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1 % $Header:
2 % $Name:
3
4 \section[P coordinate Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution in Pressure
5 Coordinates}
6 %\label{www:tutorials}
7 \label{sec:eg-globalpressure}
8 \begin{rawhtml}
9 <!-- CMIREDIR:eg-globalpressure: -->
10 \end{rawhtml}
11 \begin{center}
12 (in directory: {\it verification/tutorial\_global\_oce\_in\_p/})
13 \end{center}
14
15 \bodytext{bgcolor="#FFFFFFFF"}
16
17 This example experiment demonstrates using the MITgcm to simulate the
18 planetary ocean circulation in pressure coordinates, that is, without
19 making the Boussinesq approximations. The files for this experiment
20 can be found in the verification directory under tutorial\_global\_oce\_in\_p.
21 The simulation is configured as a near copy of
22 tutorial\_global\_oce\_latlon (Section~\ref{sec:eg-global}).
23 with realistic geography and bathymetry on a $4^{\circ} \times
24 4^{\circ}$ spherical polar grid. Fifteen levels are used in the
25 vertical, ranging in thickness from
26 $50.4089\mbox{\,dbar}\approx50\mbox{\,m}$ at the surface to
27 $710.33\mbox{\,dbar}\approx690\mbox{\,m}$ at depth, giving a maximum
28 model depth of $5302.3122\mbox{\,dbar}\approx5200\mbox{\,km}$. At
29 this resolution, the configuration can be integrated forward for
30 thousands of years on a single processor desktop computer.
31
32
33 \subsection{Overview}
34 %\label{www:tutorials}
35
36 The model is forced with climatological wind stress data from
37 \citet{trenberth90} and surface flux data from
38 \citet{jiang99}. Climatological data \citep{Levitus94} is
39 used to initialize the model hydrography. \citeauthor{Levitus94} seasonal
40 climatology data is also used throughout the calculation to provide
41 additional air-sea fluxes. These fluxes are combined with the Jiang
42 climatological estimates of surface heat flux, resulting in a mixed
43 boundary condition of the style described in \citet{Haney}.
44 Altogether, this yields the following forcing applied in the model
45 surface layer.
46
47 \begin{eqnarray}
48 \label{eq:eg-global_forcing_pcoord}
49 \label{eq:eg-global_forcing_fu_pcoord}
50 {\cal F}_{u} & = & g\frac{\tau_{x}}{\Delta p_{s}}
51 \\
52 \label{eq:eg-global_forcing_fv_pcoord}
53 {\cal F}_{v} & = & g\frac{\tau_{y}}{\Delta p_{s}}
54 \\
55 \label{eq:eg-global_forcing_ft_pcoord}
56 {\cal F}_{\theta} & = & - g\lambda_{\theta} ( \theta - \theta^{\ast} )
57 - \frac{1}{C_{p} \Delta p_{s}}{\cal Q}
58 \\
59 \label{eq:eg-global_forcing_fs_pcoord}
60 {\cal F}_{s} & = &
61 + g\rho_{FW}\frac{S}{\rho\Delta p_{s}}({\cal E} - {\cal P} - {\cal R})
62 \end{eqnarray}
63
64 \noindent where ${\cal F}_{u}$, ${\cal F}_{v}$, ${\cal F}_{\theta}$,
65 ${\cal F}_{s}$ are the forcing terms in the zonal and meridional
66 momentum and in the potential temperature and salinity equations
67 respectively. The term $\Delta p_{s}$ represents the top ocean layer
68 thickness in Pa. It is used in conjunction with a reference density,
69 $\rho_{FW}$ (here set to $999.8\,{\rm kg\,m^{-3}}$), the surface
70 salinity, $S$, and a specific heat capacity, $C_{p}$ (here set to
71 $4000~{\rm J}~^{\circ}{\rm C}^{-1}~{\rm kg}^{-1}$), to convert input
72 dataset values into time tendencies of potential temperature (with
73 units of $^{\circ}{\rm C}~{\rm s}^{-1}$), salinity (with units ${\rm
74 ppt}~s^{-1}$) and velocity (with units ${\rm m}~{\rm s}^{-2}$). The
75 externally supplied forcing fields used in this experiment are
76 $\tau_{x}$, $\tau_{y}$, $\theta^{\ast}$, $\cal{Q}$ and
77 $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$)
78 have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields
79 ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm
80 W}~{\rm m}^{-2}$ respectively. The salinity forcing fields
81 ($\cal{E}-\cal{P}-\cal{R}$) has units of ${\rm m}~{\rm s}^{-1}$
82 respectively. The source files and procedures for ingesting these data
83 into the simulation are described in the experiment configuration
84 discussion in section \ref{sec:eg-global-clim_ocn_examp_exp_config}.
