Changeset 781 for trunk/DOC/BETA/Chapters/Chap_LBC.tex
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trunk/DOC/BETA/Chapters/Chap_LBC.tex
r707 r781 128 128 \label{LBC_north_fold} 129 129 130 The north fold boundary condition ha ve been introduced in order to handle the north boundary of anthreepolar ORCA grid. Such a grid has two poles in the northern hemisphere. \colorbox{yellow}{to be completed...}130 The north fold boundary condition has been introduced in order to handle the north boundary of a threepolar ORCA grid. Such a grid has two poles in the northern hemisphere. \colorbox{yellow}{to be completed...} 131 131 132 132 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> … … 137 137 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 138 138 139 % ================================================================ 140 % Exchangedwith neighbouring processors141 % ================================================================ 142 \section{Exchange dwith neighbouring processors (\mdl{lbclnk}, \mdl{lib\_mpp})}139 % ==================================================================== 140 % SubDomain:Exchange with neighbouring processors 141 % ==================================================================== 142 \section{Exchange with neighbouring processors (\mdl{lbclnk}, \mdl{lib\_mpp})} 143 143 \label{LBC_mpp} 144 144 … … 184 184 185 185 186 The OPA model computes equation terms with the help of mask arrays ( 0 onto land points and 1 onto sea points). It is easily readable and very efficient in the context of the vectorial architecture. But in the case of scalar processor, computations over the land regions becomes more expensive in term of CPU time. It is all the more when we use a complex configuration with a realistic bathymetry like the global ocean where more than 50 \% of points are land points. For this reason, a preprocessing tool allows to search in the mpp domain decomposition strategy if a splitting can be found with a maximum number of only land points processors which could be eliminated (mppini2 program). This optimisation is made with the knowledge of the specific bathymetry in a first time and after, the OPA model, in its initialization part, take account only processors with a sea region. For that, one must indicate in the parameter file the initial cutting along i and jaxes with jpni and jpnjand the ocean processor number jpnij < jpni x jpnj. Each processor name and neighbour parameters (nbound, nono, noea,...) are modified by an algorithm in the inimpp2.F subroutine.187 186 188 187 The OPA model computes equation terms with the help of mask arrays (0 onto land points and 1 onto sea points). It is easily readable and very efficient in the context of the vectorial architecture. But in the case of scalar processor, computations over the land regions becomes more expensive in term of CPU time. It is all the more so when we use a complex configuration with a realistic bathymetry like the global ocean where more than 50 \% of points are land points. For this reason, a preprocessing tool allows to search in the mpp domain decomposition strategy if a splitting can be found with a maximum number of only land points processors which could be eliminated: the mpp\_optimiz tools (available from the DRAKKAR web site). This optimisation is made with the knowledge of the specific bathymetry. The user chooses optimal parameters \jp{jpni}, \jp{jpnj} and \jp{jpnij} with $jpnij < jpni \times jpnj$, leading to the elimination of $jpni \times jpnj  jpnij$ land processors. When those parameters are specified in module \mdl{par\_oce}, the algorithm in the \rou{inimpp2} routine set each processor name and neighbour parameters (nbound, nono, noea,...) so that the land processors are not taken into account. … … 205 204 \section{Open Boundary Conditions (\key{obc})} 206 205 \label{LBC_obc} 207 208 %gm% to be update from documentation already written by J.M. Molines + Mercator input 209 210 % ================================================================ 206 %nam_obc  207 % nobc_dta = 0 ! = 0 the obc data are equal to the initial state 208 % ! = 1 the obc data are read in 'obc .dta' files 209 % rdpein = 1. ! ??? 