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Some more Held-Suarez updates

1 cnh 1.6 % $Header: /u/gcmpack/manual/part3/case_studies/hs_atmosphere/hs_atmos.tex,v 1.5 2004/10/13 05:06:26 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    
9     \bodytext{bgcolor="#FFFFFFFF"}
10    
11     %\begin{center}
12     %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
13     %At Four Degree Resolution with Asynchronous Time Stepping}
14     %
15     %\vspace*{4mm}
16     %
17     %\vspace*{3mm}
18     %{\large May 2001}
19     %\end{center}
20    
21 cnh 1.4 This example illustrates the use of the MITgcm for large scale atmospheric
22     circulation simulation. Two simulations are described
23     \begin{itemize}
24     \item global atmospheric circulation on a latitude-longitude grid and
25     \item global atmospheric circulation on a cube-sphere grid
26     \end{itemize}
27     The examples show how to use the isomorphic 'p-coordinate' scheme in
28     MITgcm to enable atmospheric simulation.
29    
30    
31 cnh 1.1
32     \subsection{Overview}
33 adcroft 1.2 \label{www:tutorials}
34 cnh 1.1
35 cnh 1.5 This example demonstrates using the MITgcm to simulate
36     the planetary atmospheric circulation in two ways.
37 cnh 1.4 In both cases the simulation is configured with flat orography.
38     In the first case shown a $2.8^{\circ} \times 2.8^{\circ}$ spherical polar
39     horizontal grid is employed. In the second case a cube-sphere horizontal
40     grid is used that projects a cube with face size of $32 \times 32$ onto a
41     sphere.
42 cnh 1.5 Five pressure corrdinate levels are used in the vertical, ranging in thickness
43 cnh 1.4 from $100\,{\rm mb}$ at the bottom of the atmosphere to $300\,{\rm mb}$ in the middle atmosphere.
44 cnh 1.5 The total depth of the atmosphere is $1000{\rm mb}$.
45     At this resolution, the configuration can be integrated forward for many years on a
46     single processor desktop computer.
47 cnh 1.1 \\
48    
49 cnh 1.5 The model is forced by relaxation to a radiative equilibrium profile
50     from Held and Suarez \cite{held-suar:94}. Initial conditions are a
51     statically stable thermal gradient and no motion. The atmosphere
52     in these experiments is dry and the only active ``physics'' are the
53     terms in the Held and Suarez \cite{held-suar:94} formula. The
54 cnh 1.6 MITgcm intermediate atmospheric physics package (see \ref{sec:pkg:aim}) and
55 cnh 1.5 MITgcm high-end physics package ( see \ref{sec:pkg:fizhi}) are turned off.
56 cnh 1.6 Altogether, this yields the following forcing
57     (from Held and Suarez \cite{held-suar:94}) that is applied to the fluid:
58 cnh 1.1
59     \begin{eqnarray}
60     \label{EQ:eg-hs-global_forcing}
61     \label{EQ:eg-hs-global_forcing_fu}
62 cnh 1.6 \vec{{\cal F}_{u}} & = & -k_{v}(p)\vec{u}
63 cnh 1.1 \\
64     \label{EQ:eg-hs-global_forcing_ft}
65 cnh 1.6 {\cal F}_{\theta} & = & -k_{T}(\phi,p)[\theta-\theta_{eq}(\phi,p)]
66 cnh 1.1 \\
67     \end{eqnarray}
68    
69 cnh 1.6 \noindent where ${\vec{\cal F}_{u}}$, ${\cal F}_{\theta}$,
70     are the forcing terms in the zonal and meridional
71     momentum and in the potential temperature
72 cnh 1.1 equations respectively.
73 cnh 1.6 The term $k_{v}$ in equation (\ref{EQ:eg-hs-global_forcing_fu}) applies a
74     linear frictional drag (Rayleigh damping) that is active within the
75     planetary boundary layer. It is defined so as to decay with
76     height according to
77     \begin{eqnarray}
78     \label{EQ:eg-hs-define_kv}
79     k_{v} & = & k_{f}{\rm max}(0,(p_{\rm{k}}/p^{0}_{s}-\sigma_{b})/(1-\sigma_{b}))
80     \\
81     \sigma_{b} & = & 0.7
82 cnh 1.1 \\
83 cnh 1.6 k_{f} & = & 1{\rm day}^{-1}
84     \end{eqnarray}
85 cnh 1.1
86 cnh 1.6 where $p_{\rm{k}}$ is the pressure level of the cell center for level $\rm{k}$
87     and $p^{0}_{s}$ is the pressure at the base of the atmospheric column.
