Time Domain (DOM) 3 5 % ================================================================ 4 6 \chapter{Space Domain (DOM) } … … 40 42 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 41 43 \begin{figure}[!tb] \begin{center} 42 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_cell.pdf}44 \includegraphics[width=0.90\textwidth]{Fig_cell} 43 45 \caption{ \label{Fig_cell} 44 46 Arrangement of variables. $t$ indicates scalar points where temperature, … … 138 140 and $f$-points, and its divergence defined at $t$-points: 139 141 \begin{eqnarray} \label{Eq_DOM_curl} 140 \nabla \times {\rm 142 \nabla \times {\rm{\bf A}}\equiv & 141 143 \frac{1}{e_{2v}\,e_{3vw} } \ \left( \delta_{j +1/2} \left[e_{3w}\,a_3 \right] -\delta_{k+1/2} \left[e_{2v} \,a_2 \right] \right) &\ \mathbf{i} \\ 142 144 +& \frac{1}{e_{2u}\,e_{3uw}} \ \left( \delta_{k+1/2} \left[e_{1u}\,a_1 \right] -\delta_{i +1/2} \left[e_{3w}\,a_3 \right] \right) &\ \mathbf{j} \\ … … 183 185 Let $a$ and $b$ be two fields defined on the mesh, with value zero inside 184 186 continental area. Using integration by parts it can be shown that the differencing 185 operators ($\delta_i$, $\delta_j$ and $\delta_k$) are anti-symmetric linear186 operators,and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$,187 operators ($\delta_i$, $\delta_j$ and $\delta_k$) are skew-symmetric linear operators, 188 and further that the averaging operators $\overline{\,\cdot\,}^{\,i}$, 187 189 $\overline{\,\cdot\,}^{\,k}$ and $\overline{\,\cdot\,}^{\,k}$) are symmetric linear 188 190 operators, $i.e.$ … … 210 212 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 211 213 \begin{figure}[!tb] \begin{center} 212 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_index_hor.pdf}214 \includegraphics[width=0.90\textwidth]{Fig_index_hor} 213 215 \caption{ \label{Fig_index_hor} 214 216 Horizontal integer indexing used in the \textsc{Fortran} code. The dashed area indicates … … 260 262 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 261 263 \begin{figure}[!pt] \begin{center} 262 \includegraphics[width=.90\textwidth]{ ./TexFiles/Figures/Fig_index_vert.pdf}264 \includegraphics[width=.90\textwidth]{Fig_index_vert} 263 265 \caption{ \label{Fig_index_vert} 264 266 Vertical integer indexing used in the \textsc{Fortran } code. Note that … … 358 360 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 359 361 \begin{figure}[!t] \begin{center} 360 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_zgr_e3.pdf}362 \includegraphics[width=0.90\textwidth]{Fig_zgr_e3} 361 363 \caption{ \label{Fig_zgr_e3} 362 364 Comparison of (a) traditional definitions of grid-point position and grid-size in the vertical, … … 364 366 For both grids here, the same $w$-point depth has been chosen but in (a) the 365 367 $t$-points are set half way between $w$-points while in (b) they are defined from 366 an analytical function: $z(k)=5\,( i-1/2)^3 - 45\,(i-1/2)^2 + 140\,(i-1/2) - 150$.368 an analytical function: $z(k)=5\,(k-1/2)^3 - 45\,(k-1/2)^2 + 140\,(k-1/2) - 150$. 367 369 Note the resulting difference between the value of the grid-size $\Delta_k$ and 368 370 those of the scale factor $e_k$. } … … 425 427 426 428 The choice of the grid must be consistent with the boundary conditions specified 427 by the parameter \np{jperio}(see {\S\ref{LBC}).429 by \np{jperio}, a parameter found in \ngn{namcfg} namelist (see {\S\ref{LBC}). 428 430 429 431 % ------------------------------------------------------------------------------------------------------------- … … 467 469 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 468 470 \begin{figure}[!tb] \begin{center} 469 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_z_zps_s_sps.pdf}471 \includegraphics[width=1.0\textwidth]{Fig_z_zps_s_sps} 470 472 \caption{ \label{Fig_z_zps_s_sps} 471 473 The ocean bottom as seen by the model: … … 481 483 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 482 484 483 The choice of a vertical coordinate, even if it is made through a namelist parameter,485 The choice of a vertical coordinate, even if it is made through \ngn{namzgr} namelist parameters, 484 486 must be done once of all at the beginning of an experiment. It is not intended as an 485 487 option which can be enabled or disabled in the middle of an experiment. Three main … … 494 496 bathymetry or $s$-coordinate (hybrid and partial step coordinates have not 495 497 yet been tested in NEMO v2.3). If using $z$-coordinate with partial step bathymetry 496 (\np{ln\_zps}~=~true), ocean cavity beneath ice shelves can be open (\np{ln\_isfcav}~=~true). 498 (\np{ln\_zps}~=~true), ocean cavity beneath ice shelves can be open (\np{ln\_isfcav}~=~true) 499 and partial step are also applied at the ocean/ice shelf interface. 497 500 498 501 Contrary to the horizontal grid, the vertical grid is computed in the code and no 499 502 provision is made for reading it from a file. The only input file is the bathymetry 500 (in meters) (\ifile{bathy\_meter}) 503 (in meters) (\ifile{bathy\_meter}). 501 504 \footnote{N.B. in full step $z$-coordinate, a \ifile{bathy\_level} file can replace the 502 505 \ifile{bathy\_meter} file, so that the computation of the number of wet ocean point … … 540 543 541 544 Three options are possible for defining the bathymetry, according to the 542 namelist variable \np{nn\_bathy} :545 namelist variable \np{nn\_bathy} (found in \ngn{namdom} namelist): 543 546 \begin{description} 544 547 \item[\np{nn\_bathy} = 0] a flat-bottom domain is defined. The total depth $z_w (jpk)$ … … 548 551 domain width at the central latitude. This is meant for the "EEL-R5" configuration, 549 552 a periodic or open boundary channel with a seamount. 550 \item[\np{nn\_bathy} = 1] read a bathymetry . The \ifile{bathy\_meter} file (Netcdf format)551 provides the ocean depth (positive, in meters) at each grid point of the model grid. 552 The bathymetry is usually built by interpolating a standard bathymetry product553 \item[\np{nn\_bathy} = 1] read a bathymetry and ice shelf draft (if needed). 554 The \ifile{bathy\_meter} file (Netcdf format) provides the ocean depth (positive, in meters) 555 at each grid point of the model grid. The bathymetry is usually built by interpolating a standard bathymetry product 553 556 ($e.g.$ ETOPO2) onto the horizontal ocean mesh. Defining the bathymetry also 554 557 defines the coastline: where the bathymetry is zero, no model levels are defined 555 558 (all levels are masked). 559 560 The \ifile{isfdraft\_meter} file (Netcdf format) provides the ice shelf draft (positive, in meters) 561 at each grid point of the model grid. This file is only needed if \np{ln\_isfcav}~=~true. 562 Defining the ice shelf draft will also define the ice shelf edge and the grounding line position. 556 563 \end{description} 557 564 … … 573 580 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 574 581 \begin{figure}[!tb] \begin{center} 575 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_zgr.pdf}582 \includegraphics[width=0.90\textwidth]{Fig_zgr} 576 583 \caption{ \label{Fig_zgr} 577 584 Default vertical mesh for ORCA2: 30 ocean levels (L30). Vertical level functions for … … 610 617 (Fig.~\ref{Fig_zgr}). 611 618 619 If the ice shelf cavities are opened (\np{ln\_isfcav}=~true~}), the definition of $z_0$ is the same. 620 However, definition of $e_3^0$ at $t$- and $w$-points is respectively changed to: 621 \begin{equation} \label{DOM_zgr_ana} 622 \begin{split} 623 e_3^T(k) &= z_W (k+1) - z_W (k) \\ 624 e_3^W(k) &= z_T (k) - z_T (k-1) \\ 625 \end{split} 626 \end{equation} 627 This formulation decrease the self-generated circulation into the ice shelf cavity 628 (which can, in extreme case, leads to blow up).\\ 629 630 612 631 The most used vertical grid for ORCA2 has $10~m$ ($500~m)$ resolution in the 613 632 surface (bottom) layers and a depth which varies from 0 at the sea surface to a … … 721 740 usually 10\%, of the default thickness $e_{3t}(jk)$). 722 741 723 \colorbox{yellow}{Add a figure here of pstep especially at last ocean level}742 \gmcomment{ \colorbox{yellow}{Add a figure here of pstep especially at last ocean level } } 724 743 725 744 % ------------------------------------------------------------------------------------------------------------- … … 785 804 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 786 805 \begin{figure}[!ht] \begin{center} 787 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_sco_function.pdf}806 \includegraphics[width=1.0\textwidth]{Fig_sco_function} 788 807 \caption{ \label{Fig_sco_function} 789 808 Examples of the stretching function applied to a seamount; from left to right: … … 825 844 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 826 845 \begin{figure}[!ht] 827 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/FIG_DOM_compare_coordinates_surface.pdf}846 \includegraphics[width=1.0\textwidth]{FIG_DOM_compare_coordinates_surface} 828 847 \caption{A comparison of the \citet{Song_Haidvogel_JCP94} $S$-coordinate (solid lines), a 50 level $Z$-coordinate (contoured surfaces) and the \citet{Siddorn_Furner_OM12} $S$-coordinate (dashed lines) in the surface 100m for a idealised bathymetry that goes from 50m to 5500m depth. For clarity every third coordinate surface is shown.} 829 848 \label{fig_compare_coordinates_surface} … … 860 879 gives the number of ocean levels ($i.e.$ those that are not masked) at each 861 880 $t$-point. mbathy is computed from the meter bathymetry using the definiton of 862 gdept as the number of $t$-points which gdept $\leq$ bathy. 881 gdept as the number of $t$-points which gdept $\leq$ bathy. 863 882 864 883 Modifications of the model bathymetry are performed in the \textit{bat\_ctl} 865 884 routine (see \mdl{domzgr} module) after mbathy is computed. Isolated grid points 866 that do not communicate with another ocean point at the same level are eliminated. 885 that do not communicate with another ocean point at the same level are eliminated.\\ 886 887 As for the representation of bathymetry, a 2D integer array, misfdep, is created. 888 misfdep defines the level of the first wet $t$-point. All the cells between $k=1$ and $misfdep(i,j)-1$ are masked. 889 By default, misfdep(:,:)=1 and no cells are masked. 890 891 In case of ice shelf cavities (\np{ln\_isfcav}~=~true), modifications of the model bathymetry and ice shelf draft in 892 the cavities are performed through the \textit{zgr\_isf} routine. The compatibility between ice shelf draft and bathymetry is checked: 893 if only one cell on the water column is opened at $t$-, $u$- or $v$-points, the bathymetry or the ice shelf draft is dug to have a 2-level water column 894 (i.e. two unmasked levels). If the incompatibility is too strong (i.e. need to dig more than one cell), the entire water column is masked.\\ 867 895 868 896 From the \textit{mbathy} array, the mask fields are defined as follows: 869 897 \begin{align*} 870 tmask(i,j,k) &= \begin{cases} \; 1& \text{ if $k\leq mbathy(i,j)$ } \\ 871 \; 0& \text{ if $k\leq mbathy(i,j)$ } \end{cases} \\ 898 tmask(i,j,k) &= \begin{cases} \; 0& \text{ if $k < misfdep(i,j) $ } \\ 899 \; 1& \text{ if $misfdep(i,j) \leq k\leq mbathy(i,j)$ } \\ 900 \; 0& \text{ if $k > mbathy(i,j)$ } \end{cases} \\ 872 901 umask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 873 902 vmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i,j+1,k) \\ 874 903 fmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 875 & \ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) 904 & \ \ \, * tmask(i,j,k) \ * \ tmask(i+1,j,k) \\ 905 wmask(i,j,k) &= \; tmask(i,j,k) \ * \ tmask(i,j,k-1) \text{ with } wmask(i,j,1) = tmask(i,j,1) 876 906 \end{align*} 877 907 878 Note that \textit{wmask} is not defined as it is exactly equal to \textit{tmask} with 879 the numerical indexing used (\S~\ref{DOM_Num_Index}). Moreover, the 880 specification of closed lateral boundaries requires that at least the first and last 908 Note, wmask is now defined. It allows, in case of ice shelves, 909 to deal with the top boundary (ice shelf/ocean interface) exactly in the same way as for the bottom boundary. 910 911 The specification of closed lateral boundaries requires that at least the first and last 881 912 rows and columns of the \textit{mbathy} array are set to zero. In the particular 882 913 case of an east-west cyclical boundary condition, \textit{mbathy} has its last … … 910 941 (typical of the tropical ocean), see \rou{istate\_t\_s} subroutine called from \mdl{istate} module. 911 942 \end{description} 943 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_DYN.tex
r5602 r7260 1 % ================================================================ 2 % Chapter � Ocean Dynamics (DYN) 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 3 % ================================================================ 4 % Chapter ——— Ocean Dynamics (DYN) 3 5 % ================================================================ 4 6 \chapter{Ocean Dynamics (DYN)} 5 7 \label{DYN} 6 8 \minitoc 7 8 % add a figure for dynvor ens, ene latices9 9 10 10 %\vspace{2.cm} … … 165 165 %------------------------------------------------------------------------------------------------------------- 166 166 167 The vector invariant form of the momentum equations is the one most 168 often used in applications of the \NEMO ocean model. The flux form option 169 (see next section) has been present since version $2$. Options are defined 170 through the \ngn{namdyn\_adv} namelist variables 171 Coriolis and momentum advection terms are evaluated using a leapfrog 172 scheme, $i.e.$ the velocity appearing in these expressions is centred in 173 time (\textit{now} velocity). 167 The vector invariant form of the momentum equations (\np{ln\_dynhpg\_vec}~=~true) is the one most 168 often used in applications of the \NEMO ocean model. The flux form option (\np{ln\_dynhpg\_vec}~=false) 169 (see next section) has been present since version $2$. 170 Options are defined through the \ngn{namdyn\_adv} namelist variables. 171 Coriolis and momentum advection terms are evaluated using a leapfrog scheme, 172 $i.e.$ the velocity appearing in these expressions is centred in time (\textit{now} velocity). 174 173 At the lateral boundaries either free slip, no slip or partial slip boundary 175 174 conditions are applied following Chap.\ref{LBC}. … … 296 295 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 297 296 \begin{figure}[!ht] \begin{center} 298 \includegraphics[width=0.70\textwidth]{ ./TexFiles/Figures/Fig_DYN_een_triad.pdf}297 \includegraphics[width=0.70\textwidth]{Fig_DYN_een_triad} 299 298 \caption{ \label{Fig_DYN_een_triad} 300 299 Triads used in the energy and enstrophy conserving scheme (een) for … … 303 302 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 304 303 305 Note that a key point in \eqref{Eq_een_e3f} is that the averaging in the \textbf{i}- and 306 \textbf{j}- directions uses the masked vertical scale factor but is always divided by 307 $4$, not by the sum of the masks at the four $T$-points. This preserves the continuity of 308 $e_{3f}$ when one or more of the neighbouring $e_{3t}$ tends to zero and 309 extends by continuity the value of $e_{3f}$ into the land areas. This feature is essential for 310 the $z$-coordinate with partial steps. 304 A key point in \eqref{Eq_een_e3f} is how the averaging in the \textbf{i}- and \textbf{j}- directions is made. 305 It uses the sum of masked t-point vertical scale factor divided either 306 by the sum of the four t-point masks (\np{ln\_dynvor\_een\_old}~=~false), 307 or just by $4$ (\np{ln\_dynvor\_een\_old}~=~true). 308 The latter case preserves the continuity of $e_{3f}$ when one or more of the neighbouring $e_{3t}$ 309 tends to zero and extends by continuity the value of $e_{3f}$ into the land areas. 310 This case introduces a sub-grid-scale topography at f-points (with a systematic reduction of $e_{3f}$ 311 when a model level intercept the bathymetry) that tends to reinforce the topostrophy of the flow 312 ($i.e.$ the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}. 311 313 312 314 Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as … … 374 376 \end{aligned} \right. 375 377 \end{equation} 378 When \np{ln\_dynzad\_zts}~=~\textit{true}, a split-explicit time stepping with 5 sub-timesteps is used 379 on the vertical advection term. 380 This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}. 381 Note that in this case, a similar split-explicit time stepping should be used on 382 vertical advection of tracer to ensure a better stability, 383 an option which is only available with a TVD scheme (see \np{ln\_traadv\_tvd\_zts} in \S\ref{TRA_adv_tvd}). 384 376 385 377 386 % ================================================================ … … 491 500 those in the centred second order method. As the scheme already includes 492 501 a diffusion component, it can be used without explicit lateral diffusion on momentum 493 ($i.e.$ \np{ln\_dynldf\_lap}=\np{ln\_dynldf\_bilap}=false), and it is recommended to do so. 502 ($i.e.$ setting both \np{ln\_dynldf\_lap} and \np{ln\_dynldf\_bilap} to \textit{false}), 503 and it is recommended to do so. 494 504 495 505 The UBS scheme is not used in all directions. In the vertical, the centred $2^{nd}$ … … 629 639 ($e_{3w}$). 630 640 631 $\bullet$ Traditional coding with adaptation for ice shelf cavities (\np{ln\_dynhpg\_isf}=true).632 This scheme need the activation of ice shelf cavities (\np{ln\_isfcav}=true).633 634 641 $\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}=true) 635 642 … … 646 653 pressure Jacobian method is used to solve the horizontal pressure gradient. This method can provide 647 654 a more accurate calculation of the horizontal pressure gradient than the standard scheme. 655 656 \subsection{Ice shelf cavity} 657 \label{DYN_hpg_isf} 658 Beneath an ice shelf, the total pressure gradient is the sum of the pressure gradient due to the ice shelf load and 659 the pressure gradient due to the ocean load. If cavities are present (\np{ln\_isfcav}~=~true) these two terms can be 660 calculated by setting \np{ln\_dynhpg\_isf}~=~true. No other scheme is working with ice shelves.\\ 661 662 $\bullet$ The main hypothesis to compute the ice shelf load is that the ice shelf is in isostatic equilibrium. 663 The top pressure is computed integrating a reference density profile (prescribed as density of a water at 34.4 664 PSU and -1.9$^{\circ}C$) from the sea surface to the ice shelf base, which corresponds to the load of the water 665 column in which the ice shelf is floatting. This top pressure is constant over time. A detailed description of 666 this method is described in \citet{Losch2008}.\\ 667 668 $\bullet$ The ocean load is computed using the expression \eqref{Eq_dynhpg_sco} described in \ref{DYN_hpg_sco}. 669 A treatment of the top and bottom partial cells similar to the one described in \ref{DYN_hpg_zps} is done 670 to reduce the residual circulation generated by the top partial cell. 648 671 649 672 %-------------------------------------------------------------------------------------------------------------- … … 718 741 $\ $\newline %force an empty line 719 742 720 %%%721 743 Options are defined through the \ngn{namdyn\_spg} namelist variables. 722 The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}). The main distinction is between the fixed volume case (linear free surface) and the variable volume case (nonlinear free surface, \key{vvl} is defined). In the linear free surface case (\S\ref{PE_free_surface}) the vertical scale factors $e_{3}$ are fixed in time, while they are time-dependent in the nonlinear case (\S\ref{PE_free_surface}). With both linear and nonlinear free surface, external gravity waves are allowed in the equations, which imposes a very small time step when an explicit time stepping is used. Two methods are proposed to allow a longer time step for the three-dimensional equations: the filtered free surface, which is a modification of the continuous equations (see \eqref{Eq_PE_flt}), and the split-explicit free surface described below. The extra term introduced in the filtered method is calculated implicitly, so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 723 724 %%% 744 The surface pressure gradient term is related to the representation of the free surface (\S\ref{PE_hor_pg}). 745 The main distinction is between the fixed volume case (linear free surface) and the variable volume case 746 (nonlinear free surface, \key{vvl} is defined). In the linear free surface case (\S\ref{PE_free_surface}) 747 the vertical scale factors $e_{3}$ are fixed in time, while they are time-dependent in the nonlinear case 748 (\S\ref{PE_free_surface}). 749 With both linear and nonlinear free surface, external gravity waves are allowed in the equations, 750 which imposes a very small time step when an explicit time stepping is used. 751 Two methods are proposed to allow a longer time step for the three-dimensional equations: 752 the filtered free surface, which is a modification of the continuous equations (see \eqref{Eq_PE_flt}), 753 and the split-explicit free surface described below. 754 The extra term introduced in the filtered method is calculated implicitly, 755 so that the update of the next velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 725 756 726 757 … … 736 767 implicitly, so that a solver is used to compute it. As a consequence the update of the $next$ 737 768 velocities is done in module \mdl{dynspg\_flt} and not in \mdl{dynnxt}. 738 739 769 740 770 … … 779 809 $\rdt_e = \rdt / nn\_baro$. This parameter can be optionally defined automatically (\np{ln\_bt\_nn\_auto}=true) 780 810 considering that the stability of the barotropic system is essentially controled by external waves propagation. 781 Maximum allowed Courant number is in that case time independent, and easily computed online from the input bathymetry. 811 Maximum Courant number is in that case time independent, and easily computed online from the input bathymetry. 812 Therefore, $\rdt_e$ is adjusted so that the Maximum allowed Courant number is smaller than \np{rn\_bt\_cmax}. 782 813 783 814 %%% … … 798 829 %> > > > > > > > > > > > > > > > > > > > > > > > > > > > 799 830 \begin{figure}[!t] \begin{center} 800 \includegraphics[width=0.7\textwidth]{ ./TexFiles/Figures/Fig_DYN_dynspg_ts.pdf}831 \includegraphics[width=0.7\textwidth]{Fig_DYN_dynspg_ts} 801 832 \caption{ \label{Fig_DYN_dynspg_ts} 802 833 Schematic of the split-explicit time stepping scheme for the external 803 834 and internal modes. Time increases to the right. In this particular exemple, 804 a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_f ilt=1$) and $nn\_baro=5$.835 a boxcar averaging window over $nn\_baro$ barotropic time steps is used ($nn\_bt\_flt=1$) and $nn\_baro=5$. 805 836 Internal mode time steps (which are also the model time steps) are denoted 806 837 by $t-\rdt$, $t$ and $t+\rdt$. Variables with $k$ superscript refer to instantaneous barotropic variables, … … 808 839 The former are used to obtain time filtered quantities at $t+\rdt$ while the latter are used to obtain time averaged 809 840 transports to advect tracers. 810 a) Forward time integration: \np{ln\_bt\_fw}=true, \np{ln\_bt\_av e}=true.811 b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_av e}=true.812 c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_av e}=false. }841 a) Forward time integration: \np{ln\_bt\_fw}=true, \np{ln\_bt\_av}=true. 842 b) Centred time integration: \np{ln\_bt\_fw}=false, \np{ln\_bt\_av}=true. 843 c) Forward time integration with no time filtering (POM-like scheme): \np{ln\_bt\_fw}=true, \np{ln\_bt\_av}=false. } 813 844 \end{center} \end{figure} 814 845 %> > > > > > > > > > > > > > > > > > > > > > > > > > > > … … 816 847 In the default case (\np{ln\_bt\_fw}=true), the external mode is integrated 817 848 between \textit{now} and \textit{after} baroclinic time-steps (Fig.~\ref{Fig_DYN_dynspg_ts}a). To avoid aliasing of fast barotropic motions into three dimensional equations, time filtering is eventually applied on barotropic 818 quantities (\np{ln\_bt\_av e}=true). In that case, the integration is extended slightly beyond \textit{after} time step to provide time filtered quantities.849 quantities (\np{ln\_bt\_av}=true). In that case, the integration is extended slightly beyond \textit{after} time step to provide time filtered quantities. 819 850 These are used for the subsequent initialization of the barotropic mode in the following baroclinic step. 820 851 Since external mode equations written at baroclinic time steps finally follow a forward time stepping scheme, … … 837 868 %%% 838 869 839 One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_av e}=false).870 One can eventually choose to feedback instantaneous values by not using any time filter (\np{ln\_bt\_av}=false). 840 871 In that case, external mode equations are continuous in time, ie they are not re-initialized when starting a new 841 872 sub-stepping sequence. This is the method used so far in the POM model, the stability being maintained by refreshing at (almost) … … 1158 1189 1159 1190 Besides the surface and bottom stresses (see the above section) which are 1160 introduced as boundary conditions on the vertical mixing, two other forcings 1161 enter the dynamical equations. 1162 1163 One is the effect of atmospheric pressure on the ocean dynamics. 1164 Another forcing term is the tidal potential. 1165 Both of which will be introduced into the reference version soon. 1166 1167 \gmcomment{atmospheric pressure is there!!!! include its description } 1191 introduced as boundary conditions on the vertical mixing, three other forcings 1192 may enter the dynamical equations by affecting the surface pressure gradient. 1193 1194 (1) When \np{ln\_apr\_dyn}~=~true (see \S\ref{SBC_apr}), the atmospheric pressure is taken 1195 into account when computing the surface pressure gradient. 1196 1197 (2) When \np{ln\_tide\_pot}~=~true and \key{tide} is defined (see \S\ref{SBC_tide}), 1198 the tidal potential is taken into account when computing the surface pressure gradient. 1199 1200 (3) When \np{nn\_ice\_embd}~=~2 and LIM or CICE is used ($i.e.$ when the sea-ice is embedded in the ocean), 1201 the snow-ice mass is taken into account when computing the surface pressure gradient. 1202 1203 1204 \gmcomment{ missing : the lateral boundary condition !!! another external forcing 1205 } 1168 1206 1169 1207 % ================================================================ … … 1296 1334 1297 1335 % ================================================================ 1336 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_LBC.tex