210 % rdpwin = 1. ! ??? 211 % rdpnin = 30. ! ??? 212 % rdpsin = 1. ! ??? 213 % rdpeob = 1500. ! time relaxation (days) for the east open boundary 214 % rdpwob = 15. ! " " for the west open boundary 215 % rdpnob = 150. ! " " for the north open boundary 216 % rdpsob = 15. ! " " for the south open boundary 217 % zbsic1 = 140.e+6 ! barotropic stream function on first isolated coastline 218 % zbsic2 = 1.e+6 ! " " on second isolated coastline 219 % zbsic3 = 0. ! " " on thrid isolated coastline 220 % ln_obc_clim = .true. ! climatological obc data files (default T) 221 % ln_vol_cst = .true. ! total volume conserved 222 \namdisplay{namobc} 223 224 It is often necessary to implement a model configuration limited to an oceanic region or a basin, which communicates with the rest of the global ocean through ``open boundaries''. As stated by \citet{Roed1986}, an open boundary is a computational border where the aim of the calculations is to allow the perturbations generated inside the computational domain to leave it without deterioration of the inner model solution. However, an open boundary also has to let information from the outer oceans enter the model and should support inflow and outflow conditions. 225 226 The open boundary package OBC is the first open boundary option developed in NEMO (originally in OPA8.2). It allows the user to 227 \begin{itemize} 228 \item tell the model that a boundary is ``open'' and not closed by a wall, for example by modifying the calculation of the divergence of velocity there, and other necessary modifications; 229 \item impose values of tracers and velocities at that boundary (values which may be taken from a climatology): this is the``fixed OBC'' option. 230 \item calculate boundary values by a sophisticated algorithm combining radiation and relaxation (``radiative OBC'' option) 231 \end{itemize} 232 233 The package resides in the OBC directory. It is described here in four parts: the boundary geometry (parameters to be set in \mdl{obc\_par}), the forcing data at the boundaries (module \mdl{obcdta}), the radiation algorithm involving the namelist and module \mdl{obcrad}, and a brief presentation of boundary update and restart files. 234 235 % 236 \subsection{Boundary geometry} 237 \label{OBC_geom} 238 % 239 First one has to realize that open boundaries may not necessarily be located at the extremities of the computational domain. They may exist in the middle of the domain, for example at Gibraltar Straits if one wants to avoid including the Mediterranean in an Atlantic domain. This flexibility has been found necessary for the CLIPPER project \citep{Treguier2001}. Because of the complexity of the geometry of ocean basins, it may even be necessary to have more than one ``west'' open boundary, more than one ``north'', etc. This is not possible with the OBC option: only one open boundary of each kind, west, east, south and north is allowed; those names refer to the grid geometry (not to the direction of the geographical ``west'', ``east'', etc). 240 241 The open boundary geometry is set by a series of parameters in the module \mdl{obc\_par}. For an eastern open boundary, parameters are \jp{lp\_obc\_east} (true if an east open boundary exists), \jp{jpieob} the $i$index along which the eastern open boundary (eob) is located, \jp{jpjed} the $j$index at which it starts, and \jp{jpjef} the $j$index where it ends (note $d$ is for ``d\'{e}but'' and $f$ for ``fin'' in French). Similar parameters exist for the west, south and north cases (Table~\ref{Tab_obc_param}). 