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1 % $Header: /u/gcmpack/manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex,v 1.18 2010/08/27 13:25:32 jmc Exp $
2 % $Name: $
3
4 \section[Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution}
5 %\label{www:tutorials}
6 \label{sec:eg-global}
7 \begin{rawhtml}
8 <!-- CMIREDIR:eg-global: -->
9 \end{rawhtml}
10 \begin{center}
11 (in directory: {\it verification/tutorial\_global\_oce\_latlon/})
12 \end{center}
13
14 \bodytext{bgcolor="#FFFFFFFF"}
15
16 %\begin{center}
17 %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
18 %At Four Degree Resolution with Asynchronous Time Stepping}
19 %
20 %\vspace*{4mm}
21 %
22 %\vspace*{3mm}
23 %{\large May 2001}
24 %\end{center}
25
26
27 This example experiment demonstrates using the MITgcm to simulate
28 the planetary ocean circulation. The simulation is configured
29 with realistic geography and bathymetry on a
30 $4^{\circ} \times 4^{\circ}$ spherical polar grid.
31 The files for this experiment are in the verification directory
32 under tutorial\_global\_oce\_latlon.
33 Twenty levels are used in the vertical, ranging in thickness
34 from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,
35 giving a maximum model depth of $6\,{\rm km}$.
36 At this resolution, the configuration
37 can be integrated forward for thousands of years on a single
38 processor desktop computer.
39 \\
40 \subsection{Overview}
41 %\label{www:tutorials}
42
43 The model is forced with climatological wind stress data and surface
44 flux data from DaSilva \cite{DaSilva94}. Climatological data
45 from Levitus \cite{Levitus94} is used to initialize the model hydrography.
46 Levitus seasonal climatology data is also used throughout the calculation
47 to provide additional air-sea fluxes.
48 These fluxes are combined with the DaSilva climatological estimates of
49 surface heat flux and fresh water, resulting in a mixed boundary
50 condition of the style described in Haney \cite{Haney}.
51 Altogether, this yields the following forcing applied
52 in the model surface layer.
53
54 \begin{eqnarray}
55 \label{eq:eg-global-global_forcing}
56 \label{eq:eg-global-global_forcing_fu}
57 {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
58 \\
59 \label{eq:eg-global-global_forcing_fv}
60 {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
61 \\
62 \label{eq:eg-global-global_forcing_ft}
63 {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
64 - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
65 \\
66 \label{eq:eg-global-global_forcing_fs}
67 {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
68 + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
69 \end{eqnarray}
70
71 \noindent where ${\cal F}_{u}$, ${\cal F}_{v}$, ${\cal F}_{\theta}$,
72 ${\cal F}_{s}$ are the forcing terms in the zonal and meridional
73 momentum and in the potential temperature and salinity
74 equations respectively.
75 The term $\Delta z_{s}$ represents the top ocean layer thickness in
76 meters.
77 It is used in conjunction with a reference density, $\rho_{0}$
78 (here set to $999.8\,{\rm kg\,m^{-3}}$), a
79 reference salinity, $S_{0}$ (here set to 35~ppt),
80 and a specific heat capacity, $C_{p}$ (here set to
81 $4000~{\rm J}~^{\circ}{\rm C}^{-1}~{\rm kg}^{-1}$), to convert
82 input dataset values into time tendencies of
83 potential temperature (with units of $^{\circ}{\rm C}~{\rm s}^{-1}$),
84 salinity (with units ${\rm ppt}~s^{-1}$) and
85 velocity (with units ${\rm m}~{\rm s}^{-2}$).
86 The externally supplied forcing fields used in this
87 experiment are $\tau_{x}$, $\tau_{y}$, $\theta^{\ast}$, $S^{\ast}$,
88 $\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$)
89 have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields
90 ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$
91 respectively. The salinity forcing fields ($S^{\ast}$ and
92 $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
93 respectively. The source files and procedures for ingesting this data into the
94 simulation are described in the experiment configuration discussion in section
95 \ref{sec:eg-global-clim_ocn_examp_exp_config}.
