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first attempt of an introduction;
add more text about reading boundary values from a file and balancing,
reference experiments

1 heimbach 1.1 \subsection{OBCS: Open boundary conditions for regional modeling}
2    
3     \label{sec:pkg:obcs}
4     \begin{rawhtml}
5     <!-- CMIREDIR:package_obcs: -->
6     \end{rawhtml}
7    
8 heimbach 1.2 Authors:
9     Alistair Adcroft, Patrick Heimbach, Samar Katiwala, Martin Losch
10 heimbach 1.1
11     \subsubsection{Introduction
12     \label{sec:pkg:obcs:intro}}
13    
14 mlosch 1.7 The OBCS-package is fundamental to regional ocean modelling with the
15     MITgcm, but because there are so many details to be considered in
16     regional ocean modelling that this package cannot accomodate all
17     imaginable and possible options. Therefore, for a regional simulation
18     with very particular details, it is recommended to familiarize oneself
19     not only with the compile- and runtime-options of this package, but
20     also with the code itself. In many cases it will be necessary to adapt
21     the obcs-code (in particular \code{S/R OBCS\_CALC}) to the application
22     in question; in these cases the obcs-package (together with the
23     rbcs-package, section \ref{sec:pkg:rbcs}) is a very
24     useful infrastructure for implementing special regional models.
25 heimbach 1.1
26     %----------------------------------------------------------------------
27    
28     \subsubsection{OBCS configuration and compiling
29 jmc 1.4 \label{sec:pkg:obcs:comp}}
30 heimbach 1.1
31     As with all MITgcm packages, OBCS can be turned on or off
32     at compile time
33     %
34     \begin{itemize}
35     %
36     \item
37 mlosch 1.6 using the \code{packages.conf} file by adding \code{obcs} to it,
38 heimbach 1.1 %
39     \item
40 mlosch 1.6 or using \code{genmake2} adding
41     \code{-enable=obcs} or \code{-disable=obcs} switches
42 heimbach 1.1 %
43     \item
44     \textit{Required packages and CPP options:} \\
45     %
46     To alternatives are available for prescribing open boundary values,
47     which differ in the way how OB's are treated in time:
48     A simple time-management (e.g. constant in time, or cyclic with
49     fixed fequency) is provided through
50 mlosch 1.6 S/R \code{obcs\_external\_fields\_load}.
51 heimbach 1.1 More sophisticated ``real-time'' (i.e. calendar time) management is
52 mlosch 1.6 available through \code{obcs\_prescribe\_read}.
53 heimbach 1.1 The latter case requires
54 mlosch 1.6 packages \code{cal} and \code{exf} to be enabled.
55 heimbach 1.1 %
56     \end{itemize}
57 jmc 1.5 (see also Section \ref{sec:buildingCode}).
58 heimbach 1.1
59     Parts of the OBCS code can be enabled or disabled at compile time
60     via CPP preprocessor flags. These options are set in
61 mlosch 1.6 \code{OBCS\_OPTIONS.h}. Table \ref{tab:pkg:obcs:cpp} summarizes them.
62 heimbach 1.1
63 jmc 1.5 \begin{table}[!ht]
64 heimbach 1.1 \centering
65     \label{tab:pkg:obcs:cpp}
66     {\footnotesize
67     \begin{tabular}{|l|l|}
68     \hline
69     \textbf{CPP option} & \textbf{Description} \\
70     \hline \hline
71 mlosch 1.6 \code{ALLOW\_OBCS\_NORTH} &
72 heimbach 1.1 enable Northern OB \\
73 mlosch 1.6 \code{ALLOW\_OBCS\_SOUTH} &
74 heimbach 1.1 enable Southern OB \\
75 mlosch 1.6 \code{ALLOW\_OBCS\_EAST} &
76 heimbach 1.1 enable Eastern OB \\
77 mlosch 1.6 \code{ALLOW\_OBCS\_WEST} &
78 heimbach 1.1 enable Western OB \\
79     \hline
80 mlosch 1.6 \code{ALLOW\_OBCS\_PRESCRIBE} &
81 heimbach 1.1 enable code for prescribing OB's \\
82 mlosch 1.6 \code{ALLOW\_OBCS\_SPONGE} &
83 heimbach 1.1 enable sponge layer code \\
84 mlosch 1.6 \code{ALLOW\_OBCS\_BALANCE} &
85 heimbach 1.1 enable code for balancing transports through OB's \\
86 mlosch 1.6 \code{ALLOW\_ORLANSKI} &
87 heimbach 1.1 enable Orlanski radiation conditions at OB's \\
88 mlosch 1.6 \code{ALLOW\_OBCS\_STEVENS} &
89     enable Stevens (1990) boundary conditions at OB's \\
90     & (currently only implemented for eastern and western \\
91     & boundaries and NOT for ptracers) \\
92 heimbach 1.1 \hline
93     \end{tabular}
94     }
95     \caption{~}
96     \end{table}
97    
98    
99     %----------------------------------------------------------------------
100    
101     \subsubsection{Run-time parameters
102     \label{sec:pkg:obcs:runtime}}
103    
104     Run-time parameters are set in files
105 mlosch 1.6 \code{data.pkg}, \code{data.obcs}, and \code{data.exf}
106 heimbach 1.1 if ``real-time'' prescription is requested
107 mlosch 1.6 (i.e. package \code{exf} enabled).