88 cnh 1.1
89     Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
90     relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
91     the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
92     and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
93     in equations \ref{EQ:eg-hs-global_forcing_fu}-\ref{EQ:eg-hs-global_forcing_fs}. The figures
94     also indicate the lateral extent and coastline used in the experiment.
95     Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
96     domain.
97    
98    
99     \subsection{Discrete Numerical Configuration}
100 adcroft 1.2 \label{www:tutorials}
101 cnh 1.1
102    
103     The model is configured in hydrostatic form. The domain is discretised with
104     a uniform grid spacing in latitude and longitude on the sphere
105     $\Delta \phi=\Delta \lambda=4^{\circ}$, so
106     that there are ninety grid cells in the zonal and forty in the
107     meridional direction. The internal model coordinate variables
108     $x$ and $y$ are initialized according to
109     \begin{eqnarray}
110     x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
111     y=r\lambda,~\Delta x &= &r\Delta \lambda
112     \end{eqnarray}
113    
114     Arctic polar regions are not
115     included in this experiment. Meridionally the model extends from
116     $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
117     Vertically the model is configured with twenty layers with the
118     following thicknesses
119     $\Delta z_{1} = 50\,{\rm m},\,
120     \Delta z_{2} = 50\,{\rm m},\,
121     \Delta z_{3} = 55\,{\rm m},\,
122     \Delta z_{4} = 60\,{\rm m},\,
123     \Delta z_{5} = 65\,{\rm m},\,
124     $
125     $
126     \Delta z_{6}~=~70\,{\rm m},\,
127     \Delta z_{7}~=~80\,{\rm m},\,
128     \Delta z_{8}~=95\,{\rm m},\,
129     \Delta z_{9}=120\,{\rm m},\,
130     \Delta z_{10}=155\,{\rm m},\,
131     $
132     $
133     \Delta z_{11}=200\,{\rm m},\,
134     \Delta z_{12}=260\,{\rm m},\,
135     \Delta z_{13}=320\,{\rm m},\,
136     \Delta z_{14}=400\,{\rm m},\,
137     \Delta z_{15}=480\,{\rm m},\,
138     $
139     $
140     \Delta z_{16}=570\,{\rm m},\,
141     \Delta z_{17}=655\,{\rm m},\,
142     \Delta z_{18}=725\,{\rm m},\,
143     \Delta z_{19}=775\,{\rm m},\,
144     \Delta z_{20}=815\,{\rm m}
145     $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
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 for both
151     the zonal flow, $u$ and the meridional flow $v$, according to equations
152     (\ref{EQ:eg-hs-global_forcing_fu}) and (\ref{EQ:eg-hs-global_forcing_fv}).
153     Thermodynamic forcing inputs are added to the equations for
154     potential temperature, $\theta$, and salinity, $S$, according to equations
155     (\ref{EQ:eg-hs-global_forcing_ft}) and (\ref{EQ:eg-hs-global_forcing_fs}).
156     This produces a set of equations solved in this configuration as follows:
157    
158     \begin{eqnarray}
159     \label{EQ:eg-hs-model_equations}
160     \frac{Du}{Dt} - fv +
161     \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
162     \nabla_{h}\cdot A_{h}\nabla_{h}u -
163     \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}
164     & = &
165     \begin{cases}
166     {\cal F}_u & \text{(surface)} \\
167     0 & \text{(interior)}
168     \end{cases}
169     \\
170     \frac{Dv}{Dt} + fu +
171     \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
172     \nabla_{h}\cdot A_{h}\nabla_{h}v -
173     \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}
174     & = &
175     \begin{cases}
176     {\cal F}_v & \text{(surface)} \\
177     0 & \text{(interior)}
178     \end{cases}
179     \\
180     \frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
181     &=&
182     0
183     \\
184     \frac{D\theta}{Dt} -
185     \nabla_{h}\cdot K_{h}\nabla_{h}\theta
186     - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}
187     & = &
188     \begin{cases}
189     {\cal F}_\theta & \text{(surface)} \\
190     0 & \text{(interior)}
191     \end{cases}
192     \\
193     \frac{D s}{Dt} -
194     \nabla_{h}\cdot K_{h}\nabla_{h}s
195     - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}
196     & = &
197     \begin{cases}
198     {\cal F}_s & \text{(surface)} \\
199     0 & \text{(interior)}
200     \end{cases}
201     \\
202     g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
203     \end{eqnarray}
204    
205     \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
206     $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
207     are the zonal and meridional components of the
208     flow vector, $\vec{u}$, on the sphere. As described in
209     MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
210     evolution of potential temperature, $\theta$, equation is solved prognostically.
