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revision 1.4 by cnh, Wed Oct 24 19:43:07 2001 UTC revision 1.11 by adcroft, Tue Nov 13 20:13:54 2001 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}  \section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}
5  \label{sec:eg-fourlayer}  \label{sect:eg-fourlayer}
6    
7  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
8    
# Line 19  Line 19 
19  This document describes an example experiment using MITgcm  This document describes an example experiment using MITgcm
20  to simulate a baroclinic ocean gyre in spherical  to simulate a baroclinic ocean gyre in spherical
21  polar coordinates. The barotropic  polar coordinates. The barotropic
22  example experiment in section \ref{sec:eg-baro}  example experiment in section \ref{sect:eg-baro}
23  ilustrated how to configure the code for a single layer  illustrated how to configure the code for a single layer
24  simulation in a cartesian grid. In this example a similar physical problem  simulation in a Cartesian grid. In this example a similar physical problem
25  is simulated, but the code is now configured  is simulated, but the code is now configured
26  for four layers and in a spherical polar coordinate system.  for four layers and in a spherical polar coordinate system.
27    
# Line 29  for four layers and in a spherical polar Line 29  for four layers and in a spherical polar
29    
30  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
31  a baroclinic, wind-forced, ocean gyre circulation. The experiment  a baroclinic, wind-forced, ocean gyre circulation. The experiment
32  is a numerical rendition of the gyre circulation problem simliar  is a numerical rendition of the gyre circulation problem similar
33  to the problems described analytically by Stommel in 1966  to the problems described analytically by Stommel in 1966
34  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.  \cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
35  \\  \\
# Line 37  to the problems described analytically b Line 37  to the problems described analytically b
37  In this experiment the model is configured to represent a mid-latitude  In this experiment the model is configured to represent a mid-latitude
38  enclosed sector of fluid on a sphere, $60^{\circ} \times 60^{\circ}$ in  enclosed sector of fluid on a sphere, $60^{\circ} \times 60^{\circ}$ in
39  lateral extent. The fluid is $2$~km deep and is forced  lateral extent. The fluid is $2$~km deep and is forced
40  by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally  by a constant in time zonal wind stress, $\tau_{\lambda}$, that varies
41  in the north-south direction. Topologically the simulated  sinusoidally in the north-south direction. Topologically the simulated
42  domain is a sector on a sphere and the coriolis parameter, $f$, is defined  domain is a sector on a sphere and the coriolis parameter, $f$, is defined
43  according to latitude, $\varphi$  according to latitude, $\varphi$
44    
# Line 54  f(\varphi) = 2 \Omega \sin( \varphi ) Line 54  f(\varphi) = 2 \Omega \sin( \varphi )
54    
55  \begin{equation}  \begin{equation}
56  \label{EQ:taux}  \label{EQ:taux}
57  \tau_x(\varphi) = \tau_{0}\sin(\pi \frac{\varphi}{L_{\varphi}})  \tau_{\lambda}(\varphi) = \tau_{0}\sin(\pi \frac{\varphi}{L_{\varphi}})
58  \end{equation}  \end{equation}
59    
60  \noindent where $L_{\varphi}$ is the lateral domain extent ($60^{\circ}$) and  \noindent where $L_{\varphi}$ is the lateral domain extent ($60^{\circ}$) and
# Line 62  $\tau_0$ is set to $0.1N m^{-2}$. Line 62  $\tau_0$ is set to $0.1N m^{-2}$.
62  \\  \\
63    
64  Figure \ref{FIG:simulation_config}  Figure \ref{FIG:simulation_config}
65  summarises the configuration simulated.  summarizes the configuration simulated.
