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1 edhill 1.8 % $Header: /u/gcmpack/manual/part3/case_studies/hs_atmosphere/hs_atmos.tex,v 1.7 2004/10/14 14:24:28 cnh Exp $
2 cnh 1.1 % $Name: $
3    
4 cnh 1.5 \section[Held-Suarez Atmosphere MITgcm Example]{Held-Suarez forcing atmospheric simulation on a latitude-longitude grid 2.8$^\circ$ resolution and on
5 cnh 1.4 a cube-sphere grid with 32 square cube faces.}
6 adcroft 1.2 \label{www:tutorials}
7 cnh 1.1 \label{sect:eg-hs}
8 edhill 1.8 \begin{rawhtml}
9     <!-- CMIREDIR:eg-hs: -->
10     \end{rawhtml}
11 cnh 1.1
12     \bodytext{bgcolor="#FFFFFFFF"}
13    
14     %\begin{center}
15     %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
16     %At Four Degree Resolution with Asynchronous Time Stepping}
17     %
18     %\vspace*{4mm}
19     %
20     %\vspace*{3mm}
21     %{\large May 2001}
22     %\end{center}
23    
24 cnh 1.4 This example illustrates the use of the MITgcm for large scale atmospheric
25     circulation simulation. Two simulations are described
26     \begin{itemize}
27     \item global atmospheric circulation on a latitude-longitude grid and
28     \item global atmospheric circulation on a cube-sphere grid
29     \end{itemize}
30     The examples show how to use the isomorphic 'p-coordinate' scheme in
31     MITgcm to enable atmospheric simulation.
32    
33    
34 cnh 1.1
35     \subsection{Overview}
36 adcroft 1.2 \label{www:tutorials}
37 cnh 1.1
38 cnh 1.5 This example demonstrates using the MITgcm to simulate
39     the planetary atmospheric circulation in two ways.
40 cnh 1.4 In both cases the simulation is configured with flat orography.
41     In the first case shown a $2.8^{\circ} \times 2.8^{\circ}$ spherical polar
42     horizontal grid is employed. In the second case a cube-sphere horizontal
43     grid is used that projects a cube with face size of $32 \times 32$ onto a
44     sphere.
45 cnh 1.5 Five pressure corrdinate levels are used in the vertical, ranging in thickness
46 cnh 1.4 from $100\,{\rm mb}$ at the bottom of the atmosphere to $300\,{\rm mb}$ in the middle atmosphere.
47 cnh 1.5 The total depth of the atmosphere is $1000{\rm mb}$.
48     At this resolution, the configuration can be integrated forward for many years on a
49     single processor desktop computer.
50 cnh 1.1 \\
51    
52 cnh 1.5 The model is forced by relaxation to a radiative equilibrium profile
53     from Held and Suarez \cite{held-suar:94}. Initial conditions are a
54     statically stable thermal gradient and no motion. The atmosphere
55     in these experiments is dry and the only active ``physics'' are the
56     terms in the Held and Suarez \cite{held-suar:94} formula. The
57 cnh 1.6 MITgcm intermediate atmospheric physics package (see \ref{sec:pkg:aim}) and
58 cnh 1.5 MITgcm high-end physics package ( see \ref{sec:pkg:fizhi}) are turned off.
59 cnh 1.6 Altogether, this yields the following forcing
60     (from Held and Suarez \cite{held-suar:94}) that is applied to the fluid:
61 cnh 1.1
62     \begin{eqnarray}
63     \label{EQ:eg-hs-global_forcing}
64     \label{EQ:eg-hs-global_forcing_fu}
65 cnh 1.6 \vec{{\cal F}_{u}} & = & -k_{v}(p)\vec{u}
66 cnh 1.1 \\
67     \label{EQ:eg-hs-global_forcing_ft}
68 cnh 1.6 {\cal F}_{\theta} & = & -k_{T}(\phi,p)[\theta-\theta_{eq}(\phi,p)]
69 cnh 1.1 \\
70     \end{eqnarray}
71    
72 cnh 1.6 \noindent where ${\vec{\cal F}_{u}}$, ${\cal F}_{\theta}$,
73     are the forcing terms in the zonal and meridional
74     momentum and in the potential temperature
75 cnh 1.1 equations respectively.