211     The total pressure, $p$, is diagnosed by summing pressure due to surface
212     elevation $\eta$ and the hydrostatic pressure.
213     \\
214    
215     \subsubsection{Numerical Stability Criteria}
216 adcroft 1.2 \label{www:tutorials}
217 cnh 1.1
218     The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
219     This value is chosen to yield a Munk layer width \cite{adcroft:95},
220     \begin{eqnarray}
221     \label{EQ:eg-hs-munk_layer}
222     M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
223     \end{eqnarray}
224    
225     \noindent of $\approx 600$km. This is greater than the model
226     resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional
227     boundary layer is adequately resolved.
228     \\
229    
230     \noindent The model is stepped forward with a
231     time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
232     $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
233     parameter to the horizontal Laplacian friction \cite{adcroft:95}
234     \begin{eqnarray}
235     \label{EQ:eg-hs-laplacian_stability}
236     S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
237     \end{eqnarray}
238    
239     \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the
240     0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at
241     $\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.
242     \\
243    
244     \noindent The vertical dissipation coefficient, $A_{z}$, is set to
245     $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
246     \begin{eqnarray}
247     \label{EQ:eg-hs-laplacian_stability_z}
248     S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
249     \end{eqnarray}
250    
251     \noindent evaluates to $0.015$ for the smallest model
252     level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
253     the upper stability limit.
254     \\
255    
256     The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
257     for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
258     and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
259     related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
260     Here the stability parameter
261     \begin{eqnarray}
262     \label{EQ:eg-hs-laplacian_stability_xtheta}
263     S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
264     \end{eqnarray}
265     evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
266     stability parameter related to $K_{z}$
267     \begin{eqnarray}
268     \label{EQ:eg-hs-laplacian_stability_ztheta}
269     S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
270     \end{eqnarray}
271     evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
272     of $S_{l} \approx 0.5$.
273     \\
274    
275     \noindent The numerical stability for inertial oscillations
276     \cite{adcroft:95}
277    
278     \begin{eqnarray}
279     \label{EQ:eg-hs-inertial_stability}
280     S_{i} = f^{2} {\delta t_v}^2
281     \end{eqnarray}
282    
283     \noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to
284     the $S_{i} < 1$ upper limit for stability.
285     \\
286    
287     \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
288     horizontal flow
289     speed of $ | \vec{u} | = 2 ms^{-1}$
290    
291     \begin{eqnarray}
292     \label{EQ:eg-hs-cfl_stability}
293     S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
294     \end{eqnarray}
295    
296     \noindent evaluates to $6 \times 10^{-2}$. This is well below the stability
297     limit of 0.5.
298     \\
299    
300     \noindent The stability parameter for internal gravity waves propagating
301     with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
302     \cite{adcroft:95}
303    
304     \begin{eqnarray}
305     \label{EQ:eg-hs-gfl_stability}
306     S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
307     \end{eqnarray}
308    
309     \noindent evaluates to $3 \times 10^{-1}$. This is close to the linear
310     stability limit of 0.5.
311    
312     \subsection{Experiment Configuration}
313 adcroft 1.2 \label{www:tutorials}
314 cnh 1.1 \label{SEC:eg-hs_examp_exp_config}
315    
316     The model configuration for this experiment resides under the
317 edhill 1.3 directory {\it verification/hs94.128x64x5}. The experiment files
318 cnh 1.1 \begin{itemize}
319     \item {\it input/data}
320     \item {\it input/data.pkg}
321     \item {\it input/eedata},
322     \item {\it input/windx.bin},
323     \item {\it input/windy.bin},
324     \item {\it input/salt.bin},
325     \item {\it input/theta.bin},
326     \item {\it input/SSS.bin},
327     \item {\it input/SST.bin},
328     \item {\it input/topog.bin},
329     \item {\it code/CPP\_EEOPTIONS.h}
330     \item {\it code/CPP\_OPTIONS.h},
331     \item {\it code/SIZE.h}.