66  In contrast to the example in section \ref{sec:eg-baro}, the  In contrast to the example in section \ref{sect:eg-baro}, the
67  current experiment simulates a spherical polar domain. However, as indicated  current experiment simulates a spherical polar domain. As indicated
68  by the axes in the lower left of the figure the model code works internally  by the axes in the lower left of the figure the model code works internally
69  in a locally orthoganal coordinate $(x,y,z)$. For this experiment description  in a locally orthogonal coordinate $(x,y,z)$. For this experiment description
70  of this document the local orthogonal model coordinate $(x,y,z)$ is synonomous  the local orthogonal model coordinate $(x,y,z)$ is synonymous
71  with the spherical polar coordinate shown in figure  with the coordinates $(\lambda,\varphi,r)$ shown in figure
72  \ref{fig:spherical-polar-coord}  \ref{fig:spherical-polar-coord}
73  \\  \\
74    
# Line 95  linear Line 95  linear
95    
96  \noindent with $\rho_{0}=999.8\,{\rm kg\,m}^{-3}$ and  \noindent with $\rho_{0}=999.8\,{\rm kg\,m}^{-3}$ and
97  $\alpha_{\theta}=2\times10^{-4}\,{\rm degrees}^{-1} $. Integrated forward in  $\alpha_{\theta}=2\times10^{-4}\,{\rm degrees}^{-1} $. Integrated forward in
98  this configuration the model state variable {\bf theta} is synonomous with  this configuration the model state variable {\bf theta} is equivalent to
99  either in-situ temperature, $T$, or potential temperature, $\theta$. For  either in-situ temperature, $T$, or potential temperature, $\theta$. For
100  consistency with later examples, in which the equation of state is  consistency with later examples, in which the equation of state is
101  non-linear, we use $\theta$ to represent temperature here. This is  non-linear, we use $\theta$ to represent temperature here. This is
# Line 110  the quantity that is carried in the mode Line 110  the quantity that is carried in the mode
110  \caption{Schematic of simulation domain and wind-stress forcing function  \caption{Schematic of simulation domain and wind-stress forcing function
111  for the four-layer gyre numerical experiment. The domain is enclosed by solid  for the four-layer gyre numerical experiment. The domain is enclosed by solid
112  walls at $0^{\circ}$~E, $60^{\circ}$~E, $0^{\circ}$~N and $60^{\circ}$~N.  walls at $0^{\circ}$~E, $60^{\circ}$~E, $0^{\circ}$~N and $60^{\circ}$~N.
113  In the four-layer case an initial temperature stratification is  An initial stratification is
114  imposed by setting the potential temperature, $\theta$, in each layer.  imposed by setting the potential temperature, $\theta$, in each layer.
115  The vertical spacing, $\Delta z$, is constant and equal to $500$m.  The vertical spacing, $\Delta z$, is constant and equal to $500$m.
116  }  }
# Line 118  The vertical spacing, $\Delta z$, is con Line 118  The vertical spacing, $\Delta z$, is con
118  \end{figure}  \end{figure}
119    
120  \subsection{Equations solved}  \subsection{Equations solved}
121    For this problem
122  The implicit free surface form of the  the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the
123  pressure equation described in Marshall et. al \cite{Marshall97a} is  equations described in Marshall et. al \cite{marshall:97a} are
124  employed.  employed. The flow is three-dimensional with just temperature, $\theta$, as
125  A horizontal laplacian operator $\nabla_{h}^2$ provides viscous  an active tracer.  The equation of state is linear.
126  dissipation. The wind-stress momentum input is added to the momentum equation  A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
127  for the ``zonal flow'', $u$. Other terms in the model  dissipation and provides a diffusive sub-grid scale closure for the
128  are explicitly switched off for this experiement configuration (see section  temperature equation. A wind-stress momentum forcing is added to the momentum
129  \ref{SEC:code_config} ). This yields an active set of equations in  equation for the zonal flow, $u$. Other terms in the model
130    are explicitly switched off for this experiment configuration (see section
131    \ref{SEC:eg_fourl_code_config} ). This yields an active set of equations
132  solved in this configuration, written in spherical polar coordinates as  solved in this configuration, written in spherical polar coordinates as
133  follows  follows
134    
# Line 136  follows Line 138  follows
138    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} -    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} -
139    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}
