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NEMO/branches/2019/ENHANCE-02_ISF_nemo/doc/latex/NEMO/subfiles/chap_LBC.tex
r11179 r12143 2 2 3 3 \begin{document} 4 % ================================================================ 5 % Chapter — Lateral Boundary Condition (LBC) 6 % ================================================================ 4 7 5 \chapter{Lateral Boundary Condition (LBC)} 8 6 \label{chap:LBC} 9 7 10 \minitoc 11 12 \newpage 13 14 %gm% add here introduction to this chapter 15 16 % ================================================================ 17 % Boundary Condition at the Coast 18 % ================================================================ 19 \section[Boundary condition at the coast (\texttt{rn\_shlat})] 20 {Boundary condition at the coast (\protect\np{rn\_shlat})} 8 \thispagestyle{plain} 9 10 \chaptertoc 11 12 \paragraph{Changes record} ~\\ 13 14 {\footnotesize 15 \begin{tabularx}{\textwidth}{l||X|X} 16 Release & Author(s) & Modifications \\ 17 \hline 18 {\em 4.0} & {\em ...} & {\em ...} \\ 19 {\em 3.6} & {\em ...} & {\em ...} \\ 20 {\em 3.4} & {\em ...} & {\em ...} \\ 21 {\em <=3.4} & {\em ...} & {\em ...} 22 \end{tabularx} 23 } 24 25 \clearpage 26 27 \cmtgm{Add here introduction to this chapter} 28 29 %% ================================================================================================= 30 \section[Boundary condition at the coast (\forcode{rn_shlat})]{Boundary condition at the coast (\protect\np{rn_shlat}{rn\_shlat})} 21 31 \label{sec:LBC_coast} 22 %--------------------------------------------nam_lbc------------------------------------------------------- 23 24 \nlst{namlbc} 25 %-------------------------------------------------------------------------------------------------------------- 26 27 %The lateral ocean boundary conditions contiguous to coastlines are Neumann conditions for heat and salt (no flux across boundaries) and Dirichlet conditions for momentum (ranging from free-slip to "strong" no-slip). They are handled automatically by the mask system (see \autoref{subsec:DOM_msk}). 28 29 %OPA allows land and topography grid points in the computational domain due to the presence of continents or islands, and includes the use of a full or partial step representation of bottom topography. The computation is performed over the whole domain, \ie we do not try to restrict the computation to ocean-only points. This choice has two motivations. Firstly, working on ocean only grid points overloads the code and harms the code readability. Secondly, and more importantly, it drastically reduces the vector portion of the computation, leading to a dramatic increase of CPU time requirement on vector computers. The current section describes how the masking affects the computation of the various terms of the equations with respect to the boundary condition at solid walls. The process of defining which areas are to be masked is described in \autoref{subsec:DOM_msk}. 30 31 Options are defined through the \ngn{namlbc} namelist variables. 32 33 \begin{listing} 34 \nlst{namlbc} 35 \caption{\forcode{&namlbc}} 36 \label{lst:namlbc} 37 \end{listing} 38 39 %The lateral ocean boundary conditions contiguous to coastlines are Neumann conditions for heat and salt 40 %(no flux across boundaries) and Dirichlet conditions for momentum (ranging from free-slip to "strong" no-slip). 41 %They are handled automatically by the mask system (see \autoref{subsec:DOM_msk}). 42 43 %OPA allows land and topography grid points in the computational domain due to the presence of continents or islands, 44 %and includes the use of a full or partial step representation of bottom topography. 45 %The computation is performed over the whole domain, \ie\ we do not try to restrict the computation to ocean-only points. 46 %This choice has two motivations. 47 %Firstly, working on ocean only grid points overloads the code and harms the code readability. 48 %Secondly, and more importantly, it drastically reduces the vector portion of the computation, 49 %leading to a dramatic increase of CPU time requirement on vector computers. 50 %The current section describes how the masking affects the computation of the various terms of the equations 51 %with respect to the boundary condition at solid walls. 52 %The process of defining which areas are to be masked is described in \autoref{subsec:DOM_msk}. 53 54 Options are defined through the \nam{lbc}{lbc} namelist variables. 32 55 The discrete representation of a domain with complex boundaries (coastlines and bottom topography) leads to 33 56 arrays that include large portions where a computation is not required as the model variables remain at zero. … … 41 64 Since most of the boundary conditions consist of a zero flux across the solid boundaries, 42 65 they can be simply applied by multiplying variables by the correct mask arrays, 43 \ie the mask array of the grid point where the flux is evaluated.66 \ie\ the mask array of the grid point where the flux is evaluated. 44 67 For example, the heat flux in the \textbf{i}-direction is evaluated at $u$-points. 45 68 Evaluating this quantity as, 46 69 47 70 \[ 48 % \label{eq: lbc_aaaa}71 % \label{eq:LBC_aaaa} 49 72 \frac{A^{lT} }{e_1 }\frac{\partial T}{\partial i}\equiv \frac{A_u^{lT} 50 73 }{e_{1u} } \; \delta_{i+1 / 2} \left[ T \right]\;\;mask_u … … 52 75 (where mask$_{u}$ is the mask array at a $u$-point) ensures that the heat flux is zero inside land and 53 76 at the boundaries, since mask$_{u}$ is zero at solid boundaries which in this case are defined at $u$-points 54 (normal velocity $u$ remains zero at the coast) (\autoref{fig:LBC_uv}). 55 56 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 77 (normal velocity $u$ remains zero at the coast) (\autoref{fig:LBC_uv}). 78 57 79 \begin{figure}[!t] 58 \begin{center} 59 \includegraphics[width=\textwidth]{Fig_LBC_uv} 60 \caption{ 61 \protect\label{fig:LBC_uv} 62 Lateral boundary (thick line) at T-level. 63 The velocity normal to the boundary is set to zero. 64 } 65 \end{center} 80 \centering 81 \includegraphics[width=0.66\textwidth]{LBC_uv} 82 \caption[Lateral boundary at $T$-level]{ 83 Lateral boundary (thick line) at T-level. 84 The velocity normal to the boundary is set to zero.} 85 \label{fig:LBC_uv} 66 86 \end{figure} 67 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>68 87 69 88 For momentum the situation is a bit more complex as two boundary conditions must be provided along the coast … … 79 98 and is required in order to compute the vorticity at the coast. 80 99 Four different types of lateral boundary condition are available, 81 controlled by the value of the \np{rn \_shlat} namelist parameter100 controlled by the value of the \np{rn_shlat}{rn\_shlat} namelist parameter 82 101 (The value of the mask$_{f}$ array along the coastline is set equal to this parameter). 83 102 These are: 84 103 85 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>86 104 \begin{figure}[!p] 87 \begin{center} 88 \includegraphics[width=\textwidth]{Fig_LBC_shlat} 89 \caption{ 90 \protect\label{fig:LBC_shlat} 91 lateral boundary condition 92 (a) free-slip ($rn\_shlat=0$); 93 (b) no-slip ($rn\_shlat=2$); 94 (c) "partial" free-slip ($0<rn\_shlat<2$) and 95 (d) "strong" no-slip ($2<rn\_shlat$). 96 Implied "ghost" velocity inside land area is display in grey. 97 } 98 \end{center} 105 \centering 106 \includegraphics[width=0.66\textwidth]{LBC_shlat} 107 \caption[Lateral boundary conditions]{ 108 Lateral boundary conditions 109 (a) free-slip (\protect\np[=0]{rn_shlat}{rn\_shlat}); 110 (b) no-slip (\protect\np[=2]{rn_shlat}{rn\_shlat}); 111 (c) "partial" free-slip (\forcode{0<}\protect\np[<2]{rn_shlat}{rn\_shlat}) and 112 (d) "strong" no-slip (\forcode{2<}\protect\np{rn_shlat}{rn\_shlat}). 113 Implied "ghost" velocity inside land area is display in grey.} 114 \label{fig:LBC_shlat} 99 115 \end{figure} 100 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>101 116 102 117 \begin{description} 103 118 104 \item [free-slip boundary condition (\np{rn\_shlat}\forcode{ = 0}):] the tangential velocity at119 \item [free-slip boundary condition ({\np[=0]{rn_shlat}{rn\_shlat}})] the tangential velocity at 105 120 the coastline is equal to the offshore velocity, 106 \ie the normal derivative of the tangential velocity is zero at the coast,121 \ie\ the normal derivative of the tangential velocity is zero at the coast, 107 122 so the vorticity: mask$_{f}$ array is set to zero inside the land and just at the coast 108 123 (\autoref{fig:LBC_shlat}-a). 