85
86
87 \subsection{Discrete Numerical Configuration}
88 %\label{www:tutorials}
89
90
91 Due to the pressure coordinate, the model can only be hydrostatic
92 \citep{szoeke02}. The domain is discretized with a uniform grid
93 spacing in latitude and longitude on the sphere $\Delta \phi=\Delta
94 \lambda=4^{\circ}$, so that there are ninety grid cells in the zonal
95 and forty in the meridional direction. The internal model coordinate
96 variables $x$ and $y$ are initialized according to
97 \begin{eqnarray}
98 x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
99 y=r\lambda,~\Delta y &= &r\Delta \lambda
100 \end{eqnarray}
101
102 Arctic polar regions are not included in this experiment. Meridionally
103 the model extends from $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
104 Vertically the model is configured with fifteen layers with the
105 following thicknesses %
106 \begin{eqnarray*}
107 \Delta p_{1} &=& 7103300.720021\mbox{\,Pa},\\
108 \Delta p_{2} &=& 6570548.440790\mbox{\,Pa},\\
109 \Delta p_{3} &=& 6041670.010249\mbox{\,Pa},\\
110 \Delta p_{4} &=& 5516436.666057\mbox{\,Pa},\\
111 \Delta p_{5} &=& 4994602.034410\mbox{\,Pa},\\
112 \Delta p_{6} &=& 4475903.435290\mbox{\,Pa},\\
113 \Delta p_{7} &=& 3960063.245801\mbox{\,Pa},\\
114 \Delta p_{8} &=& 3446790.312651\mbox{\,Pa},\\
115 \Delta p_{9} &=& 2935781.405664\mbox{\,Pa},\\
116 \Delta p_{10}&=& 2426722.705046\mbox{\,Pa},\\
117 \Delta p_{11}&=& 1919291.315988\mbox{\,Pa},\\
118 \Delta p_{12}&=& 1413156.804970\mbox{\,Pa},\\
119 \Delta p_{13}&=& 1008846.750166\mbox{\,Pa},\\
120 \Delta p_{14}&=& 705919.025481\mbox{\,Pa},\\
121 \Delta p_{15}&=& 504089.693499\mbox{\,Pa},
122 \end{eqnarray*}
123 (here the numeric subscript indicates the model level index number,
124 ${\tt k}$; note, that the surface layer has the highest index number 15) to
125 give a total depth, $H$, of $-5200{\rm m}$. In pressure, this is
126 $p_{b}^{0}=53023122.566084\mbox{\,Pa}$.
127 The implicit free surface form of the pressure equation described in
128 \citet{marshall:97a} with the nonlinear extension by
129 \citet{campin:02} is employed. A Laplacian operator, $\nabla^2$, provides viscous
130 dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
131
132 Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations_pcoord})
133 for both the zonal flow, $u$ and the meridional flow $v$, according to equations
134 (\ref{eq:eg-global_forcing_fu_pcoord}) and (\ref{eq:eg-global_forcing_fv_pcoord}).
135 Thermodynamic forcing inputs are added to the equations
136 in (\ref{eq:eg-global-model_equations_pcoord}) for
137 potential temperature, $\theta$, and salinity, $S$, according to equations
138 (\ref{eq:eg-global_forcing_ft_pcoord}) and (\ref{eq:eg-global_forcing_fs_pcoord}).