242 243 244 %TABLE 245 246 \begin{table}[htbp] \label{Tab_obc_param} 247 \begin{center} 248 \begin{tabular}{lccc} 249 \hline 250 Boundary and & Constant index & Starting index (d\'{e}but) & Ending index (fin) \\ 251 Logical flag & & & \\ 252 \hline 253 West & \jp{jpiwob} $>= 2$ & \jp{jpjwd}$>= 2$ & \jp{jpjwf}<= \jp{jpjglo}1 \\ 254 lp\_obc\_west & $i$index of a $u$ point & $j$ of a $T$ point &$j$ of a $T$ point \\ 255 \hline 256 East & \jp{jpieob}$<=$\jp{jpiglo}2&\jp{jpjed} $>= 2$ & \jp{jpjef}$<=$ \jp{jpjglo}1 \\ 257 lp\_obc\_east & $i$index of a $u$ point & $j$ of a $T$ point & $j$ of a $T$ point \\ 258 \hline 259 South & \jp{jpjsob} $>= 2$ & \jp{jpisd} $>= 2$ & \jp{jpisf}$<=$\jp{jpiglo}1 \\ 260 lp\_obc\_south & $j$index of a $v$ point & $i$ of a $T$ point & $i$ of a $T$ point \\ 261 \hline 262 North & \jp{jpjnob} $<=$ \jp{jpjglo}2& \jp{jpind} $>= 2$ & \jp{jpinf}$<=$\jp{jpiglo}1 \\ 263 lp\_obc\_north & $j$index of a $v$ point & $i$ of a $T$ point & $i$ of a $T$ point \\ 264 \hline 265 \end{tabular} 266 \end{center} 267 \caption{Names of different indices concerning the open boundaries. In the case of a completely open ocean domain with four ocean boundaries, the parameters take exactly the values indicated.} 268 \end{table} 269 270 The open boundaries must be along coordinate lines. On the Cgrid, the boundary itself is along a line of normal velocity points: $v$ points for a zonal open boundary (the south or north one), and $u$ points for a meridional open boundary (the west or east one). Another constraint is that there still must be a row of masked points all around the domain, as if the domain were a closed basin (unless periodic conditions are used together with open boundary conditions). Therefore, an open boundary cannot be located at the first/last index, namely, 1 or \jp{jpiglo}, \jp{jpjglo}. Also, the open boundary algorithm involves calculating the normal velocity points situated just on the boundary, as well as the tangential velocity and temperature, salinity just outside the boundary. This means that for a west/south boundary, normal velocities and temperature are calculated at the same index \jp{jpiwob} and \jp{jpjsob}, respectively. For an east/north boundary, the normal velocity is calculated at index \jp{jpieob} and \jp{jpjnob}, but the ``outside'' temperature is at index \jp{jpieob}+1 and \jp{jpjnob}+1. This means that \jp{jpieob}, \jp{jpjnob} cannot be bigger than \jp{jpiglo}2, \jp{jpjglo}2. 271 272 273 The starting and ending indices are to be thought as $T$ point indices: in many cases they indicate the first land $T$point, at the extremity of an open boundary (the coast line follows the $f$ grid points, see Fig.~\ref{Fig_obc_north} for the example for a northern open boundary. All indices are relative to the global domain. In the free surface case it is possible to have ``ocean corners'', that is, an open boundary starting and ending in the ocean. 274 275 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 276 \begin{figure}[!t] \label{Fig_obc_north} \begin{center} 277 \includegraphics[width=0.70\textwidth]{./Figures/Fig_obc_north.pdf} 278 \caption {Localization of the North open boundary points.} 279 \end{center} 280 \end{figure} 281 %>>>>>>>>>>>>>>>>>>>>>>>>>>>> 282 283 Although not absolutely compulsory, it is highly recommended that the bathymetry in the vicinity of an open boundary follows the following rule: in the direction perpendicular to the open line, the water depth should be constant for 4 grid points. This is in order to ensure that the radiation condition, which involves mdoel variables next to the boundary, is calculated in a consistent way. On Fig.\ref{Fig_obc_north} we indicate by a $=$ symbol, the points which should have the same depth. It means that in the 4 points near the boundary, the bathymetry is cylindrical. The line behind the open Tline must be 0 in the bathymetry file (as shown on Fig.\ref{Fig_obc_north} for example). 284 285 % 286 \subsection{Boundary data} 287 \label{OBC_data} 288 289 It is necessary to provide information at the boundaries. The simple case happens when this information does not change in time and is equal to the initial conditions (namelist variable \np{nobc\_dta}=0). This is the case of the standard configuration EEL5 with open boundaries. When (\np{nobc\_dta}=1), open boundary information is read from netcdf files. For convenience the input files are supposed to be similar to the ''history'' NEMO output files, for dimension names and variable names. 290 Open boundary arrays must be dimensioned according to the parameters of table~\ref{Tab_obc_param}: for example, at the western boundary arrays have a dimension of \jp{jpwf}\jp{jpwd}+1 on the horizontal and \jp{jpk} on the vertical. 