76 cnh 1.6 The term $k_{v}$ in equation (\ref{EQ:eg-hs-global_forcing_fu}) applies a
77     linear frictional drag (Rayleigh damping) that is active within the
78     planetary boundary layer. It is defined so as to decay with
79     height according to
80     \begin{eqnarray}
81     \label{EQ:eg-hs-define_kv}
82     k_{v} & = & k_{f}{\rm max}(0,(p_{\rm{k}}/p^{0}_{s}-\sigma_{b})/(1-\sigma_{b}))
83     \\
84     \sigma_{b} & = & 0.7
85 cnh 1.1 \\
86 cnh 1.6 k_{f} & = & 1{\rm day}^{-1}
87     \end{eqnarray}
88 cnh 1.1
89 cnh 1.6 where $p_{\rm{k}}$ is the pressure level of the cell center for level $\rm{k}$
90     and $p^{0}_{s}$ is the pressure at the base of the atmospheric column.
91 cnh 1.1
92    
93     \subsection{Discrete Numerical Configuration}
94 adcroft 1.2 \label{www:tutorials}
95 cnh 1.1
96    
97     The model is configured in hydrostatic form. The domain is discretised with
98     a uniform grid spacing in latitude and longitude on the sphere
99     $\Delta \phi=\Delta \lambda=4^{\circ}$, so
100     that there are ninety grid cells in the zonal and forty in the
101     meridional direction. The internal model coordinate variables
102     $x$ and $y$ are initialized according to
103     \begin{eqnarray}
104     x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
105     y=r\lambda,~\Delta x &= &r\Delta \lambda
106     \end{eqnarray}
107    
108     Arctic polar regions are not
109     included in this experiment. Meridionally the model extends from
110     $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
111     Vertically the model is configured with twenty layers with the
112     following thicknesses
113     $\Delta z_{1} = 50\,{\rm m},\,
114     \Delta z_{2} = 50\,{\rm m},\,
115     \Delta z_{3} = 55\,{\rm m},\,
116     \Delta z_{4} = 60\,{\rm m},\,
117     \Delta z_{5} = 65\,{\rm m},\,
118     $
119     $
120     \Delta z_{6}~=~70\,{\rm m},\,
121     \Delta z_{7}~=~80\,{\rm m},\,
122     \Delta z_{8}~=95\,{\rm m},\,
123     \Delta z_{9}=120\,{\rm m},\,
124     \Delta z_{10}=155\,{\rm m},\,
125     $
126     $
127     \Delta z_{11}=200\,{\rm m},\,
128     \Delta z_{12}=260\,{\rm m},\,
129     \Delta z_{13}=320\,{\rm m},\,
130     \Delta z_{14}=400\,{\rm m},\,
131     \Delta z_{15}=480\,{\rm m},\,
132     $
133     $
134     \Delta z_{16}=570\,{\rm m},\,
135     \Delta z_{17}=655\,{\rm m},\,
136     \Delta z_{18}=725\,{\rm m},\,
137     \Delta z_{19}=775\,{\rm m},\,
138     \Delta z_{20}=815\,{\rm m}
139     $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
140     The implicit free surface form of the pressure equation described in Marshall et. al
141     \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
142     dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
143    
144     Wind-stress forcing is added to the momentum equations for both
145     the zonal flow, $u$ and the meridional flow $v$, according to equations
146     (\ref{EQ:eg-hs-global_forcing_fu}) and (\ref{EQ:eg-hs-global_forcing_fv}).
147     Thermodynamic forcing inputs are added to the equations for
148     potential temperature, $\theta$, and salinity, $S$, according to equations
149     (\ref{EQ:eg-hs-global_forcing_ft}) and (\ref{EQ:eg-hs-global_forcing_fs}).
150     This produces a set of equations solved in this configuration as follows:
151    
152     \begin{eqnarray}
153     \label{EQ:eg-hs-model_equations}
154     \frac{Du}{Dt} - fv +
155     \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
156     \nabla_{h}\cdot A_{h}\nabla_{h}u -
157     \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}
158     & = &
159     \begin{cases}
160     {\cal F}_u & \text{(surface)} \\
161     0 & \text{(interior)}
162     \end{cases}
163     \\
164     \frac{Dv}{Dt} + fu +
165     \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
166     \nabla_{h}\cdot A_{h}\nabla_{h}v -
167     \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}
168     & = &
169     \begin{cases}
170     {\cal F}_v & \text{(surface)} \\
171     0 & \text{(interior)}
172     \end{cases}
173     \\
174     \frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
175     &=&
176     0
177     \\
178     \frac{D\theta}{Dt} -
179     \nabla_{h}\cdot K_{h}\nabla_{h}\theta
180     - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}
181     & = &
182     \begin{cases}
183     {\cal F}_\theta & \text{(surface)} \\
184     0 & \text{(interior)}
185     \end{cases}
186     \\
187     \frac{D s}{Dt} -
188     \nabla_{h}\cdot K_{h}\nabla_{h}s
189     - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}
190     & = &
191     \begin{cases}
192     {\cal F}_s & \text{(surface)} \\
193     0 & \text{(interior)}
194     \end{cases}
195     \\
196     g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
197     \end{eqnarray}
198    
199     \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
200     $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
201     are the zonal and meridional components of the
202     flow vector, $\vec{u}$, on the sphere. As described in
203     MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
204     evolution of potential temperature, $\theta$, equation is solved prognostically.