139 This produces a set of equations solved in this configuration as follows:
140
141 \begin{eqnarray}
142 \label{eq:eg-global-model_equations_pcoord}
143 \frac{Du}{Dt} - fv +
144 \frac{1}{\rho}\frac{\partial \Phi^{'}}{\partial x} -
145 \nabla_{h}\cdot A_{h}\nabla_{h}u -
146 (g\rho_0)^2\frac{\partial}{\partial p}A_{r}\frac{\partial u}{\partial p}
147 & = &
148 \begin{cases}
149 {\cal F}_u & \text{(surface)} \\
150 0 & \text{(interior)}
151 \end{cases}
152 \\
153 \frac{Dv}{Dt} + fu +
154 \frac{1}{\rho}\frac{\partial \Phi^{'}}{\partial y} -
155 \nabla_{h}\cdot A_{h}\nabla_{h}v -
156 (g\rho_0)^2\frac{\partial}{\partial p}A_{r}\frac{\partial v}{\partial p}
157 & = &
158 \begin{cases}
159 {\cal F}_v & \text{(surface)} \\
160 0 & \text{(interior)}
161 \end{cases}
162 \\
163 \frac{\partial p_{b}}{\partial t} + \nabla_{h}\cdot \vec{u}
164 &=&
165 0
166 \\
167 \frac{D\theta}{Dt} -
168 \nabla_{h}\cdot K_{h}\nabla_{h}\theta
169 - (g\rho_0)^2\frac{\partial}{\partial p}\Gamma(K_{r})\frac{\partial\theta}{\partial p}
170 & = &
171 \begin{cases}
172 {\cal F}_\theta & \text{(surface)} \\
173 0 & \text{(interior)}
174 \end{cases}
175 \\
176 \frac{D s}{Dt} -
177 \nabla_{h}\cdot K_{h}\nabla_{h}s
178 - (g\rho_0)^2\frac{\partial}{\partial p}\Gamma(K_{r})\frac{\partial S}{\partial p}
179 & = &
180 \begin{cases}
181 {\cal F}_s & \text{(surface)} \\
182 0 & \text{(interior)}
183 \end{cases}
184 \\
185 \Phi_{-H}'^{(0)} + \alpha_{0}p_{b}+ \int^{p}_{0}\alpha' dp & = & \Phi'
186 \end{eqnarray}
187
188 \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
189 $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$ are the zonal and meridional
190 components of the flow vector, $\vec{u}$, on the sphere. As described
191 in MITgcm Numerical Solution Procedure \ref{chap:discretization}, the
192 time evolution of potential temperature, $\theta$, equation is solved
193 prognostically. The full geopotential height, $\Phi$, is diagnosed by
194 summing the geopotential height anomalies $\Phi'$ due to bottom
195 pressure $p_{b}$ and density variations. The integration of the
196 hydrostatic equation is started at the bottom of the domain. The
197 condition of $p=0$ at the sea surface requires a time-independent
198 integration constant for the height anomaly due to density variations
199 $\Phi_{-H}'^{(0)}$, which is provided as an input field.
200
201
202 \subsection{Experiment Configuration}
203 %\label{www:tutorials}
204 \label{sec:eg-globalpressure-config}
205
206 The model configuration for this experiment resides under the
207 directory {\it tutorial\_examples/global\_ocean\_circulation/}.
208 The experiment files
209
210 \begin{itemize}
211 \item {\it input/data}
212 \item {\it input/data.pkg}
213 \item {\it input/eedata},
214 \item {\it input/topog.bin},
215 \item {\it input/deltageopotjmd95.bin},
216 \item {\it input/lev\_s.bin},
217 \item {\it input/lev\_t.bin},
218 \item {\it input/trenberth\_taux.bin},
219 \item {\it input/trenberth\_tauy.bin},
220 \item {\it input/lev\_sst.bin},
221 \item {\it input/shi\_qnet.bin},
222 \item {\it input/shi\_empmr.bin},
223 \item {\it code/CPP\_EEOPTIONS.h}
224 \item {\it code/CPP\_OPTIONS.h},
225 \item {\it code/SIZE.h}.
226 \end{itemize}
227 contain the code customizations and parameter settings for these
228 experiments. Below we describe the customizations
229 to these files associated with this experiment.
230
231 \subsubsection{Driving Datasets}
232 %\label{www:tutorials}
233
234 Figures (\ref{fig:sim_config_tclim_pcoord}-\ref{fig:sim_config_empmr_pcoord}) show
235 the relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$)
236 fields, the wind stress components ($\tau_x$ and $\tau_y$), the heat
237 flux ($Q$) and the net fresh water flux (${\cal E} - {\cal P} - {\cal
238 R}$) used in equations
239 \ref{eq:eg-global_forcing_fu_pcoord}-\ref{eq:eg-global_forcing_fs_pcoord}.
