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1 adcroft 1.2 % $Header: /u/gcmpack/mitgcmdoc/part3/case_studies/hs_atmosphere/hs_atmos.tex,v 1.1 2002/02/28 19:32:19 cnh Exp $
2 cnh 1.1 % $Name: $
3    
4     \section{Held-Suarez Atmospheric Simulation at 2.8$^\circ$ Resolution}
5 adcroft 1.2 \label{www:tutorials}
6 cnh 1.1 \label{sect:eg-hs}
7    
8     \bodytext{bgcolor="#FFFFFFFF"}
9    
10     %\begin{center}
11     %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
12     %At Four Degree Resolution with Asynchronous Time Stepping}
13     %
14     %\vspace*{4mm}
15     %
16     %\vspace*{3mm}
17     %{\large May 2001}
18     %\end{center}
19    
20     \subsection{Introduction}
21 adcroft 1.2 \label{www:tutorials}
22 cnh 1.1
23     This document describes the third example MITgcm experiment. The first
24     two examples illustrated how to configure the code for hydrostatic idealized
25     geophysical fluids simulations. This example illustrates the use of
26     the MITgcm for large scale ocean circulation simulation.
27    
28     \subsection{Overview}
29 adcroft 1.2 \label{www:tutorials}
30 cnh 1.1
31     This example experiment demonstrates using the MITgcm to simulate
32     the planetary ocean circulation. The simulation is configured
33     with realistic geography and bathymetry on a
34     $4^{\circ} \times 4^{\circ}$ spherical polar grid.
35     Twenty levels are used in the vertical, ranging in thickness
36     from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,
37     giving a maximum model depth of $6\,{\rm km}$.
38     At this resolution, the configuration
39     can be integrated forward for thousands of years on a single
40     processor desktop computer.
41     \\
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-hs-global_forcing}
56     \label{EQ:eg-hs-global_forcing_fu}
57     {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
58     \\
59     \label{EQ:eg-hs-global_forcing_fv}
60     {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
61     \\
62     \label{EQ:eg-hs-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-hs-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.
94     \\
95    
96    
97     Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
98     relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
99     the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
100     and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
101     in equations \ref{EQ:eg-hs-global_forcing_fu}-\ref{EQ:eg-hs-global_forcing_fs}. The figures
102     also indicate the lateral extent and coastline used in the experiment.
103     Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
104     domain.
105    
106    
107     \subsection{Discrete Numerical Configuration}
108 adcroft 1.2 \label{www:tutorials}
109 cnh 1.1
110    
111     The model is configured in hydrostatic form. The domain is discretised with
112     a uniform grid spacing in latitude and longitude on the sphere
113     $\Delta \phi=\Delta \lambda=4^{\circ}$, so
114     that there are ninety grid cells in the zonal and forty in the
115     meridional direction. The internal model coordinate variables
116     $x$ and $y$ are initialized according to
117     \begin{eqnarray}
118     x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
119     y=r\lambda,~\Delta x &= &r\Delta \lambda
120     \end{eqnarray}
121    
122     Arctic polar regions are not
123     included in this experiment. Meridionally the model extends from
124     $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
125     Vertically the model is configured with twenty layers with the
126     following thicknesses
127     $\Delta z_{1} = 50\,{\rm m},\,
128     \Delta z_{2} = 50\,{\rm m},\,
129     \Delta z_{3} = 55\,{\rm m},\,
130     \Delta z_{4} = 60\,{\rm m},\,
131     \Delta z_{5} = 65\,{\rm m},\,
132     $
133     $
134     \Delta z_{6}~=~70\,{\rm m},\,
135     \Delta z_{7}~=~80\,{\rm m},\,
136     \Delta z_{8}~=95\,{\rm m},\,
137     \Delta z_{9}=120\,{\rm m},\,
138     \Delta z_{10}=155\,{\rm m},\,
139     $
140     $
141     \Delta z_{11}=200\,{\rm m},\,
142     \Delta z_{12}=260\,{\rm m},\,
143     \Delta z_{13}=320\,{\rm m},\,
144     \Delta z_{14}=400\,{\rm m},\,
145     \Delta z_{15}=480\,{\rm m},\,
146     $
147     $
148     \Delta z_{16}=570\,{\rm m},\,
149     \Delta z_{17}=655\,{\rm m},\,
150     \Delta z_{18}=725\,{\rm m},\,
151     \Delta z_{19}=775\,{\rm m},\,
152     \Delta z_{20}=815\,{\rm m}
153     $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
154     The implicit free surface form of the pressure equation described in Marshall et. al
155     \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
156     dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
157    
158     Wind-stress forcing is added to the momentum equations for both
159     the zonal flow, $u$ and the meridional flow $v$, according to equations
160     (\ref{EQ:eg-hs-global_forcing_fu}) and (\ref{EQ:eg-hs-global_forcing_fv}).