r4147 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 % Chapter �Lateral Boundary Condition (LBC)4 % Chapter — Lateral Boundary Condition (LBC) 3 5 % ================================================================ 4 6 \chapter{Lateral Boundary Condition (LBC) } … … 53 55 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 54 56 \begin{figure}[!t] \begin{center} 55 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_LBC_uv.pdf}57 \includegraphics[width=0.90\textwidth]{Fig_LBC_uv} 56 58 \caption{ \label{Fig_LBC_uv} 57 59 Lateral boundary (thick line) at T-level. The velocity normal to the boundary is set to zero.} … … 76 78 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 77 79 \begin{figure}[!p] \begin{center} 78 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_LBC_shlat.pdf}80 \includegraphics[width=0.90\textwidth]{Fig_LBC_shlat} 79 81 \caption{ \label{Fig_LBC_shlat} 80 82 lateral boundary condition (a) free-slip ($rn\_shlat=0$) ; (b) no-slip ($rn\_shlat=2$) … … 195 197 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 196 198 \begin{figure}[!t] \begin{center} 197 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_LBC_jperio.pdf}199 \includegraphics[width=1.0\textwidth]{Fig_LBC_jperio} 198 200 \caption{ \label{Fig_LBC_jperio} 199 201 setting of (a) east-west cyclic (b) symmetric across the equator boundary conditions.} … … 204 206 % North fold (\textit{jperio = 3 }to $6)$ 205 207 % ------------------------------------------------------------------------------------------------------------- 206 \subsection{North-fold (\textit{jperio = 3 }to $6 )$}208 \subsection{North-fold (\textit{jperio = 3 }to $6$) } 207 209 \label{LBC_north_fold} 208 210 209 211 The north fold boundary condition has been introduced in order to handle the north 210 boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere. 211 \colorbox{yellow}{to be completed...} 212 boundary of a three-polar ORCA grid. Such a grid has two poles in the northern hemisphere 213 (Fig.\ref{Fig_MISC_ORCA_msh}, and thus requires a specific treatment illustrated in Fig.\ref{Fig_North_Fold_T}. 214 Further information can be found in \mdl{lbcnfd} module which applies the north fold boundary condition. 212 215 213 216 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 214 217 \begin{figure}[!t] \begin{center} 215 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_North_Fold_T.pdf}218 \includegraphics[width=0.90\textwidth]{Fig_North_Fold_T} 216 219 \caption{ \label{Fig_North_Fold_T} 217 220 North fold boundary with a $T$-point pivot and cyclic east-west boundary condition … … 250 253 ocean model. Second order finite difference schemes lead to local discrete 251 254 operators that depend at the very most on one neighbouring point. The only 252 non-local computations concern the vertical physics (implicit diffusion, 1.5255 non-local computations concern the vertical physics (implicit diffusion, 253 256 turbulent closure scheme, ...) (delocalization over the whole water column), 254 257 and the solving of the elliptic equation associated with the surface pressure 255 258 gradient computation (delocalization over the whole horizontal domain). 256 259 Therefore, a pencil strategy is used for the data sub-structuration 257 \gmcomment{no idea what this means!}258 260 : the 3D initial domain is laid out on local processor 259 261 memories following a 2D horizontal topological splitting. Each sub-domain … … 264 266 phase starts: each processor sends to its neighbouring processors the update 265 267 values of the points corresponding to the interior overlapping area to its 266 neighbouring sub-domain (i.e. the innermost of the two overlapping rows). 267 The communication is done through message passing. Usually the parallel virtual 268 language, PVM, is used as it is a standard language available on nearly all 269 MPP computers. More specific languages (i.e. computer dependant languages) 270 can be easily used to speed up the communication, such as SHEM on a T3E 271 computer. The data exchanges between processors are required at the very 268 neighbouring sub-domain ($i.e.$ the innermost of the two overlapping rows). 269 The communication is done through the Message Passing Interface (MPI). 270 The data exchanges between processors are required at the very 272 271 place where lateral domain boundary conditions are set in the mono-domain 273 computation (\S III.10-c): the lbc\_lnk routine which manages such conditions 274 is substituted by mpplnk.F or mpplnk2.F routine when running on an MPP 275 computer (\key{mpp\_mpi} defined). It has to be pointed out that when using 276 the MPP version of the model, the east-west cyclic boundary condition is done 277 implicitly, whilst the south-symmetric boundary condition option is not available. 272 computation : the \rou{lbc\_lnk} routine (found in \mdl{lbclnk} module) 273 which manages such conditions is interfaced with routines found in \mdl{lib\_mpp} module 274 when running on an MPP computer ($i.e.$ when \key{mpp\_mpi} defined). 275 It has to be pointed out that when using the MPP version of the model, 276 the east-west cyclic boundary condition is done implicitly, 277 whilst the south-symmetric boundary condition option is not available. 278 278 279 279 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 280 280 \begin{figure}[!t] \begin{center} 281 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_mpp.pdf}281 \includegraphics[width=0.90\textwidth]{Fig_mpp} 282 282 \caption{ \label{Fig_mpp} 283 283 Positioning of a sub-domain when massively parallel processing is used. } … … 285 285 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 286 286 287 In the standard version of the OPA model, the splitting is regular and arithmetic. 288 the i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors 289 \jp{jpnij} most often equal to $jpni \times jpnj$ (model parameters set in 290 \mdl{par\_oce}). Each processor is independent and without message passing 291 or synchronous process 292 \gmcomment{how does a synchronous process relate to this?}, 293 programs run alone and access just its own local memory. For this reason, the 294 main model dimensions are now the local dimensions of the subdomain (pencil) 287 In the standard version of \NEMO, the splitting is regular and arithmetic. 288 The i-axis is divided by \jp{jpni} and the j-axis by \jp{jpnj} for a number of processors 289 \jp{jpnij} most often equal to $jpni \times jpnj$ (parameters set in 290 \ngn{nammpp} namelist). Each processor is independent and without message passing 291 or synchronous process, programs run alone and access just its own local memory. 292 For this reason, the main model dimensions are now the local dimensions of the subdomain (pencil) 295 293 that are named \jp{jpi}, \jp{jpj}, \jp{jpk}. These dimensions include the internal 296 294 domain and the overlapping rows. The number of rows to exchange (known as … … 304 302 where \jp{jpni}, \jp{jpnj} are the number of processors following the i- and j-axis. 305 303 306 \colorbox{yellow}{Figure IV.3: example of a domain splitting with 9 processors and 307 no east-west cyclic boundary conditions.} 308 309 One also defines variables nldi and nlei which correspond to the internal 310 domain bounds, and the variables nimpp and njmpp which are the position 311 of the (1,1) grid-point in the global domain. An element of $T_{l}$, a local array 312 (subdomain) corresponds to an element of $T_{g}$, a global array 313 (whole domain) by the relationship: 304 One also defines variables nldi and nlei which correspond to the internal domain bounds, 305 and the variables nimpp and njmpp which are the position of the (1,1) grid-point in the global domain. 306 An element of $T_{l}$, a local array (subdomain) corresponds to an element of $T_{g}$, 307 a global array (whole domain) by the relationship: 314 308 \begin{equation} \label{Eq_lbc_nimpp} 315 309 T_{g} (i+nimpp-1,j+njmpp-1,k) = T_{l} (i,j,k), … … 320 314 nproc. In the standard version, a processor has no more than four neighbouring 321 315 processors named nono (for north), noea (east), noso (south) and nowe (west) 322 and two variables, nbondi and nbondj, indicate the relative position of the processor 323 \colorbox{yellow}{(see Fig.IV.3)}: 316 and two variables, nbondi and nbondj, indicate the relative position of the processor : 324 317 \begin{itemize} 325 318 \item nbondi = -1 an east neighbour, no west processor, … … 332 325 processor on its overlapping row, and sends the data issued from internal 333 326 domain corresponding to the overlapping row of the other processor. 334 335 \colorbox{yellow}{Figure IV.4: pencil splitting with the additional outer halos }336 327 337 328 … … 343 334 global ocean where more than 50 \% of points are land points. For this reason, a 344 335 pre-processing tool can be used to choose the mpp domain decomposition with a 345 maximum number of only land points processors, which can then be eliminated .346 (For example, the mpp\_optimiz tools, available from the DRAKKAR web site .)336 maximum number of only land points processors, which can then be eliminated (Fig. \ref{Fig_mppini2}) 337 (For example, the mpp\_optimiz tools, available from the DRAKKAR web site). 347 338 This optimisation is dependent on the specific bathymetry employed. The user 348 339 then chooses optimal parameters \jp{jpni}, \jp{jpnj} and \jp{jpnij} with 349 340 $jpnij < jpni \times jpnj$, leading to the elimination of $jpni \times jpnj - jpnij$ 350 land processors. When those parameters are specified in module \mdl{par\_oce},341 land processors. When those parameters are specified in \ngn{nammpp} namelist, 351 342 the algorithm in the \rou{inimpp2} routine sets each processor's parameters (nbound, 352 343 nono, noea,...) so that the land-only processors are not taken into account. 353 344 354 \ colorbox{yellow}{Note that the inimpp2 routine is general so that the original inimpp345 \gmcomment{Note that the inimpp2 routine is general so that the original inimpp 355 346 routine should be suppressed from the code.} 356 347 357 348 When land processors are eliminated, the value corresponding to these locations in 358 the model output files is zero. Note that this is a problem for a mesh output file written 359 by such a model configuration, because model users often divide by the scale factors 360 ($e1t$, $e2t$, etc) and do not expect the grid size to be zero, even on land. It may be 361 best not to eliminate land processors when running the model especially to write the 362 mesh files as outputs (when \np{nn\_msh} namelist parameter differs from 0). 363 %% 364 \gmcomment{Steven : dont understand this, no land processor means no output file 365 covering this part of globe; its only when files are stitched together into one that you 366 can leave a hole} 367 %% 349 the model output files is undefined. Note that this is a problem for the meshmask file 350 which requires to be defined over the whole domain. Therefore, user should not eliminate 351 land processors when creating a meshmask file ($i.e.$ when setting a non-zero value to \np{nn\_msh}). 368 352 369 353 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 370 354 \begin{figure}[!ht] \begin{center} 371 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_mppini2.pdf}355 \includegraphics[width=0.90\textwidth]{Fig_mppini2} 372 356 \caption { \label{Fig_mppini2} 373 357 Example of Atlantic domain defined for the CLIPPER projet. Initial grid is … … 380 364 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 381 365 382 383 % ================================================================384 % Open Boundary Conditions385 % ================================================================386 \section{Open Boundary Conditions (\key{obc}) (OBC)}387 \label{LBC_obc}388 %-----------------------------------------nam_obc -------------------------------------------389 %- nobc_dta = 0 ! = 0 the obc data are equal to the initial state390 %- ! = 1 the obc data are read in 'obc .dta' files391 %- rn_dpein = 1. ! ???392 %- rn_dpwin = 1. ! ???393 %- rn_dpnin = 30. ! ???394 %- rn_dpsin = 1. ! ???395 %- rn_dpeob = 1500. ! time relaxation (days) for the east open boundary396 %- rn_dpwob = 15. ! " " for the west open boundary397 %- rn_dpnob = 150. ! " " for the north open boundary398 %- rn_dpsob = 15. ! " " for the south open boundary399 %- ln_obc_clim = .true. ! climatological obc data files (default T)400 %- ln_vol_cst = .true. ! total volume conserved401 \namdisplay{namobc}402 403 It is often necessary to implement a model configuration limited to an oceanic404 region or a basin, which communicates with the rest of the global ocean through405 ''open boundaries''. As stated by \citet{Roed1986}, an open boundary is a406 computational border where the aim of the calculations is to allow the perturbations407 generated inside the computational domain to leave it without deterioration of the408 inner model solution. However, an open boundary also has to let information from409 the outer ocean enter the model and should support inflow and outflow conditions.410 411 The open boundary package OBC is the first open boundary option developed in412 NEMO (originally in OPA8.2). It allows the user to413 \begin{itemize}414 \item tell the model that a boundary is ''open'' and not closed by a wall, for example415 by modifying the calculation of the divergence of velocity there;416 \item impose values of tracers and velocities at that boundary (values which may417 be taken from a climatology): this is the``fixed OBC'' option.418 \item calculate boundary values by a sophisticated algorithm combining radiation419 and relaxation (``radiative OBC'' option)420 \end{itemize}421 422 Options are defined through the \ngn{namobc} namelist variables.423 The package resides in the OBC directory. It is described here in four parts: the424 boundary geometry (parameters to be set in \mdl{obc\_par}), the forcing data at425 the boundaries (module \mdl{obcdta}), the radiation algorithm involving the426 namelist and module \mdl{obcrad}, and a brief presentation of boundary update427 and restart files.428 429 %----------------------------------------------430 \subsection{Boundary geometry}431 \label{OBC_geom}432 %433 First one has to realize that open boundaries may not necessarily be located434 at the extremities of the computational domain. They may exist in the middle435 of the domain, for example at Gibraltar Straits if one wants to avoid including436 the Mediterranean in an Atlantic domain. This flexibility has been found necessary437 for the CLIPPER project \citep{Treguier_al_JGR01}. Because of the complexity of the438 geometry of ocean basins, it may even be necessary to have more than one439 ''west'' open boundary, more than one ''north'', etc. This is not possible with440 the OBC option: only one open boundary of each kind, west, east, south and441 north is allowed; these names refer to the grid geometry (not to the direction442 of the geographical ''west'', ''east'', etc).443 444 The open boundary geometry is set by a series of parameters in the module445 \mdl{obc\_par}. For an eastern open boundary, parameters are \jp{lp\_obc\_east}446 (true if an east open boundary exists), \jp{jpieob} the $i$-index along which447 the eastern open boundary (eob) is located, \jp{jpjed} the $j$-index at which448 it starts, and \jp{jpjef} the $j$-index where it ends (note $d$ is for ''d\'{e}but''449 and $f$ for ''fin'' in French). Similar parameters exist for the west, south and450 north cases (Table~\ref{Tab_obc_param}).451 452 453 %--------------------------------------------------TABLE--------------------------------------------------454 \begin{table}[htbp] \begin{center} \begin{tabular}{|l|c|c|c|}455 \hline456 Boundary and & Constant index & Starting index (d\'{e}but) & Ending index (fin) \\457 Logical flag & & & \\458 \hline459 West & \jp{jpiwob} $>= 2$ & \jp{jpjwd}$>= 2$ & \jp{jpjwf}<= \np{jpjglo}-1 \\460 lp\_obc\_west & $i$-index of a $u$ point & $j$ of a $T$ point &$j$ of a $T$ point \\461 \hline462 East & \jp{jpieob}$<=$\np{jpiglo}-2&\jp{jpjed} $>= 2$ & \jp{jpjef}$<=$ \np{jpjglo}-1 \\463 lp\_obc\_east & $i$-index of a $u$ point & $j$ of a $T$ point & $j$ of a $T$ point \\464 \hline465 South & \jp{jpjsob} $>= 2$ & \jp{jpisd} $>= 2$ & \jp{jpisf}$<=$\np{jpiglo}-1 \\466 lp\_obc\_south & $j$-index of a $v$ point & $i$ of a $T$ point & $i$ of a $T$ point \\467 \hline468 North & \jp{jpjnob} $<=$ \np{jpjglo}-2& \jp{jpind} $>= 2$ & \jp{jpinf}$<=$\np{jpiglo}-1 \\469 lp\_obc\_north & $j$-index of a $v$ point & $i$ of a $T$ point & $i$ of a $T$ point \\470 \hline471 \end{tabular} \end{center}472 \caption{ \label{Tab_obc_param}473 Names of different indices relating to the open boundaries. In the case474 of a completely open ocean domain with four ocean boundaries, the parameters475 take exactly the values indicated.}476 \end{table}477 %------------------------------------------------------------------------------------------------------------478 479 The open boundaries must be along coordinate lines. On the C-grid, the boundary480 itself is along a line of normal velocity points: $v$ points for a zonal open boundary481 (the south or north one), and $u$ points for a meridional open boundary (the west482 or east one). Another constraint is that there still must be a row of masked points483 all around the domain, as if the domain were a closed basin (unless periodic conditions484 are used together with open boundary conditions). Therefore, an open boundary485 cannot be located at the first/last index, namely, 1, \jp{jpiglo} or \jp{jpjglo}. Also,486 the open boundary algorithm involves calculating the normal velocity points situated487 just on the boundary, as well as the tangential velocity and temperature and salinity488 just outside the boundary. This means that for a west/south boundary, normal489 velocities and temperature are calculated at the same index \jp{jpiwob} and490 \jp{jpjsob}, respectively. For an east/north boundary, the normal velocity is491 calculated at index \jp{jpieob} and \jp{jpjnob}, but the ``outside'' temperature is492 at index \jp{jpieob}+1 and \jp{jpjnob}+1. This means that \jp{jpieob}, \jp{jpjnob}493 cannot be bigger than \jp{jpiglo}-2, \jp{jpjglo}-2.494 495 496 The starting and ending indices are to be thought of as $T$ point indices: in many497 cases they indicate the first land $T$-point, at the extremity of an open boundary498 (the coast line follows the $f$ grid points, see Fig.~\ref{Fig_obc_north} for an example499 of a northern open boundary). All indices are relative to the global domain. In the500 free surface case it is possible to have ``ocean corners'', that is, an open boundary501 starting and ending in the ocean.502 503 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>504 \begin{figure}[!t] \begin{center}505 \includegraphics[width=0.70\textwidth]{./TexFiles/Figures/Fig_obc_north.pdf}506 \caption{ \label{Fig_obc_north}507 Localization of the North open boundary points.}508 \end{center} \end{figure}509 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>510 511 Although not compulsory, it is highly recommended that the bathymetry in the512 vicinity of an open boundary follows the following rule: in the direction perpendicular513 to the open line, the water depth should be constant for 4 grid points. This is in514 order to ensure that the radiation condition, which involves model variables next515 to the boundary, is calculated in a consistent way. On Fig.\ref{Fig_obc_north} we516 indicate by an $=$ symbol, the points which should have the same depth. It means517 that at the 4 points near the boundary, the bathymetry is cylindrical \gmcomment{not sure518 why cylindrical}. The line behind the open $T$-line must be 0 in the bathymetry file519 (as shown on Fig.\ref{Fig_obc_north} for example).520 521 %----------------------------------------------522 \subsection{Boundary data}523 \label{OBC_data}524 525 It is necessary to provide information at the boundaries. The simplest case is526 when this information does not change in time and is equal to the initial conditions527 (namelist variable \np{nn\_obcdta}=0). This is the case for the standard configuration528 EEL5 with open boundaries. When (\np{nn\_obcdta}=1), open boundary information529 is read from netcdf files. For convenience the input files are supposed to be similar530 to the ''history'' NEMO output files, for dimension names and variable names.531 Open boundary arrays must be dimensioned according to the parameters of table~532 \ref{Tab_obc_param}: for example, at the western boundary, arrays have a533 dimension of \jp{jpwf}-\jp{jpwd}+1 in the horizontal and \jp{jpk} in the vertical.534 535 When ocean observations are used to generate the boundary data (a hydrographic536 section for example, as in \citet{Treguier_al_JGR01}) it happens often that only the velocity537 normal to the boundary is known, which is the reason why the initial OBC code538 assumes that only $T$, $S$, and the normal velocity ($u$ or $v$) needs to be539 specified. As more and more global model solutions and ocean analysis products540 become available, it will be possible to provide information about all the variables541 (including the tangential velocity) so that the specification of four variables at each542 boundaries will become standard. For the sea surface height, one must distinguish543 between the filtered free surface case and the time-splitting or explicit treatment of544 the free surface.545 In the first case, it is assumed that the user does not wish to represent high546 frequency motions such as tides. The boundary condition is thus one of zero547 normal gradient of sea surface height at the open boundaries, following \citet{Marchesiello2001}.548 No information other than the total velocity needs to be provided at the open549 boundaries in that case. In the other two cases (time splitting or explicit free surface),550 the user must provide barotropic information (sea surface height and barotropic551 velocities) and the use of the Flather algorithm for barotropic variables is552 recommanded. However, this algorithm has not yet been fully tested and bugs553 remain in NEMO v2.3. Users should read the code carefully before using it. Finally,554 in the case of the rigid lid approximation the barotropic streamfunction must be555 provided, as documented in \citet{Treguier_al_JGR01}). This option is no longer556 recommended but remains in NEMO V2.3.557 558 One frequently encountered case is when an open boundary domain is constructed559 from a global or larger scale NEMO configuration. Assuming the domain corresponds560 to indices $ib:ie$, $jb:je$ of the global domain, the bathymetry and forcing of the561 small domain can be created by using the following netcdf utility on the global files:562 ncks -F $-d\;x,ib,ie$ $-d\;y,jb,je$ (part of the nco series of utilities,563 see their \href{http://nco.sourceforge.net}{website}).564 The open boundary files can be constructed using ncks565 commands, following table~\ref{Tab_obc_ind}.566 567 %--------------------------------------------------TABLE--------------------------------------------------568 \begin{table}[htbp] \begin{center} \begin{tabular}{|l|c|c|c|c|c|}569 \hline570 OBC & Variable & file name & Index & Start & end \\571 West & T,S & obcwest\_TS.nc & $ib$+1 & $jb$+1 & $je-1$ \\572 & U & obcwest\_U.nc & $ib$+1 & $jb$+1 & $je-1$ \\573 & V & obcwest\_V.nc & $ib$+1 & $jb$+1 & $je-1$ \\574 \hline575 East & T,S & obceast\_TS.nc & $ie$-1 & $jb$+1 & $je-1$ \\576 & U & obceast\_U.nc & $ie$-2 & $jb$+1 & $je-1$ \\577 & V & obceast\_V.nc & $ie$-1 & $jb$+1 & $je-1$ \\578 \hline579 South & T,S & obcsouth\_TS.nc & $jb$+1 & $ib$+1 & $ie-1$ \\580 & U & obcsouth\_U.nc & $jb$+1 & $ib$+1 & $ie-1$ \\581 & V & obcsouth\_V.nc & $jb$+1 & $ib$+1 & $ie-1$ \\582 \hline583 North & T,S & obcnorth\_TS.nc & $je$-1 & $ib$+1 & $ie-1$ \\584 & U & obcnorth\_U.nc & $je$-1 & $ib$+1 & $ie-1$ \\585 & V & obcnorth\_V.nc & $je$-2 & $ib$+1 & $ie-1$ \\586 \hline587 \end{tabular} \end{center}588 \caption{ \label{Tab_obc_ind}589 Requirements for creating open boundary files from a global configuration,590 appropriate for the subdomain of indices $ib:ie$, $jb:je$. ``Index'' designates the591 $i$ or $j$ index along which the $u$ of $v$ boundary point is situated in the global592 configuration, starting and ending with the $j$ or $i$ indices indicated.593 For example, to generate file obcnorth\_V.nc, use the command ncks594 $-F$ $-d\;y,je-2$ $-d\;x,ib+1,ie-1$ }595 \end{table}596 %-----------------------------------------------------------------------------------------------------------597 598 It is assumed that the open boundary files contain the variables for the period of599 the model integration. If the boundary files contain one time frame, the boundary600 data is held fixed in time. If the files contain 12 values, it is assumed that the input601 is a climatology for a repeated annual cycle (corresponding to the case \np{ln\_obc\_clim}602 =true). The case of an arbitrary number of time frames is not yet implemented603 correctly; the user is required to write his own code in the module \mdl{obc\_dta}604 to deal with this situation.605 606 \subsection{Radiation algorithm}607 \label{OBC_rad}608 609 The art of open boundary management consists in applying a constraint strong610 enough that the inner domain "feels" the rest of the ocean, but weak enough611 that perturbations are allowed to leave the domain with minimum false reflections612 of energy. The constraints are specified separately at each boundary as time613 scales for ''inflow'' and ''outflow'' as defined below. The time scales are set (in days)614 by namelist parameters such as \np{rn\_dpein}, \np{rn\_dpeob} for the eastern open615 boundary for example. When both time scales are zero for a given boundary616 ($e.g.