291 292 When ocean observations are used to generate the boundary data (a hydrographic section for example, as in \citet{Treguier2001}) it happens often that only the velocity normal to the boundary is known, which is the reason why the initial OBC code assumes that only $T$, $S$, and the normal velocity ($u$ or $v$) needs to be specified. As more and more global model solutions and ocean analysis products are available, it is possible to provide information about all the variables (including the tangential velocity) so that the specification of four variables at each boundaries will soon become standard. Regarding the sea surface height, one must distinguish the filtered free surface case from the timesplitting or explicit treatment of the free surface. 293 In the first case, it is assumed that the user does not wish to represent high frequency motions such as tides. The boundary condition is thus one of zero normal gradient of sea surface height at the open boundaries, following \citet{Marchesiello2001}. 294 No information other than the total velocity needs to be provided at the open boundaries in that case. In the other two cases (time stplitting or explicit free surface), the user must provides barotropic information (sea surface height and barotropic velocities) and the use of the Flather algorithm for barotropic variables is recommanded. However, this algorithm has not yet been fully tested and bugs remain in NEMO v2.3. Users should read the code carefully before using it. Finally, in the case of the rigid lid approximation the barotropic streamfunction must be provided, as documented in \citet{Treguier2001}). This option is no longer used but remains in NEMO V2.3. 295 296 One frequently encountered case is when an open boundary domain is constructed from a global or larger scale NEMO configuration. Assuming the domain corresponds to indices $ib:ie$, $jb:je$ of the global domain, the bathymetry and forcing of the small domain can be created by using the following command on the global files: ncks F $d\;x,ib,ie$ $d\;y,jb,je$. 297 The open boundary files can be constructed using ncks commands, following table~\ref{Tab_obc_ind}. 298 299 %TABLE 300 301 \begin{table}[htbp] \label{Tab_obc_ind} 302 \begin{center} 303 \begin{tabular}{lccccc} 304 \hline 305 OBC & Variable & file name & Index & Start & end \\ 306 West & T,S & obcwest\_TS.nc & $ib$+1 & $jb$+1 & $je1$ \\ 307 & U & obcwest\_U.nc & $ib$+1 & $jb$+1 & $je1$ \\ 308 & V & obcwest\_V.nc & $ib$+1 & $jb$+1 & $je1$ \\ 309 \hline 310 East & T,S & obceast\_TS.nc & $ie$1 & $jb$+1 & $je1$ \\ 311 & U & obceast\_U.nc & $ie$2 & $jb$+1 & $je1$ \\ 312 & V & obceast\_V.nc & $ie$1 & $jb$+1 & $je1$ \\ 313 \hline 314 South & T,S & obcsouth\_TS.nc & $jb$+1 & $ib$+1 & $ie1$ \\ 315 & U & obcsouth\_U.nc & $jb$+1 & $ib$+1 & $ie1$ \\ 316 & V & obcsouth\_V.nc & $jb$+1 & $ib$+1 & $ie1$ \\ 317 \hline 318 North & T,S & obcnorth\_TS.nc & $je$1 & $ib$+1 & $ie1$ \\ 319 & U & obcnorth\_U.nc & $je$1 & $ib$+1 & $ie1$ \\ 320 & V & obcnorth\_V.nc & $je$2 & $ib$+1 & $ie1$ \\ 321 \hline 322 \end{tabular} 323 \end{center} 324 \caption{Indications for creating open boundary files from a global configuration, appropriate for the subdomain of indices $ib:ie$, $jb:je$. ``Index'' designates the $i$ or $j$ index along which the $u$ of $v$ boundary point is situated in the global configuration, starting and ending with the $j$ or $i$ indices indicated. For example, to generate file obcnorth\_V.nc, use the command ncks $F$ $d\;y,je2$ $d\;x,ib+1,ie1$ } 325 \end{table} 326 327 It is assumed that the open boundary files contain the variables for the period of the model integration. If the boundary files contain one time frame, the boundary data is held fixed in time. If the files contain 12 values, it is assumed that the input is a climatology for a repeated annual cycle (corresponding to the case \np{ln\_obc\_clim} = .T.). The case of an arbitrary number of time frames is not yet implemented correctly; the user is supposed to write his own code in the module \mdl{obc\_dta} to deal with this situation. 