161     Thermodynamic forcing inputs are added to the equations for
162     potential temperature, $\theta$, and salinity, $S$, according to equations
163     (\ref{EQ:eg-hs-global_forcing_ft}) and (\ref{EQ:eg-hs-global_forcing_fs}).
164     This produces a set of equations solved in this configuration as follows:
165    
166     \begin{eqnarray}
167     \label{EQ:eg-hs-model_equations}
168     \frac{Du}{Dt} - fv +
169     \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
170     \nabla_{h}\cdot A_{h}\nabla_{h}u -
171     \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}
172     & = &
173     \begin{cases}
174     {\cal F}_u & \text{(surface)} \\
175     0 & \text{(interior)}
176     \end{cases}
177     \\
178     \frac{Dv}{Dt} + fu +
179     \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
180     \nabla_{h}\cdot A_{h}\nabla_{h}v -
181     \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}
182     & = &
183     \begin{cases}
184     {\cal F}_v & \text{(surface)} \\
185     0 & \text{(interior)}
186     \end{cases}
187     \\
188     \frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
189     &=&
190     0
191     \\
192     \frac{D\theta}{Dt} -
193     \nabla_{h}\cdot K_{h}\nabla_{h}\theta
194     - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}
195     & = &
196     \begin{cases}
197     {\cal F}_\theta & \text{(surface)} \\
198     0 & \text{(interior)}
199     \end{cases}
200     \\
201     \frac{D s}{Dt} -
202     \nabla_{h}\cdot K_{h}\nabla_{h}s
203     - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}
204     & = &
205     \begin{cases}
206     {\cal F}_s & \text{(surface)} \\
207     0 & \text{(interior)}
208     \end{cases}
209     \\
210     g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
211     \end{eqnarray}
212    
213     \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
214     $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
215     are the zonal and meridional components of the
216     flow vector, $\vec{u}$, on the sphere. As described in
217     MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
218     evolution of potential temperature, $\theta$, equation is solved prognostically.
219     The total pressure, $p$, is diagnosed by summing pressure due to surface
220     elevation $\eta$ and the hydrostatic pressure.
221     \\
222    
223     \subsubsection{Numerical Stability Criteria}
224 adcroft 1.2 \label{www:tutorials}
225 cnh 1.1
226     The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
227     This value is chosen to yield a Munk layer width \cite{adcroft:95},
228     \begin{eqnarray}
229     \label{EQ:eg-hs-munk_layer}
230     M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
231     \end{eqnarray}
232    
233     \noindent of $\approx 600$km. This is greater than the model
234     resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional
235     boundary layer is adequately resolved.
236     \\
237    
238     \noindent The model is stepped forward with a
239     time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
240     $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
241     parameter to the horizontal Laplacian friction \cite{adcroft:95}
242     \begin{eqnarray}
243     \label{EQ:eg-hs-laplacian_stability}
244     S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
245     \end{eqnarray}
246    
247     \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the
248     0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at
249     $\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.