$ for the western boundary, \jp{lp\_obc\_west}=true, \np{rn\_dpwob}=0 and617 \np{rn\_dpwin}=0) this means that the boundary in question is a ''fixed '' boundary618 where the solution is set exactly by the boundary data. This is not recommended,619 except in combination with increased viscosity in a ''sponge'' layer next to the620 boundary in order to avoid spurious reflections.621 622 623 The radiation\/relaxation \gmcomment{the / doesnt seem to appear in the output}624 algorithm is applied when either relaxation time (for ''inflow'' or ''outflow'') is625 non-zero. It has been developed and tested in the SPEM model and its626 successor ROMS \citep{Barnier1996, Marchesiello2001}, which is an627 $s$-coordinate model on an Arakawa C-grid. Although the algorithm has628 been numerically successful in the CLIPPER Atlantic models, the physics629 do not work as expected \citep{Treguier_al_JGR01}. Users are invited to consider630 open boundary conditions (OBC hereafter) with some scepticism631 \citep{Durran2001, Blayo2005}.632 633 The first part of the algorithm calculates a phase velocity to determine634 whether perturbations tend to propagate toward, or away from, the635 boundary. Let us consider a model variable $\phi$.636 The phase velocities ($C_{\phi x}$,$C_{\phi y}$) for the variable $\phi$,637 in the directions normal and tangential to the boundary are638 \begin{equation} \label{Eq_obc_cphi}639 C_{\phi x} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{x}640 \;\;\;\;\; \;\;\;641 C_{\phi y} = \frac{ -\phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{y}.642 \end{equation}643 Following \citet{Treguier_al_JGR01} and \citet{Marchesiello2001} we retain only644 the normal component of the velocity, $C_{\phi x}$, setting $C_{\phi y} =0$645 (but unlike the original Orlanski radiation algorithm we retain $\phi_{y}$ in646 the expression for $C_{\phi x}$).647 648 The discrete form of (\ref{Eq_obc_cphi}), described by \citet{Barnier1998},649 takes into account the two rows of grid points situated inside the domain650 next to the boundary, and the three previous time steps ($n$, $n-1$,651 and $n-2$). The same equation can then be discretized at the boundary at652 time steps $n-1$, $n$ and $n+1$ \gmcomment{since the original was three time-level}653 in order to extrapolate for the new boundary value $\phi^{n+1}$.654 655 In the open boundary algorithm as implemented in NEMO v2.3, the new boundary656 values are updated differently depending on the sign of $C_{\phi x}$. Let us take657 an eastern boundary as an example. The solution for variable $\phi$ at the658 boundary is given by a generalized wave equation with phase velocity $C_{\phi}$,659 with the addition of a relaxation term, as:660 \begin{eqnarray}661 \phi_{t} & = & -C_{\phi x} \phi_{x} + \frac{1}{\tau_{o}} (\phi_{c}-\phi)662 \;\;\; \;\;\; \;\;\; (C_{\phi x} > 0), \label{Eq_obc_rado} \\663 \phi_{t} & = & \frac{1}{\tau_{i}} (\phi_{c}-\phi)664 \;\;\; \;\;\; \;\;\;\;\;\; (C_{\phi x} < 0), \label{Eq_obc_radi}665 \end{eqnarray}666 where $\phi_{c}$ is the estimate of $\phi$ at the boundary, provided as boundary667 data. Note that in (\ref{Eq_obc_rado}), $C_{\phi x}$ is bounded by the ratio668 $\delta x/\delta t$ for stability reasons. When $C_{\phi x}$ is eastward (outward669 propagation), the radiation condition (\ref{Eq_obc_rado}) is used.670 When $C_{\phi x}$ is westward (inward propagation), (\ref{Eq_obc_radi}) is671 used with a strong relaxation to climatology (usually $\tau_{i}=\np{rn\_dpein}=$1~day).672 Equation (\ref{Eq_obc_radi}) is solved with a Euler time-stepping scheme. As a673 consequence, setting $\tau_{i}$ smaller than, or equal to the time step is equivalent674 to a fixed boundary condition. A time scale of one day is usually a good compromise675 which guarantees that the inflow conditions remain close to climatology while ensuring676 numerical stability.677 678 In the case of a western boundary located in the Eastern Atlantic, \citet{Penduff_al_JGR00}679 have been able to implement the radiation algorithm without any boundary data,680 using persistence from the previous time step instead. This solution has not worked681 in other cases \citep{Treguier_al_JGR01}, so that the use of boundary data is recommended.682 Even in the outflow condition (\ref{Eq_obc_rado}), we have found it desirable to683 maintain a weak relaxation to climatology. The time step is usually chosen so as to684 be larger than typical turbulent scales (of order 1000~days \gmcomment{or maybe seconds?}).685 686 The radiation condition is applied to the model variables: temperature, salinity,687 tangential and normal velocities. For normal and tangential velocities, $u$ and $v$,688 radiation is applied with phase velocities calculated from $u$ and $v$ respectively.689 For the radiation of tracers, we use the phase velocity calculated from the tangential690 velocity in order to avoid calculating too many independent radiation velocities and691 because tangential velocities and tracers have the same position along the boundary692 on a C-grid.693 694 \subsection{Domain decomposition (\key{mpp\_mpi})}695 \label{OBC_mpp}696 When \key{mpp\_mpi} is active in the code, the computational domain is divided697 into rectangles that are attributed each to a different processor. The open boundary698 code is ``mpp-compatible'' up to a certain point. The radiation algorithm will not699 work if there is an mpp subdomain boundary parallel to the open boundary at the700 index of the boundary, or the grid point after (outside), or three grid points before701 (inside). On the other hand, there is no problem if an mpp subdomain boundary702 cuts the open boundary perpendicularly. These geometrical limitations must be703 checked for by the user (there is no safeguard in the code).704 The general principle for the open boundary mpp code is that loops over the open705 boundaries {not sure what this means} are performed on local indices (nie0,706 nie1, nje0, nje1 for an eastern boundary for instance) that are initialized in module707 \mdl{obc\_ini}. Those indices have relevant values on the processors that contain708 a segment of an open boundary. For processors that do not include an open709 boundary segment, the indices are such that the calculations within the loops are710 not performed.711 \gmcomment{I dont understand most of the last few sentences}712 713 Arrays of climatological data that are read from files are seen by all processors714 and have the same dimensions for all (for instance, for the eastern boundary,715 uedta(jpjglo,jpk,2)). On the other hand, the arrays for the calculation of radiation716 are local to each processor (uebnd(jpj,jpk,3,3) for instance). This allowed the717 CLIPPER model for example, to save on memory where the eastern boundary718 crossed 8 processors so that \jp{jpj} was much smaller than (\jp{jpjef}-\jp{jpjed}+1).719 720 \subsection{Volume conservation}721 \label{OBC_vol}722 723 It is necessary to control the volume inside a domain when using open boundaries.724 With fixed boundaries, it is enough to ensure that the total inflow/outflow has725 reasonable values (either zero or a value compatible with an observed volume726 balance). When using radiative boundary conditions it is necessary to have a727 volume constraint because each open boundary works independently from the728 others. The methodology used to control this volume is identical to the one729 coded in the ROMS model \citep{Marchesiello2001}.730 731 732 %---------------------------------------- EXTRAS733 \colorbox{yellow}{Explain obc\_vol{\ldots}}734 735 \colorbox{yellow}{OBC algorithm for update, OBC restart, list of routines where obc key appears{\ldots}}736 737 \colorbox{yellow}{OBC rigid lid? {\ldots}}738 366 739 367 % ==================================================================== … … 956 584 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 957 585 \begin{figure}[!t] \begin{center} 958 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_LBC_bdy_geom.pdf}586 \includegraphics[width=1.0\textwidth]{Fig_LBC_bdy_geom} 959 587 \caption { \label{Fig_LBC_bdy_geom} 960 588 Example of geometry of unstructured open boundary} … … 997 625 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 998 626 \begin{figure}[!t] \begin{center} 999 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_LBC_nc_header.pdf}627 \includegraphics[width=1.0\textwidth]{Fig_LBC_nc_header} 1000 628 \caption { \label{Fig_LBC_nc_header} 1001 629 Example of the header for a coordinates.bdy.nc file} … … 1034 662 1035 663 664 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_LDF.tex
r4147 r7260 1 2 % ================================================================ 3 % Chapter � Lateral Ocean Physics (LDF) 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 3 4 % ================================================================ 5 % Chapter ——— Lateral Ocean Physics (LDF) 4 6 % ================================================================ 5 7 \chapter{Lateral Ocean Physics (LDF)} … … 68 70 When none of the \textbf{key\_dynldf\_...} and \textbf{key\_traldf\_...} keys are 69 71 defined, a constant value is used over the whole ocean for momentum and 70 tracers, which is specified through the \np{rn\_ahm 0} and \np{rn\_aht0} namelist72 tracers, which is specified through the \np{rn\_ahm\_0\_lap} and \np{rn\_aht\_0} namelist 71 73 parameters. 72 74 … … 77 79 mixing coefficients will require 3D arrays. In the 1D option, a hyperbolic variation 78 80 of the lateral mixing coefficient is introduced in which the surface value is 79 \np{rn\_aht 0} (\np{rn\_ahm0}), the bottom value is 1/4 of the surface value,81 \np{rn\_aht\_0} (\np{rn\_ahm\_0\_lap}), the bottom value is 1/4 of the surface value, 80 82 and the transition takes place around z=300~m with a width of 300~m 81 83 ($i.e.$ both the depth and the width of the inflection point are set to 300~m). … … 93 95 \end{equation} 94 96 where $e_{max}$ is the maximum of $e_1$ and $e_2$ taken over the whole masked 95 ocean domain, and $A_o^l$ is the \np{rn\_ahm 0} (momentum) or \np{rn\_aht0} (tracer)97 ocean domain, and $A_o^l$ is the \np{rn\_ahm\_0\_lap} (momentum) or \np{rn\_aht\_0} (tracer) 96 98 namelist parameter. This variation is intended to reflect the lesser need for subgrid 97 99 scale eddy mixing where the grid size is smaller in the domain. It was introduced in … … 105 107 Other formulations can be introduced by the user for a given configuration. 106 108 For example, in the ORCA2 global ocean model (see Configurations), the laplacian 107 viscosity operator uses \np{rn\_ahm 0}~= 4.10$^4$ m$^2$/s poleward of 20$^{\circ}$108 north and south and decreases linearly to \np{rn\_aht 0}~= 2.10$^3$ m$^2$/s109 viscosity operator uses \np{rn\_ahm\_0\_lap}~= 4.10$^4$ m$^2$/s poleward of 20\deg 110 north and south and decreases linearly to \np{rn\_aht\_0}~= 2.10$^3$ m$^2$/s 109 111 at the equator \citep{Madec_al_JPO96, Delecluse_Madec_Bk00}. This modification 110 112 can be found in routine \rou{ldf\_dyn\_c2d\_orca} defined in \mdl{ldfdyn\_c2d}. … … 120 122 \subsubsection{Space and Time Varying Mixing Coefficients} 121 123 122 There is no default specification of space and time varying mixing coefficient. 123 The only case available is specific to the ORCA2 and ORCA05 global ocean 124 configurations. It provides only a tracer 125 mixing coefficient for eddy induced velocity (ORCA2) or both iso-neutral and 126 eddy induced velocity (ORCA05) that depends on the local growth rate of 127 baroclinic instability. This specification is actually used when an ORCA key 124 There are no default specifications of space and time varying mixing coefficient. One 125 available case is specific to the ORCA2 and ORCA05 global ocean configurations. It 126 provides only a tracer mixing coefficient for eddy induced velocity (ORCA2) or both 127 iso-neutral and eddy induced velocity (ORCA05) that depends on the local growth rate of 128 baroclinic instability. This specification is actually used when an ORCA key 128 129 and both \key{traldf\_eiv} and \key{traldf\_c2d} are defined. 130 131 \subsubsection{Smagorinsky viscosity (\key{dynldf\_c3d} and \key{dynldf\_smag})} 132 133 The \key{dynldf\_smag} key activates a 3D, time-varying viscosity that depends on the 134 resolved motions. Following \citep{Smagorinsky_93} the viscosity coefficient is set 135 proportional to a local deformation rate based on the horizontal shear and tension, 136 namely: 137 138 \begin{equation} 139 A_{m_{Smag}} = \left(\frac{{\sf CM_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert 140 \end{equation} 141 142 \noindent where the deformation rate $\vert{D}\vert$ is given by 143 144 \begin{equation} 145 \vert{D}\vert=\sqrt{\left({\frac{\partial{u}} {\partial{x}}} 146 -{\frac{\partial{v}} {\partial{y}}}\right)^2 147 + \left({\frac{\partial{u}} {\partial{y}}} 148 +{\frac{\partial{v}} {\partial{x}}}\right)^2} 149 \end{equation} 150 151 \noindent and $L$ is the local gridscale given by: 152 153 \begin{equation} 154 L^2 = \frac{2{e_1}^2 {e_2}^2}{\left ( {e_1}^2 + {e_2}^2 \right )} 155 \end{equation} 156 157 \citep{Griffies_Hallberg_MWR00} suggest values in the range 2.2 to 4.0 of the coefficient 158 $\sf CM_{Smag}$ for oceanic flows. This value is set via the \np{rn\_cmsmag\_1} namelist 159 parameter. An additional parameter: \np{rn\_cmsh} is included in NEMO for experimenting 160 with the contribution of the shear term. A value of 1.0 (the default) calculates the 161 deformation rate as above; a value of 0.0 will discard the shear term entirely. 162 163 For numerical stability, the calculated viscosity is bounded according to the following: 164 165 \begin{equation} 166 {\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_ahm\_m\_lap\right ) \geq A_{m_{Smag}} 167 \geq rn\_ahm\_0\_lap 168 \end{equation} 169 170 \noindent with both parameters for the upper and lower bounds being provided via the 171 indicated namelist parameters. 172 173 \bigskip When $ln\_dynldf\_bilap = .true.$, a biharmonic version of the Smagorinsky 174 viscosity is also available which sets a coefficient for the biharmonic viscosity as: 175 176 \begin{equation} 177 B_{m_{Smag}} = - \left(\frac{{\sf CM_{bSmag}}}{\pi}\right)^2 {L^4\over 8}\vert{D}\vert 178 \end{equation} 179 180 \noindent which is bounded according to: 181 182 \begin{equation} 183 {\rm MAX}\left (-{ L^4\over {64\Delta{t}}}, rn\_ahm\_m\_blp\right ) \leq B_{m_{Smag}} 184 \leq rn\_ahm\_0\_blp 185 \end{equation} 186 187 \noindent Note the reversal of the inequalities here because NEMO requires the biharmonic 188 coefficients as negative numbers. $\sf CM_{bSmag}$ is set via the \np{rn\_cmsmag\_2} 189 namelist parameter and the bounding values have corresponding entries in the namelist too. 190 191 \bigskip The current implementation in NEMO also allows for 3D, time-varying diffusivities 192 to be set using the Smagorinsky approach. Users should note that this option is not 193 recommended for many applications since diffusivities will tend to be largest near 194 boundaries (where shears are greatest) leading to spurious upwellings 195 (\citep{Griffies_Bk04}, chapter 18.3.4). Nevertheless the option is there for those 196 wishing to experiment. This choice requires both \key{traldf\_c3d} and \key{traldf\_smag} 197 and uses the \np{rn\_chsmag} (${\sf CH_{Smag}}$), \np{rn\_smsh} and \np{rn\_aht\_m} 198 namelist parameters in an analogous way to \np{rn\_cmsmag\_1}, \np{rn\_cmsh} and 199 \np{rn\_ahm\_m\_lap} (see above) to set the diffusion coefficient: 200 201 \begin{equation} 202 A_{h_{Smag}} = \left(\frac{{\sf CH_{Smag}}}{\pi}\right)^2L^2\vert{D}\vert 203 \end{equation} 204 205 206 For numerical stability, the calculated diffusivity is bounded according to the following: 207 208 \begin{equation} 209 {\rm MIN}\left ({ L^2\over {8\Delta{t}}}, rn\_aht\_m\right ) \geq A_{h_{Smag}} 210 \geq rn\_aht\_0 211 \end{equation} 212 213 129 214 130 215 $\ $\newline % force a new ligne … … 144 229 (3) for isopycnal diffusion on momentum or tracers, an additional purely 145 230 horizontal background diffusion with uniform coefficient can be added by 146 setting a non zero value of \np{rn\_ahmb 0} or \np{rn\_ahtb0}, a background horizontal231 setting a non zero value of \np{rn\_ahmb\_0} or \np{rn\_ahtb\_0}, a background horizontal 147 232 eddy viscosity or diffusivity coefficient (namelist parameters whose default 148 233 values are $0$). However, the technique used to compute the isopycnal 149 234 slopes is intended to get rid of such a background diffusion, since it introduces 150 spurious diapycnal diffusion (see {\S\ref{LDF_slp}).235 spurious diapycnal diffusion (see \S\ref{LDF_slp}). 151 236 152 237 (4) when an eddy induced advection term is used (\key{traldf\_eiv}), $A^{eiv}$, … … 361 446 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 362 447 \begin{figure}[!ht] \begin{center} 363 \includegraphics[width=0.70\textwidth]{ ./TexFiles/Figures/Fig_LDF_ZDF1.pdf}448 \includegraphics[width=0.70\textwidth]{Fig_LDF_ZDF1} 364 449 \caption { \label{Fig_LDF_ZDF1} 365 450 averaging procedure for isopycnal slope computation.} … … 389 474 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 390 475 \begin{figure}[!ht] \begin{center} 391 \includegraphics[width=0.70\textwidth]{ ./TexFiles/Figures/Fig_eiv_slp.pdf}476 \includegraphics[width=0.70\textwidth]{Fig_eiv_slp} 392 477 \caption { \label{Fig_eiv_slp} 393 478 Vertical profile of the slope used for lateral mixing in the mixed layer : … … 431 516 diffusion along model level surfaces, i.e. using the shear computed along 432 517 the model levels and with no additional friction at the ocean bottom (see 433 {\S\ref{LBC_coast}).518 \S\ref{LBC_coast}). 434 519 435 520 … … 472 557 473 558 559 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_MISC.tex
r5602 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter � Miscellaneous Topics … … 34 36 has been made to set them in a generic way. However, examples of how 35 37 they can be set up is given in the ORCA 2\deg and 0.5\deg configurations. For example, 36 for details of implementation in ORCA2, search: 37 \vspace{-10pt} 38 \begin{alltt} 39 \tiny 40 \begin{verbatim} 41 IF( cp_cfg == "orca" .AND. jp_cfg == 2 ) 42 \end{verbatim} 43 \end{alltt} 38 for details of implementation in ORCA2, search: 39 \texttt{ IF( cp\_cfg == "orca" .AND. jp\_cfg == 2 ) } 44 40 45 41 % ------------------------------------------------------------------------------------------------------------- … … 66 62 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 67 63 \begin{figure}[!tbp] \begin{center} 68 \includegraphics[width=0.80\textwidth]{ ./TexFiles/Figures/Fig_Gibraltar.pdf}69 \includegraphics[width=0.80\textwidth]{ ./TexFiles/Figures/Fig_Gibraltar2.pdf}64 \includegraphics[width=0.80\textwidth]{Fig_Gibraltar} 65 \includegraphics[width=0.80\textwidth]{Fig_Gibraltar2} 70 66 \caption{ \label{Fig_MISC_strait_hand} 71 Example of the Gibraltar strait defined in a $1 \deg \times 1\deg$ mesh.67 Example of the Gibraltar strait defined in a $1^{\circ} \times 1^{\circ}$ mesh. 72 68 \textit{Top}: using partially open cells. The meridional scale factor at $v$-point 73 69 is reduced on both sides of the strait to account for the real width of the strait … … 89 85 %-------------------------------------------------------------------------------------------------------------- 90 86 91 \colorbox{yellow}{Add a short description of CLA staff here or in lateral boundary condition chapter?}92 87 Options are defined through the \ngn{namcla} namelist variables. 88 This option is an obsolescent feature that will be removed in version 3.7 and followings. 93 89 94 90 %The problem is resolved here by allowing the mixing of tracers and mass/volume between non-adjacent water columns at nominated regions within the model. Momentum is not mixed. The scheme conserves total tracer content, and total volume (the latter in $z*$- or $s*$-coordinate), and maintains compatibility between the tracer and mass/volume budgets. … … 200 196 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 201 197 \begin{figure}[!ht] \begin{center} 202 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_LBC_zoom.pdf}198 \includegraphics[width=0.90\textwidth]{Fig_LBC_zoom} 203 199 \caption{ \label{Fig_LBC_zoom} 204 200 Position of a model domain compared to the data input domain when the zoom functionality is used.} … … 638 634 639 635 636 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_Model_Basics.tex
r3294 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter 1 Ñ Model Basics … … 114 116 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 115 117 \begin{figure}[!ht] \begin{center} 116 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_I_ocean_bc.pdf}118 \includegraphics[width=0.90\textwidth]{Fig_I_ocean_bc} 117 119 \caption{ \label{Fig_ocean_bc} 118 120 The ocean is bounded by two surfaces, $z=-H(i,j)$ and $z=\eta(i,j,t)$, where $H$ … … 247 249 sufficient to solve a linearized version of (\ref{Eq_PE_ssh}), which still allows 248 250 to take into account freshwater fluxes applied at the ocean surface \citep{Roullet_Madec_JGR00}. 251 Nevertheless, with the linearization, an exact conservation of heat and salt contents is lost. 249 252 250 253 The filtering of EGWs in models with a free surface is usually a matter of discretisation 251 of the temporal derivatives, using the time splitting method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92} 252 or the implicit scheme \citep{Dukowicz1994}. In \NEMO, we use a slightly different approach 253 developed by \citet{Roullet_Madec_JGR00}: the damping of EGWs is ensured by introducing an 254 additional force in the momentum equation. \eqref{Eq_PE_dyn} becomes: 255 \begin{equation} \label{Eq_PE_flt} 256 \frac{\partial {\rm {\bf U}}_h }{\partial t}= {\rm {\bf M}} 257 - g \nabla \left( \tilde{\rho} \ \eta \right) 258 - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right) 259 \end{equation} 260 where $T_c$, is a parameter with dimensions of time which characterizes the force, 261 $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density, and $\rm {\bf M}$ 262 represents the collected contributions of the Coriolis, hydrostatic pressure gradient, 263 non-linear and viscous terms in \eqref{Eq_PE_dyn}. 264 265 The new force can be interpreted as a diffusion of vertically integrated volume flux divergence. 266 The time evolution of $D$ is thus governed by a balance of two terms, $-g$ \textbf{A} $\eta$ 267 and $g \, T_c \,$ \textbf{A} $D$, associated with a propagative regime and a diffusive regime 268 in the temporal spectrum, respectively. In the diffusive regime, the EGWs no longer propagate, 269 $i.e.$ they are stationary and damped. The diffusion regime applies to the modes shorter than 270 $T_c$. For longer ones, the diffusion term vanishes. Hence, the temporally unresolved EGWs 271 can be damped by choosing $T_c > \rdt$. \citet{Roullet_Madec_JGR00} demonstrate that 272 (\ref{Eq_PE_flt}) can be integrated with a leap frog scheme except the additional term which 273 has to be computed implicitly. This is not surprising since the use of a large time step has a 274 necessarily numerical cost. Two gains arise in comparison with the previous formulations. 275 Firstly, the damping of EGWs can be quantified through the magnitude of the additional term. 276 Secondly, the numerical scheme does not need any tuning. Numerical stability is ensured as 277 soon as $T_c > \rdt$. 278 279 When the variations of free surface elevation are small compared to the thickness of the first 280 model layer, the free surface equation (\ref{Eq_PE_ssh}) can be linearized. As emphasized 281 by \citet{Roullet_Madec_JGR00} the linearization of (\ref{Eq_PE_ssh}) has consequences on the 282 conservation of salt in the model. With the nonlinear free surface equation, the time evolution 283 of the total salt content is 284 \begin{equation} \label{Eq_PE_salt_content} 285 \frac{\partial }{\partial t}\int\limits_{D\eta } {S\;dv} 286 =\int\limits_S {S\;(-\frac{\partial \eta }{\partial t}-D+P-E)\;ds} 287 \end{equation} 288 where $S$ is the salinity, and the total salt is integrated over the whole ocean volume 289 $D_\eta$ bounded by the time-dependent free surface. The right hand side (which is an 290 integral over the free surface) vanishes when the nonlinear equation (\ref{Eq_PE_ssh}) 291 is satisfied, so that the salt is perfectly conserved. When the free surface equation is 292 linearized, \citet{Roullet_Madec_JGR00} show that the total salt content integrated in the fixed 293 volume $D$ (bounded by the surface $z=0$) is no longer conserved: 294 \begin{equation} \label{Eq_PE_salt_content_linear} 295 \frac{\partial }{\partial t}\int\limits_D {S\;dv} 296 = - \int\limits_S {S\;\frac{\partial \eta }{\partial t}ds} 297 \end{equation} 298 299 The right hand side of (\ref{Eq_PE_salt_content_linear}) is small in equilibrium solutions 300 \citep{Roullet_Madec_JGR00}. It can be significant when the freshwater forcing is not balanced and 301 the globally averaged free surface is drifting. An increase in sea surface height \textit{$\eta $} 302 results in a decrease of the salinity in the fixed volume $D$. Even in that case though, 303 the total salt integrated in the variable volume $D_{\eta}$ varies much less, since 304 (\ref{Eq_PE_salt_content_linear}) can be rewritten as 305 \begin{equation} \label{Eq_PE_salt_content_corrected} 306 \frac{\partial }{\partial t}\int\limits_{D\eta } {S\;dv} 307 =\frac{\partial}{\partial t} \left[ \;{\int\limits_D {S\;dv} +\int\limits_S {S\eta \;ds} } \right] 308 =\int\limits_S {\eta \;\frac{\partial S}{\partial t}ds} 309 \end{equation} 310 311 Although the total salt content is not exactly conserved with the linearized free surface, 312 its variations are driven by correlations of the time variation of surface salinity with the 313 sea surface height, which is a negligible term. This situation contrasts with the case of 314 the rigid lid approximation in which case freshwater forcing is represented by a virtual 315 salt flux, leading to a spurious source of salt at the ocean surface 316 \citep{Huang_JPO93, Roullet_Madec_JGR00}. 