205     The total pressure, $p$, is diagnosed by summing pressure due to surface
206     elevation $\eta$ and the hydrostatic pressure.
207     \\
208    
209     \subsubsection{Numerical Stability Criteria}
210 adcroft 1.2 \label{www:tutorials}
211 cnh 1.1
212     The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
213     This value is chosen to yield a Munk layer width \cite{adcroft:95},
214     \begin{eqnarray}
215     \label{EQ:eg-hs-munk_layer}
216     M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
217     \end{eqnarray}
218    
219     \noindent of $\approx 600$km. This is greater than the model
220     resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional
221     boundary layer is adequately resolved.
222     \\
223    
224     \noindent The model is stepped forward with a
225     time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
226     $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
227     parameter to the horizontal Laplacian friction \cite{adcroft:95}
228     \begin{eqnarray}
229     \label{EQ:eg-hs-laplacian_stability}
230     S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
231     \end{eqnarray}
232    
233     \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the
234     0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at
235     $\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.
236     \\
237    
238     \noindent The vertical dissipation coefficient, $A_{z}$, is set to
239     $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
240     \begin{eqnarray}
241     \label{EQ:eg-hs-laplacian_stability_z}
242     S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
243     \end{eqnarray}
244    
245     \noindent evaluates to $0.015$ for the smallest model
246     level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
247     the upper stability limit.
248     \\
249    
250     The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
251     for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
252     and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
253     related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
254     Here the stability parameter
255     \begin{eqnarray}
256     \label{EQ:eg-hs-laplacian_stability_xtheta}
257     S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
258     \end{eqnarray}
259     evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
260     stability parameter related to $K_{z}$
261     \begin{eqnarray}
262     \label{EQ:eg-hs-laplacian_stability_ztheta}
263     S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
264     \end{eqnarray}
265     evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
266     of $S_{l} \approx 0.5$.
267     \\
268    
269     \noindent The numerical stability for inertial oscillations
270     \cite{adcroft:95}
271    
272     \begin{eqnarray}
273     \label{EQ:eg-hs-inertial_stability}
274     S_{i} = f^{2} {\delta t_v}^2
275     \end{eqnarray}
276    
277     \noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to
278     the $S_{i} < 1$ upper limit for stability.
279     \\
280    
281     \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
282     horizontal flow
283     speed of $ | \vec{u} | = 2 ms^{-1}$
284    
285     \begin{eqnarray}
286     \label{EQ:eg-hs-cfl_stability}
287     S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
288     \end{eqnarray}
289    
290     \noindent evaluates to $6 \times 10^{-2}$. This is well below the stability
291     limit of 0.5.
292     \\
293    
294     \noindent The stability parameter for internal gravity waves propagating
295     with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
296     \cite{adcroft:95}
297    
298     \begin{eqnarray}
299     \label{EQ:eg-hs-gfl_stability}
300     S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
301     \end{eqnarray}
302    
303     \noindent evaluates to $3 \times 10^{-1}$. This is close to the linear
304     stability limit of 0.5.
305    
306     \subsection{Experiment Configuration}
307 adcroft 1.2 \label{www:tutorials}
308 cnh 1.1 \label{SEC:eg-hs_examp_exp_config}
309    
310     The model configuration for this experiment resides under the
311 edhill 1.3 directory {\it verification/hs94.128x64x5}. The experiment files
312 cnh 1.1 \begin{itemize}
313     \item {\it input/data}
314     \item {\it input/data.pkg}
315     \item {\it input/eedata},
316     \item {\it input/windx.bin},
317     \item {\it input/windy.bin},
318     \item {\it input/salt.bin},
319     \item {\it input/theta.bin},
320     \item {\it input/SSS.bin},
321     \item {\it input/SST.bin},
322     \item {\it input/topog.bin},
323     \item {\it code/CPP\_EEOPTIONS.h}
324     \item {\it code/CPP\_OPTIONS.h},
325     \item {\it code/SIZE.h}.