96
97
98 \subsection{Discrete Numerical Configuration}
99 %\label{www:tutorials}
100
101
102 The model is configured in hydrostatic form. The domain is discretised with
103 a uniform grid spacing in latitude and longitude on the sphere
104 $\Delta \phi=\Delta \lambda=4^{\circ}$, so
105 that there are ninety grid cells in the zonal and forty in the
106 meridional direction. The internal model coordinate variables
107 $x$ and $y$ are initialized according to
108 \begin{eqnarray}
109 x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
110 y=r\lambda,~\Delta y &= &r\Delta \lambda
111 \end{eqnarray}
112
113 Arctic polar regions are not
114 included in this experiment. Meridionally the model extends from
115 $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
116 Vertically the model is configured with twenty layers with the
117 following thicknesses
118 $\Delta z_{1} = 50\,{\rm m},\,
119 \Delta z_{2} = 50\,{\rm m},\,
120 \Delta z_{3} = 55\,{\rm m},\,
121 \Delta z_{4} = 60\,{\rm m},\,
122 \Delta z_{5} = 65\,{\rm m},\,
123 $
124 $
125 \Delta z_{6}~=~70\,{\rm m},\,
126 \Delta z_{7}~=~80\,{\rm m},\,
127 \Delta z_{8}~=95\,{\rm m},\,
128 \Delta z_{9}=120\,{\rm m},\,
129 \Delta z_{10}=155\,{\rm m},\,
130 $
131 $
132 \Delta z_{11}=200\,{\rm m},\,
133 \Delta z_{12}=260\,{\rm m},\,
134 \Delta z_{13}=320\,{\rm m},\,
135 \Delta z_{14}=400\,{\rm m},\,
136 \Delta z_{15}=480\,{\rm m},\,
137 $
138 $
139 \Delta z_{16}=570\,{\rm m},\,
140 \Delta z_{17}=655\,{\rm m},\,
141 \Delta z_{18}=725\,{\rm m},\,
142 \Delta z_{19}=775\,{\rm m},\,
143 \Delta z_{20}=815\,{\rm m}
144 $ (here the numeric subscript indicates the model level index number, ${\tt k}$) to
145 give a total depth, $H$, of $-5450{\rm m}$.
146 The implicit free surface form of the pressure equation described in Marshall et. al
147 \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
148 dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
149
150 Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations})
151 for both the zonal flow, $u$ and the meridional flow $v$, according to equations
152 (\ref{eq:eg-global-global_forcing_fu}) and (\ref{eq:eg-global-global_forcing_fv}).
153 Thermodynamic forcing inputs are added to the equations
154 in (\ref{eq:eg-global-model_equations}) for
155 potential temperature, $\theta$, and salinity, $S$, according to equations
156 (\ref{eq:eg-global-global_forcing_ft}) and (\ref{eq:eg-global-global_forcing_fs}).
157 This produces a set of equations solved in this configuration as follows:
158
159 \begin{eqnarray}
160 \label{eq:eg-global-model_equations}
161 \frac{Du}{Dt} - fv +
162 \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
163 \nabla_{h}\cdot A_{h}\nabla_{h}u -
164 \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}
165 & = &
166 \begin{cases}
167 {\cal F}_u & \text{(surface)} \\
168 0 & \text{(interior)}
169 \end{cases}
170 \\
171 \frac{Dv}{Dt} + fu +
172 \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
173 \nabla_{h}\cdot A_{h}\nabla_{h}v -
174 \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}
175 & = &
176 \begin{cases}
177 {\cal F}_v & \text{(surface)} \\
178 0 & \text{(interior)}
179 \end{cases}
180 \\
181 \frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
182 &=&
183 0
184 \\
185 \frac{D\theta}{Dt} -
186 \nabla_{h}\cdot K_{h}\nabla_{h}\theta
187 - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}
188 & = &
189 \begin{cases}
190 {\cal F}_\theta & \text{(surface)} \\
191 0 & \text{(interior)}
192 \end{cases}
193 \\
194 \frac{D s}{Dt} -
195 \nabla_{h}\cdot K_{h}\nabla_{h}s
196 - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}
197 & = &
198 \begin{cases}
199 {\cal F}_s & \text{(surface)} \\
200 0 & \text{(interior)}
201 \end{cases}
202 \\
203 g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
204 \end{eqnarray}
205
206 \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
207 $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
208 are the zonal and meridional components of the
209 flow vector, $\vec{u}$, on the sphere. As described in
210 MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
211 evolution of potential temperature, $\theta$, equation is solved prognostically.