317 318 \newpage 319 $\ $\newline % force a new ligne 254 of the temporal derivatives, using a split-explicit method \citep{Killworth_al_JPO91, Zhang_Endoh_JGR92} 255 or the implicit scheme \citep{Dukowicz1994} or the addition of a filtering force in the momentum equation 256 \citep{Roullet_Madec_JGR00}. With the present release, \NEMO offers the choice between 257 an explicit free surface (see \S\ref{DYN_spg_exp}) or a split-explicit scheme strongly 258 inspired the one proposed by \citet{Shchepetkin_McWilliams_OM05} (see \S\ref{DYN_spg_ts}). 259 260 %\newpage 261 %$\ $\newline % force a new line 320 262 321 263 % ================================================================ … … 372 314 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 373 315 \begin{figure}[!tb] \begin{center} 374 \includegraphics[width=0.60\textwidth]{ ./TexFiles/Figures/Fig_I_earth_referential.pdf}316 \includegraphics[width=0.60\textwidth]{Fig_I_earth_referential} 375 317 \caption{ \label{Fig_referential} 376 318 the geographical coordinate system $(\lambda,\varphi,z)$ and the curvilinear … … 773 715 \end{equation} 774 716 775 The equations solved by the ocean model \eqref{Eq_PE} in $s-$coordinate can be written as follows :717 The equations solved by the ocean model \eqref{Eq_PE} in $s-$coordinate can be written as follows (see Appendix~\ref{Apdx_A_momentum}): 776 718 777 719 \vspace{0.5cm} 778 * momentum equation:720 $\bullet$ Vector invariant form of the momentum equation : 779 721 \begin{multline} \label{Eq_PE_sco_u} 780 \frac{ 1}{e_3} \frac{\partial \left( e_3\,u \right)}{\partial t}=722 \frac{\partial u }{\partial t}= 781 723 + \left( {\zeta +f} \right)\,v 782 724 - \frac{1}{2\,e_1} \frac{\partial}{\partial i} \left( u^2+v^2 \right) … … 787 729 \end{multline} 788 730 \begin{multline} \label{Eq_PE_sco_v} 789 \frac{ 1}{e_3} \frac{\partial \left( e_3\,v \right)}{\partial t}=731 \frac{\partial v }{\partial t}= 790 732 - \left( {\zeta +f} \right)\,u 791 733 - \frac{1}{2\,e_2 }\frac{\partial }{\partial j}\left( u^2+v^2 \right) … … 795 737 + D_v^{\vect{U}} + F_v^{\vect{U}} \quad 796 738 \end{multline} 739 740 \vspace{0.5cm} 741 $\bullet$ Vector invariant form of the momentum equation : 742 \begin{multline} \label{Eq_PE_sco_u} 743 \frac{1}{e_3} \frac{\partial \left( e_3\,u \right) }{\partial t}= 744 + \left( { f + \frac{1}{e_1 \; e_2 } 745 \left( v \frac{\partial e_2}{\partial i} 746 -u \frac{\partial e_1}{\partial j} \right)} \right) \, v \\ 747 - \frac{1}{e_1 \; e_2 \; e_3 } \left( 748 \frac{\partial \left( {e_2 \, e_3 \, u\,u} \right)}{\partial i} 749 + \frac{\partial \left( {e_1 \, e_3 \, v\,u} \right)}{\partial j} \right) 750 - \frac{1}{e_3 }\frac{\partial \left( { \omega\,u} \right)}{\partial k} \\ 751 - \frac{1}{e_1} \frac{\partial}{\partial i} \left( \frac{p_s + p_h}{\rho _o} \right) 752 + g\frac{\rho }{\rho _o}\sigma _1 753 + D_u^{\vect{U}} + F_u^{\vect{U}} \quad 754 \end{multline} 755 \begin{multline} \label{Eq_PE_sco_v} 756 \frac{1}{e_3} \frac{\partial \left( e_3\,v \right) }{\partial t}= 757 - \left( { f + \frac{1}{e_1 \; e_2} 758 \left( v \frac{\partial e_2}{\partial i} 759 -u \frac{\partial e_1}{\partial j} \right)} \right) \, u \\ 760 - \frac{1}{e_1 \; e_2 \; e_3 } \left( 761 \frac{\partial \left( {e_2 \; e_3 \,u\,v} \right)}{\partial i} 762 + \frac{\partial \left( {e_1 \; e_3 \,v\,v} \right)}{\partial j} \right) 763 - \frac{1}{e_3 } \frac{\partial \left( { \omega\,v} \right)}{\partial k} \\ 764 - \frac{1}{e_2 }\frac{\partial }{\partial j}\left( \frac{p_s+p_h }{\rho _o} \right) 765 + g\frac{\rho }{\rho _o }\sigma _2 766 + D_v^{\vect{U}} + F_v^{\vect{U}} \quad 767 \end{multline} 768 797 769 where the relative vorticity, \textit{$\zeta $}, the surface pressure gradient, and the hydrostatic 798 770 pressure have the same expressions as in $z$-coordinates although they do not represent 799 771 exactly the same quantities. $\omega$ is provided by the continuity equation 800 772 (see Appendix~\ref{Apdx_A}): 801 802 773 \begin{equation} \label{Eq_PE_sco_continuity} 803 774 \frac{\partial e_3}{\partial t} + e_3 \; \chi + \frac{\partial \omega }{\partial s} = 0 … … 809 780 810 781 \vspace{0.5cm} 811 *tracer equations:782 $\bullet$ tracer equations: 812 783 \begin{multline} \label{Eq_PE_sco_t} 813 784 \frac{1}{e_3} \frac{\partial \left( e_3\,T \right) }{\partial t}= … … 842 813 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 843 814 \begin{figure}[!b] \begin{center} 844 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_z_zstar.pdf}815 \includegraphics[width=1.0\textwidth]{Fig_z_zstar} 845 816 \caption{ \label{Fig_z_zstar} 846 817 (a) $z$-coordinate in linear free-surface case ; … … 1023 994 \label{PE_zco_tilde} 1024 995 1025 The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM10s}. 1026 It is not available in the current version of \NEMO. 996 The $\tilde{z}$-coordinate has been developed by \citet{Leclair_Madec_OM11}. 997 It is available in \NEMO since the version 3.4. Nevertheless, it is currently not robust enough 998 to be used in all possible configurations. Its use is therefore not recommended. 999 1027 1000 1028 1001 \newpage … … 1157 1130 operator acting along $s-$surfaces (see \S\ref{LDF}). 1158 1131 1159 \subsubsection{Lateral second ordertracer diffusive operator}1160 1161 The lateral second ordertracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}):1132 \subsubsection{Lateral Laplacian tracer diffusive operator} 1133 1134 The lateral Laplacian tracer diffusive operator is defined by (see Appendix~\ref{Apdx_B}): 1162 1135 \begin{equation} \label{Eq_PE_iso_tensor} 1163 1136 D^{lT}=\nabla {\rm {\bf .}}\left( {A^{lT}\;\Re \;\nabla T} \right) \qquad … … 1180 1153 ocean (see Appendix~\ref{Apdx_B}). 1181 1154 1155 For \textit{iso-level} diffusion, $r_1$ and $r_2 $ are zero. $\Re $ reduces to the identity 1156 in the horizontal direction, no rotation is applied. 1157 1182 1158 For \textit{geopotential} diffusion, $r_1$ and $r_2 $ are the slopes between the 1183 geopotential and computational surfaces: in $z$-coordinates they are zero 1184 ($r_1 = r_2 = 0$) while in $s$-coordinate (including $\textit{z*}$ case) they are 1185 equal to $\sigma _1$ and $\sigma _2$, respectively (see \eqref{Eq_PE_sco_slope} ). 1159 geopotential and computational surfaces: they are equal to $\sigma _1$ and $\sigma _2$, 1160 respectively (see \eqref{Eq_PE_sco_slope} ). 1186 1161 1187 1162 For \textit{isoneutral} diffusion $r_1$ and $r_2$ are the slopes between the isoneutral … … 1231 1206 to zero in the vicinity of the boundaries. The latter strategy is used in \NEMO (cf. Chap.~\ref{LDF}). 1232 1207 1233 \subsubsection{Lateral fourth ordertracer diffusive operator}1234 1235 The lateral fourth ordertracer diffusive operator is defined by:1208 \subsubsection{Lateral bilaplacian tracer diffusive operator} 1209 1210 The lateral bilaplacian tracer diffusive operator is defined by: 1236 1211 \begin{equation} \label{Eq_PE_bilapT} 1237 1212 D^{lT}=\Delta \left( {A^{lT}\;\Delta T} \right) 1238 1213 \qquad \text{where} \ D^{lT}=\Delta \left( {A^{lT}\;\Delta T} \right) 1239 1214 \end{equation} 1240 1241 1215 It is the second order operator given by \eqref{Eq_PE_iso_tensor} applied twice with 1242 1216 the eddy diffusion coefficient correctly placed. 1243 1217 1244 1245 \subsubsection{Lateral second order momentum diffusive operator} 1246 1247 The second order momentum diffusive operator along $z$- or $s$-surfaces is found by 1218 \subsubsection{Lateral Laplacian momentum diffusive operator} 1219 1220 The Laplacian momentum diffusive operator along $z$- or $s$-surfaces is found by 1248 1221 applying \eqref{Eq_PE_lap_vector} to the horizontal velocity vector (see Appendix~\ref{Apdx_B}): 1249 1222 \begin{equation} \label{Eq_PE_lapU} … … 1279 1252 of the Equator in a geographical coordinate system \citep{Lengaigne_al_JGR03}. 1280 1253 1281 \subsubsection{lateral fourth ordermomentum diffusive operator}1254 \subsubsection{lateral bilaplacian momentum diffusive operator} 1282 1255 1283 1256 As for tracers, the fourth order momentum diffusive operator along $z$ or $s$-surfaces … … 1309 1282 \end{equation} 1310 1283 1284 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_Model_Basics_zstar.tex
r4147 r7260 1 % ================================================================ 2 % Chapter 1 � Model Basics 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 3 % ================================================================ 4 % Chapter 1 ——— Model Basics 3 5 % ================================================================ 4 6 % ================================================================ … … 121 123 %> > > > > > > > > > > > > > > > > > > > > > > > > > > > 122 124 \begin{figure}[!t] \begin{center} 123 \includegraphics[width=0.90\textwidth]{ ./Figures/Fig_DYN_dynspg_ts.pdf}125 \includegraphics[width=0.90\textwidth]{Fig_DYN_dynspg_ts} 124 126 \caption{ \label{Fig_DYN_dynspg_ts} 125 127 Schematic of the split-explicit time stepping scheme for the barotropic and baroclinic modes, … … 256 258 257 259 260 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_OBS.tex
r4245 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter observation operator (OBS) … … 732 734 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 733 735 \begin{figure} \begin{center} 734 \includegraphics[width=10cm,height=12cm,angle=-90.]{ ./TexFiles/Figures/Fig_ASM_obsdist_local}736 \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_local} 735 737 \caption{ \label{fig:obslocal} 736 738 Example of the distribution of observations with the geographical distribution of observational data.} … … 759 761 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 760 762 \begin{figure} \begin{center} 761 \includegraphics[width=10cm,height=12cm,angle=-90.]{ ./TexFiles/Figures/Fig_ASM_obsdist_global}763 \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_global} 762 764 \caption{ \label{fig:obsglobal} 763 765 Example of the distribution of observations with the round-robin distribution of observational data.} … … 1376 1378 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1377 1379 \begin{figure} \begin{center} 1378 %\includegraphics[width=10cm,height=12cm,angle=-90.]{ ./TexFiles/Figures/Fig_OBS_dataplot_main}1379 \includegraphics[width=9cm,angle=-90.]{ ./TexFiles/Figures/Fig_OBS_dataplot_main}1380 %\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_main} 1381 \includegraphics[width=9cm,angle=-90.]{Fig_OBS_dataplot_main} 1380 1382 \caption{ \label{fig:obsdataplotmain} 1381 1383 Main window of dataplot.} … … 1388 1390 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1389 1391 \begin{figure} \begin{center} 1390 %\includegraphics[width=10cm,height=12cm,angle=-90.]{ ./TexFiles/Figures/Fig_OBS_dataplot_prof}1391 \includegraphics[width=7cm,angle=-90.]{ ./TexFiles/Figures/Fig_OBS_dataplot_prof}1392 %\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_prof} 1393 \includegraphics[width=7cm,angle=-90.]{Fig_OBS_dataplot_prof} 1392 1394 \caption{ \label{fig:obsdataplotprofile} 1393 1395 Profile plot from dataplot produced by right clicking on a point in the main window.} … … 1398 1400 1399 1401 1402 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_SBC.tex
r5602 r7260 1 % ================================================================ 2 % Chapter � Surface Boundary Condition (SBC, ISF, ICB) 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 3 % ================================================================ 4 % Chapter —— Surface Boundary Condition (SBC, ISF, ICB) 3 5 % ================================================================ 4 6 \chapter{Surface Boundary Condition (SBC, ISF, ICB) } … … 17 19 \item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$ 18 20 \item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$ 19 \item the surface freshwater budget $\left( {\textit{emp},\;\textit{emp}_S } \right)$ 21 \item the surface freshwater budget $\left( {\textit{emp}} \right)$ 22 \item the surface salt flux associated with freezing/melting of seawater $\left( {\textit{sfx}} \right)$ 20 23 \end{itemize} 21 24 plus an optional field: … … 27 30 are controlled by namelist \ngn{namsbc} variables: an analytical formulation (\np{ln\_ana}~=~true), 28 31 a flux formulation (\np{ln\_flx}~=~true), a bulk formulae formulation (CORE 29 (\np{ln\_ core}~=~true), CLIO (\np{ln\_clio}~=~true) or MFS32 (\np{ln\_blk\_core}~=~true), CLIO (\np{ln\_blk\_clio}~=~true) or MFS 30 33 \footnote { Note that MFS bulk formulae compute fluxes only for the ocean component} 31 (\np{ln\_mfs}~=~true) bulk formulae) and a coupled 32 formulation (exchanges with a atmospheric model via the OASIS coupler) 33 (\np{ln\_cpl}~=~true). When used, the atmospheric pressure forces both 34 ocean and ice dynamics (\np{ln\_apr\_dyn}~=~true). 35 The frequency at which the six or seven fields have to be updated is the \np{nn\_fsbc} 36 namelist parameter. 34 (\np{ln\_blk\_mfs}~=~true) bulk formulae) and a coupled or mixed forced/coupled formulation 35 (exchanges with a atmospheric model via the OASIS coupler) (\np{ln\_cpl} or \np{ln\_mixcpl}~=~true). 36 When used ($i.e.$ \np{ln\_apr\_dyn}~=~true), the atmospheric pressure forces both ocean and ice dynamics. 37 38 The frequency at which the forcing fields have to be updated is given by the \np{nn\_fsbc} namelist parameter. 37 39 When the fields are supplied from data files (flux and bulk formulations), the input fields 38 need not be supplied on the model grid. 40 need not be supplied on the model grid. Instead a file of coordinates and weights can 39 41 be supplied which maps the data from the supplied grid to the model points 40 42 (so called "Interpolation on the Fly", see \S\ref{SBC_iof}). … … 42 44 can be masked to avoid spurious results in proximity of the coasts as large sea-land gradients characterize 43 45 most of the atmospheric variables. 46 44 47 In addition, the resulting fields can be further modified using several namelist options. 45 These options control the rotation of vector components supplied relative to an east-north 46 coordinate system onto the local grid directions in the model; the addition of a surface 47 restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true); the modification of fluxes 48 below ice-covered areas (using observed ice-cover or a sea-ice model) 49 (\np{nn\_ice}~=~0,1, 2 or 3); the addition of river runoffs as surface freshwater 50 fluxes or lateral inflow (\np{ln\_rnf}~=~true); the addition of isf melting as lateral inflow (parameterisation) 51 (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false) or as surface flux at the land-ice ocean interface 52 (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true); 53 the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2); the 54 transformation of the solar radiation (if provided as daily mean) into a diurnal 55 cycle (\np{ln\_dm2dc}~=~true); and a neutral drag coefficient can be read from an external wave 56 model (\np{ln\_cdgw}~=~true). The latter option is possible only in case core or mfs bulk formulas are selected. 48 These options control 49 \begin{itemize} 50 \item the rotation of vector components supplied relative to an east-north 51 coordinate system onto the local grid directions in the model ; 52 \item the addition of a surface restoring term to observed SST and/or SSS (\np{ln\_ssr}~=~true) ; 53 \item the modification of fluxes below ice-covered areas (using observed ice-cover or a sea-ice model) (\np{nn\_ice}~=~0,1, 2 or 3) ; 54 \item the addition of river runoffs as surface freshwater fluxes or lateral inflow (\np{ln\_rnf}~=~true) ; 55 \item the addition of isf melting as lateral inflow (parameterisation) (\np{nn\_isf}~=~2 or 3 and \np{ln\_isfcav}~=~false) 56 or as fluxes applied at the land-ice ocean interface (\np{nn\_isf}~=~1 or 4 and \np{ln\_isfcav}~=~true) ; 57 \item the addition of a freshwater flux adjustment in order to avoid a mean sea-level drift (\np{nn\_fwb}~=~0,~1~or~2) ; 58 \item the transformation of the solar radiation (if provided as daily mean) into a diurnal cycle (\np{ln\_dm2dc}~=~true) ; 59 and a neutral drag coefficient can be read from an external wave model (\np{ln\_cdgw}~=~true). 60 \end{itemize} 61 The latter option is possible only in case core or mfs bulk formulas are selected. 57 62 58 63 In this chapter, we first discuss where the surface boundary condition appears in the … … 73 78 74 79 The surface ocean stress is the stress exerted by the wind and the sea-ice 75 on the ocean. The two components of stress are assumed to be interpolated 76 onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction 77 at $u$- and $v$-points They are applied as a surface boundary condition of the 78 computation of the momentum vertical mixing trend (\mdl{dynzdf} module) : 79 \begin{equation} \label{Eq_sbc_dynzdf} 80 \left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1} 81 = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v } 82 \end{equation} 83 where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind 84 stress vector in the $(\textbf{i},\textbf{j})$ coordinate system. 80 on the ocean. It is applied in \mdl{dynzdf} module as a surface boundary condition of the 81 computation of the momentum vertical mixing trend (see \eqref{Eq_dynzdf_sbc} in \S\ref{DYN_zdf}). 82 As such, it has to be provided as a 2D vector interpolated 83 onto the horizontal velocity ocean mesh, $i.e.$ resolved onto the model 84 (\textbf{i},\textbf{j}) direction at $u$- and $v$-points. 85 85 86 86 The surface heat flux is decomposed into two parts, a non solar and a solar heat 87 87 flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part 88 of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes). 89 It is applied as a surface boundary condition trend of the first level temperature 90 time evolution equation (\mdl{trasbc} module). 91 \begin{equation} \label{Eq_sbc_trasbc_q} 92 \frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 93 _o \;C_p \;e_{3t} }} \right|_{k=1} \quad 94 \end{equation} 95 $Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D 96 trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True. 97 98 \begin{equation} \label{Eq_sbc_traqsr} 99 \frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho_o C_p \,e_{3t} }\delta _k \left[ {I_w } \right] 100 \end{equation} 101 where $I_w$ is a non-dimensional function that describes the way the light 102 penetrates inside the water column. It is generally a sum of decreasing 103 exponentials (see \S\ref{TRA_qsr}). 104 105 The surface freshwater budget is provided by fields: \textit{emp} and $\textit{emp}_S$ which 106 may or may not be identical. Indeed, a surface freshwater flux has two effects: 107 it changes the volume of the ocean and it changes the surface concentration of 108 salt (and other tracers). Therefore it appears in the sea surface height as a volume 109 flux, \textit{emp} (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations 110 as a concentration/dilution effect, 111 $\textit{emp}_{S}$ (\mdl{trasbc} module). 112 \begin{equation} \label{Eq_trasbc_emp} 113 \begin{aligned} 114 &\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\textit{emp}\quad \\ 115 \\ 116 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\textit{emp}_S \;S}{e_{3t} }} \right|_{k=1} \\ 117 \end{aligned} 118 \end{equation} 119 120 In the real ocean, $\textit{emp}=\textit{emp}_S$ and the ocean salt content is conserved, 121 but it exist several numerical reasons why this equality should be broken. 122 For example, when the ocean is coupled to a sea-ice model, the water exchanged between 123 ice and ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case, 124 $\textit{emp}_{S}$ take into account both concentration/dilution effect associated with 125 freezing/melting and the salt flux between ice and ocean, while \textit{emp} is 126 only the volume flux. In addition, in the current version of \NEMO, the sea-ice is 127 assumed to be above the ocean (the so-called levitating sea-ice). Freezing/melting does 128 not change the ocean volume (no impact on \textit{emp}) but it modifies the SSS. 129 %gm \colorbox{yellow}{(see {\S} on LIM sea-ice model)}. 130 131 Note that SST can also be modified by a freshwater flux. Precipitation (in 132 particular solid precipitation) may have a temperature significantly different from 133 the SST. Due to the lack of information about the temperature of 134 precipitation, we assume it is equal to the SST. Therefore, no 135 concentration/dilution term appears in the temperature equation. It has to 136 be emphasised that this absence does not mean that there is no heat flux 137 associated with precipitation! Precipitation can change the ocean volume and thus the 138 ocean heat content. It is therefore associated with a heat flux (not yet 139 diagnosed in the model) \citep{Roullet_Madec_JGR00}). 88 of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes 89 plus the heat content of the mass exchange with the atmosphere and sea-ice). 90 It is applied in \mdl{trasbc} module as a surface boundary condition trend of 91 the first level temperature time evolution equation (see \eqref{Eq_tra_sbc} 92 and \eqref{Eq_tra_sbc_lin} in \S\ref{TRA_sbc}). 93 The latter is the penetrative part of the heat flux. It is applied as a 3D 94 trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=\textit{true}. 95 The way the light penetrates inside the water column is generally a sum of decreasing 96 exponentials (see \S\ref{TRA_qsr}). 97 98 The surface freshwater budget is provided by the \textit{emp} field. 99 It represents the mass flux exchanged with the atmosphere (evaporation minus precipitation) 100 and possibly with the sea-ice and ice shelves (freezing minus melting of ice). 101 It affects both the ocean in two different ways: 102 $(i)$ it changes the volume of the ocean and therefore appears in the sea surface height 103 equation as a volume flux, and 104 $(ii)$ it changes the surface temperature and salinity through the heat and salt contents 105 of the mass exchanged with the atmosphere, the sea-ice and the ice shelves. 106 140 107 141 108 %\colorbox{yellow}{Miss: } … … 152 119 %Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields 153 120 % 154 %Fluxes update only each n f{\_}sbc time step (namsbc) explain relation155 %between n f{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one156 %n f{\_}sbc121 %Fluxes update only each nn{\_}fsbc time step (namsbc) explain relation 122 %between nn{\_}fsbc and nf{\_}ice, do we define nf{\_}blk??? ? only one 123 %nn{\_}fsbc 157 124 % 158 125 %Explain here all the namlist namsbc variable{\ldots}. 126 % 127 % explain : use or not of surface currents 159 128 % 160 129 %\colorbox{yellow}{End Miss } 161 130 162 The ocean model provides the surface currents, temperature and salinity 163 averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the 164 mean is done in \mdl{sbcmod} module. 131 The ocean model provides, at each time step, to the surface module (\mdl{sbcmod}) 132 the surface currents, temperature and salinity. 133 These variables are averaged over \np{nn\_fsbc} time-step (\ref{Tab_ssm}), 134 and it is these averaged fields which are used to computes the surface fluxes 135 at a frequency of \np{nn\_fsbc} time-step. 136 165 137 166 138 %-------------------------------------------------TABLE--------------------------------------------------- … … 175 147 \caption{ \label{Tab_ssm} 176 148 Ocean variables provided by the ocean to the surface module (SBC). 177 The variable are averaged over n f{\_}sbc time step, $i.e.$ the frequency of149 The variable are averaged over nn{\_}fsbc time step, $i.e.$ the frequency of 178 150 computation of surface fluxes.} 179 151 \end{center} \end{table} … … 459 431 %-------------------------------------------------------------------------------------------------------------- 460 432 461 In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields and simply read them in from a previous run.462 Options are defined through the \ngn{namsbc\_sas} namelist variables. 433 In some circumstances it may be useful to avoid calculating the 3D temperature, salinity and velocity fields 434 and simply read them in from a previous run or receive them from OASIS. 463 435 For example: 464 436 465 \begin{ enumerate}466 \item Multiple runs of the model are required in code development to see the affect of different algorithms in437 \begin{itemize} 438 \item Multiple runs of the model are required in code development to see the effect of different algorithms in 467 439 the bulk formulae. 468 440 \item The effect of different parameter sets in the ice model is to be examined. 469 \end{enumerate} 441 \item Development of sea-ice algorithms or parameterizations. 442 \item spinup of the iceberg floats 443 \item ocean/sea-ice simulation with both media running in parallel (\np{ln\_mixcpl}~=~\textit{true}) 444 \end{itemize} 470 445 471 446 The StandAlone Surface scheme provides this utility. 447 Its options are defined through the \ngn{namsbc\_sas} namelist variables. 472 448 A new copy of the model has to be compiled with a configuration based on ORCA2\_SAS\_LIM. 473 449 However no namelist parameters need be changed from the settings of the previous run (except perhaps nn{\_}date0) … … 475 451 Routines replaced are: 476 452 477 \begin{enumerate} 478 \item \mdl{nemogcm} 479 480 This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90) 453 \begin{itemize} 454 \item \mdl{nemogcm} : This routine initialises the rest of the model and repeatedly calls the stp time stepping routine (step.F90) 481 455 Since the ocean state is not calculated all associated initialisations have been removed. 482 \item \mdl{step} 483 484 The main time stepping routine now only needs to call the sbc routine (and a few utility functions). 485 \item \mdl{sbcmod} 486 487 This has been cut down and now only calculates surface forcing and the ice model required. New surface modules 456 \item \mdl{step} : The main time stepping routine now only needs to call the sbc routine (and a few utility functions). 457 \item \mdl{sbcmod} : This has been cut down and now only calculates surface forcing and the ice model required. New surface modules 488 458 that can function when only the surface level of the ocean state is defined can also be added (e.g. icebergs). 