108 heimbach 1.1 These parameter files are read in S/R
109 mlosch 1.6 \code{packages\_readparms.F}, \code{obcs\_readparms.F}, and
110     \code{exf\_readparms.F}, respectively.
111 heimbach 1.1 Run-time parameters may be broken into 3 categories:
112     (i) switching on/off the package at runtime,
113     (ii) OBCS package flags and parameters,
114 mlosch 1.6 (iii) additional timing flags in \code{data.exf}, if selected.
115 heimbach 1.1
116     \paragraph{Enabling the package}
117     ~ \\
118     %
119     The OBCS package is switched on at runtime by setting
120 mlosch 1.6 \code{useOBCS = .TRUE.} in \code{data.pkg}.
121 heimbach 1.1
122     \paragraph{Package flags and parameters}
123     ~ \\
124     %
125     Table \ref{tab:pkg:obcs:runtime_flags} summarizes the
126 mlosch 1.6 runtime flags that are set in \code{data.obcs}, and
127 heimbach 1.1 their default values.
128    
129 jmc 1.5 \begin{table}[!ht]
130 heimbach 1.1 \centering
131     {\footnotesize
132     \begin{tabular}{|l|c|l|}
133     \hline
134     \textbf{Flag/parameter} & \textbf{default} & \textbf{Description} \\
135     \hline \hline
136 mlosch 1.6 \multicolumn{3}{|c|}{\textit{basic flags \& parameters} (OBCS\_PARM01) } \\
137 heimbach 1.1 \hline
138     OB\_Jnorth & 0 &
139     Nx-vector of J-indices (w.r.t. Ny) of Northern OB
140     at each I-position (w.r.t. Nx) \\
141     OB\_Jsouth & 0 &
142     Nx-vector of J-indices (w.r.t. Ny) of Southern OB
143     at each I-position (w.r.t. Nx) \\
144     OB\_Ieast & 0 &
145     Ny-vector of I-indices (w.r.t. Nx) of Eastern OB
146     at each J-position (w.r.t. Ny) \\
147     OB\_Iwest & 0 &
148     Ny-vector of I-indices (w.r.t. Nx) of Western OB
149     at each J-position (w.r.t. Ny) \\
150 mlosch 1.6 useOBCSprescribe & \code{.FALSE.} &
151 heimbach 1.1 ~ \\
152 mlosch 1.6 useOBCSsponge & \code{.FALSE.} &
153 heimbach 1.1 ~ \\
154 mlosch 1.6 useOBCSbalance & \code{.FALSE.} &
155 heimbach 1.1 ~ \\
156 mlosch 1.6 useOrlanskiNorth/South/EastWest & \code{.FALSE.} &
157     turn on Orlanski boundary conditions for individual boundary\\
158     useStevensNorth/South/EastWest & \code{.FALSE.} &
159     turn on Stevens boundary conditions for individual boundary\\
160 heimbach 1.1 OB\textbf{X}\textbf{y}File & ~ &
161     file name of OB field \\
162     ~ & ~ &
163     \textbf{X}: \textbf{N}(orth), \textbf{S}(outh),
164     \textbf{E}(ast), \textbf{W}(est) \\
165     ~ & ~ &
166     \textbf{y}: \textbf{t}(emperature), \textbf{s}(salinity),
167 mlosch 1.6 \textbf{u}(-velocity), \textbf{v}(-velocity), \\
168     ~ & ~ &
169     \textbf{w}(-velocity), \textbf{eta}(sea surface height)\\
170     ~ & ~ &
171     \textbf{a}(sea ice area), \textbf{h}(sea ice thickness),
172     \textbf{sn}(snow thickness), \textbf{sl}(sea ice salinity)\\
173 heimbach 1.1 \hline
174 mlosch 1.6 \multicolumn{3}{|c|}{\textit{Orlanski parameters} (OBCS\_PARM02) } \\
175 heimbach 1.1 \hline
176     cvelTimeScale & 2000 sec &