212 The total pressure, $p$, is diagnosed by summing pressure due to surface
213 elevation $\eta$ and the hydrostatic pressure.
214 \\
215
216 \subsubsection{Numerical Stability Criteria}
217 %\label{www:tutorials}
218
219 The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
220 This value is chosen to yield a Munk layer width \cite{adcroft:95},
221 \begin{eqnarray}
222 \label{eq:eg-global-munk_layer}
223 && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
224 \end{eqnarray}
225
226 \noindent of $\approx 600$km. This is greater than the model
227 resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional
228 boundary layer is adequately resolved.
229 \\
230
231 \noindent The model is stepped forward with a
232 time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
233 $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
234 parameter to the horizontal Laplacian friction \cite{adcroft:95}
235 \begin{eqnarray}
236 \label{eq:eg-global-laplacian_stability}
237 && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
238 \end{eqnarray}
239
240 \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the
241 0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at
242 $\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.
243 \\
244
245 \noindent The vertical dissipation coefficient, $A_{z}$, is set to
246 $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
247 \begin{eqnarray}
248 \label{eq:eg-global-laplacian_stability_z}
249 S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
250 \end{eqnarray}
251
252 \noindent evaluates to $0.015$ for the smallest model
253 level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
254 the upper stability limit.
255 \\
256
257 The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
258 for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
259 and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
260 related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
261 Here the stability parameter
262 \begin{eqnarray}
263 \label{eq:eg-global-laplacian_stability_xtheta}
264 S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
265 \end{eqnarray}
266 evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
267 stability parameter related to $K_{z}$
268 \begin{eqnarray}
269 \label{eq:eg-global-laplacian_stability_ztheta}
270 S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
271 \end{eqnarray}
272 evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
273 of $S_{l} \approx 0.5$.
274 \\
275
276 \noindent The numerical stability for inertial oscillations
277 \cite{adcroft:95}
278
279 \begin{eqnarray}
280 \label{eq:eg-global-inertial_stability}
281 S_{i} = f^{2} {\delta t_v}^2
282 \end{eqnarray}
283
284 \noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to
285 the $S_{i} < 1$ upper limit for stability.
286 \\
287
288 \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
289 horizontal flow
290 speed of $ | \vec{u} | = 2 ms^{-1}$
291
292 \begin{eqnarray}
293 \label{eq:eg-global-cfl_stability}
294 S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
295 \end{eqnarray}
296
297 \noindent evaluates to $6 \times 10^{-2}$. This is well below the stability
298 limit of 0.5.
299 \\
300
301 \noindent The stability parameter for internal gravity waves propagating
302 with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
303 \cite{adcroft:95}
304
305 \begin{eqnarray}
306 \label{eq:eg-global-gfl_stability}
307 S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
308 \end{eqnarray}
309
310 \noindent evaluates to $3 \times 10^{-1}$. This is close to the linear
311 stability limit of 0.5.
312
313 \subsection{Experiment Configuration}
314 %\label{www:tutorials}
315 \label{sec:eg-global-clim_ocn_examp_exp_config}
316
317 The model configuration for this experiment resides under the
318 directory {\it tutorial\_examples/global\_ocean\_circulation/}.
319 The experiment files
320
321 \begin{itemize}
322 \item {\it input/data}
323 \item {\it input/data.pkg}
324 \item {\it input/eedata},
325 \item {\it input/windx.bin},
326 \item {\it input/windy.bin},
327 \item {\it input/salt.bin},
328 \item {\it input/theta.bin},
329 \item {\it input/SSS.bin},
330 \item {\it input/SST.bin},
331 \item {\it input/topog.bin},
332 \item {\it code/CPP\_EEOPTIONS.h}
333 \item {\it code/CPP\_OPTIONS.h},
334 \item {\it code/SIZE.h}.
335 \end{itemize}
336 contain the code customizations and parameter settings for these
337 experiments. Below we describe the customizations
338 to these files associated with this experiment.
339
340 \subsubsection{Driving Datasets}
341 %\label{www:tutorials}
342
343 Figures ({\it --- missing figures ---})
344 %(\ref{fig:sim_config_tclim}-\ref{fig:sim_config_empmr})
345 show the relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$)
346 fields, the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
347 and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
348 in equations
349 (\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}).
350 The figures also indicate the lateral extent and coastline used in the
351 experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})
352 shows the depth contours of the model domain.