109 124 110 \item [no-slip boundary condition (\np{rn\_shlat}\forcode{ = 2}):] the tangential velocity vanishes at the coastline.125 \item [no-slip boundary condition ({\np[=2]{rn_shlat}{rn\_shlat}})] the tangential velocity vanishes at the coastline. 111 126 Assuming that the tangential velocity decreases linearly from 112 127 the closest ocean velocity grid point to the coastline, … … 114 129 the closest ocean velocity gridpoint were of the same magnitude but in the opposite direction 115 130 (\autoref{fig:LBC_shlat}-b). 116 Therefore, the vorticity along the coastlines is given by: 131 Therefore, the vorticity along the coastlines is given by: 117 132 118 133 \[ … … 123 138 the no-slip boundary condition, simply by multiplying it by the mask$_{f}$ : 124 139 \[ 125 % \label{eq: lbc_bbbb}140 % \label{eq:LBC_bbbb} 126 141 \zeta \equiv \frac{1}{e_{1f} {\kern 1pt}e_{2f} }\left( {\delta_{i+1/2} 127 142 \left[ {e_{2v} \,v} \right]-\delta_{j+1/2} \left[ {e_{1u} \,u} \right]} … … 129 144 \] 130 145 131 \item ["partial" free-slip boundary condition (0$<$\np{rn\_shlat}$<$2):] the tangential velocity at132 the coastline is smaller than the offshore velocity, \ie there is a lateral friction but146 \item ["partial" free-slip boundary condition (0$<$\np{rn_shlat}{rn\_shlat}$<$2)] the tangential velocity at 147 the coastline is smaller than the offshore velocity, \ie\ there is a lateral friction but 133 148 not strong enough to make the tangential velocity at the coast vanish (\autoref{fig:LBC_shlat}-c). 134 149 This can be selected by providing a value of mask$_{f}$ strictly inbetween $0$ and $2$. 135 150 136 \item ["strong" no-slip boundary condition (2$<$\np{rn\_shlat}):] the viscous boundary layer is assumed to151 \item ["strong" no-slip boundary condition (2$<$\np{rn_shlat}{rn\_shlat})] the viscous boundary layer is assumed to 137 152 be smaller than half the grid size (\autoref{fig:LBC_shlat}-d). 138 153 The friction is thus larger than in the no-slip case. … … 140 155 \end{description} 141 156 142 Note that when the bottom topography is entirely represented by the $s$-coor -dinates (pure $s$-coordinate),157 Note that when the bottom topography is entirely represented by the $s$-coordinates (pure $s$-coordinate), 143 158 the lateral boundary condition on tangential velocity is of much less importance as 144 159 it is only applied next to the coast where the minimum water depth can be quite shallow. 145 160 146 147 % ================================================================ 148 % Boundary Condition around the Model Domain 149 % ================================================================ 150 \section[Model domain boundary condition (\texttt{jperio})] 151 {Model domain boundary condition (\protect\np{jperio})} 161 %% ================================================================================================= 162 \section[Model domain boundary condition (\forcode{jperio})]{Model domain boundary condition (\protect\jp{jperio})} 152 163 \label{sec:LBC_jperio} 153 164 … … 155 166 closed, cyclic east-west, cyclic north-south, a north-fold, and combination closed-north fold or 156 167 bi-cyclic east-west and north-fold. 157 The north-fold boundary condition is associated with the 3-pole ORCA mesh. 158 159 % ------------------------------------------------------------------------------------------------------------- 160 % Closed, cyclic (\np{jperio}\forcode{ = 0..2}) 161 % ------------------------------------------------------------------------------------------------------------- 162 \subsection[Closed, cyclic (\forcode{jperio = [0127]})] 163 {Closed, cyclic (\protect\np{jperio}\forcode{ = [0127]})} 168 The north-fold boundary condition is associated with the 3-pole ORCA mesh. 169 170 %% ================================================================================================= 171 \subsection[Closed, cyclic (\forcode{=0,1,2,7})]{Closed, cyclic (\protect\jp{jperio}\forcode{=0,1,2,7})} 164 172 \label{subsec:LBC_jperio012} 165 173 166 174 The choice of closed or cyclic model domain boundary condition is made by 167 setting \ np{jperio} to 0, 1, 2 or 7 in namelist \ngn{namcfg}.175 setting \jp{jperio} to 0, 1, 2 or 7 in namelist \nam{cfg}{cfg}. 168 176 Each time such a boundary condition is needed, it is set by a call to routine \mdl{lbclnk}. 169 177 The computation of momentum and tracer trends proceeds from $i=2$ to $i=jpi-1$ and from $j=2$ to $j=jpj-1$, 170 \ie in the model interior.178 \ie\ in the model interior. 171 179 To choose a lateral model boundary condition is to specify the first and last rows and columns of 172 the model variables. 180 the model variables. 173 181 174 182 \begin{description} 175 183 176 \item[For closed boundary (\np{jperio}\forcode{ = 0})], 177 solid walls are imposed at all model boundaries: 184 \item [For closed boundary (\jp{jperio}\forcode{=0})], solid walls are imposed at all model boundaries: 178 185 first and last rows and columns are set to zero. 179 186 180 \item[For cyclic east-west boundary (\np{jperio}\forcode{ = 1})], 181 first and last rows are set to zero (closed) whilst the first column is set to 187 \item [For cyclic east-west boundary (\jp{jperio}\forcode{=1})], first and last rows are set to zero (closed) whilst the first column is set to 182 188 the value of the last-but-one column and the last column to the value of the second one 183 189 (\autoref{fig:LBC_jperio}-a). 184 190 Whatever flows out of the eastern (western) end of the basin enters the western (eastern) end. 185 191 186 \item[For cyclic north-south boundary (\np{jperio}\forcode{ = 2})], 187 first and last columns are set to zero (closed) whilst the first row is set to 192 \item [For cyclic north-south boundary (\jp{jperio}\forcode{=2})], first and last columns are set to zero (closed) whilst the first row is set to 188 193 the value of the last-but-one row and the last row to the value of the second one 189 194 (\autoref{fig:LBC_jperio}-a). 190 195 Whatever flows out of the northern (southern) end of the basin enters the southern (northern) end. 191 196 192 \item [Bi-cyclic east-west and north-south boundary (\np{jperio}\forcode{ =7})] combines cases 1 and 2.197 \item [Bi-cyclic east-west and north-south boundary (\jp{jperio}\forcode{=7})] combines cases 1 and 2. 193 198 194 199 \end{description} 195 200 196 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>197 201 \begin{figure}[!t] 198 \begin{center} 199 \includegraphics[width=\textwidth]{Fig_LBC_jperio} 200 \caption{ 201 \protect\label{fig:LBC_jperio} 202 setting of (a) east-west cyclic (b) symmetric across the equator boundary conditions. 203 } 204 \end{center} 202 \centering 203 \includegraphics[width=0.66\textwidth]{LBC_jperio} 204 \caption[Setting of east-west cyclic and symmetric across the Equator boundary conditions]{ 205 Setting of (a) east-west cyclic (b) symmetric across the Equator boundary conditions} 206 \label{fig:LBC_jperio} 205 207 \end{figure} 206 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 207 208 % ------------------------------------------------------------------------------------------------------------- 209 % North fold (\textit{jperio = 3 }to $6)$ 210 % ------------------------------------------------------------------------------------------------------------- 211 \subsection[North-fold (\forcode{jperio = [3-6]})] 212 {North-fold (\protect\np{jperio}\forcode{ = [3-6]})} 208 209 %% ================================================================================================= 210 \subsection[North-fold (\forcode{=3,6})]{North-fold (\protect\jp{jperio}\forcode{=3,6})} 213 211 \label{subsec:LBC_north_fold} 214 212 215 213 The north fold boundary condition has been introduced in order to handle the north boundary of 216 214 a three-polar ORCA grid. 217 Such a grid has two poles in the northern hemisphere (\autoref{fig: MISC_ORCA_msh},218 and thus requires a specific treatment illustrated in \autoref{fig: North_Fold_T}.215 Such a grid has two poles in the northern hemisphere (\autoref{fig:CFGS_ORCA_msh}, 216 and thus requires a specific treatment illustrated in \autoref{fig:LBC_North_Fold_T}. 219 217 Further information can be found in \mdl{lbcnfd} module which applies the north fold boundary condition. 220 218 221 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>222 219 \begin{figure}[!t] 223 \begin{center} 224 \includegraphics[width=\textwidth]{Fig_North_Fold_T} 225 \caption{ 226 \protect\label{fig:North_Fold_T} 227 North fold boundary with a $T$-point pivot and cyclic east-west boundary condition ($jperio=4$), 228 as used in ORCA 2, 1/4, and 1/12. 229 Pink shaded area corresponds to the inner domain mask (see text). 