326     \end{itemize}
327     contain the code customizations and parameter settings for these
328     experiments. Below we describe the customizations
329     to these files associated with this experiment.
330    
331     \subsubsection{File {\it input/data}}
332 adcroft 1.2 \label{www:tutorials}
333 cnh 1.1
334     This file, reproduced completely below, specifies the main parameters
335     for the experiment. The parameters that are significant for this configuration
336     are
337    
338     \begin{itemize}
339    
340     \item Lines 7-10 and 11-14
341     \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim}
342     $\cdots$ \\
343     set reference values for potential
344     temperature and salinity at each model level in units of $^{\circ}$C and
345     ${\rm ppt}$. The entries are ordered from surface to depth.
346     Density is calculated from anomalies at each level evaluated
347     with respect to the reference values set here.\\
348     \fbox{
349     \begin{minipage}{5.0in}
350     {\it S/R INI\_THETA}({\it ini\_theta.F})
351     \end{minipage}
352     }
353    
354    
355     \item Line 15,
356     \begin{verbatim} viscAz=1.E-3, \end{verbatim}
357     this line sets the vertical Laplacian dissipation coefficient to
358     $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
359     for this operator are specified later. This variable is copied into
360     model general vertical coordinate variable {\bf viscAr}.
361    
362     \fbox{
363     \begin{minipage}{5.0in}
364     {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
365     \end{minipage}
366     }
367    
368     \item Line 16,
369     \begin{verbatim}
370     viscAh=5.E5,
371     \end{verbatim}
372     this line sets the horizontal Laplacian frictional dissipation coefficient to
373     $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
374     for this operator are specified later.
375    
376     \item Lines 17,
377     \begin{verbatim}
378     no_slip_sides=.FALSE.
379     \end{verbatim}
380     this line selects a free-slip lateral boundary condition for
381     the horizontal Laplacian friction operator
382     e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
383     $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
384    
385     \item Lines 9,
386     \begin{verbatim}
387     no_slip_bottom=.TRUE.
388     \end{verbatim}
389     this line selects a no-slip boundary condition for bottom
390     boundary condition in the vertical Laplacian friction operator
391     e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
392    
393     \item Line 19,
394     \begin{verbatim}
395     diffKhT=1.E3,
396     \end{verbatim}
397     this line sets the horizontal diffusion coefficient for temperature
398     to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
399     operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
400     all boundaries.
401    
402     \item Line 20,
403     \begin{verbatim}
404     diffKzT=3.E-5,
405     \end{verbatim}
406     this line sets the vertical diffusion coefficient for temperature
407     to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
408     condition on this operator is $\frac{\partial}{\partial z}=0$ at both
409     the upper and lower boundaries.
410    
411     \item Line 21,
412     \begin{verbatim}
413     diffKhS=1.E3,
414     \end{verbatim}
415     this line sets the horizontal diffusion coefficient for salinity
416     to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
417     operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
418     all boundaries.
419    
420     \item Line 22,
421     \begin{verbatim}
422     diffKzS=3.E-5,
423     \end{verbatim}
424     this line sets the vertical diffusion coefficient for salinity
425     to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
426     condition on this operator is $\frac{\partial}{\partial z}=0$ at both
427     the upper and lower boundaries.
428    
429     \item Lines 23-26
430     \begin{verbatim}
431     beta=1.E-11,
432     \end{verbatim}
433     \vspace{-5mm}$\cdots$\\
434     These settings do not apply for this experiment.
435    
436     \item Line 27,
437     \begin{verbatim}
438     gravity=9.81,
439     \end{verbatim}
440     Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
441     \fbox{
442     \begin{minipage}{5.0in}
443     {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
444     {\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\
445     {\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\
446     {\it S/R INI\_PARMS}~({\it ini\_parms.F})\\
447     {\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})
448     \end{minipage}
449     }
450    
451    
452     \item Line 28-29,
453     \begin{verbatim}
454     rigidLid=.FALSE.,
455     implicitFreeSurface=.TRUE.,
456     \end{verbatim}
457     Selects the barotropic pressure equation to be the implicit free surface
458     formulation.
