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branches/2017/dev_merge_2017/DOC/TexFiles/Chapters/Chap_TRA.tex
r9350 r9363 64 64 % ================================================================ 65 65 \section [Tracer Advection (\textit{traadv})] 66 {Tracer Advection (\ mdl{traadv})}66 {Tracer Advection (\protect\mdl{traadv})} 67 67 \label{TRA_adv} 68 68 %------------------------------------------namtra_adv----------------------------------------------------- … … 93 93 \begin{figure}[!t] \begin{center} 94 94 \includegraphics[width=0.9\textwidth]{Fig_adv_scheme} 95 \caption{ \ label{Fig_adv_scheme}95 \caption{ \protect\label{Fig_adv_scheme} 96 96 Schematic representation of some ways used to evaluate the tracer value 97 97 at $u$-point and the amount of tracer exchanged between two neighbouring grid … … 174 174 % 2nd and 4th order centred schemes 175 175 % ------------------------------------------------------------------------------------------------------------- 176 \subsection [Centred schemes (CEN) (\ np{ln\_traadv\_cen})]177 {Centred schemes (CEN) (\ np{ln\_traadv\_cen}=true)}176 \subsection [Centred schemes (CEN) (\protect\np{ln\_traadv\_cen})] 177 {Centred schemes (CEN) (\protect\np{ln\_traadv\_cen}=true)} 178 178 \label{TRA_adv_cen} 179 179 … … 246 246 % FCT scheme 247 247 % ------------------------------------------------------------------------------------------------------------- 248 \subsection [Flux Corrected Transport schemes (FCT) (\ np{ln\_traadv\_fct})]249 {Flux Corrected Transport schemes (FCT) (\ np{ln\_traadv\_fct}=true)}248 \subsection [Flux Corrected Transport schemes (FCT) (\protect\np{ln\_traadv\_fct})] 249 {Flux Corrected Transport schemes (FCT) (\protect\np{ln\_traadv\_fct}=true)} 250 250 \label{TRA_adv_tvd} 251 251 … … 293 293 % MUSCL scheme 294 294 % ------------------------------------------------------------------------------------------------------------- 295 \subsection[MUSCL scheme (\ np{ln\_traadv\_mus})]296 {Monotone Upstream Scheme for Conservative Laws (MUSCL) (\ np{ln\_traadv\_mus}=T)}295 \subsection[MUSCL scheme (\protect\np{ln\_traadv\_mus})] 296 {Monotone Upstream Scheme for Conservative Laws (MUSCL) (\protect\np{ln\_traadv\_mus}=T)} 297 297 \label{TRA_adv_mus} 298 298 … … 326 326 % UBS scheme 327 327 % ------------------------------------------------------------------------------------------------------------- 328 \subsection [Upstream-Biased Scheme (UBS) (\ np{ln\_traadv\_ubs})]329 {Upstream-Biased Scheme (UBS) (\ np{ln\_traadv\_ubs}=true)}328 \subsection [Upstream-Biased Scheme (UBS) (\protect\np{ln\_traadv\_ubs})] 329 {Upstream-Biased Scheme (UBS) (\protect\np{ln\_traadv\_ubs}=true)} 330 330 \label{TRA_adv_ubs} 331 331 … … 401 401 % QCK scheme 402 402 % ------------------------------------------------------------------------------------------------------------- 403 \subsection [QUICKEST scheme (QCK) (\ np{ln\_traadv\_qck})]404 {QUICKEST scheme (QCK) (\ np{ln\_traadv\_qck}=true)}403 \subsection [QUICKEST scheme (QCK) (\protect\np{ln\_traadv\_qck})] 404 {QUICKEST scheme (QCK) (\protect\np{ln\_traadv\_qck}=true)} 405 405 \label{TRA_adv_qck} 406 406 … … 429 429 % ================================================================ 430 430 \section [Tracer Lateral Diffusion (\textit{traldf})] 431 {Tracer Lateral Diffusion (\ mdl{traldf})}431 {Tracer Lateral Diffusion (\protect\mdl{traldf})} 432 432 \label{TRA_ldf} 433 433 %-----------------------------------------nam_traldf------------------------------------------------------ … … 455 455 % Type of operator 456 456 % ------------------------------------------------------------------------------------------------------------- 457 \subsection [Type of operator (\ np{ln\_traldf\{\_NONE, \_lap, \_blp\}})]458 {Type of operator (\ np{ln\_traldf\_NONE}, \np{ln\_traldf\_lap}, or\np{ln\_traldf\_blp} = true) }457 \subsection [Type of operator (\protect\np{ln\_traldf\{\_NONE, \_lap, \_blp\}})] 458 {Type of operator (\protect\np{ln\_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp} = true) } 459 459 \label{TRA_ldf_op} 460 460 … … 488 488 % Direction of action 489 489 % ------------------------------------------------------------------------------------------------------------- 490 \subsection [Direction of action (\ np{ln\_traldf\{\_lev, \_hor, \_iso, \_triad\}})]491 {Direction of action (\ np{ln\_traldf\_lev}, \textit{...\_hor}, \textit{...\_iso}, or \textit{...