230 } 231 \end{center} 220 \centering 221 \includegraphics[width=0.66\textwidth]{LBC_North_Fold_T} 222 \caption[North fold boundary in ORCA 2\deg, 1/4\deg and 1/12\deg]{ 223 North fold boundary with a $T$-point pivot and cyclic east-west boundary condition ($jperio=4$), 224 as used in ORCA 2\deg, 1/4\deg and 1/12\deg. 225 Pink shaded area corresponds to the inner domain mask (see text).} 226 \label{fig:LBC_North_Fold_T} 232 227 \end{figure} 233 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 234 235 % ==================================================================== 236 % Exchange with neighbouring processors 237 % ==================================================================== 238 \section[Exchange with neighbouring processors (\textit{lbclnk.F90}, \textit{lib\_mpp.F90})] 239 {Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})} 228 229 %% ================================================================================================= 230 \section[Exchange with neighbouring processors (\textit{lbclnk.F90}, \textit{lib\_mpp.F90})]{Exchange with neighbouring processors (\protect\mdl{lbclnk}, \protect\mdl{lib\_mpp})} 240 231 \label{sec:LBC_mpp} 241 232 233 \begin{listing} 234 \nlst{nammpp} 235 \caption{\forcode{&nammpp}} 236 \label{lst:nammpp} 237 \end{listing} 238 242 239 For massively parallel processing (mpp), a domain decomposition method is used. 243 The basic idea of the method is to split the large computation domain of a numerical experiment into 244 s everal smaller domains and solve the set of equations by addressing independent local problems.240 The basic idea of the method is to split the large computation domain of a numerical experiment into several smaller domains and 241 solve the set of equations by addressing independent local problems. 245 242 Each processor has its own local memory and computes the model equation over a subdomain of the whole model domain. 246 The subdomain boundary conditions are specified through communications between processors which 247 are organized by explicit statements (message passing method). 248 249 A big advantage is that the method does not need many modifications of the initial \fortran code. 250 From the modeller's point of view, each sub domain running on a processor is identical to the "mono-domain" code. 251 In addition, the programmer manages the communications between subdomains, 252 and the code is faster when the number of processors is increased. 253 The porting of OPA code on an iPSC860 was achieved during Guyon's PhD [Guyon et al. 1994, 1995] 254 in collaboration with CETIIS and ONERA. 255 The implementation in the operational context and the studies of performance on 256 a T3D and T3E Cray computers have been made in collaboration with IDRIS and CNRS. 243 The subdomain boundary conditions are specified through communications between processors which are organized by 244 explicit statements (message passing method). 257 245 The present implementation is largely inspired by Guyon's work [Guyon 1995]. 258 246 … … 261 249 depend at the very most on one neighbouring point. 262 250 The only non-local computations concern the vertical physics 263 (implicit diffusion, turbulent closure scheme, ...) (delocalization over the whole water column), 264 and the solving of the elliptic equation associated with the surface pressure gradient computation 265 (delocalization over the whole horizontal domain). 251 (implicit diffusion, turbulent closure scheme, ...). 266 252 Therefore, a pencil strategy is used for the data sub-structuration: 267 253 the 3D initial domain is laid out on local processor memories following a 2D horizontal topological splitting. … … 272 258 After a computation, a communication phase starts: 273 259 each processor sends to its neighbouring processors the update values of the points corresponding to 274 the interior overlapping area to its neighbouring sub-domain (\ie the innermost of the two overlapping rows). 275 The communication is done through the Message Passing Interface (MPI). 260 the interior overlapping area to its neighbouring sub-domain (\ie\ the innermost of the two overlapping rows). 261 Communications are first done according to the east-west direction and next according to the north-south direction. 262 There is no specific communications for the corners. 263 The communication is done through the Message Passing Interface (MPI) and requires \key{mpp\_mpi}. 264 Use also \key{mpi2} if MPI3 is not available on your computer. 276 265 The data exchanges between processors are required at the very place where 277 266 lateral domain boundary conditions are set in the mono-domain computation: 278 267 the \rou{lbc\_lnk} routine (found in \mdl{lbclnk} module) which manages such conditions is interfaced with 279 routines found in \mdl{lib\_mpp} module when running on an MPP computer (\ie when \key{mpp\_mpi} defined). 280 It has to be pointed out that when using the MPP version of the model, 281 the east-west cyclic boundary condition is done implicitly, 282 whilst the south-symmetric boundary condition option is not available. 283 284 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 268 routines found in \mdl{lib\_mpp} module. 269 The output file \textit{communication\_report.txt} provides the list of which routines do how 270 many communications during 1 time step of the model.\\ 271 285 272 \begin{figure}[!t] 286 \begin{center} 287 \includegraphics[width=\textwidth]{Fig_mpp} 288 \caption{ 289 \protect\label{fig:mpp} 290 Positioning of a sub-domain when massively parallel processing is used. 291 } 292 \end{center} 273 \centering 274 \includegraphics[width=0.66\textwidth]{LBC_mpp} 275 \caption{Positioning of a sub-domain when massively parallel processing is used} 276 \label{fig:LBC_mpp} 293 277 \end{figure} 294 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 295 296 In the standard version of \NEMO, the splitting is regular and arithmetic. 297 The i-axis is divided by \jp{jpni} and 298 the j-axis by \jp{jpnj} for a number of processors \jp{jpnij} most often equal to $jpni \times jpnj$ 299 (parameters set in \ngn{nammpp} namelist). 300 Each processor is independent and without message passing or synchronous process, 301 programs run alone and access just its own local memory. 302 For this reason, the main model dimensions are now the local dimensions of the subdomain (pencil) that 303 are named \jp{jpi}, \jp{jpj}, \jp{jpk}. 278 279 In \NEMO, the splitting is regular and arithmetic. 280 The total number of subdomains corresponds to the number of MPI processes allocated to \NEMO\ when the model is launched 281 (\ie\ mpirun -np x ./nemo will automatically give x subdomains). 282 The i-axis is divided by \np{jpni}{jpni} and the j-axis by \np{jpnj}{jpnj}. 283 These parameters are defined in \nam{mpp}{mpp} namelist. 284 If \np{jpni}{jpni} and \np{jpnj}{jpnj} are < 1, they will be automatically redefined in the code to give the best domain decomposition 285 (see bellow). 286 287 Each processor is independent and without message passing or synchronous process, programs run alone and access just its own local memory. 288 For this reason, 289 the main model dimensions are now the local dimensions of the subdomain (pencil) that are named \jp{jpi}, \jp{jpj}, \jp{jpk}. 304 290 These dimensions include the internal domain and the overlapping rows. 305 The number of rows to exchange (known as the halo) is usually set to one (\jp{jpreci}=1, in \mdl{par\_oce}). 306 The whole domain dimensions are named \np{jpiglo}, \np{jpjglo} and \jp{jpk}. 291 The number of rows to exchange (known as the halo) is usually set to one (nn\_hls=1, in \mdl{par\_oce}, 292 and must be kept to one until further notice). 293 The whole domain dimensions are named \jp{jpiglo}, \jp{jpjglo} and \jp{jpk}. 307 294 The relationship between the whole domain and a sub-domain is: 295 \begin{gather*} 296 jpi = ( jpiglo-2\times nn\_hls + (jpni-1) ) / jpni + 2\times nn\_hls \\ 297 jpj = ( jpjglo-2\times nn\_hls + (jpnj-1) ) / jpnj + 2\times nn\_hls 298 \end{gather*} 299 300 One also defines variables nldi and nlei which correspond to the internal domain bounds, and the variables nimpp and njmpp which are the position of the (1,1) grid-point in the global domain (\autoref{fig:LBC_mpp}). Note that since the version 4, there is no more extra-halo area as defined in \autoref{fig:LBC_mpp} so \jp{jpi} is now always equal to nlci and \jp{jpj} equal to nlcj. 301 302 An element of $T_{l}$, a local array (subdomain) corresponds to an element of $T_{g}$, 303 a global array (whole domain) by the relationship: 308 304 \[ 309 jpi = ( jpiglo-2*jpreci + (jpni-1) ) / jpni + 2*jpreci 310 jpj = ( jpjglo-2*jprecj + (jpnj-1) ) / jpnj + 2*jprecj 311 \] 312 where \jp{jpni}, \jp{jpnj} are the number of processors following the i- and j-axis. 313 314 One also defines variables nldi and nlei which correspond to the internal domain bounds, 315 and the variables nimpp and njmpp which are the position of the (1,1) grid-point in the global domain. 