459    
460     \item Line 30,
461     \begin{verbatim}
462     eosType='POLY3',
463     \end{verbatim}
464     Selects the third order polynomial form of the equation of state.\\
465     \fbox{
466     \begin{minipage}{5.0in}
467     {\it S/R FIND\_RHO}~({\it find\_rho.F})\\
468     {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})
469     \end{minipage}
470     }
471    
472     \item Line 31,
473     \begin{verbatim}
474     readBinaryPrec=32,
475     \end{verbatim}
476     Sets format for reading binary input datasets holding model fields to
477     use 32-bit representation for floating-point numbers.\\
478     \fbox{
479     \begin{minipage}{5.0in}
480     {\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\
481     {\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})
482     \end{minipage}
483     }
484    
485     \item Line 36,
486     \begin{verbatim}
487     cg2dMaxIters=1000,
488     \end{verbatim}
489     Sets maximum number of iterations the two-dimensional, conjugate
490     gradient solver will use, {\bf irrespective of convergence
491     criteria being met}.\\
492     \fbox{
493     \begin{minipage}{5.0in}
494     {\it S/R CG2D}~({\it cg2d.F})
495     \end{minipage}
496     }
497    
498     \item Line 37,
499     \begin{verbatim}
500     cg2dTargetResidual=1.E-13,
501     \end{verbatim}
502     Sets the tolerance which the two-dimensional, conjugate
503     gradient solver will use to test for convergence in equation
504     \ref{EQ:eg-hs-congrad_2d_resid} to $1 \times 10^{-13}$.
505     Solver will iterate until
506     tolerance falls below this value or until the maximum number of
507     solver iterations is reached.\\
508     \fbox{
509     \begin{minipage}{5.0in}
510     {\it S/R CG2D}~({\it cg2d.F})
511     \end{minipage}
512     }
513    
514     \item Line 42,
515     \begin{verbatim}
516     startTime=0,
517     \end{verbatim}
518     Sets the starting time for the model internal time counter.
519     When set to non-zero this option implicitly requests a
520     checkpoint file be read for initial state.
521     By default the checkpoint file is named according to
522     the integer number of time steps in the {\bf startTime} value.
523     The internal time counter works in seconds.
524    
525     \item Line 43,
526     \begin{verbatim}
527     endTime=2808000.,
528     \end{verbatim}
529     Sets the time (in seconds) at which this simulation will terminate.
530     At the end of a simulation a checkpoint file is automatically
531     written so that a numerical experiment can consist of multiple
532     stages.
533    
534     \item Line 44,
535     \begin{verbatim}
536     #endTime=62208000000,
537     \end{verbatim}
538     A commented out setting for endTime for a 2000 year simulation.
539    
540     \item Line 45,
541     \begin{verbatim}
542     deltaTmom=2400.0,
543     \end{verbatim}
544     Sets the timestep $\delta t_{v}$ used in the momentum equations to
545     $20~{\rm mins}$.
546     See section \ref{SEC:mom_time_stepping}.
547    
548     \fbox{
549     \begin{minipage}{5.0in}
550     {\it S/R TIMESTEP}({\it timestep.F})
551     \end{minipage}
552     }
553    
554     \item Line 46,
555     \begin{verbatim}
556     tauCD=321428.,
557     \end{verbatim}
558     Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.
559     See section \ref{SEC:cd_scheme}.
560    
561     \fbox{
562     \begin{minipage}{5.0in}
563     {\it S/R INI\_PARMS}({\it ini\_parms.F})\\
564     {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})
565     \end{minipage}
566     }
567    
568     \item Line 47,
569     \begin{verbatim}
570     deltaTtracer=108000.,
571     \end{verbatim}
572     Sets the default timestep, $\delta t_{\theta}$, for tracer equations to
573     $30~{\rm hours}$.
574     See section \ref{SEC:tracer_time_stepping}.
575    
576     \fbox{
577     \begin{minipage}{5.0in}
578     {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})
579     \end{minipage}
580     }
581    
582     \item Line 47,
583     \begin{verbatim}
584     bathyFile='topog.box'
585     \end{verbatim}
586     This line specifies the name of the file from which the domain
587     bathymetry is read. This file is a two-dimensional ($x,y$) map of
588     depths. This file is assumed to contain 64-bit binary numbers
589     giving the depth of the model at each grid cell, ordered with the x
590     coordinate varying fastest. The points are ordered from low coordinate
591     to high coordinate for both axes. The units and orientation of the
592     depths in this file are the same as used in the MITgcm code. In this
593     experiment, a depth of $0m$ indicates a solid wall and a depth
594     of $-2000m$ indicates open ocean. The matlab program
595     {\it input/gendata.m} shows an example of how to generate a
596     bathymetry file.