489 \item \mdl{daymod} 490 491 No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions 459 \item \mdl{daymod} : No ocean restarts are read or written (though the ice model restarts are retained), so calls to restart functions 492 460 have been removed. This also means that the calendar cannot be controlled by time in a restart file, so the user 493 461 must make sure that nn{\_}date0 in the model namelist is correct for his or her purposes. 494 \item \mdl{stpctl} 495 496 Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module. 497 \item \mdl{diawri} 498 499 All 3D data have been removed from the output. The surface temperature, salinity and velocity components (which 462 \item \mdl{stpctl} : Since there is no free surface solver, references to it have been removed from \rou{stp\_ctl} module. 463 \item \mdl{diawri} : All 3D data have been removed from the output. The surface temperature, salinity and velocity components (which 500 464 have been read in) are written along with relevant forcing and ice data. 501 \end{ enumerate}465 \end{itemize} 502 466 503 467 One new routine has been added: 504 468 505 \begin{enumerate} 506 \item \mdl{sbcsas} 507 This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface. 469 \begin{itemize} 470 \item \mdl{sbcsas} : This module initialises the input files needed for reading temperature, salinity and velocity arrays at the surface. 508 471 These filenames are supplied in namelist namsbc{\_}sas. Unfortunately because of limitations with the \mdl{iom} module, 509 472 the full 3D fields from the mean files have to be read in and interpolated in time, before using just the top level. 510 473 Since fldread is used to read in the data, Interpolation on the Fly may be used to change input data resolution. 511 \end{enumerate} 474 \end{itemize} 475 476 477 % Missing the description of the 2 following variables: 478 % ln_3d_uve = .true. ! specify whether we are supplying a 3D u,v and e3 field 479 % ln_read_frq = .false. ! specify whether we must read frq or not 480 481 512 482 513 483 % ================================================================ … … 590 560 reanalysis and satellite data. They use an inertial dissipative method to compute 591 561 the turbulent transfer coefficients (momentum, sensible heat and evaporation) 592 from the 10 met rewind speed, air temperature and specific humidity.562 from the 10 meters wind speed, air temperature and specific humidity. 593 563 This \citet{Large_Yeager_Rep04} dataset is available through the 594 564 \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/CORE.html}{GFDL web site}. … … 625 595 or larger than the one of the input atmospheric fields. 626 596 597 The \np{sn\_wndi}, \np{sn\_wndj}, \np{sn\_qsr}, \np{sn\_qlw}, \np{sn\_tair},\np{sn\_humi},\np{sn\_prec}, \np{sn\_snow}, \np{sn\_tdif} parameters describe the fields and the way they have to be used (spatial and temporal interpolations). 598 599 \np{cn\_dir} is the directory of location of bulk files 600 \np{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.) 601 \np{rn\_zqt}: is the height of humidity and temperature measurements (m) 602 \np{rn\_zu}: is the height of wind measurements (m) 603 The multiplicative factors to activate (value is 1) or deactivate (value is 0) : 604 \np{rn\_pfac} for precipitations (total and snow) 605 \np{rn\_efac} for evaporation 606 \np{rn\_vfac} for for ice/ocean velocities in the calculation of wind stress 607 627 608 % ------------------------------------------------------------------------------------------------------------- 628 609 % CLIO Bulk formulea … … 720 701 are sent to the atmospheric component. 721 702 722 A generalised coupled interface has been developed. It is currently interfaced with OASIS 3 723 (\key{oasis3}) and does not support OASIS 4 724 \footnote{The \key{oasis4} exist. It activates portion of the code that are still under development.}. 703 A generalised coupled interface has been developed. 704 It is currently interfaced with OASIS-3-MCT (\key{oasis3}). 725 705 It has been successfully used to interface \NEMO to most of the European atmospheric 726 706 GCM (ARPEGE, ECHAM, ECMWF, HadAM, HadGAM, LMDz), … … 787 767 \label{SBC_tide} 788 768 789 A module is available to use the tidal potential forcing and is activated with with \key{tide}. 790 791 792 %------------------------------------------nam_tide---------------------------------------------------- 769 %------------------------------------------nam_tide--------------------------------------- 793 770 \namdisplay{nam_tide} 794 %------------------------------------------------------------------------------------------------------------- 795 796 Concerning the tidal potential, some parameters are available in namelist \ngn{nam\_tide}: 771 %----------------------------------------------------------------------------------------- 772 773 A module is available to compute the tidal potential and use it in the momentum equation. 774 This option is activated when \key{tide} is defined. 775 776 Some parameters are available in namelist \ngn{nam\_tide}: 797 777 798 778 - \np{ln\_tide\_pot} activate the tidal potential forcing … … 801 781 802 782 - \np{clname} is the name of constituent 803 804 783 805 784 The tide is generated by the forces of gravity ot the Earth-Moon and Earth-Sun sytem; … … 895 874 lowest box the river water is being added to (i.e. the total depth that river water is being added to in the model). 896 875 876 %Christian: 877 If the depth information is not provide in the NetCDF file, it can be estimate from the runoff input file at the initial time-step, by setting the namelist parameter \np{ln\_rnf\_depth\_ini} to true. 878 879 This estimation is a simple linear relation between the runoff and a given depth : 880 \begin{equation} 881 h\_dep = \frac{rn\_dep\_max} {rn\_rnf\_max} rnf 882 \end{equation} 883 where \np{rn\_dep\_max} is the given maximum depth over which the runoffs is spread, 884 \np{rn\_rnf\_max} is the maximum value of the runoff climatologie over the global domain 885 and rnf is the maximum value in time of the runoff climatology at each grid cell (computed online). 886 887 The estimated depth array can be output if needed in a NetCDF file by setting the namelist parameter \np{nn\_rnf\_depth\_file} to 1. 888 897 889 The mass/volume addition due to the river runoff is, at each relevant depth level, added to the horizontal divergence 898 890 (\textit{hdivn}) in the subroutine \rou{sbc\_rnf\_div} (called from \mdl{divcur}). … … 958 950 \namdisplay{namsbc_isf} 959 951 %-------------------------------------------------------------------------------------------------------- 960 Namelist variable in \ngn{namsbc}, \np{nn\_isf}, control the kind of ice shelf representation used. 952 Namelist variable in \ngn{namsbc}, \np{nn\_isf}, controls the ice shelf representation used (Fig. \ref{Fig_SBC_isf}): 953 954 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 955 \begin{figure}[!h] \begin{center} 956 \includegraphics[width=0.8\textwidth]{Fig_SBC_isf} 957 \caption{ \label{Fig_SBC_isf} 958 Schematic for all the options available trough \np{nn\_isf}.} 959 \end{center} \end{figure} 960 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 961 961 962 \begin{description} 963 \item[\np{nn\_isf}~=~0] 964 The ice shelf routines are not used. The ice shelf melting is not computed or prescribed, the cavity have to be closed. 965 If needed, the ice shelf melting should be added to the runoff or the precipitation file. 966 962 967 \item[\np{nn\_isf}~=~1] 963 The ice shelf cavity is represented. The fwf and heat flux are computed. 964 Full description, sensitivity and validation in preparation. 968 The ice shelf cavity is represented. The fwf and heat flux are computed. Two different bulk formula are available: 969 \begin{description} 970 \item[\np{nn\_isfblk}~=~1] 971 The bulk formula used to compute the melt is based the one described in \citet{Hunter2006}. 972 This formulation is based on a balance between the upward ocean heat flux and the latent heat flux at the ice shelf base. 973 974 \item[\np{nn\_isfblk}~=~2] 975 The bulk formula used to compute the melt is based the one described in \citet{Jenkins1991}. 976 This formulation is based on a 3 equations formulation (a heat flux budget, a salt flux budget and a linearised freezing point temperature equation). 977 \end{description} 978 979 For this 2 bulk formulations, there are 3 different ways to compute the exchange coeficient: 980 \begin{description} 981 \item[\np{nn\_gammablk~=~0~}] 982 The salt and heat exchange coefficients are constant and defined by \np{rn\_gammas0} and \np{rn\_gammat0} 983 984 \item[\np{nn\_gammablk~=~1~}] 985 The salt and heat exchange coefficients are velocity dependent and defined as $\np{rn\_gammas0} \times u_{*}$ and $\np{rn\_gammat0} \times u_{*}$ 986 where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters). 987 See \citet{Jenkins2010} for all the details on this formulation. 988 989 \item[\np{nn\_gammablk~=~2~}] 990 The salt and heat exchange coefficients are velocity and stability dependent and defined as 991 $\gamma_{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}}$ 992 where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn\_hisf\_tbl} meters), 993 $\Gamma_{Turb}$ the contribution of the ocean stability and 994 $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 995 See \citet{Holland1999} for all the details on this formulation. 996 \end{description} 965 997 966 998 \item[\np{nn\_isf}~=~2] … … 968 1000 The fwf is distributed along the ice shelf edge between the depth of the average grounding line (GL) 969 1001 (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}) as in (\np{nn\_isf}~=~3). 970 Furthermore the fwf iscomputed using the \citet{Beckmann2003} parameterisation of isf melting.1002 Furthermore the fwf and heat flux are computed using the \citet{Beckmann2003} parameterisation of isf melting. 971 1003 The effective melting length (\np{sn\_Leff\_isf}) is read from a file. 972 1004 973 1005 \item[\np{nn\_isf}~=~3] 974 1006 A simple parameterisation of isf is used. The ice shelf cavity is not represented. 975 The fwf (\np{sn\_rnfisf}) is distributed along the ice shelf edge between the depth of the average grounding line (GL)976 (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}). 977 Full description, sensitivity and validation in preparation.1007 The fwf (\np{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between the depth of the average grounding line (GL) 1008 (\np{sn\_depmax\_isf}) and the base of the ice shelf along the calving front (\np{sn\_depmin\_isf}). 1009 The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 978 1010 979 1011 \item[\np{nn\_isf}~=~4] 980 The ice shelf cavity is represented. However, the fwf (\np{sn\_fwfisf}) and heat flux (\np{sn\_qisf}) are981 not computed but specified from file. 1012 The ice shelf cavity is opened. However, the fwf is not computed but specified from file \np{sn\_fwfisf}). 1013 The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$.\\ 982 1014 \end{description} 983 1015 984 \np{nn\_isf}~=~1 and \np{nn\_isf}~=~2 compute a melt rate based on the water masse properties, ocean velocities and depth. 985 This flux is thus highly dependent of the model resolution (horizontal and vertical), realism of the water masse onto the shelf ... 986 987 \np{nn\_isf}~=~3 and \np{nn\_isf}~=~4 read the melt rate and heat flux from a file. You have total control of the fwf scenario. 988 989 This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too 990 coarse to have realistic melting or for sensitivity studies where you want to control your input. 991 Full description, sensitivity and validation in preparation. 992 993 There is 2 ways to apply the fwf to NEMO. The first possibility (\np{ln\_divisf}~=~false) applied the fwf 994 and heat flux directly on the salinity and temperature tendancy. The second possibility (\np{ln\_divisf}~=~true) 995 apply the fwf as for the runoff fwf (see \S\ref{SBC_rnf}). The mass/volume addition due to the ice shelf melting is, 996 at each relevant depth level, added to the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div} 997 (called from \mdl{divcur}). 1016 1017 $\bullet$ \np{nn\_isf}~=~1 and \np{nn\_isf}~=~2 compute a melt rate based on the water mass properties, ocean velocities and depth. 1018 This flux is thus highly dependent of the model resolution (horizontal and vertical), realism of the water masses onto the shelf ...\\ 1019 1020 $\bullet$ \np{nn\_isf}~=~3 and \np{nn\_isf}~=~4 read the melt rate from a file. You have total control of the fwf forcing. 1021 This can be usefull if the water masses on the shelf are not realistic or the resolution (horizontal/vertical) are too 1022 coarse to have realistic melting or for studies where you need to control your heat and fw input.\\ 1023 1024 Two namelist parameters control how the heat and fw fluxes are passed to NEMO: \np{rn\_hisf\_tbl} and \np{ln\_divisf} 1025 \begin{description} 1026 \item[\np{rn\_hisf\_tbl}] is the top boundary layer thickness as defined in \citet{Losch2008}. 1027 This parameter is only used if \np{nn\_isf}~=~1 or \np{nn\_isf}~=~4 1028 It allows you to control over which depth you want to spread the heat and fw fluxes. 1029 1030 If \np{rn\_hisf\_tbl} = 0.0, the fluxes are put in the top level whatever is its tickness. 1031 1032 If \np{rn\_hisf\_tbl} $>$ 0.0, the fluxes are spread over the first \np{rn\_hisf\_tbl} m (ie over one or several cells). 1033 1034 \item[\np{ln\_divisf}] is a flag to apply the fw flux as a volume flux or as a salt flux. 1035 1036 \np{ln\_divisf}~=~true applies the fwf as a volume flux. This volume flux is implemented with in the same way as for the runoff. 1037 The fw addition due to the ice shelf melting is, at each relevant depth level, added to the horizontal divergence 1038 (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divcur}. 1039 See the runoff section \ref{SBC_rnf} for all the details about the divergence correction. 1040 1041 \np{ln\_divisf}~=~false applies the fwf and heat flux directly on the salinity and temperature tendancy. 1042 1043 \item[\np{ln\_conserve}] is a flag for \np{nn\_isf}~=~1. A conservative boundary layer scheme as described in \citet{Jenkins2001} 1044 is used if \np{ln\_conserve}=true. It takes into account the fact that the melt water is at freezing T and needs to be warm up to ocean temperature. 1045 It is only relevant for \np{ln\_divisf}~=~false. 1046 If \np{ln\_divisf}~=~true, \np{ln\_conserve} has to be set to false to avoid a double counting of the contribution. 1047 1048 \end{description} 998 1049 % 999 1050 % ================================================================ 1000 1051 % Handling of icebergs 1001 1052 % ================================================================ 1002 \section{ Handling of icebergs (ICB)}1053 \section{Handling of icebergs (ICB)} 1003 1054 \label{ICB_icebergs} 1004 1055 %------------------------------------------namberg---------------------------------------------------- … … 1006 1057 %------------------------------------------------------------------------------------------------------------- 1007 1058 1008 Icebergs are modelled as lagrangian particles in NEMO. 1009 Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ). 1010 (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO.) 1011 Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described in the \ngn{namberg} namelist: 1059 Icebergs are modelled as lagrangian particles in NEMO \citep{Marsh_GMD2015}. 1060 Their physical behaviour is controlled by equations as described in \citet{Martin_Adcroft_OM10} ). 1061 (Note that the authors kindly provided a copy of their code to act as a basis for implementation in NEMO). 1062 Icebergs are initially spawned into one of ten classes which have specific mass and thickness as described 1063 in the \ngn{namberg} namelist: 1012 1064 \np{rn\_initial\_mass} and \np{rn\_initial\_thickness}. 1013 1065 Each class has an associated scaling (\np{rn\_mass\_scaling}), which is an integer representing how many icebergs … … 1079 1131 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1080 1132 \begin{figure}[!t] \begin{center} 1081 \includegraphics[width=0.8\textwidth]{ ./TexFiles/Figures/Fig_SBC_diurnal.pdf}1133 \includegraphics[width=0.8\textwidth]{Fig_SBC_diurnal} 1082 1134 \caption{ \label{Fig_SBC_diurnal} 1083 1135 Example of recontruction of the diurnal cycle variation of short wave flux … … 1112 1164 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1113 1165 \begin{figure}[!t] \begin{center} 1114 \includegraphics[width=0.7\textwidth]{ ./TexFiles/Figures/Fig_SBC_dcy.pdf}1166 \includegraphics[width=0.7\textwidth]{Fig_SBC_dcy} 1115 1167 \caption{ \label{Fig_SBC_dcy} 1116 1168 Example of recontruction of the diurnal cycle variation of short wave flux … … 1193 1245 The presence at the sea surface of an ice covered area modifies all the fluxes 1194 1246 transmitted to the ocean. There are several way to handle sea-ice in the system 1195 depending on the value of the \np{nn {\_}ice} namelist parameter.1247 depending on the value of the \np{nn\_ice} namelist parameter found in \ngn{namsbc} namelist. 1196 1248 \begin{description} 1197 1249 \item[nn{\_}ice = 0] there will never be sea-ice in the computational domain. … … 1268 1320 % ------------------------------------------------------------------------------------------------------------- 1269 1321 \subsection [Neutral drag coefficient from external wave model (\textit{sbcwave})] 1270 1322 {Neutral drag coefficient from external wave model (\mdl{sbcwave})} 1271 1323 \label{SBC_wave} 1272 1324 %------------------------------------------namwave---------------------------------------------------- 1273 1325 \namdisplay{namsbc_wave} 1274 1326 %------------------------------------------------------------------------------------------------------------- 1275 \begin{description} 1276 1277 \item [??] In order to read a neutral drag coeff, from an external data source (i.e. a wave model), the 1278 logical variable \np{ln\_cdgw} 1279 in $namsbc$ namelist must be defined ${.true.}$. 1327 1328 In order to read a neutral drag coeff, from an external data source ($i.e.$ a wave model), the 1329 logical variable \np{ln\_cdgw} in \ngn{namsbc} namelist must be set to \textit{true}. 1280 1330 The \mdl{sbcwave} module containing the routine \np{sbc\_wave} reads the 1281 1331 namelist \ngn{namsbc\_wave} (for external data names, locations, frequency, interpolation and all 1282 1332 the miscellanous options allowed by Input Data generic Interface see \S\ref{SBC_input}) 1283 and a 2D field of neutral drag coefficient. Then using the routine 1284 TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, the drag coefficient is computed according 1285 to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}. 1286 1287 \end{description} 1333 and a 2D field of neutral drag coefficient. 1334 Then using the routine TURB\_CORE\_1Z or TURB\_CORE\_2Z, and starting from the neutral drag coefficent provided, 1335 the drag coefficient is computed according to stable/unstable conditions of the air-sea interface following \citet{Large_Yeager_Rep04}. 1336 1288 1337 1289 1338 % Griffies doc: 1290 % When running ocean-ice simulations, we are not explicitly representing land processes, such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, it is important to balance the hydrological cycle in ocean-ice models. We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. The result of the normalization should be a global integrated zero net water input to the ocean-ice system over a chosen time scale. 1291 %How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, so that there is always a zero net input of water to the ocean-ice system. Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing. 1292 %When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean and ice models when aiming to balance the hydrological cycle. The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running ocean-ice models, not the water in any one sub-component. As an extreme example to illustrate the issue, consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up, there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. The total water contained in the ocean plus ice system is constant, but there is an exchange of water between the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle in ocean-ice models. 1293 1294 1339 % When running ocean-ice simulations, we are not explicitly representing land processes, 1340 % such as rivers, catchment areas, snow accumulation, etc. However, to reduce model drift, 1341 % it is important to balance the hydrological cycle in ocean-ice models. 1342 % We thus need to prescribe some form of global normalization to the precipitation minus evaporation plus river runoff. 1343 % The result of the normalization should be a global integrated zero net water input to the ocean-ice system over 1344 % a chosen time scale. 1345 %How often the normalization is done is a matter of choice. In mom4p1, we choose to do so at each model time step, 1346 % so that there is always a zero net input of water to the ocean-ice system. 1347 % Others choose to normalize over an annual cycle, in which case the net imbalance over an annual cycle is used 1348 % to alter the subsequent year�s water budget in an attempt to damp the annual water imbalance. 1349 % Note that the annual budget approach may be inappropriate with interannually varying precipitation forcing. 1350 % When running ocean-ice coupled models, it is incorrect to include the water transport between the ocean 1351 % and ice models when aiming to balance the hydrological cycle. 1352 % The reason is that it is the sum of the water in the ocean plus ice that should be balanced when running ocean-ice models, 1353 % not the water in any one sub-component. As an extreme example to illustrate the issue, 1354 % consider an ocean-ice model with zero initial sea ice. As the ocean-ice model spins up, 1355 % there should be a net accumulation of water in the growing sea ice, and thus a net loss of water from the ocean. 1356 % The total water contained in the ocean plus ice system is constant, but there is an exchange of water between 1357 % the subcomponents. This exchange should not be part of the normalization used to balance the hydrological cycle 1358 % in ocean-ice models. 1359 1360 1361 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_STO.tex