250     \\
251    
252     \noindent The vertical dissipation coefficient, $A_{z}$, is set to
253     $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
254     \begin{eqnarray}
255     \label{EQ:eg-hs-laplacian_stability_z}
256     S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
257     \end{eqnarray}
258    
259     \noindent evaluates to $0.015$ for the smallest model
260     level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
261     the upper stability limit.
262     \\
263    
264     The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
265     for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
266     and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
267     related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
268     Here the stability parameter
269     \begin{eqnarray}
270     \label{EQ:eg-hs-laplacian_stability_xtheta}
271     S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
272     \end{eqnarray}
273     evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
274     stability parameter related to $K_{z}$
275     \begin{eqnarray}
276     \label{EQ:eg-hs-laplacian_stability_ztheta}
277     S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
278     \end{eqnarray}
279     evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
280     of $S_{l} \approx 0.5$.
281     \\
282    
283     \noindent The numerical stability for inertial oscillations
284     \cite{adcroft:95}
285    
286     \begin{eqnarray}
287     \label{EQ:eg-hs-inertial_stability}
288     S_{i} = f^{2} {\delta t_v}^2
289     \end{eqnarray}
290    
291     \noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to
292     the $S_{i} < 1$ upper limit for stability.
293     \\
294    
295     \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
296     horizontal flow
297     speed of $ | \vec{u} | = 2 ms^{-1}$
298    
299     \begin{eqnarray}
300     \label{EQ:eg-hs-cfl_stability}
301     S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
302     \end{eqnarray}
303    
304     \noindent evaluates to $6 \times 10^{-2}$. This is well below the stability
305     limit of 0.5.
306     \\
307    
308     \noindent The stability parameter for internal gravity waves propagating
309     with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
310     \cite{adcroft:95}
311    
312     \begin{eqnarray}
313     \label{EQ:eg-hs-gfl_stability}
314     S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
315     \end{eqnarray}
316    
317     \noindent evaluates to $3 \times 10^{-1}$. This is close to the linear
318     stability limit of 0.5.
319    
320     \subsection{Experiment Configuration}
321 adcroft 1.2 \label{www:tutorials}
322 cnh 1.1 \label{SEC:eg-hs_examp_exp_config}
323    
324     The model configuration for this experiment resides under the
325     directory {\it verification/exp2/}. The experiment files
326     \begin{itemize}
327     \item {\it input/data}
328     \item {\it input/data.pkg}
329     \item {\it input/eedata},
330     \item {\it input/windx.bin},
331     \item {\it input/windy.bin},
332     \item {\it input/salt.bin},
333     \item {\it input/theta.bin},
334     \item {\it input/SSS.bin},
335     \item {\it input/SST.bin},
336     \item {\it input/topog.bin},
337     \item {\it code/CPP\_EEOPTIONS.h}
338     \item {\it code/CPP\_OPTIONS.h},
339     \item {\it code/SIZE.h}.
340     \end{itemize}
341     contain the code customizations and parameter settings for these
342     experiments. Below we describe the customizations
343     to these files associated with this experiment.
344    
345     \subsubsection{File {\it input/data}}
346 adcroft 1.2 \label{www:tutorials}
347 cnh 1.1
348     This file, reproduced completely below, specifies the main parameters
349     for the experiment. The parameters that are significant for this configuration
350     are
351    
352     \begin{itemize}
353    
354     \item Lines 7-10 and 11-14
355     \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim}
356     $\cdots$ \\
357     set reference values for potential
358     temperature and salinity at each model level in units of $^{\circ}$C and
359     ${\rm ppt}$. The entries are ordered from surface to depth.
360     Density is calculated from anomalies at each level evaluated
361     with respect to the reference values set here.\\
362     \fbox{
363     \begin{minipage}{5.0in}
364     {\it S/R INI\_THETA}({\it ini\_theta.F})
365     \end{minipage}
366     }
367    
368    
369     \item Line 15,
370     \begin{verbatim} viscAz=1.E-3, \end{verbatim}
371     this line sets the vertical Laplacian dissipation coefficient to
372     $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
373     for this operator are specified later. This variable is copied into
374     model general vertical coordinate variable {\bf viscAr}.