240 The figures also indicate the lateral extent and coastline used in the
241 experiment. Figure ({\ref{fig:model_bathymetry_pcoord}) shows the depth
242 contours of the model domain.
243 \begin{figure}[t]
244 \begin{center}
245 \includegraphics[width=.9\textwidth]{s_examples/global_oce_in_p/sst}
246 \caption{Annual mean of relaxation temperature [$^{\circ}\mathrm{C}$]}
247 \label{fig:sim_config_tclim_pcoord}
248 \end{center}
249 \end{figure}
250 \begin{figure}[t]
251 \begin{center}
252 \includegraphics[width=.9\textwidth]{s_examples/global_oce_in_p/sss}
253 \caption{Annual mean of relaxation salinity [PSU]}
254 \label{fig:sim_config_sclim_pcoord}
255 \end{center}
256 \end{figure}
257 \begin{figure}[t]
258 \begin{center}
259 \includegraphics[width=.9\textwidth]{s_examples/global_oce_in_p/tx}
260 \caption{Annual mean of zonal wind stress component [Nm\,m$^{-2}$]}
261 \label{fig:sim_config_taux_pcoord}
262 \end{center}
263 \end{figure}
264 \begin{figure}[t]
265 \begin{center}
266 \includegraphics[width=.9\textwidth]{s_examples/global_oce_in_p/ty}
267 \caption{Annual mean of meridional wind stress component [Nm\,m$^{-2}$]}
268 \label{fig:sim_config_tauy_pcoord}
269 \end{center}
270 \end{figure}
271 \begin{figure}[t]
272 \begin{center}
273 \includegraphics[width=.9\textwidth]{s_examples/global_oce_in_p/qnet}
274 \caption{Annual mean heat flux [W\,m$^{-2}$]}
275 \label{fig:sim_config_qnet_pcoord}
276 \end{center}
277 \end{figure}
278 \begin{figure}[t]
279 \begin{center}
280 \includegraphics[width=.9\textwidth]{s_examples/global_oce_in_p/emp}
281 \caption{Annual mean fresh water flux (Evaporation-Precipitation) [m\,s$^{-1}$]}
282 \label{fig:sim_config_empmr_pcoord}
283 \end{center}
284 \end{figure}
285 \begin{figure}[t]
286 \begin{center}
287 \includegraphics[width=.9\textwidth]{s_examples/global_oce_in_p/pb0}
288 \caption{Model bathymetry in pressure units [Pa]}
289 \label{fig:model_bathymetry_pcoord}
290 \end{center}
291 \end{figure}
292
293 \subsubsection{File {\it input/data}}
294 %\label{www:tutorials}
295
296 This file, reproduced completely below, specifies the main parameters
297 for the experiment. The parameters that are significant for this configuration
298 are
299
300 \begin{itemize}
301
302 \item Line 15,
303 \begin{verbatim} viscAr=1.721611620915750E+05, \end{verbatim}
304 this line sets the vertical Laplacian dissipation coefficient to
305 $1.72161162091575 \times 10^{5} {\rm Pa^{2}s^{-1}}$. Note that, the factor
306 $(g\rho)^2$ needs to be included in this line. Boundary conditions
307 for this operator are specified later. This variable is copied into
308 model general vertical coordinate variable {\bf viscAr}.
309
310 \fbox{
311 \begin{minipage}{5.0in}
312 {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
313 \end{minipage}
314 }
315
316 \item Line 9--10,
317 \begin{verbatim}
318 viscAh=3.E5,
319 no_slip_sides=.TRUE.
320 \end{verbatim}
321 these lines set the horizontal Laplacian frictional dissipation
322 coefficient to $3 \times 10^{5} {\rm m^{2}s^{-1}}$ and specify a
323 no-slip boundary condition for this operator, that is, $u=0$ along
324 boundaries in $y$ and $v=0$ along boundaries in $x$.