\_triad} = true) }490 \subsection [Direction of action (\protect\np{ln\_traldf\{\_lev, \_hor, \_iso, \_triad\}})] 491 {Direction of action (\protect\np{ln\_traldf\_lev}, \textit{...\_hor}, \textit{...\_iso}, or \textit{...\_triad} = true) } 492 492 \label{TRA_ldf_dir} 493 493 … … 515 515 % iso-level operator 516 516 % ------------------------------------------------------------------------------------------------------------- 517 \subsection [Iso-level (bi-)laplacian operator ( \ np{ln\_traldf\_iso})]518 {Iso-level (bi-)laplacian operator ( \ np{ln\_traldf\_iso}) }517 \subsection [Iso-level (bi-)laplacian operator ( \protect\np{ln\_traldf\_iso})] 518 {Iso-level (bi-)laplacian operator ( \protect\np{ln\_traldf\_iso}) } 519 519 \label{TRA_ldf_lev} 520 520 … … 555 555 %&& Standard rotated (bi-)laplacian operator 556 556 %&& ---------------------------------------------- 557 \subsubsection [Standard rotated (bi-)laplacian operator (\ mdl{traldf\_iso})]558 {Standard rotated (bi-)laplacian operator (\ mdl{traldf\_iso})}557 \subsubsection [Standard rotated (bi-)laplacian operator (\protect\mdl{traldf\_iso})] 558 {Standard rotated (bi-)laplacian operator (\protect\mdl{traldf\_iso})} 559 559 \label{TRA_ldf_iso} 560 560 The general form of the second order lateral tracer subgrid scale physics … … 609 609 %&& Triad rotated (bi-)laplacian operator 610 610 %&& ------------------------------------------- 611 \subsubsection [Triad rotated (bi-)laplacian operator (\ np{ln\_traldf\_triad})]612 {Triad rotated (bi-)laplacian operator (\ np{ln\_traldf\_triad})}611 \subsubsection [Triad rotated (bi-)laplacian operator (\protect\np{ln\_traldf\_triad})] 612 {Triad rotated (bi-)laplacian operator (\protect\np{ln\_traldf\_triad})} 613 613 \label{TRA_ldf_triad} 614 614 … … 649 649 % ================================================================ 650 650 \section [Tracer Vertical Diffusion (\textit{trazdf})] 651 {Tracer Vertical Diffusion (\ mdl{trazdf})}651 {Tracer Vertical Diffusion (\protect\mdl{trazdf})} 652 652 \label{TRA_zdf} 653 653 %--------------------------------------------namzdf--------------------------------------------------------- … … 703 703 % ------------------------------------------------------------------------------------------------------------- 704 704 \subsection [Surface boundary condition (\textit{trasbc})] 705 {Surface boundary condition (\ mdl{trasbc})}705 {Surface boundary condition (\protect\mdl{trasbc})} 706 706 \label{TRA_sbc} 707 707 … … 774 774 % ------------------------------------------------------------------------------------------------------------- 775 775 \subsection [Solar Radiation Penetration (\textit{traqsr})] 776 {Solar Radiation Penetration (\ mdl{traqsr})}776 {Solar Radiation Penetration (\protect\mdl{traqsr})} 777 777 \label{TRA_qsr} 778 778 %--------------------------------------------namqsr-------------------------------------------------------- … … 872 872 \begin{figure}[!t] \begin{center} 873 873 \includegraphics[width=1.0\textwidth]{Fig_TRA_Irradiance} 874 \caption{ \ label{Fig_traqsr_irradiance}874 \caption{ \protect\label{Fig_traqsr_irradiance} 875 875 Penetration profile of the downward solar irradiance calculated by four models. 876 876 Two waveband chlorophyll-independent formulation (blue), a chlorophyll-dependent … … 885 885 % ------------------------------------------------------------------------------------------------------------- 886 886 \subsection [Bottom Boundary Condition (\textit{trabbc})] 887 {Bottom Boundary Condition (\ mdl{trabbc})}887 {Bottom Boundary Condition (\protect\mdl{trabbc})} 888 888 \label{TRA_bbc} 889 889 %--------------------------------------------nambbc-------------------------------------------------------- … … 893 893 \begin{figure}[!t] \begin{center} 894 894 \includegraphics[width=1.0\textwidth]{Fig_TRA_geoth} 895 \caption{ \ label{Fig_geothermal}895 \caption{ \protect\label{Fig_geothermal} 896 896 Geothermal Heat flux (in $mW.m^{-2}$) used by \cite{Emile-Geay_Madec_OS09}. 897 897 It is inferred from the age of the sea floor and the formulae of \citet{Stein_Stein_Nat92}.