375    
376     \fbox{
377     \begin{minipage}{5.0in}
378     {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
379     \end{minipage}
380     }
381    
382     \item Line 16,
383     \begin{verbatim}
384     viscAh=5.E5,
385     \end{verbatim}
386     this line sets the horizontal Laplacian frictional dissipation coefficient to
387     $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
388     for this operator are specified later.
389    
390     \item Lines 17,
391     \begin{verbatim}
392     no_slip_sides=.FALSE.
393     \end{verbatim}
394     this line selects a free-slip lateral boundary condition for
395     the horizontal Laplacian friction operator
396     e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
397     $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
398    
399     \item Lines 9,
400     \begin{verbatim}
401     no_slip_bottom=.TRUE.
402     \end{verbatim}
403     this line selects a no-slip boundary condition for bottom
404     boundary condition in the vertical Laplacian friction operator
405     e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
406    
407     \item Line 19,
408     \begin{verbatim}
409     diffKhT=1.E3,
410     \end{verbatim}
411     this line sets the horizontal diffusion coefficient for temperature
412     to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
413     operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
414     all boundaries.
415    
416     \item Line 20,
417     \begin{verbatim}
418     diffKzT=3.E-5,
419     \end{verbatim}
420     this line sets the vertical diffusion coefficient for temperature
421     to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
422     condition on this operator is $\frac{\partial}{\partial z}=0$ at both
423     the upper and lower boundaries.
424    
425     \item Line 21,
426     \begin{verbatim}
427     diffKhS=1.E3,
428     \end{verbatim}
429     this line sets the horizontal diffusion coefficient for salinity
430     to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
431     operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
432     all boundaries.
433    
434     \item Line 22,
435     \begin{verbatim}
436     diffKzS=3.E-5,
437     \end{verbatim}
438     this line sets the vertical diffusion coefficient for salinity
439     to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
440     condition on this operator is $\frac{\partial}{\partial z}=0$ at both
441     the upper and lower boundaries.
442    
443     \item Lines 23-26
444     \begin{verbatim}
445     beta=1.E-11,
446     \end{verbatim}
447     \vspace{-5mm}$\cdots$\\
448     These settings do not apply for this experiment.
449    
450     \item Line 27,
451     \begin{verbatim}
452     gravity=9.81,
453     \end{verbatim}
454     Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
455     \fbox{
456     \begin{minipage}{5.0in}
457     {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
458     {\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\
459     {\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\
460     {\it S/R INI\_PARMS}~({\it ini\_parms.F})\\
461     {\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})
462     \end{minipage}
463     }
464    
465    
466     \item Line 28-29,
467     \begin{verbatim}
468     rigidLid=.FALSE.,
469     implicitFreeSurface=.TRUE.,
470     \end{verbatim}
471     Selects the barotropic pressure equation to be the implicit free surface
472     formulation.
473    
474     \item Line 30,
475     \begin{verbatim}
476     eosType='POLY3',
477     \end{verbatim}
478     Selects the third order polynomial form of the equation of state.\\
479     \fbox{
480     \begin{minipage}{5.0in}
481     {\it S/R FIND\_RHO}~({\it find\_rho.F})\\
482     {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})
483     \end{minipage}
484     }
485    
486     \item Line 31,
487     \begin{verbatim}
488     readBinaryPrec=32,
489     \end{verbatim}
490     Sets format for reading binary input datasets holding model fields to
491     use 32-bit representation for floating-point numbers.\\
492     \fbox{
493     \begin{minipage}{5.0in}
494     {\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\
495     {\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})
496     \end{minipage}
497     }
498    
499     \item Line 36,
500     \begin{verbatim}
501     cg2dMaxIters=1000,
502     \end{verbatim}
503     Sets maximum number of iterations the two-dimensional, conjugate
504     gradient solver will use, {\bf irrespective of convergence
505     criteria being met}.\\
506     \fbox{
507     \begin{minipage}{5.0in}
508     {\it S/R CG2D}~({\it cg2d.F})
509     \end{minipage}
510     }
511    
512     \item Line 37,
513     \begin{verbatim}
514     cg2dTargetResidual=1.E-13,
515     \end{verbatim}
516     Sets the tolerance which the two-dimensional, conjugate
517     gradient solver will use to test for convergence in equation
518     \ref{EQ:eg-hs-congrad_2d_resid} to $1 \times 10^{-13}$.