325
326 \item Lines 11-13,
327 \begin{verbatim}
328 viscAr =1.721611620915750e5,
329 #viscAz =1.67E-3,
330 no_slip_bottom=.FALSE.,
331 \end{verbatim}
332 These lines set the vertical Laplacian frictional dissipation
333 coefficient to $1.721611620915750 \times
334 10^{5}\mbox{\,Pa$^{2}$s$^{-1}$}$, which corresponds to
335 $1.67\times10^{-3}\mbox{\,m$^{2}$s$^{-1}$}$ in the commented line, and
336 specify a free slip boundary condition for this operator, that is,
337 $\frac{\partial u}{\partial p}=\frac{\partial v}{\partial p}=0$ at
338 $p=p_{b}^{0}$, where $p_{b}^{0}$ is the local bottom pressure of the
339 domain at rest. Note that, the factor $(g\rho)^2$ needs to be
340 included in this line.
341
342 \item Line 14,
343 \begin{verbatim}
344 diffKhT=1.E3,
345 \end{verbatim}
346 this line sets the horizontal diffusion coefficient for temperature
347 to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
348 operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial
349 y}=0$ on all boundaries.
350
351 \item Line 15--16,
352 \begin{verbatim}
353 diffKrT=5.154525811125000e3,
354 #diffKzT=0.5E-4,
355 \end{verbatim}
356 this line sets the vertical diffusion coefficient for temperature to
357 $5.154525811125 \times 10^{3}\,{\rm Pa^{2}s^{-1}}$, which
358 corresponds to $5\times10^{-4}\mbox{\,m$^{2}$s$^{-1}$}$ in the commented
359 line. Note that, the factor $(g\rho)^2$ needs to be included in this
360 line. The boundary condition on this operator is
361 $\frac{\partial}{\partial p}=0$ at both the upper and lower
362 boundaries.
363
364 \item Line 17--19,
365 \begin{verbatim}
366 diffKhS=1.E3,
367 diffKrS=5.154525811125000e3,
368 #diffKzS=0.5E-4,
369 \end{verbatim}
370 These lines set the same values for the diffusion coefficients for
371 salinity as for temperature.
372
373 \item Line 20--22,
374 \begin{verbatim}
375 implicitDiffusion=.TRUE.,
376 ivdc_kappa=1.030905162225000E9,
377 #ivdc_kappa=10.0,
378 \end{verbatim}
379 Select implicit diffusion as a convection scheme and set coefficient
380 for implicit vertical diffusion to $1.030905162225\times10^{9}\,{\rm
381 Pa^{2}s^{-1}}$, which corresponds to $10\mbox{\,m$^{2}$\,s$^{-1}$}$.
382
383 \item Line 23-24,
384 \begin{verbatim}
385 gravity=9.81,
386 gravitySign=-1.D0,
387 \end{verbatim}
388 These lines set the gravitational acceleration coefficient to
389 $9.81{\rm m}{\rm s}^{-1}$ and define the upward direction relative
390 to the direction of increasing vertical coordinate (in pressure
391 coordinates, up is in the direction of decreasing pressure)
392 \item Line 25,
393 \begin{verbatim}
394 rhoNil=1035.,
395 \end{verbatim}
396 sets the reference density of sea water to $1035\mbox{\,kg\,m$^{-3}$}$.\\
397 \fbox{
398 \begin{minipage}{5.0in}
399 {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
400 {\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\
401 {\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\
402 {\it S/R INI\_PARMS}~({\it ini\_parms.F})\\
403 {\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})
404 \end{minipage}
405 }
406
407 \item Line 28
408 \begin{verbatim}
409 eosType='JMD95P',
410 \end{verbatim}
411 Selects the full equation of state according to
412 \citet{jackett95}. The only other sensible choice is the equation of
413 state by \citet{mcdougall03}, 'MDJFW'. All other
414 equations of state do not make sense in this configuration.\\
415 \fbox{
416 \begin{minipage}{5.0in}
417 {\it S/R FIND\_RHO}~({\it find\_rho.F})\\
418 {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})
419 \end{minipage}
420 }
421
422 \item Line 28-29,
423 \begin{verbatim}
424 rigidLid=.FALSE.,
425 implicitFreeSurface=.TRUE.,
426 \end{verbatim}
427 Selects the barotropic pressure equation to be the implicit free
428 surface formulation.
429 \item Line 30
430 \begin{verbatim}
431 exactConserv=.TRUE.,
432 \end{verbatim}
433 Select a more accurate conservation of properties at the surface
434 layer by including the horizontal velocity divergence to update the
435 free surface.