328 329 \subsection{Radiation algorithm} 330 \label{OBC_rad} 331 332 The art of open boundary management consists in applying a constraint strong enough so that the inner domain "feels" the rest of the ocean, but not too strong 333 in order to allow perturbations to leave the domain with minimum false reflexions of energy. The cosntraint to the specified boundary data is set by time scales 334 specified separately for each boundary and for ``inflow'' and `outflow'' conditions as defined below. These time scales are set (in days) by namelist parameters such as \np{rdpein}, \np{rdpeob} for the eastern open boundary, for example. When both time scales are zero for a given boundary, for example 335 \jp{lp\_obc\_west}=.T., \np{rdpwob}=0, \np{rdpwin}=0, this means that the boundary in question (western boundary here) is a ``fixed '' boundary where the solution is set exactly by the boundary data. This is not recommanded, excepted in compination with increased viscosity in a ``sponge'' layer next to the boundary in order to avois spurious reflexions. 336 337 338 The radiation\/relaxation algorithm is applied when either relxation time (for ``inflow'' or `outflow'') is nonzero. It has been developed and tested in the SPEM model and its successor ROMS \citep{Barnier1996, Marchesiello2001}, a $s$coordinate model on an Arakawa Cgrid. Although the algorithm has been numerically successful in the CLIPPER Atlantic models, the physics do not work as expected \citep{Treguier2001}. Users are invited to consider open boundary conditions (OBC hereafter) with some skepticism \citep{Durran2001, Blayo2005}. 339 340 The first part of the algorithm consists in calculating a phase 341 velocity to determine whether perturbations tend to propagate toward, 342 or away from, the boundary. 343 Let us consider a model variable $\phi$. 344 The phase velocity ($C_{\phi x}$,$C_{\phi y}$) for the variable 345 $\phi$, in the directions normal and tangential to 346 the boundary is 347 \begin{equation} \label{Eq_obc_cphi} 348 C_{\phi x} = \frac{ \phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{x} 349 \;\;\;\;\; \;\;\; 350 C_{\phi y} = \frac{ \phi_{t} }{ ( \phi_{x}^{2} + \phi_{y}^{2}) } \phi_{y}. 351 \end{equation} 352 Following \citet{Treguier2001} and \citet{Marchesiello2001} retain only the normal 353 projection of the total velocity, $C_{\phi x}$, setting 354 $C_{\phi y} =0$ (but unlike the original Orlanski radiation algorithm we retain $\phi_{y}$ in the expression 355 for $C_{\phi x}$). 356 357 The discrete form of (\ref{Eq_obc_cphi}), described by \citet{Barnier1998}, 358 takes into account the two rows of grid points situated inside the domain 359 next to the boundary, and the three previous time steps ($n$, $n1$, 360 and $n2$). 361 The same equation can then be discretized at the boundary at 362 time steps $n$ and $n+1$ in order to extrapolate the new boundary 363 value $\phi^{n+1}$. 364 365 In the present open boundary algorithm, the new boundary values are 366 updated differently according to the sign of $C_{\phi x}$. 367 Let us take an East boundary as an example. The solution for variable $\phi$ at the boundary is given from a generalized wave equation 368 with phase velocity $C_{\phi}$, with the addition of a relaxation term: 369 \begin{eqnarray} 370 \phi_{t} & = & C_{\phi x} \phi_{x} + \frac{1}{\tau_{o}} (\phi_{c}\phi) 371 \;\;\; \;\;\; \;\;\; (C_{\phi x} > 0), \label{Eq_obc_rado} \\ 372 \phi_{t} & = & \frac{1}{\tau_{i}} (\phi_{c}\phi) 373 \;\;\; \;\;\; \;\;\;\;\;\; (C_{\phi x} < 0), \label{Eq_obc_radi} 374 \end{eqnarray} 375 where $\phi_{c}$ is the estimate of $\phi$ at the boundary, provided as boundary data. 376 Note that in (\ref{Eq_obc_rado}), $C_{\phi x}$ 377 is bounded by the ratio $\delta x/\delta t$ for stability reasons. 378 When $C_{\phi x}$ is eastward (outward propagation), 379 the radiation condition (\ref{Eq_obc_rado}) is used. 380 When $C_{\phi x}$ is westward (inward propagation), (\ref{Eq_obc_radi}) is used with 381 a strong relaxation to climatology (usually $\tau_{i}=\np{rdpein}=$1~day). 382 The time derivative in (\ref{Eq_obc_radi}) is calculated with a Euler timestepping 383 scheme. It results from this choice that setting 384 $\tau_{i}$ smaller than, or equal to the time step is in fact equivalent to a fixed boundary condition; 385 a time scale of one day is usually a good compromise which guarantees that the inflow conditions remain close to 386 climatology while ensuring numerical stability. 