519     Solver will iterate until
520     tolerance falls below this value or until the maximum number of
521     solver iterations is reached.\\
522     \fbox{
523     \begin{minipage}{5.0in}
524     {\it S/R CG2D}~({\it cg2d.F})
525     \end{minipage}
526     }
527    
528     \item Line 42,
529     \begin{verbatim}
530     startTime=0,
531     \end{verbatim}
532     Sets the starting time for the model internal time counter.
533     When set to non-zero this option implicitly requests a
534     checkpoint file be read for initial state.
535     By default the checkpoint file is named according to
536     the integer number of time steps in the {\bf startTime} value.
537     The internal time counter works in seconds.
538    
539     \item Line 43,
540     \begin{verbatim}
541     endTime=2808000.,
542     \end{verbatim}
543     Sets the time (in seconds) at which this simulation will terminate.
544     At the end of a simulation a checkpoint file is automatically
545     written so that a numerical experiment can consist of multiple
546     stages.
547    
548     \item Line 44,
549     \begin{verbatim}
550     #endTime=62208000000,
551     \end{verbatim}
552     A commented out setting for endTime for a 2000 year simulation.
553    
554     \item Line 45,
555     \begin{verbatim}
556     deltaTmom=2400.0,
557     \end{verbatim}
558     Sets the timestep $\delta t_{v}$ used in the momentum equations to
559     $20~{\rm mins}$.
560     See section \ref{SEC:mom_time_stepping}.
561    
562     \fbox{
563     \begin{minipage}{5.0in}
564     {\it S/R TIMESTEP}({\it timestep.F})
565     \end{minipage}
566     }
567    
568     \item Line 46,
569     \begin{verbatim}
570     tauCD=321428.,
571     \end{verbatim}
572     Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.
573     See section \ref{SEC:cd_scheme}.
574    
575     \fbox{
576     \begin{minipage}{5.0in}
577     {\it S/R INI\_PARMS}({\it ini\_parms.F})\\
578     {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})
579     \end{minipage}
580     }
581    
582     \item Line 47,
583     \begin{verbatim}
584     deltaTtracer=108000.,
585     \end{verbatim}
586     Sets the default timestep, $\delta t_{\theta}$, for tracer equations to
587     $30~{\rm hours}$.
588     See section \ref{SEC:tracer_time_stepping}.
589    
590     \fbox{
591     \begin{minipage}{5.0in}
592     {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})
593     \end{minipage}
594     }
595    
596     \item Line 47,
597     \begin{verbatim}
598     bathyFile='topog.box'
599     \end{verbatim}
600     This line specifies the name of the file from which the domain
601     bathymetry is read. This file is a two-dimensional ($x,y$) map of
602     depths. This file is assumed to contain 64-bit binary numbers
603     giving the depth of the model at each grid cell, ordered with the x
604     coordinate varying fastest. The points are ordered from low coordinate
605     to high coordinate for both axes. The units and orientation of the
606     depths in this file are the same as used in the MITgcm code. In this
607     experiment, a depth of $0m$ indicates a solid wall and a depth
608     of $-2000m$ indicates open ocean. The matlab program
609     {\it input/gendata.m} shows an example of how to generate a
610     bathymetry file.