436 \item Line 31--33
437 \begin{verbatim}
438 nonlinFreeSurf=3,
439 hFacInf=0.2,
440 hFacSup=2.0,
441 \end{verbatim}
442 Select the nonlinear free surface formulation and set lower and
443 upper limits for the free surface excursions.
444 \item Line 34
445 \begin{verbatim}
446 useRealFreshWaterFlux=.FALSE.,
447 \end{verbatim}
448 Select virtual salt flux boundary condition for salinity. The
449 freshwater flux at the surface only affect the surface salinity, but
450 has no mass flux associated with it
451
452 \item Line 35--36,
453 \begin{verbatim}
454 readBinaryPrec=64,
455 writeBinaryPrec=64,
456 \end{verbatim}
457 Sets format for reading binary input datasets and
458 writing binary output datasets holding model fields to
459 use 64-bit representation for floating-point numbers.\\
460 \fbox{
461 \begin{minipage}{5.0in}
462 {\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\
463 {\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})
464 \end{minipage}
465 }
466
467 \item Line 42,
468 \begin{verbatim}
469 cg2dMaxIters=200,
470 \end{verbatim}
471 Sets maximum number of iterations the two-dimensional, conjugate
472 gradient solver will use, {\bf irrespective of convergence
473 criteria being met}.\\
474 \fbox{
475 \begin{minipage}{5.0in}
476 {\it S/R CG2D}~({\it cg2d.F})
477 \end{minipage}
478 }
479
480 \item Line 43,
481 \begin{verbatim}
482 cg2dTargetResidual=1.E-13,
483 \end{verbatim}
484 Sets the tolerance which the two-dimensional, conjugate
485 gradient solver will use to test for convergence in equation
486 %- note: Description of Conjugate gradient method (& related params) is missing
487 % in the mean time, substitute this eq ref:
488 \ref{eq:elliptic-backward-free-surface} %\ref{eq:congrad_2d_resid}
489 to $1 \times 10^{-9}$.
490 Solver will iterate until tolerance falls below this value or until the
491 maximum number of solver iterations is reached.\\
492 \fbox{
493 \begin{minipage}{5.0in}
494 {\it S/R CG2D}~({\it cg2d.F})
495 \end{minipage}
496 }
497
498 \item Line 48,
499 \begin{verbatim}
500 startTime=0,
501 \end{verbatim}
502 Sets the starting time for the model internal time counter.
503 When set to non-zero this option implicitly requests a
504 checkpoint file be read for initial state.
505 By default the checkpoint file is named according to
506 the integer number of time steps in the {\bf startTime} value.
507 The internal time counter works in seconds.
508
509 \item Line 49--50,
510 \begin{verbatim}
511 endTime=8640000.,
512 #endTime=62208000000,
513 \end{verbatim}
514 Sets the time (in seconds) at which this simulation will terminate.
515 At the end of a simulation a checkpoint file is automatically
516 written so that a numerical experiment can consist of multiple
517 stages. The commented out setting for endTime is for a 2000 year
518 simulation.
519
520 \item Line 51--53,
521 \begin{verbatim}
522 deltaTmom = 1200.0,
523 deltaTtracer = 172800.0,
524 deltaTfreesurf = 172800.0,
525 \end{verbatim}
526 Sets the timestep $\delta t_{v}$ used in the momentum equations to
527 $20~{\rm mins}$ and the timesteps $\delta t_{\theta}$ in the tracer
528 equations and $\delta t_{\eta}$ in the implicit free surface
529 equation to $48\mbox{\,hours}$.
530 %- note: Distord Physics (using different time-steps) is not described
531 % in the mean time, put this section ref:
532 See section \ref{sec:time_stepping}.%\ref{sec:mom_time_stepping}
533 \\
534
535 \fbox{
536 \begin{minipage}{5.0in}
537 {\it S/R TIMESTEP}({\it timestep.F}) \\
538 {\it S/R INI\_PARMS}({\it ini\_parms.F})\\
539 {\it S/R MOM\_FLUXFORM}({\it mom\_fluxform.F}) \\
540 {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})
541 \end{minipage}
542 }
543
544 \item Line 55,
545 \begin{verbatim}
546 pChkptFreq =3110400000.,
547 \end{verbatim}
548 write a pick-up file every 100 years of integration.