353
354 \subsubsection{File {\it input/data}}
355 %\label{www:tutorials}
356
357 This file, reproduced completely below, specifies the main parameters
358 for the experiment. The parameters that are significant for this configuration
359 are
360
361 \begin{itemize}
362
363 \item Lines 7-10 and 11-14
364 \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim}
365 $\cdots$ \\
366 set reference values for potential
367 temperature and salinity at each model level in units of $^{\circ}\mathrm{C}$ and
368 ${\rm ppt}$. The entries are ordered from surface to depth.
369 Density is calculated from anomalies at each level evaluated
370 with respect to the reference values set here.\\
371 \fbox{
372 \begin{minipage}{5.0in}
373 {\it S/R INI\_THETA}({\it ini\_theta.F})
374 \end{minipage}
375 }
376
377
378 \item Line 15,
379 \begin{verbatim} viscAz=1.E-3, \end{verbatim}
380 this line sets the vertical Laplacian dissipation coefficient to
381 $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
382 for this operator are specified later. This variable is copied into
383 model general vertical coordinate variable {\bf viscAr}.
384
385 \fbox{
386 \begin{minipage}{5.0in}
387 {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
388 \end{minipage}
389 }
390
391 \item Line 16,
392 \begin{verbatim}
393 viscAh=5.E5,
394 \end{verbatim}
395 this line sets the horizontal Laplacian frictional dissipation coefficient to
396 $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
397 for this operator are specified later.
398
399 \item Lines 17,
400 \begin{verbatim}
401 no_slip_sides=.FALSE.
402 \end{verbatim}
403 this line selects a free-slip lateral boundary condition for
404 the horizontal Laplacian friction operator
405 e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
406 $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
407
408 \item Lines 9,
409 \begin{verbatim}
410 no_slip_bottom=.TRUE.
411 \end{verbatim}
412 this line selects a no-slip boundary condition for bottom
413 boundary condition in the vertical Laplacian friction operator
414 e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
415
416 \item Line 19,
417 \begin{verbatim}
418 diffKhT=1.E3,
419 \end{verbatim}
420 this line sets the horizontal diffusion coefficient for temperature
421 to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
422 operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
423 all boundaries.
424
425 \item Line 20,
426 \begin{verbatim}
427 diffKzT=3.E-5,
428 \end{verbatim}
429 this line sets the vertical diffusion coefficient for temperature
430 to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
431 condition on this operator is $\frac{\partial}{\partial z}=0$ at both
432 the upper and lower boundaries.
433
434 \item Line 21,
435 \begin{verbatim}
436 diffKhS=1.E3,
437 \end{verbatim}
438 this line sets the horizontal diffusion coefficient for salinity
439 to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
440 operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
441 all boundaries.
442
443 \item Line 22,
444 \begin{verbatim}
445 diffKzS=3.E-5,
446 \end{verbatim}
447 this line sets the vertical diffusion coefficient for salinity
448 to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
449 condition on this operator is $\frac{\partial}{\partial z}=0$ at both
450 the upper and lower boundaries.
451
452 \item Lines 23-26
453 \begin{verbatim}
454 beta=1.E-11,
455 \end{verbatim}
456 \vspace{-5mm}$\cdots$\\
457 These settings do not apply for this experiment.
458
459 \item Line 27,
460 \begin{verbatim}
461 gravity=9.81,
462 \end{verbatim}
463 Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
464 \fbox{
465 \begin{minipage}{5.0in}
466 {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
467 {\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\
468 {\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\
469 {\it S/R INI\_PARMS}~({\it ini\_parms.F})\\
470 {\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})
471 \end{minipage}
472 }
473
474
475 \item Line 28-29,
476 \begin{verbatim}
477 rigidLid=.FALSE.,
478 implicitFreeSurface=.TRUE.,
479 \end{verbatim}
480 Selects the barotropic pressure equation to be the implicit free surface
481 formulation.