316 An element of $T_{l}$, a local array (subdomain) corresponds to an element of $T_{g}$, 317 a global array (whole domain) by the relationship: 318 \[ 319 % \label{eq:lbc_nimpp} 305 % \label{eq:LBC_nimpp} 320 306 T_{g} (i+nimpp-1,j+njmpp-1,k) = T_{l} (i,j,k), 321 307 \] 322 with $1 \leq i \leq jpi$, $1 \leq j \leq jpj $ , and $1 \leq k \leq jpk$. 323 324 Processors are numbered from 0 to $jpnij-1$, the number is saved in the variable nproc. 325 In the standard version, a processor has no more than 326 four neighbouring processors named nono (for north), noea (east), noso (south) and nowe (west) and 327 two variables, nbondi and nbondj, indicate the relative position of the processor: 328 \begin{itemize} 329 \item nbondi = -1 an east neighbour, no west processor, 330 \item nbondi = 0 an east neighbour, a west neighbour, 331 \item nbondi = 1 no east processor, a west neighbour, 332 \item nbondi = 2 no splitting following the i-axis. 333 \end{itemize} 334 During the simulation, processors exchange data with their neighbours. 335 If there is effectively a neighbour, the processor receives variables from this processor on its overlapping row, 336 and sends the data issued from internal domain corresponding to the overlapping row of the other processor. 337 338 339 The \NEMO model computes equation terms with the help of mask arrays (0 on land points and 1 on sea points). 340 It is easily readable and very efficient in the context of a computer with vectorial architecture. 341 However, in the case of a scalar processor, computations over the land regions become more expensive in 342 terms of CPU time. 343 It is worse when we use a complex configuration with a realistic bathymetry like the global ocean where 344 more than 50 \% of points are land points. 345 For this reason, a pre-processing tool can be used to choose the mpp domain decomposition with a maximum number of 346 only land points processors, which can then be eliminated (\autoref{fig:mppini2}) 347 (For example, the mpp\_optimiz tools, available from the DRAKKAR web site). 348 This optimisation is dependent on the specific bathymetry employed. 349 The user then chooses optimal parameters \jp{jpni}, \jp{jpnj} and \jp{jpnij} with $jpnij < jpni \times jpnj$, 350 leading to the elimination of $jpni \times jpnj - jpnij$ land processors. 351 When those parameters are specified in \ngn{nammpp} namelist, 352 the algorithm in the \rou{inimpp2} routine sets each processor's parameters (nbound, nono, noea,...) so that 353 the land-only processors are not taken into account. 354 355 \gmcomment{Note that the inimpp2 routine is general so that the original inimpp 356 routine should be suppressed from the code.} 357 358 When land processors are eliminated, 359 the value corresponding to these locations in the model output files is undefined. 360 Note that this is a problem for the meshmask file which requires to be defined over the whole domain. 361 Therefore, user should not eliminate land processors when creating a meshmask file 362 (\ie when setting a non-zero value to \np{nn\_msh}). 363 364 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 308 with $1 \leq i \leq jpi$, $1 \leq j \leq jpj $ , and $1 \leq k \leq jpk$. 309 310 The 1-d arrays $mig(1:\jp{jpi})$ and $mjg(1:\jp{jpj})$, defined in \rou{dom\_glo} routine (\mdl{domain} module), should be used to get global domain indices from local domain indices. The 1-d arrays, $mi0(1:\jp{jpiglo})$, $mi1(1:\jp{jpiglo})$ and $mj0(1:\jp{jpjglo})$, $mj1(1:\jp{jpjglo})$ have the reverse purpose and should be used to define loop indices expressed in global domain indices (see examples in \mdl{dtastd} module).\\ 311 312 The \NEMO\ model computes equation terms with the help of mask arrays (0 on land points and 1 on sea points). It is therefore possible that an MPI subdomain contains only land points. To save ressources, we try to supress from the computational domain as much land subdomains as possible. For example if $N_{mpi}$ processes are allocated to NEMO, the domain decomposition will be given by the following equation: 313 \[ 314 N_{mpi} = jpni \times jpnj - N_{land} + N_{useless} 315 \] 316 $N_{land}$ is the total number of land subdomains in the domain decomposition defined by \np{jpni}{jpni} and \np{jpnj}{jpnj}. $N_{useless}$ is the number of land subdomains that are kept in the compuational domain in order to make sure that $N_{mpi}$ MPI processes are indeed allocated to a given subdomain. The values of $N_{mpi}$, \np{jpni}{jpni}, \np{jpnj}{jpnj}, $N_{land}$ and $N_{useless}$ are printed in the output file \texttt{ocean.output}. $N_{useless}$ must, of course, be as small as possible to limit the waste of ressources. A warning is issued in \texttt{ocean.output} if $N_{useless}$ is not zero. Note that non-zero value of $N_{useless}$ is uselly required when using AGRIF as, up to now, the parent grid and each of the child grids must use all the $N_{mpi}$ processes. 317 318 If the domain decomposition is automatically defined (when \np{jpni}{jpni} and \np{jpnj}{jpnj} are < 1), the decomposition chosen by the model will minimise the sub-domain size (defined as $max_{all domains}(jpi \times jpj)$) and maximize the number of eliminated land subdomains. This means that no other domain decomposition (a set of \np{jpni}{jpni} and \np{jpnj}{jpnj} values) will use less processes than $(jpni \times jpnj - N_{land})$ and get a smaller subdomain size. 319 In order to specify $N_{mpi}$ properly (minimize $N_{useless}$), you must run the model once with \np{ln_list}{ln\_list} activated. In this case, the model will start the initialisation phase, print the list of optimum decompositions ($N_{mpi}$, \np{jpni}{jpni} and \np{jpnj}{jpnj}) in \texttt{ocean.output} and directly abort. The maximum value of $N_{mpi}$ tested in this list is given by $max(N_{MPI\_tasks}, jpni \times jpnj)$. For example, run the model on 40 nodes with ln\_list activated and $jpni = 10000$ and $jpnj = 1$, will print the list of optimum domains decomposition from 1 to about 10000. 320 321 Processors are numbered from 0 to $N_{mpi} - 1$. Subdomains containning some ocean points are numbered first from 0 to $jpni * jpnj - N_{land} -1$. The remaining $N_{useless}$ land subdomains are numbered next, which means that, for a given (\np{jpni}{jpni}, \np{jpnj}{jpnj}), the numbers attributed to he ocean subdomains do not vary with $N_{useless}$. 322 323 When land processors are eliminated, the value corresponding to these locations in the model output files is undefined. \np{ln_mskland}{ln\_mskland} must be activated in order avoid Not a Number values in output files. Note that it is better to not eliminate land processors when creating a meshmask file (\ie\ when setting a non-zero value to \np{nn_msh}{nn\_msh}). 324 365 325 \begin{figure}[!ht] 366 \begin{center} 367 \includegraphics[width=\textwidth]{Fig_mppini2} 368 \caption { 369 \protect\label{fig:mppini2} 370 Example of Atlantic domain defined for the CLIPPER projet. 371 Initial grid is composed of 773 x 1236 horizontal points. 372 (a) the domain is split onto 9 \time 20 subdomains (jpni=9, jpnj=20). 373 52 subdomains are land areas. 374 (b) 52 subdomains are eliminated (white rectangles) and 375 the resulting number of processors really used during the computation is jpnij=128. 376 } 377 \end{center} 326 \centering 327 \includegraphics[width=0.66\textwidth]{LBC_mppini2} 328 \caption[Atlantic domain defined for the CLIPPER projet]{ 329 Example of Atlantic domain defined for the CLIPPER projet. 330 Initial grid is composed of 773 x 1236 horizontal points. 331 (a) the domain is split onto 9 $times$ 20 subdomains (jpni=9, jpnj=20). 332 52 subdomains are land areas. 333 (b) 52 subdomains are eliminated (white rectangles) and 334 the resulting number of processors really used during the computation is jpnij=128.