549
550 \item Line 56--58
551 \begin{verbatim}
552 dumpFreq = 3110400000.,
553 taveFreq = 3110400000.,
554 monitorFreq = 31104000.,
555 \end{verbatim}
556 write model output and time-averaged model output every 100 years,
557 and monitor statisitics every year.
558
559 \item Line 59--61
560 \begin{verbatim}
561 periodicExternalForcing=.TRUE.,
562 externForcingPeriod=2592000.,
563 externForcingCycle=31104000.,
564 \end{verbatim}
565 Allow periodic external forcing, set forcing period, during which
566 one set of data is valid, to 1 month and the repeat cycle to 1 year.\\
567 \fbox{
568 \begin{minipage}{5.0in}
569 {\it S/R EXTERNAL\_FORCING\_SURF}({\it external\_forcing\_surf.F})
570 \end{minipage}
571 }
572 \item Line 62
573 \begin{verbatim}
574 tauThetaClimRelax=5184000.0,
575 \end{verbatim}
576 Set the restoring timescale to 2 months.\\
577 \fbox{
578 \begin{minipage}{5.0in}
579 {\it S/R EXTERNAL\_FORCING\_SURF}({\it external\_forcing\_surf.F})
580 \end{minipage}
581 }
582
583 \item Line 63
584 \begin{verbatim}
585 abEps=0.1,
586 \end{verbatim}
587 Adams-Bashford factor (see section \ref{sec:adams-bashforth})
588
589 \item Line 68--69
590 \begin{verbatim}
591 usingCartesianGrid=.FALSE.,
592 usingSphericalPolarGrid=.TRUE.,
593 \end{verbatim}
594 Select spherical grid.
595 \item Line 70--71
596 \begin{verbatim}
597 dXspacing=4.,
598 dYspacing=4.,
599 \end{verbatim}
600 Set the horizontal grid spacing in degrees spherical distance.
601 \item Line 72
602 \begin{verbatim}
603 Ro_SeaLevel=53023122.566084,
604 \end{verbatim}
605 specifies the total height (in $r$-units, i.e., pressure units) of the
606 sea surface at rest. This is a reference value.
607 \item Line 73
608 \begin{verbatim}
609 groundAtK1=.TRUE.,
610 \end{verbatim}
611 specifies the reversal of the vertical indexing. The vertical index is
612 1 at the bottom of the doman and maximal (i.e., 15) at the surface.
613 \item Line 74--78
614 \begin{verbatim}
615 delR=7103300.720021, \ldots
616 \end{verbatim}
617 set the layer thickness in pressure units, starting with the bottom
618 layer.
619
620 \item Line 84--93,
621 \begin{verbatim}
622 bathyFile='topog.box'
623 ploadFile='deltageopotjmd95.bin'
624 hydrogThetaFile='lev_t.bin',
625 hydrogSaltFile ='lev_s.bin',
626 zonalWindFile ='trenberth_taux.bin',
627 meridWindFile ='trenberth_tauy.bin',
628 thetaClimFile ='lev_sst.bin',
629 surfQFile ='shi_qnet.bin',
630 EmPmRFile ='shi_empmr.bin',
631 \end{verbatim}
632 This line specifies the names of the files holding the bathymetry
633 data set, the
634 time-independent geopotential height anomaly at the bottom, initial
635 conditions of temperature and salinity, wind stress forcing fields,
636 sea surface temperature climatology, heat flux, and fresh water flux
637 (evaporation minus precipitation minus run-off) at the surface.
638 See file descriptions in section \ref{sec:eg-globalpressure-config}.
639
640 \end{itemize}
641
642 \noindent other lines in the file {\it input/data} are standard values
643 that are described in the MITgcm Getting Started and MITgcm Parameters
644 notes.
645
646 \begin{small}
647 \input{s_examples/global_oce_in_p/input/data}
648 \end{small}
649
650 \subsubsection{File {\it input/data.pkg}}
651 %\label{www:tutorials}
652
653 This file uses standard default values and does not contain
654 customisations for this experiment.
655
656 \subsubsection{File {\it input/eedata}}
657 %\label{www:tutorials}
658
659 This file uses standard default values and does not contain
660 customisations for this experiment.