177     averaging period for phase speed \\
178     CMAX & 0.45 m/s &
179     maximum allowable phase speed-CFL for AB-II \\
180     CFIX & 0.8 m/s &
181     fixed boundary phase speed \\
182 mlosch 1.6 useFixedCEast & \code{.FALSE.} &
183 heimbach 1.1 ~ \\
184 mlosch 1.6 useFixedCWest & \code{.FALSE.} &
185 heimbach 1.1 ~ \\
186     \hline
187 mlosch 1.6 \multicolumn{3}{|c|}{\textit{Sponge-layer parameters} (OBCS\_PARM03)} \\
188 heimbach 1.1 \hline
189     spongeThickness & 0 &
190     sponge layer thickness (in \# grid points) \\
191     Urelaxobcsinner & 0 sec &
192     relaxation time scale at the
193     innermost sponge layer point of a meridional OB \\
194     Vrelaxobcsinner & 0 sec &
195     relaxation time scale at the
196     innermost sponge layer point of a zonal OB \\
197     Urelaxobcsbound & 0 sec &
198     relaxation time scale at the
199     outermost sponge layer point of a meridional OB \\
200     Vrelaxobcsbound & 0 sec &
201     relaxation time scale at the
202     outermost sponge layer point of a zonal OB \\
203 mlosch 1.6 \hline
204     \multicolumn{3}{|c|}{\textit{Stevens parameters} (OBCS\_PARM04) } \\
205     \hline
206     T/SrelaxStevens & 0~sec & relaxation time scale for
207     temperature/salinity \\
208     useStevensPhaseVel & \code{.TRUE.} & \\
209     useStevensAdvection & \code{.TRUE.} & \\
210 heimbach 1.1 \hline
211     \hline
212     \end{tabular}
213     }
214 jmc 1.5 \caption{pkg OBCS run-time parameters}
215     \label{tab:pkg:obcs:runtime_flags}
216 heimbach 1.1 \end{table}
217    
218    
219    
220     %----------------------------------------------------------------------
221    
222 heimbach 1.2 \subsubsection{Defining open boundary positions
223     \label{sec:pkg:obcs:defining}}
224    
225     There are four open boundaries (OBs), a
226     Northern, Southern, Eastern, and Western.
227     All OB locations are specified by their absolute
228     meridional (Northern/Southern) or zonal (Eastern/Western) indices.
229 mlosch 1.6 Thus, for each zonal position $i=1,\ldots,N_x$ a meridional index
230 heimbach 1.2 $j$ specifies the Northern/Southern OB position,
231 mlosch 1.6 and for each meridional position $j=1,\ldots,N_y$, a zonal index
232 heimbach 1.2 $i$ specifies the Eastern/Western OB position.
233 mlosch 1.6 For Northern/Southern OB this defines an $N_x$-dimensional
234 heimbach 1.2 ``row'' array $\tt OB\_Jnorth(Ny)$ / $\tt OB\_Jsouth(Ny)$,
235 mlosch 1.6 and an $N_y$-dimenisonal
236     ``column'' array $\tt OB\_Ieast(Nx)$ / $\tt OB\_Iwest(Nx)$.
237 heimbach 1.2 Positions determined in this way allows Northern/Southern
238     OBs to be at variable $j$ (or $y$) positions, and Eastern/Western
239     OBs at variable $i$ (or $x$) positions.
240     Here, indices refer to tracer points on the C-grid.
241     A zero (0) element in $\tt OB\_I\ldots$, $\tt OB\_J\ldots$
242     means there is no corresponding OB in that column/row.