r5602 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter stochastic parametrization of EOS (STO) … … 5 7 \label{STO} 6 8 9 Authors: P.-A. Bouttier 10 7 11 \minitoc 8 9 12 10 13 \newpage 11 14 $\ $\newline % force a new line 15 16 The stochastic parametrization module aims to explicitly simulate uncertainties in the model. More particularly, \cite{Brankart_OM2013} has shown that, because of the nonlinearity of the seawater equation of state, unresolved scales represent a major source of uncertainties in the computation of the large scale horizontal density gradient (from T/S large scale fields), and that the impact of these uncertainties can be simulated by random processes representing unresolved T/S fluctuations. 17 18 The stochastic formulation of the equation of state can be written as: 19 \begin{equation} 20 \label{eq:eos_sto} 21 \rho = \frac{1}{2} \sum_{i=1}^m\{ \rho[T+\Delta T_i,S+\Delta S_i,p_o(z)] + \rho[T-\Delta T_i,S-\Delta S_i,p_o(z)] \} 22 \end{equation} 23 where $p_o(z)$ is the reference pressure depending on the depth and $\Delta T_i$ and $\Delta S_i$ are a set of T/S perturbations defined as the scalar product of the respective local T/S gradients with random walks $\mathbf{\xi}$: 24 \begin{equation} 25 \label{eq:sto_pert} 26 \Delta T_i = \mathbf{\xi}_i \cdot \nabla T \qquad \hbox{and} \qquad \Delta S_i = \mathbf{\xi}_i \cdot \nabla S 27 \end{equation} 28 $\mathbf{\xi}_i$ are produced by a first-order autoregressive processes (AR-1) with a parametrized decorrelation time scale, and horizontal and vertical standard deviations $\sigma_s$. $\mathbf{\xi}$ are uncorrelated over the horizontal and fully correlated along the vertical. 29 30 31 \section{Stochastic processes} 32 \label{STO_the_details} 33 34 The starting point of our implementation of stochastic parameterizations 35 in NEMO is to observe that many existing parameterizations are based 36 on autoregressive processes, which are used as a basic source of randomness 37 to transform a deterministic model into a probabilistic model. 38 A generic approach is thus to add one single new module in NEMO, 39 generating processes with appropriate statistics 40 to simulate each kind of uncertainty in the model 41 (see \cite{Brankart_al_GMD2015} for more details). 42 43 In practice, at every model grid point, independent Gaussian autoregressive 44 processes~$\xi^{(i)},\,i=1,\ldots,m$ are first generated 45 using the same basic equation: 46 47 \begin{equation} 48 \label{eq:autoreg} 49 \xi^{(i)}_{k+1} = a^{(i)} \xi^{(i)}_k + b^{(i)} w^{(i)} + c^{(i)} 50 \end{equation} 51 52 \noindent 53 where $k$ is the index of the model timestep; and 54 $a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are parameters defining 55 the mean ($\mu^{(i)}$) standard deviation ($\sigma^{(i)}$) 56 and correlation timescale ($\tau^{(i)}$) of each process: 57 58 \begin{itemize} 59 \item for order~1 processes, $w^{(i)}$ is a Gaussian white noise, 60 with zero mean and standard deviation equal to~1, and the parameters 61 $a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are given by: 62 63 \begin{equation} 64 \label{eq:ord1} 65 \left\{ 66 \begin{array}{l} 67 a^{(i)} = \varphi \\ 68 b^{(i)} = \sigma^{(i)} \sqrt{ 1 - \varphi^2 } 69 \qquad\qquad\mbox{with}\qquad\qquad 70 \varphi = \exp \left( - 1 / \tau^{(i)} \right) \\ 71 c^{(i)} = \mu^{(i)} \left( 1 - \varphi \right) \\ 72 \end{array} 73 \right. 74 \end{equation} 75 76 \item for order~$n>1$ processes, $w^{(i)}$ is an order~$n-1$ autoregressive process, 77 with zero mean, standard deviation equal to~$\sigma^{(i)}$; correlation timescale 78 equal to~$\tau^{(i)}$; and the parameters 79 $a^{(i)}$, $b^{(i)}$, $c^{(i)}$ are given by: 80 81 \begin{equation} 82 \label{eq:ord2} 83 \left\{ 84 \begin{array}{l} 85 a^{(i)} = \varphi \\ 86 b^{(i)} = \frac{n-1}{2(4n-3)} \sqrt{ 1 - \varphi^2 } 87 \qquad\qquad\mbox{with}\qquad\qquad 88 \varphi = \exp \left( - 1 / \tau^{(i)} \right) \\ 89 c^{(i)} = \mu^{(i)} \left( 1 - \varphi \right) \\ 90 \end{array} 91 \right. 92 \end{equation} 93 94 \end{itemize} 95 96 \noindent 97 In this way, higher order processes can be easily generated recursively using the same piece of code implementing Eq.~(\ref{eq:autoreg}), and using succesively processes from order $0$ to~$n-1$ as~$w^{(i)}$. 98 The parameters in Eq.~(\ref{eq:ord2}) are computed so that this recursive application 99 of Eq.~(\ref{eq:autoreg}) leads to processes with the required standard deviation 100 and correlation timescale, with the additional condition that 101 the $n-1$ first derivatives of the autocorrelation function 102 are equal to zero at~$t=0$, so that the resulting processes 103 become smoother and smoother as $n$ is increased. 104 105 Overall, this method provides quite a simple and generic way of generating a wide class of stochastic processes. However, this also means that new model parameters are needed to specify each of these stochastic processes. As in any parameterization of lacking physics, a very important issues then to tune these new parameters using either first principles, model simulations, or real-world observations. 106 107 \section{Implementation details} 108 \label{STO_thech_details} 109 The computer code implementing stochastic parametrisations is made of one single FORTRAN module, 110 with 3 public routines to be called by the model (in our case, NEMO): 111 112 The first routine ({sto\_par}) is a direct implementation of Eq.~(\ref{eq:autoreg}), 113 applied at each model grid point (in 2D or 3D), 114 and called at each model time step ($k$) to update 115 every autoregressive process ($i=1,\ldots,m$). 116 This routine also includes a filtering operator, applied to $w^{(i)}$, 117 to introduce a spatial correlation between the stochastic processes. 118 119 The second routine ({sto\_par\_init}) 120 is an initialization routine mainly dedicated 121 to the computation of parameters $a^{(i)}, b^{(i)}, c^{(i)}$ 122 for each autoregressive process, as a function of the statistical properties 123 required by the model user (mean, standard deviation, time correlation, 124 order of the process,\ldots). Parameters for the processes can be specified through the following namelist parameters: 125 \begin{alltt} 126 \tiny 127 \begin{verbatim} 128 nn_sto_eos = 1 ! number of independent random walks 129 rn_eos_stdxy = 1.4 ! random walk horz. standard deviation (in grid points) 130 rn_eos_stdz = 0.7 ! random walk vert. standard deviation (in grid points) 131 rn_eos_tcor = 1440.0 ! random walk time correlation (in timesteps) 132 nn_eos_ord = 1 ! order of autoregressive processes 133 nn_eos_flt = 0 ! passes of Laplacian filter 134 rn_eos_lim = 2.0 ! limitation factor (default = 3.0) 135 \end{verbatim} 136 \end{alltt} 137 This routine also includes the initialization (seeding) 138 of the random number generator. 139 140 The third routine ({sto\_rst\_write}) writes a ``restart file'' 141 with the current value of all autoregressive processes 142 to allow restarting a simulation from where it has been interrupted. 143 This file also contains the current state of the random number generator. 144 In case of a restart, this file is then read by the initialization routine 145 ({sto\_par\_init}), so that the simulation can continue exactly 146 as if it was not interrupted. 147 Restart capabilities of the module are driven by the following namelist parameters: 148 \begin{alltt} 149 \tiny 150 \begin{verbatim} 151 ln_rststo = .false. ! start from mean parameter (F) or from restart file (T) 152 ln_rstseed = .true. ! read seed of RNG from restart file 153 cn_storst_in = "restart_sto" ! suffix of stochastic parameter restart file (input) 154 cn_storst_out = "restart_sto" ! suffix of stochastic parameter restart file (output) 155 \end{verbatim} 156 \end{alltt} 157 158 In the particular case of the stochastic equation of state, there is also an additional module ({sto\_pts}) implementing Eq~\ref{eq:sto_pert} and specific piece of code in the equation of state implementing Eq~\ref{eq:eos_sto}. 159 160 161 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_STP.tex
r4147 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 2 4 % ================================================================ … … 196 198 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 197 199 \begin{figure}[!t] \begin{center} 198 \includegraphics[width=0.7\textwidth]{ ./TexFiles/Figures/Fig_TimeStepping_flowchart.pdf}200 \includegraphics[width=0.7\textwidth]{Fig_TimeStepping_flowchart} 199 201 \caption{ \label{Fig_TimeStep_flowchart} 200 202 Sketch of the leapfrog time stepping sequence in \NEMO from \citet{Leclair_Madec_OM09}. … … 288 290 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 289 291 \begin{figure}[!t] \begin{center} 290 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_MLF_forcing.pdf}292 \includegraphics[width=0.90\textwidth]{Fig_MLF_forcing} 291 293 \caption{ \label{Fig_MLF_forcing} 292 294 Illustration of forcing integration methods. … … 424 426 } 425 427 %% 428 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_TRA.tex
r5602 r7260 1 % ================================================================ 2 % Chapter 1 � Ocean Tracers (TRA) 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 3 % ================================================================ 4 % Chapter 1 ——— Ocean Tracers (TRA) 3 5 % ================================================================ 4 6 \chapter{Ocean Tracers (TRA)} … … 36 38 (BBL) parametrisation, and an internal damping (DMP) term. The terms QSR, 37 39 BBC, BBL and DMP are optional. The external forcings and parameterisations 38 require complex inputs and complex calculations ( e.g.bulk formulae, estimation40 require complex inputs and complex calculations ($e.g.$ bulk formulae, estimation 39 41 of mixing coefficients) that are carried out in the SBC, LDF and ZDF modules and 40 42 described in chapters \S\ref{SBC}, \S\ref{LDF} and \S\ref{ZDF}, respectively. 41 Note that \mdl{tranpc}, the non-penetrative convection module, although 42 (temporarily) located in the NEMO/OPA/TRA directory, is described with the 43 model vertical physics (ZDF). 44 %%% 45 \gmcomment{change the position of eosbn2 in the reference code} 46 %%% 43 Note that \mdl{tranpc}, the non-penetrative convection module, although 44 located in the NEMO/OPA/TRA directory as it directly modifies the tracer fields, 45 is described with the model vertical physics (ZDF) together with other available 46 parameterization of convection. 47 47 48 48 In the present chapter we also describe the diagnostic equations used to compute 49 the sea-water properties (density, Brunt-V ais\"{a}l\"{a} frequency, specific heat and49 the sea-water properties (density, Brunt-V\"{a}is\"{a}l\"{a} frequency, specific heat and 50 50 freezing point with associated modules \mdl{eosbn2} and \mdl{phycst}). 51 51 … … 56 56 found in the \textit{trattt} or \textit{trattt\_xxx} module, in the NEMO/OPA/TRA directory. 57 57 58 The user has the option of extracting each tendency term on the rhsof the tracer59 equation for output (\ key{trdtra} is defined), as described in Chap.~\ref{MISC}.58 The user has the option of extracting each tendency term on the RHS of the tracer 59 equation for output (\np{ln\_tra\_trd} or \np{ln\_tra\_mxl}~=~true), as described in Chap.~\ref{DIA}. 60 60 61 61 $\ $\newline % force a new ligne … … 91 91 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 92 92 \begin{figure}[!t] \begin{center} 93 \includegraphics[width=0.9\textwidth]{ ./TexFiles/Figures/Fig_adv_scheme.pdf}93 \includegraphics[width=0.9\textwidth]{Fig_adv_scheme} 94 94 \caption{ \label{Fig_adv_scheme} 95 95 Schematic representation of some ways used to evaluate the tracer value … … 125 125 \end{description} 126 126 In all cases, this boundary condition retains local conservation of tracer. 127 Global conservation is obtained in both rigid-lid and non-linear free surface128 cases, but not in the linear free surface case. Nevertheless, in the latter 129 case,it is achieved to a good approximation since the non-conservative127 Global conservation is obtained in non-linear free surface case, 128 but \textit{not} in the linear free surface case. Nevertheless, in the latter case, 129 it is achieved to a good approximation since the non-conservative 130 130 term is the product of the time derivative of the tracer and the free surface 131 131 height, two quantities that are not correlated (see \S\ref{PE_free_surface}, … … 133 133 134 134 The velocity field that appears in (\ref{Eq_tra_adv}) and (\ref{Eq_tra_adv_zco}) 135 is the centred (\textit{now}) \textit{eulerian} ocean velocity (see Chap.~\ref{DYN}). 136 When eddy induced velocity (\textit{eiv}) parameterisation is used it is the \textit{now} 137 \textit{effective} velocity ($i.e.$ the sum of the eulerian and eiv velocities) which is used. 135 is the centred (\textit{now}) \textit{effective} ocean velocity, $i.e.$ the \textit{eulerian} velocity 136 (see Chap.~\ref{DYN}) plus the eddy induced velocity (\textit{eiv}) 137 and/or the mixed layer eddy induced velocity (\textit{eiv}) 138 when those parameterisations are used (see Chap.~\ref{LDF}). 138 139 139 140 The choice of an advection scheme is made in the \textit{\ngn{nam\_traadv}} namelist, by … … 146 147 147 148 Note that 148 (1) cen2 , cen4and TVD schemes require an explicit diffusion149 (1) cen2 and TVD schemes require an explicit diffusion 149 150 operator while the other schemes are diffusive enough so that they do not 150 151 require additional diffusion ; 151 (2) cen2, cen4,MUSCL2, and UBS are not \textit{positive} schemes152 (2) cen2, MUSCL2, and UBS are not \textit{positive} schemes 152 153 \footnote{negative values can appear in an initially strictly positive tracer field 153 154 which is advected} … … 189 190 temperature is close to the freezing point). 190 191 This combined scheme has been included for specific grid points in the ORCA2 191 and ORCA4 configurationsonly. This is an obsolescent feature as the recommended192 configuration only. This is an obsolescent feature as the recommended 192 193 advection scheme for the ORCA configuration is TVD (see \S\ref{TRA_adv_tvd}). 193 194 … … 196 197 have this order of accuracy. \gmcomment{Note also that ... blah, blah} 197 198 198 % -------------------------------------------------------------------------------------------------------------199 % 4nd order centred scheme200 % -------------------------------------------------------------------------------------------------------------201 \subsection [$4^{nd}$ order centred scheme (cen4) (\np{ln\_traadv\_cen4})]202 {$4^{nd}$ order centred scheme (cen4) (\np{ln\_traadv\_cen4}=true)}203 \label{TRA_adv_cen4}204 205 In the $4^{th}$ order formulation (to be implemented), tracer values are206 evaluated at velocity points as a $4^{th}$ order interpolation, and thus depend on207 the four neighbouring $T$-points. For example, in the $i$-direction:208 \begin{equation} \label{Eq_tra_adv_cen4}209 \tau _u^{cen4}210 =\overline{ T - \frac{1}{6}\,\delta _i \left[ \delta_{i+1/2}[T] \,\right] }^{\,i+1/2}211 \end{equation}212 213 Strictly speaking, the cen4 scheme is not a $4^{th}$ order advection scheme214 but a $4^{th}$ order evaluation of advective fluxes, since the divergence of215 advective fluxes \eqref{Eq_tra_adv} is kept at $2^{nd}$ order. The phrase ``$4^{th}$216 order scheme'' used in oceanographic literature is usually associated217 with the scheme presented here. Introducing a \textit{true} $4^{th}$ order advection218 scheme is feasible but, for consistency reasons, it requires changes in the219 discretisation of the tracer advection together with changes in both the220 continuity equation and the momentum advection terms.221 222 A direct consequence of the pseudo-fourth order nature of the scheme is that223 it is not non-diffusive, i.e. the global variance of a tracer is not preserved using224 \textit{cen4}. Furthermore, it must be used in conjunction with an explicit225 diffusion operator to produce a sensible solution. The time-stepping is also226 performed using a leapfrog scheme in conjunction with an Asselin time-filter,227 so $T$ in (\ref{Eq_tra_adv_cen4}) is the \textit{now} tracer.228 229 At a $T$-grid cell adjacent to a boundary (coastline, bottom and surface), an230 additional hypothesis must be made to evaluate $\tau _u^{cen4}$. This231 hypothesis usually reduces the order of the scheme. Here we choose to set232 the gradient of $T$ across the boundary to zero. Alternative conditions can be233 specified, such as a reduction to a second order scheme for these near boundary234 grid points.235 199 236 200 % ------------------------------------------------------------------------------------------------------------- … … 270 234 used for the diffusive part. 271 235 236 An additional option has been added controlled by \np{ln\_traadv\_tvd\_zts}. 237 By setting this logical to true, a TVD scheme is used on both horizontal and vertical direction, 238 but on the latter, a split-explicit time stepping is used, with 5 sub-timesteps. 239 This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}. 240 Note that in this case, a similar split-explicit time stepping should be used on 241 vertical advection of momentum to ensure a better stability (see \np{ln\_dynzad\_zts} in \S\ref{DYN_zad}). 242 243 272 244 % ------------------------------------------------------------------------------------------------------------- 273 245 % MUSCL scheme … … 296 268 297 269 For an ocean grid point adjacent to land and where the ocean velocity is 298 directed toward land, two choices are available: an upstream flux 299 (\np{ln\_traadv\_muscl}=true) or a second order flux 300 (\np{ln\_traadv\_muscl2}=true). Note that the latter choice does not ensure 301 the \textit{positive} character of the scheme. Only the former can be used 302 on both active and passive tracers. The two MUSCL schemes are implemented 303 in the \mdl{traadv\_tvd} and \mdl{traadv\_tvd2} modules. 270 directed toward land, two choices are available: an upstream flux (\np{ln\_traadv\_muscl}=true) 271 or a second order flux (\np{ln\_traadv\_muscl2}=true). 272 Note that the latter choice does not ensure the \textit{positive} character of the scheme. 273 Only the former can be used on both active and passive tracers. 274 The two MUSCL schemes are implemented in the \mdl{traadv\_tvd} and \mdl{traadv\_tvd2} modules. 275 276 Note that when using np{ln\_traadv\_msc\_ups}~=~true in addition to \np{ln\_traadv\_muscl}=true, 277 the MUSCL fluxes are replaced by upstream fluxes in vicinity of river mouths. 304 278 305 279 % ------------------------------------------------------------------------------------------------------------- … … 416 390 direction (as for the UBS case) should be implemented to restore this property. 417 391 418 419 % -------------------------------------------------------------------------------------------------------------420 % PPM scheme421 % -------------------------------------------------------------------------------------------------------------422 \subsection [Piecewise Parabolic Method (PPM) (\np{ln\_traadv\_ppm})]423 {Piecewise Parabolic Method (PPM) (\np{ln\_traadv\_ppm}=true)}424 \label{TRA_adv_ppm}425 426 The Piecewise Parabolic Method (PPM) proposed by Colella and Woodward (1984)427 \sgacomment{reference?}428 is based on a quadradic piecewise construction. Like the QCK scheme, it is associated429 with the ULTIMATE QUICKEST limiter \citep{Leonard1991}. It has been implemented430 in \NEMO by G. Reffray (MERCATOR-ocean) but is not yet offered in the reference431 version 3.3.432 392 433 393 % ================================================================ … … 464 424 surfaces is given by: 465 425 \begin{equation} \label{Eq_tra_ldf_lap} 466 D_T^{lT} =\frac{1}{b_t T} \left( \;426 D_T^{lT} =\frac{1}{b_t} \left( \; 467 427 \delta _{i}\left[ A_u^{lT} \; \frac{e_{2u}\,e_{3u}}{e_{1u}} \;\delta _{i+1/2} [T] \right] 468 428 + \delta _{j}\left[ A_v^{lT} \; \frac{e_{1v}\,e_{3v}}{e_{2v}} \;\delta _{j+1/2} [T] \right] \;\right) … … 661 621 the thickness of the top model layer. 662 622 663 Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components ($i.e.$ atmosphere, sea-ice, land), 664 the change in the heat and salt content of the surface layer of the ocean is due both 665 to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$) 666 and to the heat and salt content of the mass exchange. 667 \sgacomment{ the following does not apply to the release to which this documentation is 668 attached and so should not be included .... 669 In a forthcoming release, these two parts, computed in the surface module (SBC), will be included directly 670 in $Q_{ns}$, the surface heat flux and $F_{salt}$, the surface salt flux. 671 The specification of these fluxes is further detailed in the SBC chapter (see \S\ref{SBC}). 672 This change will provide a forcing formulation which is the same for any tracer (including temperature and salinity). 673 674 In the current version, the situation is a little bit more complicated. } 623 Due to interactions and mass exchange of water ($F_{mass}$) with other Earth system components 624 ($i.e.$ atmosphere, sea-ice, land), the change in the heat and salt content of the surface layer 625 of the ocean is due both to the heat and salt fluxes crossing the sea surface (not linked with $F_{mass}$) 626 and to the heat and salt content of the mass exchange. They are both included directly in $Q_{ns}$, 627 the surface heat flux, and $F_{salt}$, the surface salt flux (see \S\ref{SBC} for further details). 628 By doing this, the forcing formulation is the same for any tracer (including temperature and salinity). 675 629 676 630 The surface module (\mdl{sbcmod}, see \S\ref{SBC}) provides the following … … 679 633 $\bullet$ $Q_{ns}$, the non-solar part of the net surface heat flux that crosses the sea surface 680 634 (i.e. the difference between the total surface heat flux and the fraction of the short wave flux that 681 penetrates into the water column, see \S\ref{TRA_qsr}) 682 683 $\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation) 684 685 $\bullet$ $\textit{emp}_S$, an equivalent mass flux taking into account the effect of ice-ocean mass exchange 686 687 $\bullet$ \textit{rnf}, the mass flux associated with runoff (see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies) 688 689 The $\textit{emp}_S$ field is not simply the budget of evaporation-precipitation+freezing-melting because 690 the sea-ice is not currently embedded in the ocean but levitates above it. There is no mass 691 exchanged between the sea-ice and the ocean. Instead we only take into account the salt 692 flux associated with the non-zero salinity of sea-ice, and the concentration/dilution effect 693 due to the freezing/melting (F/M) process. These two parts of the forcing are then converted into 694 an equivalent mass flux given by $\textit{emp}_S - \textit{emp}$. As a result of this mess, 695 the surface boundary condition on temperature and salinity is applied as follows: 696 697 In the nonlinear free surface case (\key{vvl} is defined): 635 penetrates into the water column, see \S\ref{TRA_qsr}) plus the heat content associated with 636 of the mass exchange with the atmosphere and lands. 637 638 $\bullet$ $\textit{sfx}$, the salt flux resulting from ice-ocean mass exchange (freezing, melting, ridging...) 639 640 $\bullet$ \textit{emp}, the mass flux exchanged with the atmosphere (evaporation minus precipitation) 641 and possibly with the sea-ice and ice-shelves. 642 643 $\bullet$ \textit{rnf}, the mass flux associated with runoff 644 (see \S\ref{SBC_rnf} for further detail of how it acts on temperature and salinity tendencies) 645 646 $\bullet$ \textit{fwfisf}, the mass flux associated with ice shelf melt, (see \S\ref{SBC_isf} for further details 647 on how the ice shelf melt is computed and applied).\\ 648 649 In the non-linear free surface case (\key{vvl} is defined), the surface boundary condition 650 on temperature and salinity is applied as follows: 698 651 \begin{equation} \label{Eq_tra_sbc} 652 \begin{aligned} 653 &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} } &\overline{ Q_{ns} }^t & \\ 654 & F^S =\frac{ 1 }{\rho _o \, \left. e_{3t} \right|_{k=1} } &\overline{ \textit{sfx} }^t & \\ 655 \end{aligned} 656 \end{equation} 657 where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps 658 ($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the 659 divergence of odd and even time step (see \S\ref{STP}). 660 661 In the linear free surface case (\key{vvl} is \textit{not} defined), 662 an additional term has to be added on both temperature and salinity. 663 On temperature, this term remove the heat content associated with mass exchange 664 that has been added to $Q_{ns}$. On salinity, this term mimics the concentration/dilution effect that 665 would have resulted from a change in the volume of the first level. 666 The resulting surface boundary condition is applied as follows: 667 \begin{equation} \label{Eq_tra_sbc_lin} 699 668 \begin{aligned} 700 669 &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} } … … 702 671 % 703 672 & F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} } 704 &\overline{ \left( (\textit{emp}_S - \textit{emp})\;\left. S \right|_{k=1} \right) }^t & \\673 &\overline{ \left( \;\textit{sfx} - \textit{emp} \;\left. S \right|_{k=1} \right) }^t & \\ 705 674 \end{aligned} 706 675 \end{equation} 707 708 In the linear free surface case (\key{vvl} not defined): 709 \begin{equation} \label{Eq_tra_sbc_lin} 710 \begin{aligned} 711 &F^T = \frac{ 1 }{\rho _o \;C_p \,\left. e_{3t} \right|_{k=1} } &\overline{ Q_{ns} }^t & \\ 712 % 713 & F^S =\frac{ 1 }{\rho _o \,\left. e_{3t} \right|_{k=1} } 714 &\overline{ \left( \textit{emp}_S\;\left. S \right|_{k=1} \right) }^t & \\ 715 \end{aligned} 716 \end{equation} 717 where $\overline{x }^t$ means that $x$ is averaged over two consecutive time steps 718 ($t-\rdt/2$ and $t+\rdt/2$). Such time averaging prevents the 719 divergence of odd and even time step (see \S\ref{STP}). 720 721 The two set of equations, \eqref{Eq_tra_sbc} and \eqref{Eq_tra_sbc_lin}, are obtained 722 by assuming that the temperature of precipitation and evaporation are equal to 723 the ocean surface temperature and that their salinity is zero. Therefore, the heat content 724 of the \textit{emp} budget must be added to the temperature equation in the variable volume case, 725 while it does not appear in the constant volume case. Similarly, the \textit{emp} budget affects 726 the ocean surface salinity in the constant volume case (through the concentration dilution effect) 727 while it does not appears explicitly in the variable volume case since salinity change will be 728 induced by volume change. In both constant and variable volume cases, surface salinity 729 will change with ice-ocean salt flux and F/M flux (both contained in $\textit{emp}_S - \textit{emp}$) without mass exchanges. 730 731 Note that the concentration/dilution effect due to F/M is computed using 732 a constant ice salinity as well as a constant ocean salinity. 733 This approximation suppresses the correlation between \textit{SSS} 734 and F/M flux, allowing the ice-ocean salt exchanges to be conservative. 735 Indeed, if this approximation is not made, even if the F/M budget is zero 736 on average over the whole ocean domain and over the seasonal cycle, 737 the associated salt flux is not zero, since sea-surface salinity and F/M flux are 738 intrinsically correlated (high \textit{SSS} are found where freezing is 739 strong whilst low \textit{SSS} is usually associated with high melting areas). 740 741 Even using this approximation, an exact conservation of heat and salt content 742 is only achieved in the variable volume case. In the constant volume case, 743 there is a small imbalance associated with the product $(\partial_t\eta - \textit{emp}) * \textit{SSS}$. 744 Nevertheless, the salt content variation is quite small and will not induce 745 a long term drift as there is no physical reason for $(\partial_t\eta - \textit{emp})$ 746 and \textit{SSS} to be correlated \citep{Roullet_Madec_JGR00}. 747 Note that, while quite small, the imbalance in the constant volume case is larger 676 Note that an exact conservation of heat and salt content is only achieved with non-linear free surface. 677 In the linear free surface case, there is a small imbalance. The imbalance is larger 748 678 than the imbalance associated with the Asselin time filter \citep{Leclair_Madec_OM09}. 749 This is the reason why the modified filter is not applied in the constant volume case.679 This is the reason why the modified filter is not applied in the linear free surface case (see \S\ref{STP}). 750 680 751 681 % ------------------------------------------------------------------------------------------------------------- … … 821 751 ($i.e.$ the inverses of the extinction length scales) are tabulated over 61 nonuniform 822 752 chlorophyll classes ranging from 0.01 to 10 g.Chl/L (see the routine \rou{trc\_oce\_rgb} 823 in \mdl{trc\_oce} module). Three types of chlorophyll can be chosen in the RGB formulation: 824 (1) a constant 0.05 g.Chl/L value everywhere (\np{nn\_chdta}=0) ; (2) an observed 825 time varying chlorophyll (\np{nn\_chdta}=1) ; (3) simulated time varying chlorophyll 826 by TOP biogeochemical model (\np{ln\_qsr\_bio}=true). In the latter case, the RGB 827 formulation is used to calculate both the phytoplankton light limitation in PISCES 828 or LOBSTER and the oceanic heating rate. 829 753 in \mdl{trc\_oce} module). Four types of chlorophyll can be chosen in the RGB formulation: 754 \begin{description} 755 \item[\np{nn\_chdta}=0] 756 a constant 0.05 g.Chl/L value everywhere ; 757 \item[\np{nn\_chdta}=1] 758 an observed time varying chlorophyll deduced from satellite surface ocean color measurement 759 spread uniformly in the vertical direction ; 760 \item[\np{nn\_chdta}=2] 761 same as previous case except that a vertical profile of chlorophyl is used. 762 Following \cite{Morel_Berthon_LO89}, the profile is computed from the local surface chlorophyll value ; 763 \item[\np{ln\_qsr\_bio}=true] 764 simulated time varying chlorophyll by TOP biogeochemical model. 