661
662 \subsubsection{File {\it input/topog.bin}}
663 %\label{www:tutorials}
664
665 This file is a two-dimensional ($x,y$) map of
666 depths. This file is assumed to contain 64-bit binary numbers giving
667 the depth of the model at each grid cell, ordered with the x
668 coordinate varying fastest. The points are ordered from low
669 coordinate to high coordinate for both axes. The units and
670 orientation of the depths in this file are the same as used in the
671 MITgcm code (Pa for this experiment). In this experiment, a depth of
672 $0\mbox{\,Pa}$ indicates a land point wall and a depth of
673 $>0\mbox{\,Pa}$ indicates open ocean.
674
675 \subsubsection{File {\it input/deltageopotjmd95.box}}
676 %\label{www:tutorials}
677
678 The file contains 12 identical two dimensional maps ($x,y$) of
679 geopotential height anomaly at the bottom at rest. The values have
680 been obtained by vertically integrating the hydrostatic equation with
681 the initial density field (from {\it input/lev\_t/s.bin}). This file
682 has to be consitent with the temperature and salinity field at rest
683 and the choice of equation of state!
684
685 \subsubsection{File {\it input/lev\_t/s.bin}}
686 %\label{www:tutorials}
687
688 The files {\it input/lev\_t/s.bin} specify the initial conditions for
689 temperature and salinity for every grid point in a three dimensional
690 array ($x,y,z$). The data are obtain by interpolating
691 monthly mean values \citep{Levitus94} for January onto the model
692 grid. Keep in mind, that the first index corresponds to the bottom
693 layer and highest index to the surface layer.
694
695 \subsubsection{File {\it input/trenberth\_taux/y.bin}}
696 %\label{www:tutorials}
697
698 Each of the {\it input/trenberth\_taux/y.bin} files specifies 12
699 two-dimensional ($x,y,t$) maps of zonal and meridional wind stress
700 values, $\tau_{x}$ and $\tau_{y}$, that is monthly mean values from
701 \citet{trenberth90}. The units used are $Nm^{-2}$.
702
703 \subsubsection{File {\it input/lev\_sst.bin}}
704 %\label{www:tutorials}
705
706 The file {\it input/lev\_sst.bin} contains 12 monthly surface
707 temperature climatologies \citep{Levitus94} in a three
708 dimensional array ($x,y,t$).
709
710 \subsubsection{File {\it input/shi\_qnet/empmr.bin}}
711 %\label{www:tutorials}
712
713 The files {\it input/shi\_qnet/empmr.bin} contain 12 monthly surface
714 fluxes of heat (qnet) and freshwater (empmr) by
715 \citet{jiang99} in three dimensional arrays ($x,y,t$). Both fluxes are
716 normalized so that of one year there is no net flux into the
717 ocean. The freshwater flux is actually constant in time.
718
719 \subsubsection{File {\it code/SIZE.h}}
720 %\label{www:tutorials}
721
722 Three lines are customized in this file for the current experiment
723
724 \begin{itemize}
725
726 \item Line 39,
727 \begin{verbatim} sNx=90, \end{verbatim} this line sets
728 the lateral domain extent in grid points for the
729 axis aligned with the x-coordinate.
730
731 \item Line 40,
732 \begin{verbatim} sNy=40, \end{verbatim} this line sets
733 the lateral domain extent in grid points for the
734 axis aligned with the y-coordinate.
735
736 \item Line 49,
737 \begin{verbatim} Nr=15, \end{verbatim} this line sets
738 the vertical domain extent in grid points.
739
740 \end{itemize}
741
742 \begin{small}
743 \input{s_examples/global_oce_in_p/code/SIZE.h}
744 \end{small}
745
746 \subsubsection{File {\it code/CPP\_OPTIONS.h}}
747 %\label{www:tutorials}
748
749 This file uses mostly standard default values except for:
750 \begin{itemize}
751 \item \verb+#define ATMOSPHERIC_LOADING+\\
752 enable pressure loading which is abused to include the initial
753 geopotential height anomaly
754 \item \verb+#define EXACT_CONSERV+\\
755 enable more accurate conservation properties to include the
756 horizontal mass divergence in the free surface
757 \item \verb+#define NONLIN_FRSURF+\\
758 enable the nonlinear free surface
759 \end{itemize}
760
761
762 \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
763 %\label{www:tutorials}
764
765 This file uses standard default values and does not contain
766 customisations for this experiment.
767
768

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