} 335 \label{fig:LBC_mppini2} 378 336 \end{figure} 379 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 380 381 382 % ==================================================================== 383 % Unstructured open boundaries BDY 384 % ==================================================================== 337 338 %% ================================================================================================= 385 339 \section{Unstructured open boundary conditions (BDY)} 386 340 \label{sec:LBC_bdy} 387 341 388 %-----------------------------------------nambdy-------------------------------------------- 389 390 \nlst{nambdy} 391 %----------------------------------------------------------------------------------------------- 392 %-----------------------------------------nambdy_dta-------------------------------------------- 393 394 \nlst{nambdy_dta} 395 %----------------------------------------------------------------------------------------------- 396 397 Options are defined through the \ngn{nambdy} \ngn{nambdy\_dta} namelist variables. 398 The BDY module is the core implementation of open boundary conditions for regional configurations on 399 temperature, salinity, barotropic and baroclinic velocities, as well as ice concentration, ice and snow thicknesses). 400 401 The BDY module was modelled on the OBC module (see NEMO 3.4) and shares many features and 342 \begin{listing} 343 \nlst{nambdy} 344 \caption{\forcode{&nambdy}} 345 \label{lst:nambdy} 346 \end{listing} 347 348 \begin{listing} 349 \nlst{nambdy_dta} 350 \caption{\forcode{&nambdy_dta}} 351 \label{lst:nambdy_dta} 352 \end{listing} 353 354 Options are defined through the \nam{bdy}{bdy} and \nam{bdy_dta}{bdy\_dta} namelist variables. 355 The BDY module is the core implementation of open boundary conditions for regional configurations on 356 ocean temperature, salinity, barotropic-baroclinic velocities, ice-snow concentration, thicknesses, temperatures, salinity and melt ponds concentration and thickness. 357 358 The BDY module was modelled on the OBC module (see \NEMO\ 3.4) and shares many features and 402 359 a similar coding structure \citep{chanut_rpt05}. 403 360 The specification of the location of the open boundary is completely flexible and 404 allows for example the open boundary to follow an isobath or other irregular contour.405 Boundary data files used with versions of NEMOprior to Version 3.4 may need to be re-ordered to work with this version.361 allows any type of setup, from regular boundaries to irregular contour (it includes the possibility to set an open boundary able to follow an isobath). 362 Boundary data files used with versions of \NEMO\ prior to Version 3.4 may need to be re-ordered to work with this version. 406 363 See the section on the Input Boundary Data Files for details. 407 364 408 % ----------------------------------------------365 %% ================================================================================================= 409 366 \subsection{Namelists} 410 \label{subsec: BDY_namelist}411 412 The BDY module is activated by setting \np {ln\_bdy}\forcode{ = .true.} .367 \label{subsec:LBC_bdy_namelist} 368 369 The BDY module is activated by setting \np[=.true.]{ln_bdy}{ln\_bdy} . 413 370 It is possible to define more than one boundary ``set'' and apply different boundary conditions to each set. 414 The number of boundary sets is defined by \np{nb\_bdy}. 415 Each boundary set may be defined as a set of straight line segments in a namelist 416 (\np{ln\_coords\_file}\forcode{ = .false.}) or read in from a file (\np{ln\_coords\_file}\forcode{ = .true.}). 417 If the set is defined in a namelist, then the namelists \ngn{nambdy\_index} must be included separately, one for each set. 418 If the set is defined by a file, then a ``\ifile{coordinates.bdy}'' file must be provided. 419 The coordinates.bdy file is analagous to the usual NEMO ``\ifile{coordinates}'' file. 371 The number of boundary sets is defined by \np{nb_bdy}{nb\_bdy}. 372 Each boundary set can be either defined as a series of straight line segments directly in the namelist 373 (\np[=.false.]{ln_coords_file}{ln\_coords\_file}, and a namelist block \nam{bdy_index}{bdy\_index} must be included for each set) or read in from a file (\np[=.true.]{ln_coords_file}{ln\_coords\_file}, and a ``\ifile{coordinates.bdy}'' file must be provided). 374 The coordinates.bdy file is analagous to the usual \NEMO\ ``\ifile{coordinates}'' file. 420 375 In the example above, there are two boundary sets, the first of which is defined via a file and 421 the second is defined in anamelist.422 For more details of the definition of the boundary geometry see section \autoref{subsec: BDY_geometry}.376 the second is defined in the namelist. 377 For more details of the definition of the boundary geometry see section \autoref{subsec:LBC_bdy_geometry}. 423 378 424 379 For each boundary set a boundary condition has to be chosen for the barotropic solution 425 (``u2d'':sea-surface height and barotropic velocities), for the baroclinic velocities (``u3d''), 426 for the active tracers \footnote{The BDY module does not deal with passive tracers at this version} (``tra''), and sea-ice (``ice''). 427 For each set of variables there is a choice of algorithm and a choice for the data, 428 eg. for the active tracers the algorithm is set by \np{cn\_tra} and the choice of data is set by \np{nn\_tra\_dta}.\\ 380 (``u2d'':sea-surface height and barotropic velocities), for the baroclinic velocities (``u3d''), 381 for the active tracers \footnote{The BDY module does not deal with passive tracers at this version} (``tra''), and for sea-ice (``ice''). 382 For each set of variables one has to choose an algorithm and the boundary data (set resp. by \np{cn_tra}{cn\_tra} and \np{nn_tra_dta}{nn\_tra\_dta} for tracers).\\ 429 383 430 384 The choice of algorithm is currently as follows: 431 385 432 386 \begin{description} 433 \item [\forcode{'none'}:] No boundary condition applied.387 \item [\forcode{'none'}:] No boundary condition applied. 434 388 So the solution will ``see'' the land points around the edge of the edge of the domain. 435 \item [\forcode{'specified'}:] Specified boundary condition applied (only available for baroclinic velocity and tracer variables).436 \item [\forcode{'neumann'}:] Value at the boundary are duplicated (No gradient). Only available for baroclinic velocity and tracer variables.437 \item [\forcode{'frs'}:] Flow Relaxation Scheme (FRS) available for all variables.438 \item [\forcode{'Orlanski'}:] Orlanski radiation scheme (fully oblique) for barotropic, baroclinic and tracer variables.439 \item [\forcode{'Orlanski_npo'}:] Orlanski radiation scheme for barotropic, baroclinic and tracer variables.440 \item [\forcode{'flather'}:] Flather radiation scheme for the barotropic variables only.389 \item [\forcode{'specified'}:] Specified boundary condition applied (only available for baroclinic velocity and tracer variables). 390 \item [\forcode{'neumann'}:] Value at the boundary are duplicated (No gradient). Only available for baroclinic velocity and tracer variables. 391 \item [\forcode{'frs'}:] Flow Relaxation Scheme (FRS) available for all variables. 392 \item [\forcode{'Orlanski'}:] Orlanski radiation scheme (fully oblique) for barotropic, baroclinic and tracer variables. 393 \item [\forcode{'Orlanski_npo'}:] Orlanski radiation scheme for barotropic, baroclinic and tracer variables. 394 \item [\forcode{'flather'}:] Flather radiation scheme for the barotropic variables only. 441 395 \end{description} 442 396 443 The main choice for the boundary data is to use initial conditions as boundary data444 (\np {nn\_tra\_dta}\forcode{ = 0}) or to use external data from a file (\np{nn\_tra\_dta}\forcode{ = 1}).445 In case the 3d velocity data contain the total velocity (ie, baroclinic and barotropic velocity), 446 the bdy code can derived baroclinic and barotropic velocities by setting \np {ln\_full\_vel}\forcode{ = .true.}397 The boundary data is either set to initial conditions 398 (\np[=0]{nn_tra_dta}{nn\_tra\_dta}) or forced with external data from a file (\np[=1]{nn_tra_dta}{nn\_tra\_dta}). 399 In case the 3d velocity data contain the total velocity (ie, baroclinic and barotropic velocity), 400 the bdy code can derived baroclinic and barotropic velocities by setting \np[=.true.]{ln_full_vel}{ln\_full\_vel} 447 401 For the barotropic solution there is also the option to use tidal harmonic forcing either by 448 itself (\np{nn\_dyn2d\_dta}\forcode{ = 2}) or in addition to other external data (\np{nn\_dyn2d\_dta}\forcode{ = 3}).\\ 449 Sea-ice salinity, temperature and age data at the boundary are constant and defined repectively by \np{rn\_ice\_sal}, \np{rn\_ice\_tem} and \np{rn\_ice\_age}. 450 451 If external boundary data is required then the \ngn{nambdy\_dta} namelist must be defined. 452 One \ngn{nambdy\_dta} namelist is required for each boundary set in the order in which 453 the boundary sets are defined in nambdy. 