611    
612    
613     \item Line 50,
614     \begin{verbatim}
615     zonalWindFile='windx.sin_y'
616     \end{verbatim}
617     This line specifies the name of the file from which the x-direction
618     surface wind stress is read. This file is also a two-dimensional
619     ($x,y$) map and is enumerated and formatted in the same manner as the
620     bathymetry file. The matlab program {\it input/gendata.m} includes example
621     code to generate a valid
622     {\bf zonalWindFile}
623     file.
624    
625     \end{itemize}
626    
627     \noindent other lines in the file {\it input/data} are standard values
628     that are described in the MITgcm Getting Started and MITgcm Parameters
629     notes.
630    
631     \begin{small}
632     \input{part3/case_studies/climatalogical_ogcm/input/data}
633     \end{small}
634    
635     \subsubsection{File {\it input/data.pkg}}
636 adcroft 1.2 \label{www:tutorials}
637 cnh 1.1
638     This file uses standard default values and does not contain
639     customisations for this experiment.
640    
641     \subsubsection{File {\it input/eedata}}
642 adcroft 1.2 \label{www:tutorials}
643 cnh 1.1
644     This file uses standard default values and does not contain
645     customisations for this experiment.
646    
647     \subsubsection{File {\it input/windx.sin\_y}}
648 adcroft 1.2 \label{www:tutorials}
649 cnh 1.1
650     The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
651     map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
652     Although $\tau_{x}$ is only a function of $y$n in this experiment
653     this file must still define a complete two-dimensional map in order
654     to be compatible with the standard code for loading forcing fields
655     in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
656     code for creating the {\it input/windx.sin\_y} file.
657    
658     \subsubsection{File {\it input/topog.box}}
659 adcroft 1.2 \label{www:tutorials}
660 cnh 1.1
661    
662     The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
663     map of depth values. For this experiment values are either
664     $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep
665     ocean. The file contains a raw binary stream of data that is enumerated
666     in the same way as standard MITgcm two-dimensional, horizontal arrays.
667     The included matlab program {\it input/gendata.m} gives a complete
668     code for creating the {\it input/topog.box} file.
669    
670     \subsubsection{File {\it code/SIZE.h}}
671 adcroft 1.2 \label{www:tutorials}
672 cnh 1.1
673     Two lines are customized in this file for the current experiment
674    
675     \begin{itemize}
676    
677     \item Line 39,
678     \begin{verbatim} sNx=60, \end{verbatim} this line sets
679     the lateral domain extent in grid points for the
680     axis aligned with the x-coordinate.
681    
682     \item Line 40,
683     \begin{verbatim} sNy=60, \end{verbatim} this line sets
684     the lateral domain extent in grid points for the
685     axis aligned with the y-coordinate.
686    
687     \item Line 49,
688     \begin{verbatim} Nr=4, \end{verbatim} this line sets
689     the vertical domain extent in grid points.
690    
691     \end{itemize}
692    
693     \begin{small}
694     \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}
695     \end{small}
696    
697     \subsubsection{File {\it code/CPP\_OPTIONS.h}}
698 adcroft 1.2 \label{www:tutorials}
699 cnh 1.1
700     This file uses standard default values and does not contain
701     customisations for this experiment.
702    
703    
704     \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
705 adcroft 1.2 \label{www:tutorials}
706 cnh 1.1
707     This file uses standard default values and does not contain
708     customisations for this experiment.
709    
710     \subsubsection{Other Files }
711 adcroft 1.2 \label{www:tutorials}
712 cnh 1.1
713     Other files relevant to this experiment are
714     \begin{itemize}
715     \item {\it model/src/ini\_cori.F}. This file initializes the model
716     coriolis variables {\bf fCorU}.
717     \item {\it model/src/ini\_spherical\_polar\_grid.F}
718     \item {\it model/src/ini\_parms.F},
719     \item {\it input/windx.sin\_y},
720     \end{itemize}
721     contain the code customisations and parameter settings for this
722     experiments. Below we describe the customisations
723     to these files associated with this experiment.

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