765 In this case, the RGB formulation is used to calculate both the phytoplankton 766 light limitation in PISCES or LOBSTER and the oceanic heating rate. 767 \end{description} 830 768 The trend in \eqref{Eq_tra_qsr} associated with the penetration of the solar radiation 831 769 is added to the temperature trend, and the surface heat flux is modified in routine \mdl{traqsr}. … … 842 780 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 843 781 \begin{figure}[!t] \begin{center} 844 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_TRA_Irradiance.pdf}782 \includegraphics[width=1.0\textwidth]{Fig_TRA_Irradiance} 845 783 \caption{ \label{Fig_traqsr_irradiance} 846 784 Penetration profile of the downward solar irradiance calculated by four models. … … 859 797 \label{TRA_bbc} 860 798 %--------------------------------------------nambbc-------------------------------------------------------- 861 \namdisplay{nam tra_bbc}799 \namdisplay{nambbc} 862 800 %-------------------------------------------------------------------------------------------------------------- 863 801 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 864 802 \begin{figure}[!t] \begin{center} 865 \includegraphics[width=1.0\textwidth]{ ./TexFiles/Figures/Fig_TRA_geoth.pdf}803 \includegraphics[width=1.0\textwidth]{Fig_TRA_geoth} 866 804 \caption{ \label{Fig_geothermal} 867 805 Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{Emile-Geay_Madec_OS09}. … … 973 911 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 974 912 \begin{figure}[!t] \begin{center} 975 \includegraphics[width=0.7\textwidth]{ ./TexFiles/Figures/Fig_BBL_adv.pdf}913 \includegraphics[width=0.7\textwidth]{Fig_BBL_adv} 976 914 \caption{ \label{Fig_bbl} 977 915 Advective/diffusive Bottom Boundary Layer. The BBL parameterisation is … … 1103 1041 \subsection[DMP\_TOOLS]{Generating resto.nc using DMP\_TOOLS} 1104 1042 1105 DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$. Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled and run on the same machine as the NEMO model. A mesh\_mask.nc file for the model configuration is required as an input. This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1. The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work. The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 1043 DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$. 1044 Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled 1045 and run on the same machine as the NEMO model. A mesh\_mask.nc file for the model configuration is required as an input. 1046 This can be generated by carrying out a short model run with the namelist parameter \np{nn\_msh} set to 1. 1047 The namelist parameter \np{ln\_tradmp} will also need to be set to .false. for this to work. 1048 The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 1106 1049 1107 1050 %--------------------------------------------nam_dmp_create------------------------------------------------- … … 1111 1054 \np{cp\_cfg}, \np{cp\_cpz}, \np{jp\_cfg} and \np{jperio} specify the model configuration being used and should be the same as specified in \nl{namcfg}. The variable \nl{lzoom} is used to specify that the damping is being used as in case \textit{a} above to provide boundary conditions to a zoom configuration. In the case of the arctic or antarctic zoom configurations this includes some specific treatment. Otherwise damping is applied to the 6 grid points along the ocean boundaries. The open boundaries are specified by the variables \np{lzoom\_n}, \np{lzoom\_e}, \np{lzoom\_s}, \np{lzoom\_w} in the \nl{nam\_zoom\_dmp} name list. 1112 1055 1113 The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations. \np{ln\_full\_field} specifies that newtonian damping should be applied to the whole model domain. \np{ln\_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea for the ORCA4, ORCA2 and ORCA05 configurations. If \np{ln\_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference configurations with previous model versions. \np{ln\_coast} specifies that the restoration coefficient should be reduced near to coastlines. This option only has an effect if \np{ln\_full\_field} is true. \np{ln\_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer. Finally \np{ln\_custom} specifies that the custom module will be called. This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region. 1114 1115 The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn\_hdmp}. Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to the full values of a 10$^{\circ}$ latitud band. This is often used because of the short adjustment time scale in the equatorial region \citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a hyperbolic tangent, with \np{rn\_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}. 1056 The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations. 1057 \np{ln\_full\_field} specifies that newtonian damping should be applied to the whole model domain. 1058 \np{ln\_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea 1059 for the ORCA4, ORCA2 and ORCA05 configurations. 1060 If \np{ln\_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as 1061 a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference 1062 configurations with previous model versions. 1063 \np{ln\_coast} specifies that the restoration coefficient should be reduced near to coastlines. 1064 This option only has an effect if \np{ln\_full\_field} is true. 1065 \np{ln\_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer. 1066 Finally \np{ln\_custom} specifies that the custom module will be called. 1067 This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region. 1068 1069 The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn\_hdmp}. 1070 Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to 1071 the full values of a 10\deg latitud band. 1072 This is often used because of the short adjustment time scale in the equatorial region 1073 \citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a 1074 hyperbolic tangent, with \np{rn\_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}. 1116 1075 1117 1076 % ================================================================ … … 1167 1126 % Equation of State 1168 1127 % ------------------------------------------------------------------------------------------------------------- 1169 \subsection{Equation of State (\np{nn\_eos} = 0, 1 or 2)}1128 \subsection{Equation Of Seawater (\np{nn\_eos} = -1, 0, or 1)} 1170 1129 \label{TRA_eos} 1171 1130 1172 It is necessary to know the equation of state for the ocean very accurately 1173 to determine stability properties (especially the Brunt-Vais\"{a}l\"{a} frequency), 1174 particularly in the deep ocean. The ocean seawater volumic mass, $\rho$, 1175 abusively called density, is a non linear empirical function of \textit{in situ} 1176 temperature, salinity and pressure. The reference equation of state is that 1177 defined by the Joint Panel on Oceanographic Tables and Standards 1178 \citep{UNESCO1983}. It was the standard equation of state used in early 1179 releases of OPA. However, even though this computation is fully vectorised, 1180 it is quite time consuming ($15$ to $20${\%} of the total CPU time) since 1181 it requires the prior computation of the \textit{in situ} temperature from the 1182 model \textit{potential} temperature using the \citep{Bryden1973} polynomial 1183 for adiabatic lapse rate and a $4^th$ order Runge-Kutta integration scheme. 1184 Since OPA6, we have used the \citet{JackMcD1995} equation of state for 1185 seawater instead. It allows the computation of the \textit{in situ} ocean density 1186 directly as a function of \textit{potential} temperature relative to the surface 1187 (an \NEMO variable), the practical salinity (another \NEMO variable) and the 1188 pressure (assuming no pressure variation along geopotential surfaces, $i.e.$ 1189 the pressure in decibars is approximated by the depth in meters). 1190 Both the \citet{UNESCO1983} and \citet{JackMcD1995} equations of state 1191 have exactly the same except that the values of the various coefficients have 1192 been adjusted by \citet{JackMcD1995} in order to directly use the \textit{potential} 1193 temperature instead of the \textit{in situ} one. This reduces the CPU time of the 1194 \textit{in situ} density computation to about $3${\%} of the total CPU time, 1195 while maintaining a quite accurate equation of state. 1196 1197 In the computer code, a \textit{true} density anomaly, $d_a= \rho / \rho_o - 1$, 1198 is computed, with $\rho_o$ a reference volumic mass. Called \textit{rau0} 1199 in the code, $\rho_o$ is defined in \mdl{phycst}, and a value of $1,035~Kg/m^3$. 1131 The Equation Of Seawater (EOS) is an empirical nonlinear thermodynamic relationship 1132 linking seawater density, $\rho$, to a number of state variables, 1133 most typically temperature, salinity and pressure. 1134 Because density gradients control the pressure gradient force through the hydrostatic balance, 1135 the equation of state provides a fundamental bridge between the distribution of active tracers 1136 and the fluid dynamics. Nonlinearities of the EOS are of major importance, in particular 1137 influencing the circulation through determination of the static stability below the mixed layer, 1138 thus controlling rates of exchange between the atmosphere and the ocean interior \citep{Roquet_JPO2015}. 1139 Therefore an accurate EOS based on either the 1980 equation of state (EOS-80, \cite{UNESCO1983}) 1140 or TEOS-10 \citep{TEOS10} standards should be used anytime a simulation of the real 1141 ocean circulation is attempted \citep{Roquet_JPO2015}. 1142 The use of TEOS-10 is highly recommended because 1143 \textit{(i)} it is the new official EOS, 1144 \textit{(ii)} it is more accurate, being based on an updated database of laboratory measurements, and 1145 \textit{(iii)} it uses Conservative Temperature and Absolute Salinity (instead of potential temperature 1146 and practical salinity for EOS-980, both variables being more suitable for use as model variables 1147 \citep{TEOS10, Graham_McDougall_JPO13}. 1148 EOS-80 is an obsolescent feature of the NEMO system, kept only for backward compatibility. 1149 For process studies, it is often convenient to use an approximation of the EOS. To that purposed, 1150 a simplified EOS (S-EOS) inspired by \citet{Vallis06} is also available. 1151 1152 In the computer code, a density anomaly, $d_a= \rho / \rho_o - 1$, 1153 is computed, with $\rho_o$ a reference density. Called \textit{rau0} 1154 in the code, $\rho_o$ is set in \mdl{phycst} to a value of $1,026~Kg/m^3$. 1200 1155 This is a sensible choice for the reference density used in a Boussinesq ocean 1201 1156 climate model, as, with the exception of only a small percentage of the ocean, 1202 density in the World Ocean varies by no more than 2$\%$ from $1,035~kg/m^3$ 1203 \citep{Gill1982}. 1204 1205 Options are defined through the \ngn{nameos} namelist variables. 1206 The default option (namelist parameter \np{nn\_eos}=0) is the \citet{JackMcD1995} 1207 equation of state. Its use is highly recommended. However, for process studies, 1208 it is often convenient to use a linear approximation of the density. 1157 density in the World Ocean varies by no more than 2$\%$ from that value \citep{Gill1982}. 1158 1159 Options are defined through the \ngn{nameos} namelist variables, and in particular \np{nn\_eos} 1160 which controls the EOS used (=-1 for TEOS10 ; =0 for EOS-80 ; =1 for S-EOS). 1161 \begin{description} 1162 1163 \item[\np{nn\_eos}$=-1$] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used. 1164 The accuracy of this approximation is comparable to the TEOS-10 rational function approximation, 1165 but it is optimized for a boussinesq fluid and the polynomial expressions have simpler 1166 and more computationally efficient expressions for their derived quantities 1167 which make them more adapted for use in ocean models. 1168 Note that a slightly higher precision polynomial form is now used replacement of the TEOS-10 1169 rational function approximation for hydrographic data analysis \citep{TEOS10}. 1170 A key point is that conservative state variables are used: 1171 Absolute Salinity (unit: g/kg, notation: $S_A$) and Conservative Temperature (unit: \degC, notation: $\Theta$). 1172 The pressure in decibars is approximated by the depth in meters. 1173 With TEOS10, the specific heat capacity of sea water, $C_p$, is a constant. It is set to 1174 $C_p=3991.86795711963~J\,Kg^{-1}\,^{\circ}K^{-1}$, according to \citet{TEOS10}. 1175 1176 Choosing polyTEOS10-bsq implies that the state variables used by the model are 1177 $\Theta$ and $S_A$. In particular, the initial state deined by the user have to be given as 1178 \textit{Conservative} Temperature and \textit{Absolute} Salinity. 1179 In addition, setting \np{ln\_useCT} to \textit{true} convert the Conservative SST to potential SST 1180 prior to either computing the air-sea and ice-sea fluxes (forced mode) 1181 or sending the SST field to the atmosphere (coupled mode). 1182 1183 \item[\np{nn\_eos}$=0$] the polyEOS80-bsq equation of seawater is used. 1184 It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized 1185 to accurately fit EOS80 (Roquet, personal comm.). The state variables used in both the EOS80 1186 and the ocean model are: 1187 the Practical Salinity ((unit: psu, notation: $S_p$)) and Potential Temperature (unit: $^{\circ}C$, notation: $\theta$). 1188 The pressure in decibars is approximated by the depth in meters. 1189 With thsi EOS, the specific heat capacity of sea water, $C_p$, is a function of temperature, 1190 salinity and pressure \citep{UNESCO1983}. Nevertheless, a severe assumption is made in order to 1191 have a heat content ($C_p T_p$) which is conserved by the model: $C_p$ is set to a constant 1192 value, the TEOS10 value. 1193 1194 \item[\np{nn\_eos}$=1$] a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen, 1195 the coefficients of which has been optimized to fit the behavior of TEOS10 (Roquet, personal comm.) 1196 (see also \citet{Roquet_JPO2015}). It provides a simplistic linear representation of both 1197 cabbeling and thermobaricity effects which is enough for a proper treatment of the EOS 1198 in theoretical studies \citep{Roquet_JPO2015}. 1209 1199 With such an equation of state there is no longer a distinction between 1210 \textit{in situ} and \textit{potential} density and both cabbeling and thermobaric 1211 effects are removed. 1212 Two linear formulations are available: a function of $T$ only (\np{nn\_eos}=1) 1213 and a function of both $T$ and $S$ (\np{nn\_eos}=2): 1214 \begin{equation} \label{Eq_tra_eos_linear} 1200 \textit{conservative} and \textit{potential} temperature, as well as between \textit{absolute} 1201 and \textit{practical} salinity. 1202 S-EOS takes the following expression: 1203 \begin{equation} \label{Eq_tra_S-EOS} 1215 1204 \begin{split} 1216 d_a(T) &= \rho (T) / \rho_o - 1 = \ 0.0285 - \alpha \;T \\ 1217 d_a(T,S) &= \rho (T,S) / \rho_o - 1 = \ \beta \; S - \alpha \;T 1205 d_a(T,S,z) = ( & - a_0 \; ( 1 + 0.5 \; \lambda_1 \; T_a + \mu_1 \; z ) * T_a \\ 1206 & + b_0 \; ( 1 - 0.5 \; \lambda_2 \; S_a - \mu_2 \; z ) * S_a \\ 1207 & - \nu \; T_a \; S_a \; ) \; / \; \rho_o \\ 1208 with \ \ T_a = T-10 \; ; & \; S_a = S-35 \; ;\; \rho_o = 1026~Kg/m^3 1218 1209 \end{split} 1219 1210 \end{equation} 1220 where $\alpha$ and $\beta$ are the thermal and haline expansion 1221 coefficients, and $\rho_o$, the reference volumic mass, $rau0$. 1222 ($\alpha$ and $\beta$ can be modified through the \np{rn\_alpha} and 1223 \np{rn\_beta} namelist variables). Note that when $d_a$ is a function 1224 of $T$ only (\np{nn\_eos}=1), the salinity is a passive tracer and can be 1225 used as such. 1226 1227 % ------------------------------------------------------------------------------------------------------------- 1228 % Brunt-Vais\"{a}l\"{a} Frequency 1229 % ------------------------------------------------------------------------------------------------------------- 1230 \subsection{Brunt-Vais\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)} 1211 where the computer name of the coefficients as well as their standard value are given in \ref{Tab_SEOS}. 1212 In fact, when choosing S-EOS, various approximation of EOS can be specified simply by changing 1213 the associated coefficients. 1214 Setting to zero the two thermobaric coefficients ($\mu_1$, $\mu_2$) remove thermobaric effect from S-EOS. 1215 setting to zero the three cabbeling coefficients ($\lambda_1$, $\lambda_2$, $\nu$) remove cabbeling effect from S-EOS. 1216 Keeping non-zero value to $a_0$ and $b_0$ provide a linear EOS function of T and S. 1217 1218 \end{description} 1219 1220 1221 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1222 \begin{table}[!tb] 1223 \begin{center} \begin{tabular}{|p{26pt}|p{72pt}|p{56pt}|p{136pt}|} 1224 \hline 1225 coeff. & computer name & S-EOS & description \\ \hline 1226 $a_0$ & \np{rn\_a0} & 1.6550 $10^{-1}$ & linear thermal expansion coeff. \\ \hline 1227 $b_0$ & \np{rn\_b0} & 7.6554 $10^{-1}$ & linear haline expansion coeff. \\ \hline 1228 $\lambda_1$ & \np{rn\_lambda1}& 5.9520 $10^{-2}$ & cabbeling coeff. in $T^2$ \\ \hline 1229 $\lambda_2$ & \np{rn\_lambda2}& 5.4914 $10^{-4}$ & cabbeling coeff. in $S^2$ \\ \hline 1230 $\nu$ & \np{rn\_nu} & 2.4341 $10^{-3}$ & cabbeling coeff. in $T \, S$ \\ \hline 1231 $\mu_1$ & \np{rn\_mu1} & 1.4970 $10^{-4}$ & thermobaric coeff. in T \\ \hline 1232 $\mu_2$ & \np{rn\_mu2} & 1.1090 $10^{-5}$ & thermobaric coeff. in S \\ \hline 1233 \end{tabular} 1234 \caption{ \label{Tab_SEOS} 1235 Standard value of S-EOS coefficients. } 1236 \end{center} 1237 \end{table} 1238 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1239 1240 1241 % ------------------------------------------------------------------------------------------------------------- 1242 % Brunt-V\"{a}is\"{a}l\"{a} Frequency 1243 % ------------------------------------------------------------------------------------------------------------- 1244 \subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\np{nn\_eos} = 0, 1 or 2)} 1231 1245 \label{TRA_bn2} 1232 1246 1233 An accurate computation of the ocean stability (i.e. of $N$, the brunt-Vais\"{a}l\"{a} 1234 frequency) is of paramount importance as it is used in several ocean 1235 parameterisations (namely TKE, KPP, Richardson number dependent 1236 vertical diffusion, enhanced vertical diffusion, non-penetrative convection, 1237 iso-neutral diffusion). In particular, one must be aware that $N^2$ has to 1238 be computed with an \textit{in situ} reference. The expression for $N^2$ 1239 depends on the type of equation of state used (\np{nn\_eos} namelist parameter). 1240 1241 For \np{nn\_eos}=0 (\citet{JackMcD1995} equation of state), the \citet{McDougall1987} 1242 polynomial expression is used (with the pressure in decibar approximated by 1243 the depth in meters): 1247 An accurate computation of the ocean stability (i.e. of $N$, the brunt-V\"{a}is\"{a}l\"{a} 1248 frequency) is of paramount importance as determine the ocean stratification and 1249 is used in several ocean parameterisations (namely TKE, GLS, Richardson number dependent 1250 vertical diffusion, enhanced vertical diffusion, non-penetrative convection, tidal mixing 1251 parameterisation, iso-neutral diffusion). In particular, $N^2$ has to be computed at the local pressure 1252 (pressure in decibar being approximated by the depth in meters). The expression for $N^2$ 1253 is given by: 1244 1254 \begin{equation} \label{Eq_tra_bn2} 1245 N^2 = \frac{g}{e_{3w}} \; \beta \1246 \left( \alpha / \beta \ \delta_{k+1/2}[T] - \delta_{k+1/2}[S] \right)1247 \end{equation}1248 where $\alpha$ and $\beta$ are the thermal and haline expansion coefficients.1249 They are a function of $\overline{T}^{\,k+1/2},\widetilde{S}=\overline{S}^{\,k+1/2} - 35.$,1250 and $z_w$, with $T$ the \textit{potential} temperature and $\widetilde{S}$ a salinity anomaly.1251 Note that both $\alpha$ and $\beta$ depend on \textit{potential}1252 temperature and salinity which are averaged at $w$-points prior1253 to the computation instead of being computed at $T$-points and1254 then averaged to $w$-points.1255 1256 When a linear equation of state is used (\np{nn\_eos}=1 or 2,1257 \eqref{Eq_tra_bn2} reduces to:1258 \begin{equation} \label{Eq_tra_bn2_linear}1259 1255 N^2 = \frac{g}{e_{3w}} \left( \beta \;\delta_{k+1/2}[S] - \alpha \;\delta_{k+1/2}[T] \right) 1260 1256 \end{equation} 1261 where $\alpha$ and $\beta $ are the constant coefficients used to 1262 defined the linear equation of state \eqref{Eq_tra_eos_linear}. 1263 1264 % ------------------------------------------------------------------------------------------------------------- 1265 % Specific Heat 1266 % ------------------------------------------------------------------------------------------------------------- 1267 \subsection [Specific Heat (\textit{phycst})] 1268 {Specific Heat (\mdl{phycst})} 1269 \label{TRA_adv_ldf} 1270 1271 The specific heat of sea water, $C_p$, is a function of temperature, salinity 1272 and pressure \citep{UNESCO1983}. It is only used in the model to convert 1273 surface heat fluxes into surface temperature increase and so the pressure 1274 dependence is neglected. The dependence on $T$ and $S$ is weak. 1275 For example, with $S=35~psu$, $C_p$ increases from $3989$ to $4002$ 1276 when $T$ varies from -2~\degres C to 31~\degres C. Therefore, $C_p$ has 1277 been chosen as a constant: $C_p=4.10^3~J\,Kg^{-1}\,\degres K^{-1}$. 1278 Its value is set in \mdl{phycst} module. 1279 1257 where $(T,S) = (\Theta, S_A)$ for TEOS10, $= (\theta, S_p)$ for TEOS-80, or $=(T,S)$ for S-EOS, 1258 and, $\alpha$ and $\beta$ are the thermal and haline expansion coefficients. 1259 The coefficients are a polynomial function of temperature, salinity and depth which expression 1260 depends on the chosen EOS. They are computed through \textit{eos\_rab}, a \textsc{Fortran} 1261 function that can be found in \mdl{eosbn2}. 1280 1262 1281 1263 % ------------------------------------------------------------------------------------------------------------- … … 1298 1280 sea water ($i.e.$ referenced to the surface $p=0$), thus the pressure dependent 1299 1281 terms in \eqref{Eq_tra_eos_fzp} (last term) have been dropped. The freezing 1300 point is computed through \textit{ tfreez}, a \textsc{Fortran} function that can be found1282 point is computed through \textit{eos\_fzp}, a \textsc{Fortran} function that can be found 1301 1283 in \mdl{eosbn2}. 1302 1284 … … 1308 1290 \label{TRA_zpshde} 1309 1291 1310 \gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators, I've changed "derivative" to "difference" and "mean" to "average"} 1311 1312 With partial bottom cells (\np{ln\_zps}=true), in general, tracers in horizontally 1292 \gmcomment{STEVEN: to be consistent with earlier discussion of differencing and averaging operators, 1293 I've changed "derivative" to "difference" and "mean" to "average"} 1294 1295 With partial cells (\np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true), in general, tracers in horizontally 1313 1296 adjacent cells live at different depths. Horizontal gradients of tracers are needed 1314 1297 for horizontal diffusion (\mdl{traldf} module) and for the hydrostatic pressure 1315 1298 gradient (\mdl{dynhpg} module) to be active. 1316 1299 \gmcomment{STEVEN from gm : question: not sure of what -to be active- means} 1300 1317 1301 Before taking horizontal gradients between the tracers next to the bottom, a linear 1318 1302 interpolation in the vertical is used to approximate the deeper tracer as if it actually … … 1323 1307 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1324 1308 \begin{figure}[!p] \begin{center} 1325 \includegraphics[width=0.9\textwidth]{ ./TexFiles/Figures/Partial_step_scheme.pdf}1309 \includegraphics[width=0.9\textwidth]{Partial_step_scheme} 1326 1310 \caption{ \label{Fig_Partial_step_scheme} 1327 1311 Discretisation of the horizontal difference and average of tracers in the $z$-partial … … 1390 1374 \gmcomment{gm : this last remark has to be done} 1391 1375 %%% 1376 1377 If under ice shelf seas opened (\np{ln\_isfcav}=true), the partial cell properties 1378 at the top are computed in the same way as for the bottom. Some extra variables are, 1379 however, computed to reduce the flow generated at the top and bottom if $z*$ coordinates activated. 1380 The extra variables calculated and used by \S\ref{DYN_hpg_isf} are: 1381 1382 $\bullet$ $\overline{T}_k^{\,i+1/2}$ as described in \eqref{Eq_zps_hde} 1383 1384 $\bullet$ $\delta _{i+1/2} Z_{T_k} = \widetilde {Z}^{\,i}_{T_k}-Z^{\,i}_{T_k}$ to compute 1385 the pressure gradient correction term used by \eqref{Eq_dynhpg_sco} in \S\ref{DYN_hpg_isf}, 1386 with $\widetilde {Z}_{T_k}$ the depth of the point $\widetilde {T}_{k}$ in case of $z^*$ coordinates 1387 (this term = 0 in z-coordinates) 1388 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Chap_ZDF.tex