482
483 \item Line 30,
484 \begin{verbatim}
485 eosType='POLY3',
486 \end{verbatim}
487 Selects the third order polynomial form of the equation of state.\\
488 \fbox{
489 \begin{minipage}{5.0in}
490 {\it S/R FIND\_RHO}~({\it find\_rho.F})\\
491 {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})
492 \end{minipage}
493 }
494
495 \item Line 31,
496 \begin{verbatim}
497 readBinaryPrec=32,
498 \end{verbatim}
499 Sets format for reading binary input datasets holding model fields to
500 use 32-bit representation for floating-point numbers.\\
501 \fbox{
502 \begin{minipage}{5.0in}
503 {\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\
504 {\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})
505 \end{minipage}
506 }
507
508 \item Line 36,
509 \begin{verbatim}
510 cg2dMaxIters=1000,
511 \end{verbatim}
512 Sets maximum number of iterations the two-dimensional, conjugate
513 gradient solver will use, {\bf irrespective of convergence
514 criteria being met}.\\
515 \fbox{
516 \begin{minipage}{5.0in}
517 {\it S/R CG2D}~({\it cg2d.F})
518 \end{minipage}
519 }
520
521 \item Line 37,
522 \begin{verbatim}
523 cg2dTargetResidual=1.E-13,
524 \end{verbatim}
525 Sets the tolerance which the two-dimensional, conjugate
526 gradient solver will use to test for convergence in equation
527 %- note: Description of Conjugate gradient method (& related params) is missing
528 % in the mean time, substitute this eq ref:
529 \ref{eq:elliptic-backward-free-surface} %\ref{eq:congrad_2d_resid}
530 to $1 \times 10^{-13}$.
531 Solver will iterate until tolerance falls below this value or until the
532 maximum number of solver iterations is reached.\\
533 \fbox{
534 \begin{minipage}{5.0in}
535 {\it S/R CG2D}~({\it cg2d.F})
536 \end{minipage}
537 }
538
539 \item Line 42,
540 \begin{verbatim}
541 startTime=0,
542 \end{verbatim}
543 Sets the starting time for the model internal time counter.
544 When set to non-zero this option implicitly requests a
545 checkpoint file be read for initial state.
546 By default the checkpoint file is named according to
547 the integer number of time steps in the {\bf startTime} value.
548 The internal time counter works in seconds.
549
550 \item Line 43,
551 \begin{verbatim}
552 endTime=2808000.,
553 \end{verbatim}
554 Sets the time (in seconds) at which this simulation will terminate.
555 At the end of a simulation a checkpoint file is automatically
556 written so that a numerical experiment can consist of multiple
557 stages.
558
559 \item Line 44,
560 \begin{verbatim}
561 #endTime=62208000000,
562 \end{verbatim}
563 A commented out setting for endTime for a 2000 year simulation.
564
565 \item Line 45,
566 \begin{verbatim}
567 deltaTmom=2400.0,
568 \end{verbatim}
569 Sets the timestep $\delta t_{v}$ used in the momentum equations to
570 $20~{\rm mins}$.
571 %- note: Distord Physics (using different time-steps) is not described
572 % in the mean time, put this section ref:
573 See section \ref{sec:time_stepping}. %\ref{sec:mom_time_stepping}.
574
575 \fbox{
576 \begin{minipage}{5.0in}
577 {\it S/R TIMESTEP}({\it timestep.F})
578 \end{minipage}
579 }
580
581 \item Line 46,
582 \begin{verbatim}
583 tauCD=321428.,
584 \end{verbatim}
585 Sets the D-grid to C-grid coupling time scale $\tau_{CD}$
586 used in the momentum equations.
587 %- note: description of CD-scheme pkg (and related params) is missing;
588 % in the mean time, comment out this ref.
589 %See section \ref{sec:cd_scheme}.
590
591 \fbox{
592 \begin{minipage}{5.0in}
593 {\it S/R INI\_PARMS}({\it ini\_parms.F})\\
594 {\it S/R MOM\_FLUXFORM}({\it mom\_fluxform.F})
595 \end{minipage}
596 }
597
598 \item Line 47,
599 \begin{verbatim}
600 deltaTtracer=108000.,
601 \end{verbatim}
602 Sets the default timestep, $\delta t_{\theta}$, for tracer equations to
603 $30~{\rm hours}$.