454 In the example given, two boundary sets have been defined. The first one is reading data file in the \ngn{nambdy\_dta} namelist shown above 455 and the second one is using data from intial condition (no namelist bloc needed). 402 itself (\np[=2]{nn_dyn2d_dta}{nn\_dyn2d\_dta}) or in addition to other external data (\np[=3]{nn_dyn2d_dta}{nn\_dyn2d\_dta}).\\ 403 If not set to initial conditions, sea-ice salinity, temperatures and melt ponds data at the boundary can either be read in a file or defined as constant (by \np{rn_ice_sal}{rn\_ice\_sal}, \np{rn_ice_tem}{rn\_ice\_tem}, \np{rn_ice_apnd}{rn\_ice\_apnd}, \np{rn_ice_hpnd}{rn\_ice\_hpnd}). Ice age is constant and defined by \np{rn_ice_age}{rn\_ice\_age}. 404 405 If external boundary data is required then the \nam{bdy_dta}{bdy\_dta} namelist must be defined. 406 One \nam{bdy_dta}{bdy\_dta} namelist is required for each boundary set, adopting the same order of indexes in which the boundary sets are defined in nambdy. 407 In the example given, two boundary sets have been defined. The first one is reading data file in the \nam{bdy_dta}{bdy\_dta} namelist shown above 408 and the second one is using data from intial condition (no namelist block needed). 456 409 The boundary data is read in using the fldread module, 457 so the \ngn{nambdy\_dta} namelist is in the format required for fldread. 458 For each variable required, the filename, the frequency of the files and 459 the frequency of the data in the files is given. 460 Also whether or not time-interpolation is required and whether the data is climatological (time-cyclic) data.\\ 410 so the \nam{bdy_dta}{bdy\_dta} namelist is in the format required for fldread. 411 For each required variable, the filename, the frequency of the files and 412 the frequency of the data in the files are given. 413 Also whether or not time-interpolation is required and whether the data is climatological (time-cyclic) data. 414 For sea-ice salinity, temperatures and melt ponds, reading the files are skipped and constant values are used if filenames are defined as {'NOT USED'}.\\ 461 415 462 416 There is currently an option to vertically interpolate the open boundary data onto the native grid at run-time. 463 If \np{nn \_bdy\_jpk} $< -1$, it is assumed that the lateral boundary data are already on the native grid.464 However, if \np{nn \_bdy\_jpk} is set to the number of vertical levels present in the boundary data,465 a bilinear interpolation onto the native grid will be triggered at runtime. 466 For this to be successful the additional variables: $gdept$, $gdepu$, $gdepv$, $e3t$, $e3u$ and $e3v$, are required to be present in the lateral boundary files. 467 These correspond to the depths and scale factors of the input data, 417 If \np{nn_bdy_jpk}{nn\_bdy\_jpk}$<-1$, it is assumed that the lateral boundary data are already on the native grid. 418 However, if \np{nn_bdy_jpk}{nn\_bdy\_jpk} is set to the number of vertical levels present in the boundary data, 419 a bilinear interpolation onto the native grid will be triggered at runtime. 420 For this to be successful the additional variables: $gdept$, $gdepu$, $gdepv$, $e3t$, $e3u$ and $e3v$, are required to be present in the lateral boundary files. 421 These correspond to the depths and scale factors of the input data, 468 422 the latter used to make any adjustment to the velocity fields due to differences in the total water depths between the two vertical grids.\\ 469 423 470 In the example namelists given, two boundary sets are defined.424 In the example of given namelists, two boundary sets are defined. 471 425 The first set is defined via a file and applies FRS conditions to temperature and salinity and 472 426 Flather conditions to the barotropic variables. No condition specified for the baroclinic velocity and sea-ice. … … 474 428 Tidal harmonic forcing is also used. 475 429 The second set is defined in a namelist. 476 FRS conditions are applied on temperature and salinity and climatological data is read from initial condition files. 477 478 % ----------------------------------------------430 FRS conditions are applied on temperature and salinity and climatological data is read from initial condition files. 431 432 %% ================================================================================================= 479 433 \subsection{Flow relaxation scheme} 480 \label{subsec: BDY_FRS_scheme}434 \label{subsec:LBC_bdy_FRS_scheme} 481 435 482 436 The Flow Relaxation Scheme (FRS) \citep{davies_QJRMS76,engedahl_T95}, … … 485 439 Given a model prognostic variable $\Phi$ 486 440 \[ 487 % \label{eq: bdy_frs1}441 % \label{eq:LBC_bdy_frs1} 488 442 \Phi(d) = \alpha(d)\Phi_{e}(d) + (1-\alpha(d))\Phi_{m}(d)\;\;\;\;\; d=1,N 489 443 \] … … 494 448 the prognostic equation for $\Phi$ of the form: 495 449 \[ 496 % \label{eq: bdy_frs2}450 % \label{eq:LBC_bdy_frs2} 497 451 -\frac{1}{\tau}\left(\Phi - \Phi_{e}\right) 498 452 \] 499 453 where the relaxation time scale $\tau$ is given by a function of $\alpha$ and the model time step $\Delta t$: 500 454 \[ 501 % \label{eq: bdy_frs3}455 % \label{eq:LBC_bdy_frs3} 502 456 \tau = \frac{1-\alpha}{\alpha} \,\rdt 503 457 \] … … 505 459 is relaxed towards the external conditions over the rest of the FRS zone. 506 460 The application of a relaxation zone helps to prevent spurious reflection of 507 outgoing signals from the model boundary. 461 outgoing signals from the model boundary. 508 462 509 463 The function $\alpha$ is specified as a $tanh$ function: 510 464 \[ 511 % \label{eq: bdy_frs4}465 % \label{eq:LBC_bdy_frs4} 512 466 \alpha(d) = 1 - \tanh\left(\frac{d-1}{2}\right), \quad d=1,N 513 467 \] 514 The width of the FRS zone is specified in the namelist as \np{nn \_rimwidth}.468 The width of the FRS zone is specified in the namelist as \np{nn_rimwidth}{nn\_rimwidth}. 515 469 This is typically set to a value between 8 and 10. 516 470 517 % ----------------------------------------------471 %% ================================================================================================= 518 472 \subsection{Flather radiation scheme} 519 \label{subsec: BDY_flather_scheme}473 \label{subsec:LBC_bdy_flather_scheme} 520 474 521 475 The \citet{flather_JPO94} scheme is a radiation condition on the normal, 522 476 depth-mean transport across the open boundary. 523 477 It takes the form 524 \begin{equation} \label{eq:bdy_fla1} 525 U = U_{e} + \frac{c}{h}\left(\eta - \eta_{e}\right), 478 \begin{equation} 479 \label{eq:LBC_bdy_fla1} 480 U = U_{e} + \frac{c}{h}\left(\eta - \eta_{e}\right), 526 481 \end{equation} 527 482 where $U$ is the depth-mean velocity normal to the boundary and $\eta$ is the sea surface height, … … 532 487 the external depth-mean normal velocity, 533 488 plus a correction term that allows gravity waves generated internally to exit the model boundary. 534 Note that the sea-surface height gradient in \autoref{eq: bdy_fla1} is a spatial gradient across the model boundary,489 Note that the sea-surface height gradient in \autoref{eq:LBC_bdy_fla1} is a spatial gradient across the model boundary, 535 490 so that $\eta_{e}$ is defined on the $T$ points with $nbr=1$ and $\eta$ is defined on the $T$ points with $nbr=2$. 536 $U$ and $U_{e}$ are defined on the $U$ or $V$ points with $nbr=1$, \ie between the two $T$ grid points.537 538 % ----------------------------------------------491 $U$ and $U_{e}$ are defined on the $U$ or $V$ points with $nbr=1$, \ie\ between the two $T$ grid points. 492 493 %% ================================================================================================= 539 494 \subsection{Orlanski radiation scheme} 540 \label{subsec: BDY_orlanski_scheme}495 \label{subsec:LBC_bdy_orlanski_scheme} 541 496 542 497 The Orlanski scheme is based on the algorithm described by \citep{marchesiello.mcwilliams.ea_OM01}, hereafter MMS. … … 544 499 The adaptive Orlanski condition solves a wave plus relaxation equation at the boundary: 545 500 \begin{equation} 546 \frac{\partial\phi}{\partial t} + c_x \frac{\partial\phi}{\partial x} + c_y \frac{\partial\phi}{\partial y} = 547 -\frac{1}{\tau}(\phi - \phi^{ext})548 \label{eq:wave_continuous} 501 \label{eq:LBC_wave_continuous} 502 \frac{\partial\phi}{\partial t} + c_x \frac{\partial\phi}{\partial x} + c_y \frac{\partial\phi}{\partial y} = 503 -\frac{1}{\tau}(\phi - \phi^{ext}) 549 504 \end{equation} 550 505 … … 552 507 velocities are diagnosed from the model fields as: 553 508 554 \begin{equation} \label{eq:cx} 555 c_x = -\frac{\partial\phi}{\partial t}\frac{\partial\phi / \partial x}{(\partial\phi /\partial x)^2 + (\partial\phi /\partial y)^2} 509 \begin{equation} 510 \label{eq:LBC_cx} 511 c_x = -\frac{\partial\phi}{\partial t}\frac{\partial\phi / \partial x}{(\partial\phi /\partial x)^2 + (\partial\phi /\partial y)^2} 556 512 \end{equation} 557 513 \begin{equation} 558 \label{eq:cy}559 c_y = -\frac{\partial\phi}{\partial t}\frac{\partial\phi / \partial y}{(\partial\phi /\partial x)^2 + (\partial\phi /\partial y)^2}514 \label{eq:LBC_cy} 515 c_y = -\frac{\partial\phi}{\partial t}\frac{\partial\phi / \partial y}{(\partial\phi /\partial x)^2 + (\partial\phi /\partial y)^2} 560 516 \end{equation} 561 517 562 518 (As noted by MMS, this is a circular diagnosis of the phase speeds which only makes sense on a discrete grid). 