r5602 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 % ================================================================ 2 4 % Chapter Vertical Ocean Physics (ZDF) … … 33 35 points, respectively (see \S\ref{TRA_zdf} and \S\ref{DYN_zdf}). These 34 36 coefficients can be assumed to be either constant, or a function of the local 35 Richardson number, or computed from a turbulent closure model (either 36 TKE or KPP formulation). The computation of these coefficients is initialized 37 in the \mdl{zdfini} module and performed in the \mdl{zdfric}, \mdl{zdftke} or 38 \mdl{zdfkpp} modules. The trends due to the vertical momentum and tracer 39 diffusion, including the surface forcing, are computed and added to the 40 general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 37 Richardson number, or computed from a turbulent closure model (TKE, GLS or KPP formulation). 38 The computation of these coefficients is initialized in the \mdl{zdfini} module 39 and performed in the \mdl{zdfric}, \mdl{zdftke}, \mdl{zdfgls} or \mdl{zdfkpp} modules. 40 The trends due to the vertical momentum and tracer diffusion, including the surface forcing, 41 are computed and added to the general trend in the \mdl{dynzdf} and \mdl{trazdf} modules, respectively. 41 42 These trends can be computed using either a forward time stepping scheme 42 43 (namelist parameter \np{ln\_zdfexp}=true) or a backward time stepping … … 234 235 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 235 236 \begin{figure}[!t] \begin{center} 236 \includegraphics[width=1.00\textwidth]{ ./TexFiles/Figures/Fig_mixing_length.pdf}237 \includegraphics[width=1.00\textwidth]{Fig_mixing_length} 237 238 \caption{ \label{Fig_mixing_length} 238 239 Illustration of the mixing length computation. } … … 262 263 \end{equation} 263 264 264 At the ocean surface, a non zero length scale is set through the \np{rn\_ lmin0} namelist265 At the ocean surface, a non zero length scale is set through the \np{rn\_mxl0} namelist 265 266 parameter. Usually the surface scale is given by $l_o = \kappa \,z_o$ 266 267 where $\kappa = 0.4$ is von Karman's constant and $z_o$ the roughness 267 268 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 interior269 leads to a 0.04~m, the default value of \np{rn\_mxl0}. In the ocean interior 269 270 a minimum length scale is set to recover the molecular viscosity when $\bar{e}$ 270 271 reach its minimum value ($1.10^{-6}= C_k\, l_{min} \,\sqrt{\bar{e}_{min}}$ ). … … 295 296 As the surface boundary condition on TKE is prescribed through $\bar{e}_o = e_{bb} |\tau| / \rho_o$, 296 297 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 Stace t's value.298 to $\alpha_{CB} = 100$. Further setting \np{ln\_mxl0} to true applies \eqref{ZDF_Lsbc} 299 as surface boundary condition on length scale, with $\beta$ hard coded to the Stacey's value. 299 300 Note that a minimal threshold of \np{rn\_emin0}$=10^{-4}~m^2.s^{-2}$ (namelist parameters) 300 301 is applied on surface $\bar{e}$ value. … … 355 356 %--------------------------------------------------------------% 356 357 357 To be add here a description of "penetration of TKE" and the associated namelist parameters 358 \np{nn\_etau}, \np{rn\_efr} and \np{nn\_htau}. 358 Vertical mixing parameterizations commonly used in ocean general circulation models 359 tend to produce mixed-layer depths that are too shallow during summer months and windy conditions. 360 This bias is particularly acute over the Southern Ocean. 361 To overcome this systematic bias, an ad hoc parameterization is introduced into the TKE scheme \cite{Rodgers_2014}. 362 The parameterization is an empirical one, $i.e.$ not derived from theoretical considerations, 363 but rather is meant to account for observed processes that affect the density structure of 364 the ocean’s planetary boundary layer that are not explicitly captured by default in the TKE scheme 365 ($i.e.$ near-inertial oscillations and ocean swells and waves). 366 367 When using this parameterization ($i.e.$ when \np{nn\_etau}~=~1), the TKE input to the ocean ($S$) 368 imposed by the winds in the form of near-inertial oscillations, swell and waves is parameterized 369 by \eqref{ZDF_Esbc} the standard TKE surface boundary condition, plus a depth depend one given by: 370 \begin{equation} \label{ZDF_Ehtau} 371 S = (1-f_i) \; f_r \; e_s \; e^{-z / h_\tau} 372 \end{equation} 373 where 374 $z$ is the depth, 375 $e_s$ is TKE surface boundary condition, 376 $f_r$ is the fraction of the surface TKE that penetrate in the ocean, 377 $h_\tau$ is a vertical mixing length scale that controls exponential shape of the penetration, 378 and $f_i$ is the ice concentration (no penetration if $f_i=1$, that is if the ocean is entirely 379 covered by sea-ice). 380 The value of $f_r$, usually a few percents, is specified through \np{rn\_efr} namelist parameter. 381 The vertical mixing length scale, $h_\tau$, can be set as a 10~m uniform value (\np{nn\_etau}~=~0) 382 or a latitude dependent value (varying from 0.5~m at the Equator to a maximum value of 30~m 383 at high latitudes (\np{nn\_etau}~=~1). 384 385 Note that two other option existe, \np{nn\_etau}~=~2, or 3. They correspond to applying 386 \eqref{ZDF_Ehtau} only at the base of the mixed layer, or to using the high frequency part 387 of the stress to evaluate the fraction of TKE that penetrate the ocean. 388 Those two options are obsolescent features introduced for test purposes. 389 They will be removed in the next release. 390 391 359 392 360 393 % from Burchard et al OM 2008 : 361 % the most critical process not reproduced by statistical turbulence models is the activity of internal waves and their interaction with turbulence. After the Reynolds decomposition, internal waves are in principle included in the RANS equations, but later partially excluded by the hydrostatic assumption and the model resolution. Thus far, the representation of internal wave mixing in ocean models has been relatively crude (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 394 % the most critical process not reproduced by statistical turbulence models is the activity of 395 % internal waves and their interaction with turbulence. After the Reynolds decomposition, 396 % internal waves are in principle included in the RANS equations, but later partially 397 % excluded by the hydrostatic assumption and the model resolution. 398 % Thus far, the representation of internal wave mixing in ocean models has been relatively crude 399 % (e.g. Mellor, 1989; Large et al., 1994; Meier, 2001; Axell, 2002; St. Laurent and Garrett, 2002). 362 400 363 401 … … 371 409 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 372 410 \begin{figure}[!t] \begin{center} 373 \includegraphics[width=1.00\textwidth]{ ./TexFiles/Figures/Fig_ZDF_TKE_time_scheme.pdf}411 \includegraphics[width=1.00\textwidth]{Fig_ZDF_TKE_time_scheme} 374 412 \caption{ \label{Fig_TKE_time_scheme} 375 413 Illustration of the TKE time integration and its links to the momentum and tracer time integration. } … … 550 588 value near physical boundaries (logarithmic boundary layer law). $C_{\mu}$ and $C_{\mu'}$ 551 589 are calculated from stability function proposed by \citet{Galperin_al_JAS88}, or by \citet{Kantha_Clayson_1994} 552 or one of the two functions suggested by \citet{Canuto_2001} (\np{nn\_stab\_func} = 0, 1, 2 or 3, resp. }).590 or one of the two functions suggested by \citet{Canuto_2001} (\np{nn\_stab\_func} = 0, 1, 2 or 3, resp.). 553 591 The value of $C_{0\mu}$ depends of the choice of the stability function. 554 592 … … 586 624 Options are defined through the \ngn{namzdf\_kpp} namelist variables. 587 625 588 \colorbox{yellow}{Add a description of KPP here.} 626 Note that KPP is an obsolescent feature of the \NEMO system. 627 It will be removed in the next release (v3.7 and followings). 589 628 590 629 … … 621 660 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 622 661 \begin{figure}[!htb] \begin{center} 623 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_npc.pdf}662 \includegraphics[width=0.90\textwidth]{Fig_npc} 624 663 \caption{ \label{Fig_npc} 625 664 Example of an unstable density profile treated by the non penetrative … … 636 675 637 676 Options are defined through the \ngn{namzdf} namelist variables. 638 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc} =true.677 The non-penetrative convective adjustment is used when \np{ln\_zdfnpc}~=~\textit{true}. 639 678 It is applied at each \np{nn\_npc} time step and mixes downwards instantaneously 640 679 the statically unstable portion of the water column, but only until the density … … 644 683 (Fig. \ref{Fig_npc}): starting from the top of the ocean, the first instability is 645 684 found. Assume in the following that the instability is located between levels 646 $k$ and $k+1$. The potentialtemperature and salinity in the two levels are685 $k$ and $k+1$. The temperature and salinity in the two levels are 647 686 vertically mixed, conserving the heat and salt contents of the water column. 648 687 The new density is then computed by a linear approximation. If the new … … 664 703 \citep{Madec_al_JPO91, Madec_al_DAO91, Madec_Crepon_Bk91}. 665 704 666 Note that in the current implementation of this algorithm presents several 667 limitations. First, potential density referenced to the sea surface is used to 668 check whether the density profile is stable or not. This is a strong 669 simplification which leads to large errors for realistic ocean simulations. 670 Indeed, many water masses of the world ocean, especially Antarctic Bottom 671 Water, are unstable when represented in surface-referenced potential density. 672 The scheme will erroneously mix them up. Second, the mixing of potential 673 density is assumed to be linear. This assures the convergence of the algorithm 674 even when the equation of state is non-linear. Small static instabilities can thus 675 persist due to cabbeling: they will be treated at the next time step. 676 Third, temperature and salinity, and thus density, are mixed, but the 677 corresponding velocity fields remain unchanged. When using a Richardson 678 Number dependent eddy viscosity, the mixing of momentum is done through 679 the vertical diffusion: after a static adjustment, the Richardson Number is zero 680 and thus the eddy viscosity coefficient is at a maximum. When this convective 681 adjustment algorithm is used with constant vertical eddy viscosity, spurious 682 solutions can occur since the vertical momentum diffusion remains small even 683 after a static adjustment. In that case, we recommend the addition of momentum 684 mixing in a manner that mimics the mixing in temperature and salinity 685 \citep{Speich_PhD92, Speich_al_JPO96}. 705 The current implementation has been modified in order to deal with any non linear 706 equation of seawater (L. Brodeau, personnal communication). 707 Two main differences have been introduced compared to the original algorithm: 708 $(i)$ the stability is now checked using the Brunt-V\"{a}is\"{a}l\"{a} frequency 709 (not the the difference in potential density) ; 710 $(ii)$ when two levels are found unstable, their thermal and haline expansion coefficients 711 are vertically mixed in the same way their temperature and salinity has been mixed. 712 These two modifications allow the algorithm to perform properly and accurately 713 with TEOS10 or EOS-80 without having to recompute the expansion coefficients at each 714 mixing iteration. 686 715 687 716 % ------------------------------------------------------------------------------------------------------------- … … 689 718 % ------------------------------------------------------------------------------------------------------------- 690 719 \subsection [Enhanced Vertical Diffusion (\np{ln\_zdfevd})] 691 720 {Enhanced Vertical Diffusion (\np{ln\_zdfevd}=true)} 692 721 \label{ZDF_evd} 693 722 … … 787 816 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 788 817 \begin{figure}[!t] \begin{center} 789 \includegraphics[width=0.99\textwidth]{ ./TexFiles/Figures/Fig_zdfddm.pdf}818 \includegraphics[width=0.99\textwidth]{Fig_zdfddm} 790 819 \caption{ \label{Fig_zdfddm} 791 820 From \citet{Merryfield1999} : (a) Diapycnal diffusivities $A_f^{vT}$ … … 830 859 % Bottom Friction 831 860 % ================================================================ 832 \section [Bottom and top Friction (\textit{zdfbfr})] {BottomFriction (\mdl{zdfbfr} module)}861 \section [Bottom and Top Friction (\textit{zdfbfr})] {Bottom and Top Friction (\mdl{zdfbfr} module)} 833 862 \label{ZDF_bfr} 834 863 … … 838 867 839 868 Options to define the top and bottom friction are defined through the \ngn{nambfr} namelist variables. 840 The top friction is activated only if the ice shelf cavities are opened (\np{ln\_isfcav}~=~true). 841 As the friction processes at the top and bottom are the represented similarly, only the bottom friction is described in detail. 869 The bottom friction represents the friction generated by the bathymetry. 870 The top friction represents the friction generated by the ice shelf/ocean interface. 871 As the friction processes at the top and bottom are represented similarly, only the bottom friction is described in detail below.\\ 872 842 873 843 874 Both the surface momentum flux (wind stress) and the bottom momentum … … 912 943 $H = 4000$~m, the resulting friction coefficient is $r = 4\;10^{-4}$~m\;s$^{-1}$. 913 944 This is the default value used in \NEMO. It corresponds to a decay time scale 914 of 115~days. It can be changed by specifying \np{rn\_bfri c1} (namelist parameter).945 of 115~days. It can be changed by specifying \np{rn\_bfri1} (namelist parameter). 915 946 916 947 For the linear friction case the coefficients defined in the general … … 922 953 \end{split} 923 954 \end{equation} 924 When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri c1}.955 When \np{nn\_botfr}=1, the value of $r$ used is \np{rn\_bfri1}. 925 956 Setting \np{nn\_botfr}=0 is equivalent to setting $r=0$ and leads to a free-slip 926 957 bottom boundary condition. These values are assigned in \mdl{zdfbfr}. … … 929 960 in the \ifile{bfr\_coef} input NetCDF file. The mask values should vary from 0 to 1. 930 961 Locations with a non-zero mask value will have the friction coefficient increased 931 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri c1}.962 by $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri1}. 932 963 933 964 % ------------------------------------------------------------------------------------------------------------- … … 949 980 $e_b = 2.5\;10^{-3}$m$^2$\;s$^{-2}$, while the FRAM experiment \citep{Killworth1992} 950 981 uses $C_D = 1.4\;10^{-3}$ and $e_b =2.5\;\;10^{-3}$m$^2$\;s$^{-2}$. 951 The CME choices have been set as default values (\np{rn\_bfri c2} and \np{rn\_bfeb2}982 The CME choices have been set as default values (\np{rn\_bfri2} and \np{rn\_bfeb2} 952 983 namelist parameters). 953 984 … … 964 995 \end{equation} 965 996 966 The coefficients that control the strength of the non-linear bottom friction are 967 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 968 Note for applications which treat tides explicitly a low or even zero value of 969 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ 970 is possible via an externally defined 2D mask array (\np{ln\_bfr2d}=true). 971 See previous section for details. 997 The coefficients that control the strength of the non-linear bottom friction are 998 initialised as namelist parameters: $C_D$= \np{rn\_bfri2}, and $e_b$ =\np{rn\_bfeb2}. 999 Note for applications which treat tides explicitly a low or even zero value of 1000 \np{rn\_bfeb2} is recommended. From v3.2 onwards a local enhancement of $C_D$ is possible 1001 via an externally defined 2D mask array (\np{ln\_bfr2d}=true). This works in the same way 1002 as for the linear bottom friction case with non-zero masked locations increased by 1003 $mask\_value$*\np{rn\_bfrien}*\np{rn\_bfri2}. 1004 1005 % ------------------------------------------------------------------------------------------------------------- 1006 % Bottom Friction Log-layer 1007 % ------------------------------------------------------------------------------------------------------------- 1008 \subsection{Log-layer Bottom Friction enhancement (\np{nn\_botfr} = 2, \np{ln\_loglayer} = .true.)} 1009 \label{ZDF_bfr_loglayer} 1010 1011 In the non-linear bottom friction case, the drag coefficient, $C_D$, can be optionally 1012 enhanced using a "law of the wall" scaling. If \np{ln\_loglayer} = .true., $C_D$ is no 1013 longer constant but is related to the thickness of the last wet layer in each column by: 1014 1015 \begin{equation} 1016 C_D = \left ( {\kappa \over {\rm log}\left ( 0.5e_{3t}/rn\_bfrz0 \right ) } \right )^2 1017 \end{equation} 1018 1019 \noindent where $\kappa$ is the von-Karman constant and \np{rn\_bfrz0} is a roughness 1020 length provided via the namelist. 1021 1022 For stability, the drag coefficient is bounded such that it is kept greater or equal to 1023 the base \np{rn\_bfri2} value and it is not allowed to exceed the value of an additional 1024 namelist parameter: \np{rn\_bfri2\_max}, i.e.: 1025 1026 \begin{equation} 1027 rn\_bfri2 \leq C_D \leq rn\_bfri2\_max 1028 \end{equation} 1029 1030 \noindent Note also that a log-layer enhancement can also be applied to the top boundary 1031 friction if under ice-shelf cavities are in use (\np{ln\_isfcav}=.true.). In this case, the 1032 relevant namelist parameters are \np{rn\_tfrz0}, \np{rn\_tfri2} 1033 and \np{rn\_tfri2\_max}. 972 1034 973 1035 % ------------------------------------------------------------------------------------------------------------- … … 1083 1145 baroclinic and barotropic components which is appropriate when using either the 1084 1146 explicit or filtered surface pressure gradient algorithms (\key{dynspg\_exp} or 1085 {\key{dynspg\_flt}). Extra attention is required, however, when using1147 \key{dynspg\_flt}). Extra attention is required, however, when using 1086 1148 split-explicit time stepping (\key{dynspg\_ts}). In this case the free surface 1087 1149 equation is solved with a small time step \np{rn\_rdt}/\np{nn\_baro}, while the three … … 1198 1260 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1199 1261 \begin{figure}[!t] \begin{center} 1200 \includegraphics[width=0.90\textwidth]{ ./TexFiles/Figures/Fig_ZDF_M2_K1_tmx.pdf}1262 \includegraphics[width=0.90\textwidth]{Fig_ZDF_M2_K1_tmx} 1201 1263 \caption{ \label{Fig_ZDF_M2_K1_tmx} 1202 1264 (a) M2 and (b) K1 internal wave drag energy from \citet{Carrere_Lyard_GRL03} ($W/m^2$). } … … 1253 1315 1254 1316 % ================================================================ 1317 % Internal wave-driven mixing 1318 % ================================================================ 1319 \section{Internal wave-driven mixing (\key{zdftmx\_new})} 1320 \label{ZDF_tmx_new} 1321 1322 %--------------------------------------------namzdf_tmx_new------------------------------------------ 1323 \namdisplay{namzdf_tmx_new} 1324 %-------------------------------------------------------------------------------------------------------------- 1325 1326 The parameterization of mixing induced by breaking internal waves is a generalization 1327 of the approach originally proposed by \citet{St_Laurent_al_GRL02}. 1328 A three-dimensional field of internal wave energy dissipation $\epsilon(x,y,z)$ is first constructed, 1329 and the resulting diffusivity is obtained as 1330 \begin{equation} \label{Eq_Kwave} 1331 A^{vT}_{wave} = R_f \,\frac{ \epsilon }{ \rho \, N^2 } 1332 \end{equation} 1333 where $R_f$ is the mixing efficiency and $\epsilon$ is a specified three dimensional distribution 1334 of the energy available for mixing. If the \np{ln\_mevar} namelist parameter is set to false, 1335 the mixing efficiency is taken as constant and equal to 1/6 \citep{Osborn_JPO80}. 1336 In the opposite (recommended) case, $R_f$ is instead a function of the turbulence intensity parameter 1337 $Re_b = \frac{ \epsilon}{\nu \, N^2}$, with $\nu$ the molecular viscosity of seawater, 1338 following the model of \cite{Bouffard_Boegman_DAO2013} 1339 and the implementation of \cite{de_lavergne_JPO2016_efficiency}. 1340 Note that $A^{vT}_{wave}$ is bounded by $10^{-2}\,m^2/s$, a limit that is often reached when the mixing efficiency is constant. 1341 1342 In addition to the mixing efficiency, the ratio of salt to heat diffusivities can chosen to vary 1343 as a function of $Re_b$ by setting the \np{ln\_tsdiff} parameter to true, a recommended choice). 1344 This parameterization of differential mixing, due to \cite{Jackson_Rehmann_JPO2014}, 1345 is implemented as in \cite{de_lavergne_JPO2016_efficiency}. 1346 1347 The three-dimensional distribution of the energy available for mixing, $\epsilon(i,j,k)$, is constructed 1348 from three static maps of column-integrated internal wave energy dissipation, $E_{cri}(i,j)$, 1349 $E_{pyc}(i,j)$, and $E_{bot}(i,j)$, combined to three corresponding vertical structures 1350 (de Lavergne et al., in prep): 1351 \begin{align*} 1352 F_{cri}(i,j,k) &\propto e^{-h_{ab} / h_{cri} }\\ 1353 F_{pyc}(i,j,k) &\propto N^{n\_p}\\ 1354 F_{bot}(i,j,k) &\propto N^2 \, e^{- h_{wkb} / h_{bot} } 1355 \end{align*} 1356 In the above formula, $h_{ab}$ denotes the height above bottom, 1357 $h_{wkb}$ denotes the WKB-stretched height above bottom, defined by 1358 \begin{equation*} 1359 h_{wkb} = H \, \frac{ \int_{-H}^{z} N \, dz' } { \int_{-H}^{\eta} N \, dz' } \; , 1360 \end{equation*} 1361 The $n_p$ parameter (given by \np{nn\_zpyc} in \ngn{namzdf\_tmx\_new} namelist) controls the stratification-dependence of the pycnocline-intensified dissipation. 1362 It can take values of 1 (recommended) or 2. 1363 Finally, the vertical structures $F_{cri}$ and $F_{bot}$ require the specification of 1364 the decay scales $h_{cri}(i,j)$ and $h_{bot}(i,j)$, which are defined by two additional input maps. 1365 $h_{cri}$ is related to the large-scale topography of the ocean (etopo2) 1366 and $h_{bot}$ is a function of the energy flux $E_{bot}$, the characteristic horizontal scale of 1367 the abyssal hill topography \citep{Goff_JGR2010} and the latitude. 1368 1369 % ================================================================ 1370 1371 1372 1373 \end{document} -
branches/2015/dev_r5003_MERCATOR6_CRS/DOC/TexFiles/Chapters/Introduction.tex
r4661 r7260 1 \documentclass[NEMO_book]{subfiles} 2 \begin{document} 1 3 2 4 % ================================================================ … … 24 26 release 8.2, described in \citet{Madec1998}. This model has been used for a wide 25 27 range of applications, both regional or global, as a forced ocean model and as a 26 model coupled with the atmosphere. A complete list of references is found on the 27 \NEMO web site. 28 model coupled with the sea-ice and/or the atmosphere. 28 29 29 30 This manual is organised in as follows. Chapter~\ref{PE} presents the model basics, 30 31 $i.e.$ the equations and their assumptions, the vertical coordinates used, and the 31 32 subgrid scale physics. This part deals with the continuous equations of the model 32 (primitive equations, with potential temperature, salinity and an equation of state).33 (primitive equations, with temperature, salinity and an equation of seawater). 33 34 The equations are written in a curvilinear coordinate system, with a choice of vertical 34 35 coordinates ($z$ or $s$, with the rescaled height coordinate formulation \textit{z*}, or … … 79 80 space and time variable coefficient \citet{Treguier1997}. The model has vertical harmonic 80 81 viscosity and diffusion with a space and time variable coefficient, with options to compute 81 the coefficients with \citet{Blanke1993}, \citet{ Large_al_RG94}, \citet{Pacanowski_Philander_JPO81},82 the coefficients with \citet{Blanke1993}, \citet{Pacanowski_Philander_JPO81}, 82 83 or \citet{Umlauf_Burchard_JMS03} mixing schemes. 83 84 \vspace{1cm} 84 85 85 86 %%gm To be put somewhere else .... 87 86 88 \noindent CPP keys and namelists are used for inputs to the code. \newline 87 89 … … 112 114 \vspace{1cm} 113 115 116 %%gm end 114 117 115 118 Model outputs management and specific online diagnostics are described in chapters~\ref{DIA}. … … 227 230 \item a deep re-writting and simplification of the off-line tracer component (OFF\_SRC) ; 228 231 \item the merge of passive and active advection and diffusion modules ; 229 \item 232 \item Use of the Flexible Configuration Manager (FCM) to build configurations, generate the Makefile and produce the executable ; 230 233 \item Linear-tangent and Adjoint component (TAM) added, phased with v3.0 231 234 \end{enumerate} … … 249 252 250 253 254 \vspace{1cm} 255 $\bullet$ The main modifications from NEMO/OPA v3.4 and v3.6 are :\\ 256 \begin{enumerate} 257 \item I/O management: NEMO in now interfaced with XIOS, a Input/Output server having a versatile xml user interface, and 258 allowing I/O to be performed on dedicated processors thus improving scalability and performance on massively parallel platforms. 259 \item ICB module \citep{Marsh_GMD2015}: icebergs as lagrangian floats ; 260 \item SAS: Stand Alone Surface module allowing testing of forcing set with bulk formulae, to run sea-ice models without ocean, to run ICB icebergs module alone, and to test AGRIF with sea-ice 261 \item ISF : Under ice-selves cavities (parametrisation and/or explicit representation) 262 \item Coupled interface for next IPCC requirements (multi category sea-ice, calving and iceberg module) 263 \item Ocean and ice allowed to be explicitly coupled through OASIS, using StandAlone Surface module) 264 \item On line coarsening of ocean I/O 265 \item Major evolution of LIM3 sea-ice model \citep{Rousset_GMD2015} 266 \item Open boundaries: completion of BDY/OBC merge : BDY is now the only Open boundary module available 267 \item re-visit of the specification of heat/salt(tracers)/mass fluxes ; 268 \item levitating or fully embedded sea-ice (for LIM and CICE) ; 269 \item a new parameterization of mixing induced by breaking internal waves (de Lavergne et al. in prep.) 270 And also: 271 \item update of AGRIF package and AGRIF compatibility with LIM2 sea-ice model ; 272 \item A new vertical sigma coordinate stretching function \citep{Siddorn_Furner_OM12} ; 273 \item Smagorinsky eddy coefficients: the \cite{Griffies_Hallberg_MWR00} Smagorinsky type diffusivity/viscosity for lateral mixing has been introduced ; 274 \item Standard Fox Kemper parametrisation 275 \item Analytical tropical cyclones taken in account using track and magnitude observations (Vincent et al. JGR 2012a,b) ; 276 \item OBS: observation operators improved and now available in Standalone mode ; 277 \item Log layer option for bottom friction 278 \item Faster split-explicit time stepping ; 279 \item Z-tilde ALE coordinates \citep{Leclair_Madec_OM11} ; 280 \item implicit bottom friction ; 281 \item Runoff improved and SBC with BGC 282 \item MPP assessment and optimisation 283 \item First steps of wave coupling 284 285 Features becoming obsolete: LIM2 (replaced by LIM3 monocategory) ; IOIPSL (replaced by XIOS) ; 286 287 Features that has been removed : LOBSTER (now included in PISCES) ; OBC, replaced by BDY ; 288 289 290 291 \end{enumerate} 292 293 294 \end{document}
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