243     For a Northern/Southern OB, the OB V point is to the South/North.
244     For an Eastern/Western OB, the OB U point is to the West/East.
245    
246     \begin{verbatim}
247     For example
248     OB_Jnorth(3)=34 means that:
249     T( 3 ,34) is a an OB point
250     U(3:4,34) is a an OB point
251     V( 4 ,34) is a an OB point
252     while
253     OB_Jsouth(3)=1 means that:
254     T( 3 ,1) is a an OB point
255     U(3:4,1) is a an OB point
256     V( 4 ,2) is a an OB point
257     \end{verbatim}
258    
259     For convenience, negative values for Jnorth/Ieast refer to
260     points relative to the Northern/Eastern edges of the model
261     eg. $\tt OB\_Jnorth(3)=-1$ means that the point $\tt (3,Ny)$
262     is a northern OB.
263    
264     \noindent
265     \textsf{Add special comments for case \#define NONLIN\_FRSURF,
266     see obcs\_ini\_fixed.F}
267    
268     %----------------------------------------------------------------------
269    
270 heimbach 1.1 \subsubsection{Equations and key routines
271     \label{sec:pkg:obcs:equations}}
272    
273 heimbach 1.2 \paragraph{OBCS\_READPARMS:} ~ \\
274     Set OB positions through arrays
275     {\tt OB\_Jnorth(Ny), OB\_Jsouth(Ny), OB\_Ieast(Nx), OB\_Iwest(Nx)},
276 jmc 1.5 and runtime flags (see Table \ref{tab:pkg:obcs:runtime_flags}).
277 heimbach 1.1
278     \paragraph{OBCS\_CALC:} ~ \\
279 heimbach 1.2 %
280     Top-level routine for filling values to be applied at OB for
281     $T,S,U,V,\eta$ into corresponding
282     ``slice'' arrays $(x,z)$, $(y,z)$ for each OB:
283     $\tt OB[N/S/E/W][t/s/u/v]$; e.g. for salinity array at
284     Southern OB, array name is $\tt OBSt$.
285     Values filled are either
286     %
287     \begin{itemize}
288     %
289     \item
290     constant vertical $T,S$ profiles as specified in file
291     {\tt data} ({\tt tRef(Nr), sRef(Nr)}) with zero velocities $U,V$,
292     %
293     \item
294     $T,S,U,V$ values determined via Orlanski radiation conditions
295     (see below),
296     %
297     \item
298     prescribed time-constant or time-varying fields (see below).
299     %
300 mlosch 1.6 \item
301     use prescribed boundary fields to compute Stevens boundary conditions.
302 heimbach 1.2 \end{itemize}
303    
304 mlosch 1.6 \paragraph{ORLANSKI:} ~ \\
305 heimbach 1.2 %
306 mlosch 1.6 Orlanski radiation conditions \citep{orl:76}, examples can be found in
307     \code{verification/dome} and
308     \code{verification/tutorial\_plume\_on\_slope}
309     (\ref{sec:eg-gravityplume}).
310    
311     \paragraph{OBCS\_PRESCRIBE\_READ:} ~ \\
312     %
313     When \code{useOBCSprescribe = .TRUE.} the model tries to read
314     temperature, salinity, u- and v-velocities from files specified in the
315     runtime parameters \code{OB[N/S/E/W][t/s/u/v]File}. These files are
316     the usual IEEE, big-endian files with dimensions of a section along an
317     open boundary:
318     \begin{itemize}
319     \item For North/South boundary files the dimensions are
320     $(N_x\times N_r\times\mbox{time levels})$, for East/West boundary
321     files the dimensions are $(N_y\times N_r\times\mbox{time levels})$.
322     \item If a non-linear free surface is used
323     (\ref{sec:nonlinear-freesurface}), additional files
324     \code{OB[N/S/E/W]etaFile} for the sea surface height $\eta$ with
325     dimension $(N_{x/y}\times\mbox{time levels})$ may be specified.