332     \end{itemize}
333     contain the code customizations and parameter settings for these
334     experiments. Below we describe the customizations
335     to these files associated with this experiment.
336    
337     \subsubsection{File {\it input/data}}
338 adcroft 1.2 \label{www:tutorials}
339 cnh 1.1
340     This file, reproduced completely below, specifies the main parameters
341     for the experiment. The parameters that are significant for this configuration
342     are
343    
344     \begin{itemize}
345    
346     \item Lines 7-10 and 11-14
347     \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim}
348     $\cdots$ \\
349     set reference values for potential
350     temperature and salinity at each model level in units of $^{\circ}$C and
351     ${\rm ppt}$. The entries are ordered from surface to depth.
352     Density is calculated from anomalies at each level evaluated
353     with respect to the reference values set here.\\
354     \fbox{
355     \begin{minipage}{5.0in}
356     {\it S/R INI\_THETA}({\it ini\_theta.F})
357     \end{minipage}
358     }
359    
360    
361     \item Line 15,
362     \begin{verbatim} viscAz=1.E-3, \end{verbatim}
363     this line sets the vertical Laplacian dissipation coefficient to
364     $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
365     for this operator are specified later. This variable is copied into
366     model general vertical coordinate variable {\bf viscAr}.
367    
368     \fbox{
369     \begin{minipage}{5.0in}
370     {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
371     \end{minipage}
372     }
373    
374     \item Line 16,
375     \begin{verbatim}
376     viscAh=5.E5,
377     \end{verbatim}
378     this line sets the horizontal Laplacian frictional dissipation coefficient to
379     $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
380     for this operator are specified later.
381    
382     \item Lines 17,
383     \begin{verbatim}
384     no_slip_sides=.FALSE.
385     \end{verbatim}
386     this line selects a free-slip lateral boundary condition for
387     the horizontal Laplacian friction operator
388     e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
389     $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
390    
391     \item Lines 9,
392     \begin{verbatim}
393     no_slip_bottom=.TRUE.
394     \end{verbatim}
395     this line selects a no-slip boundary condition for bottom
396     boundary condition in the vertical Laplacian friction operator
397     e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
398    
399     \item Line 19,
400     \begin{verbatim}
401     diffKhT=1.E3,
402     \end{verbatim}
403     this line sets the horizontal diffusion coefficient for temperature
404     to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
405     operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
406     all boundaries.
407    
408     \item Line 20,
409     \begin{verbatim}
410     diffKzT=3.E-5,
411     \end{verbatim}
412     this line sets the vertical diffusion coefficient for temperature
413     to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
414     condition on this operator is $\frac{\partial}{\partial z}=0$ at both
415     the upper and lower boundaries.
416    
417     \item Line 21,
418     \begin{verbatim}
419     diffKhS=1.E3,
420     \end{verbatim}
421     this line sets the horizontal diffusion coefficient for salinity
422     to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this
423     operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on
424     all boundaries.
425    
426     \item Line 22,
427     \begin{verbatim}
428     diffKzS=3.E-5,
429     \end{verbatim}
430     this line sets the vertical diffusion coefficient for salinity
431     to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary
432     condition on this operator is $\frac{\partial}{\partial z}=0$ at both
433     the upper and lower boundaries.
434    
435     \item Lines 23-26
436     \begin{verbatim}
437     beta=1.E-11,
438     \end{verbatim}
439     \vspace{-5mm}$\cdots$\\
440     These settings do not apply for this experiment.
441    
442     \item Line 27,
443     \begin{verbatim}
444     gravity=9.81,
445     \end{verbatim}
446     Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
447     \fbox{
448     \begin{minipage}{5.0in}
449     {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
450     {\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\
451     {\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\
452     {\it S/R INI\_PARMS}~({\it ini\_parms.F})\\
453     {\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})
454     \end{minipage}
455     }
456    
457    
458     \item Line 28-29,
459     \begin{verbatim}
460     rigidLid=.FALSE.,
461     implicitFreeSurface=.TRUE.,
462     \end{verbatim}
463     Selects the barotropic pressure equation to be the implicit free surface
464     formulation.