597    
598    
599     \item Line 50,
600     \begin{verbatim}
601     zonalWindFile='windx.sin_y'
602     \end{verbatim}
603     This line specifies the name of the file from which the x-direction
604     surface wind stress is read. This file is also a two-dimensional
605     ($x,y$) map and is enumerated and formatted in the same manner as the
606     bathymetry file. The matlab program {\it input/gendata.m} includes example
607     code to generate a valid
608     {\bf zonalWindFile}
609     file.
610    
611     \end{itemize}
612    
613     \noindent other lines in the file {\it input/data} are standard values
614     that are described in the MITgcm Getting Started and MITgcm Parameters
615     notes.
616    
617     \begin{small}
618     \input{part3/case_studies/climatalogical_ogcm/input/data}
619     \end{small}
620    
621     \subsubsection{File {\it input/data.pkg}}
622 adcroft 1.2 \label{www:tutorials}
623 cnh 1.1
624     This file uses standard default values and does not contain
625     customisations for this experiment.
626    
627     \subsubsection{File {\it input/eedata}}
628 adcroft 1.2 \label{www:tutorials}
629 cnh 1.1
630     This file uses standard default values and does not contain
631     customisations for this experiment.
632    
633     \subsubsection{File {\it input/windx.sin\_y}}
634 adcroft 1.2 \label{www:tutorials}
635 cnh 1.1
636     The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
637     map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
638     Although $\tau_{x}$ is only a function of $y$n in this experiment
639     this file must still define a complete two-dimensional map in order
640     to be compatible with the standard code for loading forcing fields
641     in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
642     code for creating the {\it input/windx.sin\_y} file.
643    
644     \subsubsection{File {\it input/topog.box}}
645 adcroft 1.2 \label{www:tutorials}
646 cnh 1.1
647    
648     The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
649     map of depth values. For this experiment values are either
650     $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep
651     ocean. The file contains a raw binary stream of data that is enumerated
652     in the same way as standard MITgcm two-dimensional, horizontal arrays.
653     The included matlab program {\it input/gendata.m} gives a complete
654     code for creating the {\it input/topog.box} file.
655    
656     \subsubsection{File {\it code/SIZE.h}}
657 adcroft 1.2 \label{www:tutorials}
658 cnh 1.1
659     Two lines are customized in this file for the current experiment
660    
661     \begin{itemize}
662    
663     \item Line 39,
664     \begin{verbatim} sNx=60, \end{verbatim} this line sets
665     the lateral domain extent in grid points for the
666     axis aligned with the x-coordinate.
667    
668     \item Line 40,
669     \begin{verbatim} sNy=60, \end{verbatim} this line sets
670     the lateral domain extent in grid points for the
671     axis aligned with the y-coordinate.
672    
673     \item Line 49,
674     \begin{verbatim} Nr=4, \end{verbatim} this line sets
675     the vertical domain extent in grid points.
676    
677     \end{itemize}
678    
679     \begin{small}
680     \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}
681     \end{small}
682    
683     \subsubsection{File {\it code/CPP\_OPTIONS.h}}
684 adcroft 1.2 \label{www:tutorials}
685 cnh 1.1
686     This file uses standard default values and does not contain
687     customisations for this experiment.
688    
689    
690     \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
691 adcroft 1.2 \label{www:tutorials}
692 cnh 1.1
693     This file uses standard default values and does not contain
694     customisations for this experiment.
695    
696     \subsubsection{Other Files }
697 adcroft 1.2 \label{www:tutorials}
698 cnh 1.1
699     Other files relevant to this experiment are
700     \begin{itemize}
701     \item {\it model/src/ini\_cori.F}. This file initializes the model
702     coriolis variables {\bf fCorU}.
703     \item {\it model/src/ini\_spherical\_polar\_grid.F}
704     \item {\it model/src/ini\_parms.F},
705     \item {\it input/windx.sin\_y},
706     \end{itemize}
707     contain the code customisations and parameter settings for this
708     experiments. Below we describe the customisations
709     to these files associated with this experiment.

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