604 %- note: Distord Physics (using different time-steps) is not described
605 % in the mean time, put this section ref:
606 See section \ref{sec:time_stepping}. %\ref{sec:tracer_time_stepping}.
607
608 \fbox{
609 \begin{minipage}{5.0in}
610 {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})
611 \end{minipage}
612 }
613
614 \item Line 47,
615 \begin{verbatim}
616 bathyFile='topog.box'
617 \end{verbatim}
618 This line specifies the name of the file from which the domain
619 bathymetry is read. This file is a two-dimensional ($x,y$) map of
620 depths. This file is assumed to contain 64-bit binary numbers
621 giving the depth of the model at each grid cell, ordered with the x
622 coordinate varying fastest. The points are ordered from low coordinate
623 to high coordinate for both axes. The units and orientation of the
624 depths in this file are the same as used in the MITgcm code. In this
625 experiment, a depth of $0m$ indicates a solid wall and a depth
626 of $-2000m$ indicates open ocean. The matlab program
627 {\it input/gendata.m} shows an example of how to generate a
628 bathymetry file.
629
630
631 \item Line 50,
632 \begin{verbatim}
633 zonalWindFile='windx.sin_y'
634 \end{verbatim}
635 This line specifies the name of the file from which the x-direction
636 surface wind stress is read. This file is also a two-dimensional
637 ($x,y$) map and is enumerated and formatted in the same manner as the
638 bathymetry file. The matlab program {\it input/gendata.m} includes example
639 code to generate a valid
640 {\bf zonalWindFile}
641 file.
642
643 \end{itemize}
644
645 \noindent other lines in the file {\it input/data} are standard values
646 that are described in the MITgcm Getting Started and MITgcm Parameters
647 notes.
648
649 \begin{small}
650 \input{s_examples/global_oce_latlon/input/data}
651 \end{small}
652
653 \subsubsection{File {\it input/data.pkg}}
654 %\label{www:tutorials}
655
656 This file uses standard default values and does not contain
657 customisations for this experiment.
658
659 \subsubsection{File {\it input/eedata}}
660 %\label{www:tutorials}
661
662 This file uses standard default values and does not contain
663 customisations for this experiment.
664
665 \subsubsection{File {\it input/windx.sin\_y}}
666 %\label{www:tutorials}
667
668 The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
669 map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
670 Although $\tau_{x}$ is only a function of $y$n in this experiment
671 this file must still define a complete two-dimensional map in order
672 to be compatible with the standard code for loading forcing fields
673 in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
674 code for creating the {\it input/windx.sin\_y} file.
675
676 \subsubsection{File {\it input/topog.box}}
677 %\label{www:tutorials}
678
679
680 The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
681 map of depth values. For this experiment values are either
682 $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep
683 ocean. The file contains a raw binary stream of data that is enumerated
684 in the same way as standard MITgcm two-dimensional, horizontal arrays.
685 The included matlab program {\it input/gendata.m} gives a complete
686 code for creating the {\it input/topog.box} file.
687
688 \subsubsection{File {\it code/SIZE.h}}
689 %\label{www:tutorials}
690
691 Two lines are customized in this file for the current experiment
692
693 \begin{itemize}
694
695 \item Line 39,
696 \begin{verbatim} sNx=60, \end{verbatim} this line sets
697 the lateral domain extent in grid points for the
698 axis aligned with the x-coordinate.
699
700 \item Line 40,
701 \begin{verbatim} sNy=60, \end{verbatim} this line sets
702 the lateral domain extent in grid points for the
703 axis aligned with the y-coordinate.
704
705 \item Line 49,
706 \begin{verbatim} Nr=4, \end{verbatim} this line sets
707 the vertical domain extent in grid points.
708
709 \end{itemize}
710
711 \begin{small}
712 \input{s_examples/global_oce_latlon/code/SIZE.h}
713 \end{small}
714
715 \subsubsection{File {\it code/CPP\_OPTIONS.h}}
716 %\label{www:tutorials}
717
718 This file uses standard default values and does not contain
719 customisations for this experiment.
720
721
722 \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
723 %\label{www:tutorials}
724
725 This file uses standard default values and does not contain
726 customisations for this experiment.
727
728 \subsubsection{Other Files }
729 %\label{www:tutorials}
730
731 Other files relevant to this experiment are
732 \begin{itemize}
733 \item {\it model/src/ini\_cori.F}. This file initializes the model
734 coriolis variables {\bf fCorU}.
735 \item {\it model/src/ini\_spherical\_polar\_grid.F}
736 \item {\it model/src/ini\_parms.F},
737 \item {\it input/windx.sin\_y},
738 \end{itemize}
739 contain the code customisations and parameter settings for this
740 experiments. Below we describe the customisations
741 to these files associated with this experiment.

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