563 Equation (\autoref{eq: wave_continuous}) is defined adaptively depending on the sign of the phase velocity normal to the boundary $c_x$.519 Equation (\autoref{eq:LBC_wave_continuous}) is defined adaptively depending on the sign of the phase velocity normal to the boundary $c_x$. 564 520 For $c_x$ outward, we have 565 521 … … 571 527 572 528 \begin{equation} 573 \tau = \tau_{in}\,\,\,;\,\,\, c_x = c_y = 0 574 \label{eq:tau_in} 529 \label{eq:LBC_tau_in} 530 \tau = \tau_{in}\,\,\,;\,\,\, c_x = c_y = 0 575 531 \end{equation} 576 532 577 Generally the relaxation time scale at inward propagation points \np{(rn\_time\_dmp}) is set much shorter than the time scale at outward propagation578 points (\np{rn \_time\_dmp\_out}) so that the solution is constrained more strongly by the external data at inward propagation points.579 See \autoref{subsec: BDY_relaxation} for detailed on the spatial shape of the scaling.\\580 The ``normal propagation of oblique radiation'' or NPO approximation (called \forcode{'orlanski_npo'}) involves assuming 581 that $c_y$ is zero in equation (\autoref{eq: wave_continuous}), but including582 this term in the denominator of equation (\autoref{eq: cx}). Both versions of the scheme are options in BDY. Equations583 (\autoref{eq: wave_continuous}) - (\autoref{eq:tau_in}) correspond to equations (13) - (15) and (2) - (3) in MMS.\\584 585 % ----------------------------------------------533 Generally the relaxation time scale at inward propagation points (\np{rn_time_dmp}{rn\_time\_dmp}) is set much shorter than the time scale at outward propagation 534 points (\np{rn_time_dmp_out}{rn\_time\_dmp\_out}) so that the solution is constrained more strongly by the external data at inward propagation points. 535 See \autoref{subsec:LBC_bdy_relaxation} for detailed on the spatial shape of the scaling.\\ 536 The ``normal propagation of oblique radiation'' or NPO approximation (called \forcode{'orlanski_npo'}) involves assuming 537 that $c_y$ is zero in equation (\autoref{eq:LBC_wave_continuous}), but including 538 this term in the denominator of equation (\autoref{eq:LBC_cx}). Both versions of the scheme are options in BDY. Equations 539 (\autoref{eq:LBC_wave_continuous}) - (\autoref{eq:LBC_tau_in}) correspond to equations (13) - (15) and (2) - (3) in MMS.\\ 540 541 %% ================================================================================================= 586 542 \subsection{Relaxation at the boundary} 587 \label{subsec: BDY_relaxation}588 589 In addition to a specific boundary condition specified as \np{cn \_tra} and \np{cn\_dyn3d}, relaxation on baroclinic velocities and tracers variables are available.590 It is control by the namelist parameter \np{ln \_tra\_dmp} and \np{ln\_dyn3d\_dmp} for each boundary set.591 592 The relaxation time scale value (\np{rn \_time\_dmp} and \np{rn\_time\_dmp\_out}, $\tau$) are defined at the boundaries itself.593 This time scale ($\alpha$) is weighted by the distance ($d$) from the boundary over \np{nn \_rimwidth} cells ($N$):543 \label{subsec:LBC_bdy_relaxation} 544 545 In addition to a specific boundary condition specified as \np{cn_tra}{cn\_tra} and \np{cn_dyn3d}{cn\_dyn3d}, relaxation on baroclinic velocities and tracers variables are available. 546 It is control by the namelist parameter \np{ln_tra_dmp}{ln\_tra\_dmp} and \np{ln_dyn3d_dmp}{ln\_dyn3d\_dmp} for each boundary set. 547 548 The relaxation time scale value (\np{rn_time_dmp}{rn\_time\_dmp} and \np{rn_time_dmp_out}{rn\_time\_dmp\_out}, $\tau$) are defined at the boundaries itself. 549 This time scale ($\alpha$) is weighted by the distance ($d$) from the boundary over \np{nn_rimwidth}{nn\_rimwidth} cells ($N$): 594 550 595 551 \[ … … 597 553 \] 598 554 599 The same scaling is applied in the Orlanski damping. 600 601 % ----------------------------------------------555 The same scaling is applied in the Orlanski damping. 556 557 %% ================================================================================================= 602 558 \subsection{Boundary geometry} 603 \label{subsec: BDY_geometry}559 \label{subsec:LBC_bdy_geometry} 604 560 605 561 Each open boundary set is defined as a list of points. 606 562 The information is stored in the arrays $nbi$, $nbj$, and $nbr$ in the $idx\_bdy$ structure. 607 The $nbi$ and $nbj$ arrays define the local $(i,j)$ ind ices of each point in the boundary zone and608 the $nbr$ array defines the discrete distance from the boundary with $nbr=1$ meaningthat609 the point is next to the edge of the model domain and $nbr>1$ showingthat610 the point is increasingly further away from the edge of the model domain.563 The $nbi$ and $nbj$ arrays define the local $(i,j)$ indexes of each point in the boundary zone and 564 the $nbr$ array defines the discrete distance from the boundary: $nbr=1$ means that 565 the boundary point is next to the edge of the model domain, while $nbr>1$ means that 566 the boundary point is increasingly further away from the edge of the model domain. 611 567 A set of $nbi$, $nbj$, and $nbr$ arrays is defined for each of the $T$, $U$ and $V$ grids. 612 Figure \autoref{fig:LBC_bdy_geom} shows an example of an irregular boundary. 568 \autoref{fig:LBC_bdy_geom} shows an example of an irregular boundary. 613 569 614 570 The boundary geometry for each set may be defined in a namelist nambdy\_index or 615 571 by reading in a ``\ifile{coordinates.bdy}'' file. 616 572 The nambdy\_index namelist defines a series of straight-line segments for north, east, south and west boundaries. 617 One nambdy\_index namelist bloc is needed for each boundary condition defined by indexes.618 For the northern boundary, \ np{nbdysegn} gives the number of segments,619 \ np{jpjnob} gives the $j$ index for each segment and \np{jpindt} and620 \ np{jpinft} give the start and end $i$ indices for each segment with similar for the other boundaries.573 One nambdy\_index namelist block is needed for each boundary condition defined by indexes. 574 For the northern boundary, \texttt{nbdysegn} gives the number of segments, 575 \jp{jpjnob} gives the $j$ index for each segment and \jp{jpindt} and 576 \jp{jpinft} give the start and end $i$ indices for each segment with similar for the other boundaries. 621 577 These segments define a list of $T$ grid points along the outermost row of the boundary ($nbr\,=\, 1$). 622 The code deduces the $U$ and $V$ points and also the points for $nbr\,>\, 1$ if \np {nn\_rimwidth}\forcode{ > 1}.578 The code deduces the $U$ and $V$ points and also the points for $nbr\,>\, 1$ if \np[>1]{nn_rimwidth}{nn\_rimwidth}. 623 579 624 580 The boundary geometry may also be defined from a ``\ifile{coordinates.bdy}'' file. 625 Figure \autoref{fig:LBC_nc_header} gives an example of the header information from such a file.581 \autoref{fig:LBC_nc_header} gives an example of the header information from such a file, based on the description of geometrical setup given above. 626 582 The file should contain the index arrays for each of the $T$, $U$ and $V$ grids. 627 583 The arrays must be in order of increasing $nbr$. … … 629 585 Typically this file will be used to generate external boundary data via interpolation and so 630 586 will also contain the latitudes and longitudes of each point as shown. 631 However, this is not necessary to run the model. 587 However, this is not necessary to run the model. 632 588 633 589 For some choices of irregular boundary the model domain may contain areas of ocean which 634 590 are not part of the computational domain. 635 For example if an open boundary is defined along an isobath, say at the shelf break,591 For example, if an open boundary is defined along an isobath, say at the shelf break, 636 592 then the areas of ocean outside of this boundary will need to be masked out. 637 This can be done by reading a mask file defined as \np{cn \_mask\_file} in the nam\_bdy namelist.593 This can be done by reading a mask file defined as \np{cn_mask_file}{cn\_mask\_file} in the nam\_bdy namelist. 