} … … 923 923 % Bottom Boundary Layer 924 924 % ================================================================ 925 \section [Bottom Boundary Layer (\ mdl{trabbl} -\key{trabbl})]926 {Bottom Boundary Layer (\ mdl{trabbl} -\key{trabbl})}925 \section [Bottom Boundary Layer (\protect\mdl{trabbl} - \protect\key{trabbl})] 926 {Bottom Boundary Layer (\protect\mdl{trabbl} - \protect\key{trabbl})} 927 927 \label{TRA_bbl} 928 928 %--------------------------------------------nambbl--------------------------------------------------------- … … 959 959 % Diffusive BBL 960 960 % ------------------------------------------------------------------------------------------------------------- 961 \subsection{Diffusive Bottom Boundary layer (\ np{nn\_bbl\_ldf}=1)}961 \subsection{Diffusive Bottom Boundary layer (\protect\np{nn\_bbl\_ldf}=1)} 962 962 \label{TRA_bbl_diff} 963 963 … … 994 994 % Advective BBL 995 995 % ------------------------------------------------------------------------------------------------------------- 996 \subsection {Advective Bottom Boundary Layer (\ np{nn\_bbl\_adv}= 1 or 2)}996 \subsection {Advective Bottom Boundary Layer (\protect\np{nn\_bbl\_adv}= 1 or 2)} 997 997 \label{TRA_bbl_adv} 998 998 … … 1003 1003 \begin{figure}[!t] \begin{center} 1004 1004 \includegraphics[width=0.7\textwidth]{Fig_BBL_adv} 1005 \caption{ \ label{Fig_bbl}1005 \caption{ \protect\label{Fig_bbl} 1006 1006 Advective/diffusive Bottom Boundary Layer. The BBL parameterisation is 1007 1007 activated when $\rho^i_{kup}$ is larger than $\rho^{i+1}_{kdnw}$. … … 1084 1084 % ================================================================ 1085 1085 \section [Tracer damping (\textit{tradmp})] 1086 {Tracer damping (\ mdl{tradmp})}1086 {Tracer damping (\protect\mdl{tradmp})} 1087 1087 \label{TRA_dmp} 1088 1088 %--------------------------------------------namtra_dmp------------------------------------------------- … … 1169 1169 % ================================================================ 1170 1170 \section [Tracer time evolution (\textit{tranxt})] 1171 {Tracer time evolution (\ mdl{tranxt})}1171 {Tracer time evolution (\protect\mdl{tranxt})} 1172 1172 \label{TRA_nxt} 1173 1173 %--------------------------------------------namdom----------------------------------------------------- … … 1208 1208 % ================================================================ 1209 1209 \section [Equation of State (\textit{eosbn2}) ] 1210 {Equation of State (\ mdl{eosbn2}) }1210 {Equation of State (\protect\mdl{eosbn2}) } 1211 1211 \label{TRA_eosbn2} 1212 1212 %--------------------------------------------nameos----------------------------------------------------- … … 1217 1217 % Equation of State 1218 1218 % ------------------------------------------------------------------------------------------------------------- 1219 \subsection{Equation Of Seawater (\ np{nn\_eos} = -1, 0, or 1)}1219 \subsection{Equation Of Seawater (\protect\np{nn\_eos} = -1, 0, or 1)} 1220 1220 \label{TRA_eos} 1221 1221 … … 1323 1323 $\mu_2$ & \np{rn\_mu2} & 1.1090 $10^{-5}$ & thermobaric coeff. in S \\ \hline 1324 1324 \end{tabular} 1325 \caption{ \ label{Tab_SEOS}1325 \caption{ \protect\label{Tab_SEOS} 1326 1326 Standard value of S-EOS coefficients. } 1327 1327 \end{center} … … 1333 1333 % Brunt-V\"{a}is\"{a}l\"{a} Frequency 1334 1334 % ------------------------------------------------------------------------------------------------------------- 1335 \subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\ np{nn\_eos} = 0, 1 or 2)}1335 \subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\protect\np{nn\_eos} = 0, 1 or 2)} 1336 1336 \label{TRA_bn2} 1337 1337 … … 1389 1389 % ================================================================ 1390 1390 \section [Horizontal Derivative in \textit{zps}-coordinate (\textit{zpshde})] 1391 {Horizontal Derivative in \textit{zps}-coordinate (\ mdl{zpshde})}1391 {Horizontal Derivative in \textit{zps}-coordinate (\protect\mdl{zpshde})} 1392 1392 \label{TRA_zpshde} 1393 1393 … … 1411 1411 \begin{figure}[!p] \begin{center} 1412 1412 \includegraphics[width=0.9\textwidth]{Partial_step_scheme} 1413 \caption{ \ label{Fig_Partial_step_scheme}1413 \caption{ \protect\label{Fig_Partial_step_scheme} 1414 1414 Discretisation of the horizontal difference and average of tracers in the $z$-partial 1415 step coordinate (\ np{ln\_zps}=true) in the case $( e3w_k^{i+1} - e3w_k^i )>0$.1415 step coordinate (\protect\np{ln\_zps}=true) in the case $( e3w_k^{i+1} - e3w_k^i )>0$. 1416 1416 A linear interpolation is used to estimate $\widetilde{T}_k^{i+1}$, the tracer value 1417 1417 at the depth of the shallower tracer point of the two adjacent bottom $T$-points.
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