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branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_DOM.tex
r2349 r2376 1 2 1 % ================================================================ 3 2 % Chapter 2 Ñ Space and Time Domain (DOM) … … 40 39 41 40 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 42 \begin{figure}[!tb] \label{Fig_cell}\begin{center}41 \begin{figure}[!tb] \begin{center} 43 42 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_cell.pdf} 44 \caption{Arrangement of variables. $t$ indicates scalar points where temperature, 43 \caption{ \label{Fig_cell} 44 Arrangement of variables. $t$ indicates scalar points where temperature, 45 45 salinity, density, pressure and horizontal divergence are defined. ($u$,$v$,$w$) 46 46 indicates vector points, and $f$ indicates vorticity points where both relative and … … 80 80 as the sum of the relevant scale factors (see \eqref{DOM_bar}) in the next section). 81 81 82 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 82 83 \begin{table}[!tb] \label{Tab_cell} 83 84 \begin{center} \begin{tabular}{|p{46pt}|p{56pt}|p{56pt}|p{56pt}|} … … 92 93 fw & $i+1/2$ & $j+1/2$ & $k+1/2$ \\ \hline 93 94 \end{tabular} 94 \caption{Location of grid-points as a function of integer or integer and a half value 95 of the column, line or level. This indexing is only used for the writing of the semi- 96 discrete equation. In the code, the indexing uses integer values only and has a 97 reverse direction in the vertical (see \S\ref{DOM_Num_Index})} 95 \caption{ \label{Tab_cell} 96 Location of grid-points as a function of integer or integer and a half value of the column, 97 line or level. This indexing is only used for the writing of the semi-discrete equation. 98 In the code, the indexing uses integer values only and has a reverse direction 99 in the vertical (see \S\ref{DOM_Num_Index})} 98 100 \end{center} 99 101 \end{table} 102 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 100 103 101 104 % ------------------------------------------------------------------------------------------------------------- … … 206 209 207 210 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 208 \begin{figure}[!tb] \label{Fig_index_hor}\begin{center}211 \begin{figure}[!tb] \begin{center} 209 212 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_index_hor.pdf} 210 \caption{ Horizontal integer indexing used in the \textsc{Fortran} code. The dashed211 area indicates the cell in which variables contained in arrays have the same212 $i$- and $j$-indices}213 \caption{ \label{Fig_index_hor} 214 Horizontal integer indexing used in the \textsc{Fortran} code. The dashed area indicates 215 the cell in which variables contained in arrays have the same $i$- and $j$-indices} 213 216 \end{center} \end{figure} 214 217 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 256 259 257 260 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 258 \begin{figure}[!pt] \label{Fig_index_vert}\begin{center}261 \begin{figure}[!pt] \begin{center} 259 262 \includegraphics[width=.90\textwidth]{./TexFiles/Figures/Fig_index_vert.pdf} 260 \caption{Vertical integer indexing used in the \textsc{Fortran } code. Note that 263 \caption{ \label{Fig_index_vert} 264 Vertical integer indexing used in the \textsc{Fortran } code. Note that 261 265 the $k$-axis is orientated downward. The dashed area indicates the cell in 262 266 which variables contained in arrays have the same $k$-index.} … … 364 368 Fig.~\ref{Fig_zgr_e3}. 365 369 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 366 \begin{figure}[!t] \label{Fig_zgr_e3}\begin{center}370 \begin{figure}[!t] \begin{center} 367 371 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_zgr_e3.pdf} 368 \caption{Comparison of (a) traditional definitions of grid-point position and grid-size 369 in the vertical, and (b) analytically derived grid-point position and scale factors. For 370 both grids here, the same $w$-point depth has been chosen but in (a) the 372 \caption{ \label{Fig_zgr_e3} 373 Comparison of (a) traditional definitions of grid-point position and grid-size in the vertical, 374 and (b) analytically derived grid-point position and scale factors. 375 For both grids here, the same $w$-point depth has been chosen but in (a) the 371 376 $t$-points are set half way between $w$-points while in (b) they are defined from 372 377 an analytical function: $z(k)=5\,(i-1/2)^3 - 45\,(i-1/2)^2 + 140\,(i-1/2) - 150$. … … 471 476 472 477 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 473 \begin{figure}[!tb] \label{Fig_z_zps_s_sps}\begin{center}478 \begin{figure}[!tb] \begin{center} 474 479 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_z_zps_s_sps.pdf} 475 \caption{The ocean bottom as seen by the model: 480 \caption{ \label{Fig_z_zps_s_sps} 481 The ocean bottom as seen by the model: 476 482 (a) $z$-coordinate with full step, 477 483 (b) $z$-coordinate with partial step, … … 575 581 576 582 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 577 \begin{figure}[!tb] \label{Fig_zgr}\begin{center}583 \begin{figure}[!tb] \begin{center} 578 584 \includegraphics[width=0.90\textwidth]{./TexFiles/Figures/Fig_zgr.pdf} 579 \caption{Default vertical mesh for ORCA2: 30 ocean levels (L30). Vertical level 580 functions for (a) T-point depth and (b) the associated scale factor as computed 585 \caption{ \label{Fig_zgr} 586 Default vertical mesh for ORCA2: 30 ocean levels (L30). Vertical level functions for 587 (a) T-point depth and (b) the associated scale factor as computed 581 588 from \eqref{DOM_zgr_ana} using \eqref{DOM_zgr_coef} in $z$-coordinate.} 582 589 \end{center} \end{figure} … … 651 658 652 659 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 653 \begin{table} \label{Tab_orca_zgr} 654 \begin{center} \begin{tabular}{c||r|r|r|r} 660 \begin{table} \begin{center} \begin{tabular}{c||r|r|r|r} 655 661 \hline 656 662 \textbf{LEVEL}& \textbf{gdept}& \textbf{gdepw}& \textbf{e3t }& \textbf{e3w } \\ \hline … … 687 693 31 & \textbf{5250.23}& 5000.00 & \textbf{500.56} & 500.33 \\ \hline 688 694 \end{tabular} \end{center} 689 \caption{ Default vertical mesh in $z$-coordinate for 30 layers ORCA2 configuration690 as computed from \eqref{DOM_zgr_ana} using the coefficients given in691 \eqref{DOM_zgr_coef}}695 \caption{ \label{Tab_orca_zgr} 696 Default vertical mesh in $z$-coordinate for 30 layers ORCA2 configuration as computed 697 from \eqref{DOM_zgr_ana} using the coefficients given in \eqref{DOM_zgr_coef}} 692 698 \end{table} 693 699 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 766 772 767 773 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 768 \begin{figure}[!tb] \label{Fig_sco_function}\begin{center}774 \begin{figure}[!tb] \begin{center} 769 775 \includegraphics[width=1.0\textwidth]{./TexFiles/Figures/Fig_sco_function.pdf} 770 \caption{Examples of the stretching function applied to a sea mont; from left to right: 776 \caption{ \label{Fig_sco_function} 777 Examples of the stretching function applied to a sea mont; from left to right: 771 778 surface, surface and bottom, and bottom intensified resolutions} 772 779 \end{center} \end{figure}
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