326     \item If non-hydrostatic dynamics are used
327     (\ref{sec:non-hydrostatic}), additional files
328     \code{OB[N/S/E/W]wFile} for the vertical velocity $w$ with
329 mlosch 1.7 dimensions $(N_{x/y}\times N_r\times\mbox{time levels})$ can be
330 mlosch 1.6 specified.
331     \item If \code{useSEAICE=.TRUE.} then additional files
332     \code{OB[N/S/E/W][a,h,sl,sn,uice,vice]} for sea ice area, thickness
333     (\code{HEFF}), seaice salinity, snow and ice velocities
334 mlosch 1.7 $(N_{x/y}\times\mbox{time levels})$ can be specified.
335 mlosch 1.6 \end{itemize}
336 mlosch 1.7 As in \code{S/R external\_fields\_load} or the \code{exf}-package, the
337     code reads two time levels for each variable, e.g.\ \code{OBNu0} and
338     \code{OBNu1}, and interpolates linearly between these time levels to
339     obtain the value \code{OBNu} at the current model time (step). When the
340     \code{exf}-package is used, the time levels are controlled for each
341     boundary separately in the same way as the \code{exf}-fields in
342     \code{data.exf}, namelist \code{EXF\_NML\_OBCS}. The runtime flags
343 mlosch 1.6 follow the above naming conventions, e.g. for the western boundary the
344     corresponding flags are \code{OBCWstartdate1/2} and
345     \code{OBCWperiod}. Sea-ice boundary values are controlled separately
346 mlosch 1.7 with \code{siobWstartdate1/2} and \code{siobWperiod}. When the
347     \code{exf}-package is not used, the time levels are controlled by the
348     runtime flags \code{externForcingPeriod} and \code{externForcingCycle}
349     in \code{data}, see \code{verification/exp4} for an example.
350 mlosch 1.6
351     \paragraph{OBCS\_CALC\_STEVENS:} ~ \\
352     (THE IMPLEMENTATION OF THESE BOUNDARY CONDITIONS IS NOT COMPLETE. SO
353     FAR ONLY EASTERN AND WESTERN BOUNDARIES ARE SUPPORTED.) \\
354     The boundary conditions following \citet{stevens:90} require the
355     vertically averaged normal velocity (originally specified as a stream
356     function along the open boundary) $\bar{u}_{ob}$ and the tracer fields
357     $\chi_{ob}$ (note: passive tracers are currently not implemented and
358     the code stops when package \code{ptracers} is used together with this
359     option). Currently, the code vertically averages the normal velocity
360     as specified. From these prescribed values the code computes the
361     boundary values for the next timestep $n+1$ as follows (as an
362     example, we use the notation for an eastern or western boundary):
363     \begin{itemize}
364     \item $u^{n+1}(y,z) = \bar{u}_{ob}(y) + u'(y,z)$, where $u_{n}'$ is the
365     deviation from the vertically averaged velocity one grid point
366     inward from the boundary.
367     \item If $u^{n+1}$ is directed into the model domain, the boudary
368     value for tracer $\chi$ is restored to the prescribed values:
369     \[\chi^{n+1} = \chi^{n} + \frac{\Delta{t}}{\tau_\chi} (\chi_{ob} -
370     \chi^{n}),\] where $\tau_\chi$ is the relaxation time
371     scale \texttt{T/SrelaxStevens}.
372     \item If $u^{n+1}$ is directed out of the model domain, the tracer is
373     advected out of the domain with $u^{n+1}+c$, where $c$ is a phase
374     velocity estimated as
375     $\frac{1}{2}\frac{\partial\chi}{\partial{t}}/\frac{\partial\chi}{\partial{x}}$.
376     For test purposes, the phase velocity contribution or the entire
377     advection can
378     be turned off by setting the corresponding parameters
379     \texttt{useStevensPhaseVel} and \texttt{useStevensAdvection} to
380     \texttt{.FALSE.}.\end{itemize} See \citet{stevens:90} for details.