387 388 In the case of a west boundary located in the Eastern Atlantic, \citet{Penduff2000} have been able to implement the radiation algorithm 389 without any boundary data, using persistence from the previous time step instead. This solution did not work in other cases \citep{Treguier2001} so that the use of boundary data is recommended. 390 Even in the outflow condition (\ref{Eq_obc_rado}), we have found desireable to maintain a weak relaxation to climatology. 391 The time step is usually chosen so as to be larger than typical turbulent scales (of order 1000~days). 392 393 The radiation condition is applied to the different model variables: temperature, salinity, tangential and normal velocities. 394 For normal and tangential velocities $u$ and $v$ radiation is applied with phase velocities calculated from $u$ and $v$ respectively. 395 For the radiation of tracers, we use the phase velocity calculated from the tangential velocity, to avoid calculating too many independent 396 radiation velocities and because tangential velocities and tracers have the same position along the boundary on a C grid. 397 398 \subsection{Domain decomposition (\key{mpp\_mpi})} 399 \label{OBC_mpp} 400 When \key{mpp\_mpi} is active in the code, the computational domain is divided into rectangles that are attributed each to a different processor. The open boundary code is ``mppcompatible'' up to a certain point. The radiation algorithm will not work if there is a mpp subdomain boundary parallel to the open boundary at the index of the boundary, or the grid point after (outside), or three grid points before (inside). On the other hand, there is no problem if a mpp subdomain boundary cuts the open boundary perpendicularly. Those geometry constraints must be checked by the user (there is no safeguard in the code). 401 The general principle for the open boundary mpp code is that loops over the open boundaries are performed on local indices (nie0, nie1, nje0, nje1 for the eastern boundary for instance) that are initialized in module \mdl{obc\_ini}. Those indices have relevant values on the processors that contain a segment of an open boundary. For processors that do not include an open boundary segment, the indices are such that the calculations within the loops are not performed. 402 403 Arrays of climatological data that are read in files are seen by all processors and have the same dimensions for all (for instance, for the eastern boundary, uedta(jpjglo,jpk,2)). On the other hand, the arrays for the calculation of radiation are local to each processor (uebnd(jpj,jpk,3,3) for instance). This allowed to spare memory in the CLIPPER model, where the eastern boundary crossed 8 processors so that \jp{jpj} was must smaller than (\jp{jpjef}\jp{jpjed}+1). 404 405 \subsection{Volume conservation} 406 \label{OBC_vol} 407 408 It is necessary to control the volume inside a domain with open boundaries. With fixed boundaries, it is enough to ensure that the total inflow/outflow has reasonable values (either zero or a value compatible with an observed volume balance). When using radiative boundary conditions it is necessary to have a volume constraint because each open boundary works independently from the others. The methodology used to control this volume is identical to the one coded in the ROMS model \citep{Marchesiello2001}. 409 410 411 % EXTRAS 412 \colorbox{yellow}{Explain obc\_vol{\ldots}} 413 414 \colorbox{yellow}{OBC algorithm for update, OBC restart, list of routines where obc key appears{\ldots}} 415 416 \colorbox{yellow}{OBC rigid lid? {\ldots}} 417 418 419 420 421 % ==================================================================== 211 422 % Flow Relaxation Scheme 212 % ================================================================ 423 % ==================================================================== 213 424 \section{Flow Relaxation Scheme (???)} 214 425 \label{LBC_bdy}
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