465    
466     \item Line 30,
467     \begin{verbatim}
468     eosType='POLY3',
469     \end{verbatim}
470     Selects the third order polynomial form of the equation of state.\\
471     \fbox{
472     \begin{minipage}{5.0in}
473     {\it S/R FIND\_RHO}~({\it find\_rho.F})\\
474     {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})
475     \end{minipage}
476     }
477    
478     \item Line 31,
479     \begin{verbatim}
480     readBinaryPrec=32,
481     \end{verbatim}
482     Sets format for reading binary input datasets holding model fields to
483     use 32-bit representation for floating-point numbers.\\
484     \fbox{
485     \begin{minipage}{5.0in}
486     {\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\
487     {\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})
488     \end{minipage}
489     }
490    
491     \item Line 36,
492     \begin{verbatim}
493     cg2dMaxIters=1000,
494     \end{verbatim}
495     Sets maximum number of iterations the two-dimensional, conjugate
496     gradient solver will use, {\bf irrespective of convergence
497     criteria being met}.\\
498     \fbox{
499     \begin{minipage}{5.0in}
500     {\it S/R CG2D}~({\it cg2d.F})
501     \end{minipage}
502     }
503    
504     \item Line 37,
505     \begin{verbatim}
506     cg2dTargetResidual=1.E-13,
507     \end{verbatim}
508     Sets the tolerance which the two-dimensional, conjugate
509     gradient solver will use to test for convergence in equation
510     \ref{EQ:eg-hs-congrad_2d_resid} to $1 \times 10^{-13}$.
511     Solver will iterate until
512     tolerance falls below this value or until the maximum number of
513     solver iterations is reached.\\
514     \fbox{
515     \begin{minipage}{5.0in}
516     {\it S/R CG2D}~({\it cg2d.F})
517     \end{minipage}
518     }
519    
520     \item Line 42,
521     \begin{verbatim}
522     startTime=0,
523     \end{verbatim}
524     Sets the starting time for the model internal time counter.
525     When set to non-zero this option implicitly requests a
526     checkpoint file be read for initial state.
527     By default the checkpoint file is named according to
528     the integer number of time steps in the {\bf startTime} value.
529     The internal time counter works in seconds.
530    
531     \item Line 43,
532     \begin{verbatim}
533     endTime=2808000.,
534     \end{verbatim}
535     Sets the time (in seconds) at which this simulation will terminate.
536     At the end of a simulation a checkpoint file is automatically
537     written so that a numerical experiment can consist of multiple
538     stages.
539    
540     \item Line 44,
541     \begin{verbatim}
542     #endTime=62208000000,
543     \end{verbatim}
544     A commented out setting for endTime for a 2000 year simulation.
545    
546     \item Line 45,
547     \begin{verbatim}
548     deltaTmom=2400.0,
549     \end{verbatim}
550     Sets the timestep $\delta t_{v}$ used in the momentum equations to
551     $20~{\rm mins}$.
552     See section \ref{SEC:mom_time_stepping}.
553    
554     \fbox{
555     \begin{minipage}{5.0in}
556     {\it S/R TIMESTEP}({\it timestep.F})
557     \end{minipage}
558     }
559    
560     \item Line 46,
561     \begin{verbatim}
562     tauCD=321428.,
563     \end{verbatim}
564     Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.
565     See section \ref{SEC:cd_scheme}.
566    
567     \fbox{
568     \begin{minipage}{5.0in}
569     {\it S/R INI\_PARMS}({\it ini\_parms.F})\\
570     {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})
571     \end{minipage}
572     }
573    
574     \item Line 47,
575     \begin{verbatim}
576     deltaTtracer=108000.,
577     \end{verbatim}
578     Sets the default timestep, $\delta t_{\theta}$, for tracer equations to
579     $30~{\rm hours}$.