381 heimbach 1.1
382 mlosch 1.7 \paragraph{OBCS\_BALANCE:} ~ \\
383 heimbach 1.1 %
384 mlosch 1.7 This is not (yet) a separate routine in the code, but it may become
385     one to make this code more transparent. The code is part of
386     \code{S/R~OBCS\_CALC}. When turned on (\code{ALLOW\_OBCS\_BALANCE}
387     defined in \code{OBCS\_OPTIONS.h} and \code{useOBCSbalance=.true.} in
388     \code{data.obcs/OBCS\_PARM01}), the normal velocities across each of
389     the four boundaries are modified separately, so that the net volume
390     transport across \emph{each} boundary is zero. For example, for the
391     western boundary at $i=i_{b}$, the modified velocity is:
392     \[
393     u(y,z) - \int_{\mbox{western boundary}}u\,dy\,dz \approx OBNu(j,k) - \sum_{j,k}
394     OBNu(j,k) h_{w}(i_{b},j,k)\Delta{y_G(i_{b},j)}\Delta{z(k)}.
395     \]
396     This also ensures a net total inflow of zero through all boundaries to
397     make it a useful flag to prevent infinite sea-level change within the
398     domain, but the flag is \emph{not} useful if you want to simulate,
399     say, a sector of the Southern Ocean with a strong ACC entering through
400     the western and leaving through the eastern boundary, because this
401     flag will make sure that the strong inflow is removed. It is
402     recommended that this part of the code is adapted to the particular
403     needs of the simulation in question.
404 heimbach 1.1
405 heimbach 1.2 \paragraph{OBCS\_APPLY\_*:} ~ \\
406 heimbach 1.1 ~
407    
408 heimbach 1.2 \paragraph{OBCS\_SPONGE} Setting sponge layer characteristics \\
409 heimbach 1.1 %
410     ~
411    
412     \paragraph{OB's with nonlinear free surface} ~ \\
413     %
414     ~
415    
416    
417     %----------------------------------------------------------------------
418    
419     \subsubsection{Flow chart
420     \label{sec:pkg:obcs:flowchart}}
421    
422    
423     {\footnotesize
424     \begin{verbatim}
425    
426     C !CALLING SEQUENCE:
427     c ...
428    
429     \end{verbatim}
430     }
431    
432     %----------------------------------------------------------------------
433    
434     \subsubsection{OBCS diagnostics
435     \label{sec:pkg:obcs:diagnostics}}
436    
437     Diagnostics output is available via the diagnostics package
438     (see Section \ref{sec:pkg:diagnostics}).
439     Available output fields are summarized in
440     Table \ref{tab:pkg:obcs:diagnostics}.
441    
442 jmc 1.5 \begin{table}[!ht]
443 heimbach 1.1 \centering
444     \label{tab:pkg:obcs:diagnostics}
445     {\footnotesize
446     \begin{verbatim}
447     ------------------------------------------------------
448     <-Name->|Levs|grid|<-- Units -->|<- Tile (max=80c)
449     ------------------------------------------------------
450    
451     \end{verbatim}
452     }
453     \caption{~}
454     \end{table}
455    
456     %----------------------------------------------------------------------
457    
458     \subsubsection{Reference experiments}
459 mlosch 1.7 In the directory \code{verifcation}, the following experiments use
460     \code{obcs}:
461     \begin{itemize}
462     \item \code{exp4}: box with 4 open boundaries, simulating flow over a
463     Gaussian bump based on \citet{adcroft:97}, also tests
464     Stevens-boundary conditions;
465     \item \code{dome}: based on ``Denmark Strait Overflow Model
466     Experiment'', use Orlanski-BCs;
467     \item \code{internal\_wave}: uses a heavily modified \code{S/R~OBCS\_CALC}
468     \item \code{seaice\_obcs}: simple example who to use the sea-ice
469     related code, based on \code{lab\_sea};
470     \item \code{tutorial\_plume\_on\_slope}: uses Orlanski-BCs, see also
471     section~\ref{sec:eg-gravityplume}.
472     \end{itemize}
473 heimbach 1.1
474    
475    
476     %----------------------------------------------------------------------
477    
478     \subsubsection{References}
479    
480 molod 1.3 \subsubsection{Experiments and tutorials that use obcs}
481     \label{sec:pkg:obcs:experiments}
482    
483     \begin{itemize}
484 mlosch 1.7 \item \code{tutorial\_plume\_on\_slope} (section~\ref{sec:eg-gravityplume})
485 molod 1.3 \end{itemize}
486    
487 mlosch 1.6
488     %%% Local Variables:
489     %%% mode: latex
490     %%% TeX-master: "../../manual"
491     %%% End:

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