638 594 Only one mask file is used even if multiple boundary sets are defined. 639 595 640 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>641 596 \begin{figure}[!t] 642 \begin{center} 643 \includegraphics[width=\textwidth]{Fig_LBC_bdy_geom} 644 \caption { 645 \protect\label{fig:LBC_bdy_geom} 646 Example of geometry of unstructured open boundary 647 } 648 \end{center} 597 \centering 598 \includegraphics[width=0.66\textwidth]{LBC_bdy_geom} 599 \caption[Geometry of unstructured open boundary]{Example of geometry of unstructured open boundary} 600 \label{fig:LBC_bdy_geom} 649 601 \end{figure} 650 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 651 652 %---------------------------------------------- 602 603 %% ================================================================================================= 653 604 \subsection{Input boundary data files} 654 \label{subsec: BDY_data}605 \label{subsec:LBC_bdy_data} 655 606 656 607 The data files contain the data arrays in the order in which the points are defined in the $nbi$ and $nbj$ arrays. … … 658 609 a time dimension; 659 610 $xb$ which is the index of the boundary data point in the horizontal; 660 and $yb$ which is a degenerate dimension of 1 to enable the file to be read by the standard NEMOI/O routines.661 The 3D fields also have a depth dimension. 611 and $yb$ which is a degenerate dimension of 1 to enable the file to be read by the standard \NEMO\ I/O routines. 612 The 3D fields also have a depth dimension. 662 613 663 614 From Version 3.4 there are new restrictions on the order in which the boundary points are defined … … 670 621 \item All the data for a particular boundary set must be in the same order. 671 622 (Prior to 3.4 it was possible to define barotropic data in a different order to 672 the data for tracers and baroclinic velocities). 623 the data for tracers and baroclinic velocities). 673 624 \end{enumerate} 674 625 675 626 These restrictions mean that data files used with versions of the 676 627 model prior to Version 3.4 may not work with Version 3.4 onwards. 677 A \fortran utility {\itshape bdy\_reorder} exists in the TOOLS directory which628 A \fortran\ utility {\itshape bdy\_reorder} exists in the TOOLS directory which 678 629 will re-order the data in old BDY data files. 679 630 680 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>681 631 \begin{figure}[!t] 682 \begin{center} 683 \includegraphics[width=\textwidth]{Fig_LBC_nc_header} 684 \caption { 685 \protect\label{fig:LBC_nc_header} 686 Example of the header for a \protect\ifile{coordinates.bdy} file 687 } 688 \end{center} 632 \centering 633 \includegraphics[width=0.66\textwidth]{LBC_nc_header} 634 \caption[Header for a \protect\ifile{coordinates.bdy} file]{ 635 Example of the header for a \protect\ifile{coordinates.bdy} file} 636 \label{fig:LBC_nc_header} 689 637 \end{figure} 690 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 691 692 %---------------------------------------------- 638 639 %% ================================================================================================= 693 640 \subsection{Volume correction} 694 \label{subsec: BDY_vol_corr}641 \label{subsec:LBC_bdy_vol_corr} 695 642 696 643 There is an option to force the total volume in the regional model to be constant. 697 This is controlled by the \np{ln \_vol} parameter in the namelist.698 A value of \np {ln\_vol}\forcode{ = .false.} indicates that this option is not used.699 Two options to control the volume are available (\np{nn \_volctl}).700 If \np {nn\_volctl}\forcode{ = 0} then a correction is applied to the normal barotropic velocities around the boundary at644 This is controlled by the \np{ln_vol}{ln\_vol} parameter in the namelist. 645 A value of \np[=.false.]{ln_vol}{ln\_vol} indicates that this option is not used. 646 Two options to control the volume are available (\np{nn_volctl}{nn\_volctl}). 647 If \np[=0]{nn_volctl}{nn\_volctl} then a correction is applied to the normal barotropic velocities around the boundary at 701 648 each timestep to ensure that the integrated volume flow through the boundary is zero. 702 If \np {nn\_volctl}\forcode{ = 1} then the calculation of the volume change on649 If \np[=1]{nn_volctl}{nn\_volctl} then the calculation of the volume change on 703 650 the timestep includes the change due to the freshwater flux across the surface and 704 651 the correction velocity corrects for this as well. … … 707 654 applied to all boundaries at once. 708 655 709 % ----------------------------------------------656 %% ================================================================================================= 710 657 \subsection{Tidal harmonic forcing} 711 \label{subsec:BDY_tides} 712 713 %-----------------------------------------nambdy_tide-------------------------------------------- 714 715 \nlst{nambdy_tide} 716 %----------------------------------------------------------------------------------------------- 658 \label{subsec:LBC_bdy_tides} 659 660 \begin{listing} 661 \nlst{nambdy_tide} 662 \caption{\forcode{&nambdy_tide}} 663 \label{lst:nambdy_tide} 664 \end{listing} 717 665 718 666 Tidal forcing at open boundaries requires the activation of surface 719 tides (i.e., in \n gn{nam\_tide}, \np{ln\_tide} needs to be set to667 tides (i.e., in \nam{_tide}{\_tide}, \np{ln_tide}{ln\_tide} needs to be set to 720 668 \forcode{.true.} and the required constituents need to be activated by 721 including their names in the \np{c name} array; see669 including their names in the \np{clname}{clname} array; see 722 670 \autoref{sec:SBC_tide}). Specific options related to the reading in of 723 671 the complex harmonic amplitudes of elevation (SSH) and barotropic 724 672 velocity (u,v) at open boundaries are defined through the 725 \n gn{nambdy\_tide} namelist parameters.\\673 \nam{bdy_tide}{bdy\_tide} namelist parameters.\\ 726 674 727 675 The tidal harmonic data at open boundaries can be specified in two 728 676 different ways, either on a two-dimensional grid covering the entire 729 677 model domain or along open boundary segments; these two variants can 730 be selected by setting \np{ln \_bdytide\_2ddta } to \forcode{.true.} or678 be selected by setting \np{ln_bdytide_2ddta }{ln\_bdytide\_2ddta } to \forcode{.true.} or 731 679 \forcode{.false.}, respectively. In either case, the real and 732 680 imaginary parts of SSH and the two barotropic velocity components for … … 734 682 separately: when two-dimensional data is used, variables 735 683 \textit{tcname\_z1} and \textit{tcname\_z2} for real and imaginary SSH, 736 respectively, are expected in input file \np{filtide} with suffix684 respectively, are expected in input file \np{filtide}{filtide} with suffix 737 685 \ifile{\_grid\_T}, variables \textit{tcname\_u1} and 738 686 \textit{tcname\_u2} for real and imaginary u, respectively, are 739 expected in input file \np{filtide} with suffix \ifile{\_grid\_U}, and687 expected in input file \np{filtide}{filtide} with suffix \ifile{\_grid\_U}, and 740 688 \textit{tcname\_v1} and \textit{tcname\_v2} for real and imaginary v, 741 respectively, are expected in input file \np{filtide} with suffix689 respectively, are expected in input file \np{filtide}{filtide} with suffix 742 690 \ifile{\_grid\_V}; when data along open boundary segments is used, 743 691 variables \textit{z1} and \textit{z2} (real and imaginary part of SSH) 744 are expected to be available from file \np{filtide} with suffix692 are expected to be available from file \np{filtide}{filtide} with suffix 745 693 \ifile{tcname\_grid\_T}, variables \textit{u1} and \textit{u2} (real 746 694 and imaginary part of u) are expected to be available from file 747 \np{filtide} with suffix \ifile{tcname\_grid\_U}, and variables695 \np{filtide}{filtide} with suffix \ifile{tcname\_grid\_U}, and variables 748 696 \textit{v1} and \textit{v2} (real and imaginary part of v) are 749 expected to be available from file \np{filtide} with suffix750 \ifile{tcname\_grid\_V}. If \np{ln \_bdytide\_conj} is set to697 expected to be available from file \np{filtide}{filtide} with suffix 698 \ifile{tcname\_grid\_V}. If \np{ln_bdytide_conj}{ln\_bdytide\_conj} is set to 751 699 \forcode{.true.}, the data is expected to be in complex conjugate 752 700 form. … … 760 708 direction of rotation). %, e.g. anticlockwise or clockwise. 761 709 762 \biblio 763 764 \pindex 710 \subinc{\input{../../global/epilogue}} 765 711 766 712 \end{document}
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