580     See section \ref{SEC:tracer_time_stepping}.
581    
582     \fbox{
583     \begin{minipage}{5.0in}
584     {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})
585     \end{minipage}
586     }
587    
588     \item Line 47,
589     \begin{verbatim}
590     bathyFile='topog.box'
591     \end{verbatim}
592     This line specifies the name of the file from which the domain
593     bathymetry is read. This file is a two-dimensional ($x,y$) map of
594     depths. This file is assumed to contain 64-bit binary numbers
595     giving the depth of the model at each grid cell, ordered with the x
596     coordinate varying fastest. The points are ordered from low coordinate
597     to high coordinate for both axes. The units and orientation of the
598     depths in this file are the same as used in the MITgcm code. In this
599     experiment, a depth of $0m$ indicates a solid wall and a depth
600     of $-2000m$ indicates open ocean. The matlab program
601     {\it input/gendata.m} shows an example of how to generate a
602     bathymetry file.
603    
604    
605     \item Line 50,
606     \begin{verbatim}
607     zonalWindFile='windx.sin_y'
608     \end{verbatim}
609     This line specifies the name of the file from which the x-direction
610     surface wind stress is read. This file is also a two-dimensional
611     ($x,y$) map and is enumerated and formatted in the same manner as the
612     bathymetry file. The matlab program {\it input/gendata.m} includes example
613     code to generate a valid
614     {\bf zonalWindFile}
615     file.
616    
617     \end{itemize}
618    
619     \noindent other lines in the file {\it input/data} are standard values
620     that are described in the MITgcm Getting Started and MITgcm Parameters
621     notes.
622    
623     \begin{small}
624     \input{part3/case_studies/climatalogical_ogcm/input/data}
625     \end{small}
626    
627     \subsubsection{File {\it input/data.pkg}}
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/eedata}}
634 adcroft 1.2 \label{www:tutorials}
635 cnh 1.1
636     This file uses standard default values and does not contain
637     customisations for this experiment.
638    
639     \subsubsection{File {\it input/windx.sin\_y}}
640 adcroft 1.2 \label{www:tutorials}
641 cnh 1.1
642     The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
643     map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
644     Although $\tau_{x}$ is only a function of $y$n in this experiment
645     this file must still define a complete two-dimensional map in order
646     to be compatible with the standard code for loading forcing fields
647     in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
648     code for creating the {\it input/windx.sin\_y} file.
649    
650     \subsubsection{File {\it input/topog.box}}
651 adcroft 1.2 \label{www:tutorials}
652 cnh 1.1
653    
654     The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
655     map of depth values. For this experiment values are either
656     $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep
657     ocean. The file contains a raw binary stream of data that is enumerated
658     in the same way as standard MITgcm two-dimensional, horizontal arrays.
659     The included matlab program {\it input/gendata.m} gives a complete
660     code for creating the {\it input/topog.box} file.
661    
662     \subsubsection{File {\it code/SIZE.h}}
663 adcroft 1.2 \label{www:tutorials}
664 cnh 1.1
665     Two lines are customized in this file for the current experiment
666    
667     \begin{itemize}
668    
669     \item Line 39,
670     \begin{verbatim} sNx=60, \end{verbatim} this line sets
671     the lateral domain extent in grid points for the
672     axis aligned with the x-coordinate.
673    
674     \item Line 40,
675     \begin{verbatim} sNy=60, \end{verbatim} this line sets
676     the lateral domain extent in grid points for the
677     axis aligned with the y-coordinate.
678    
679     \item Line 49,
680     \begin{verbatim} Nr=4, \end{verbatim} this line sets
681     the vertical domain extent in grid points.
682    
683     \end{itemize}
684    
685     \begin{small}
686     \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}
687     \end{small}
688    
689     \subsubsection{File {\it code/CPP\_OPTIONS.h}}
690 adcroft 1.2 \label{www:tutorials}
691 cnh 1.1
692     This file uses standard default values and does not contain
693     customisations for this experiment.
694    
695    
696     \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
697 adcroft 1.2 \label{www:tutorials}
698 cnh 1.1
699     This file uses standard default values and does not contain
700     customisations for this experiment.
701    
702     \subsubsection{Other Files }
703 adcroft 1.2 \label{www:tutorials}
704 cnh 1.1
705     Other files relevant to this experiment are
706     \begin{itemize}
707     \item {\it model/src/ini\_cori.F}. This file initializes the model
708     coriolis variables {\bf fCorU}.
709     \item {\it model/src/ini\_spherical\_polar\_grid.F}
710     \item {\it model/src/ini\_parms.F},
711     \item {\it input/windx.sin\_y},
712     \end{itemize}
713     contain the code customisations and parameter settings for this
714     experiments. Below we describe the customisations
715     to these files associated with this experiment.

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