140  & = &  & = &
141  \cal{F}  \cal{F}_{\lambda}
142  \\  \\
143  \frac{Dv}{Dt} + fu +  \frac{Dv}{Dt} + fu +
144    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \varphi} -    \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \varphi} -
# Line 144  follows Line 146  follows
146  & = &  & = &
147  0  0
148  \\  \\
149  \frac{\partial \eta}{\partial t} + \frac{\partial H \hat{u}}{\partial \lambda} +  \frac{\partial \eta}{\partial t} + \frac{\partial H \widehat{u}}{\partial \lambda} +
150  \frac{\partial H \hat{v}}{\partial \varphi}  \frac{\partial H \widehat{v}}{\partial \varphi}
151  &=&  &=&
152  0  0
153    \label{eq:fourl_example_continuity}
154  \\  \\
155  \frac{D\theta}{Dt} -  \frac{D\theta}{Dt} -
156   K_{h}\nabla_{h}^2\theta  - K_{z}\frac{\partial^{2}\theta}{\partial z^{2}}   K_{h}\nabla_{h}^2\theta  - K_{z}\frac{\partial^{2}\theta}{\partial z^{2}}
157  & = &  & = &
158  0  0
159    \label{eq:eg_fourl_theta}
160  \\  \\
161  p^{\prime} & = &  p^{\prime} & = &
162  g\rho_{0} \eta + \int^{0}_{-z}\rho^{\prime} dz  g\rho_{0} \eta + \int^{0}_{-z}\rho^{\prime} dz
163  \\  \\
164  \rho^{\prime} & = &- \alpha_{\theta}\rho_{0}\theta^{\prime}  \rho^{\prime} & = &- \alpha_{\theta}\rho_{0}\theta^{\prime}
165  \\  \\
166  {\cal F} |_{s} & = & \frac{\tau_{x}}{\rho_{0}\Delta z_{s}}  {\cal F}_{\lambda} |_{s} & = & \frac{\tau_{\lambda}}{\rho_{0}\Delta z_{s}}
167  \\  \\
168  {\cal F} |_{i} & = & 0  {\cal F}_{\lambda} |_{i} & = & 0
169  \end{eqnarray}  \end{eqnarray}
170    
171  \noindent where $u$ and $v$ are the components of the horizontal  \noindent where $u$ and $v$ are the components of the horizontal
172  flow vector $\vec{u}$ on the sphere ($u=\dot{\lambda},v=\dot{\varphi}$).  flow vector $\vec{u}$ on the sphere ($u=\dot{\lambda},v=\dot{\varphi}$).
173  The terms $H\hat{u}$ and $H\hat{v}$ are the components of the term  The terms $H\widehat{u}$ and $H\widehat{v}$ are the components of the vertical
174  integrated in eqaution \ref{eq:free-surface}, as descirbed in section  integral term given in equation \ref{eq:free-surface} and
175    explained in more detail in section \ref{sect:pressure-method-linear-backward}.
176    However, for the problem presented here, the continuity relation (equation
177    \ref{eq:fourl_example_continuity}) differs from the general form given
178    in section \ref{sect:pressure-method-linear-backward},
179    equation \ref{eq:linear-free-surface=P-E+R}, because the source terms
180    ${\cal P}-{\cal E}+{\cal R}$
181    are all $0$.
182    
 The suffices ${s},{i}$ indicate surface and interior of the domain.  
 The forcing $\cal F$ is only applied at the surface.  
183  The pressure field, $p^{\prime}$, is separated into a barotropic part  The pressure field, $p^{\prime}$, is separated into a barotropic part
184  due to variations in sea-surface height, $\eta$, and a hydrostatic  due to variations in sea-surface height, $\eta$, and a hydrostatic
185  part due to variations in density, $\rho^{\prime}$, over the water column.  part due to variations in density, $\rho^{\prime}$, integrated
186    through the water column.
187    
188    The suffices ${s},{i}$ indicate surface layer and the interior of the domain.
189    The windstress forcing, ${\cal F}_{\lambda}$, is applied in the surface layer
190    by a source term in the zonal momentum equation. In the ocean interior
191    this term is zero.
192    
193    In the momentum equations
194    lateral and vertical boundary conditions for the $\nabla_{h}^{2}$
195    and $\frac{\partial^{2}}{\partial z^{2}}$ operators are specified
196    when the numerical simulation is run - see section
197    \ref{SEC:eg_fourl_code_config}. For temperature
198    the boundary condition is ``zero-flux''
199    e.g. $\frac{\partial \theta}{\partial \varphi}=
200    \frac{\partial \theta}{\partial \lambda}=\frac{\partial \theta}{\partial z}=0$.
201    
202    
203    
204  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
205    
206   The model is configured in hydrostatic form.  The domain is discretised with   The domain is discretised with
207  a uniform grid spacing in latitude and longitude  a uniform grid spacing in latitude and longitude
208   $\Delta \lambda=\Delta \varphi=1^{\circ}$, so   $\Delta \lambda=\Delta \varphi=1^{\circ}$, so
209  that there are sixty grid cells in the zonal and meridional directions.  that there are sixty grid cells in the zonal and meridional directions.
210  Vertically the  Vertically the
211  model is configured with four layers with constant depth,  model is configured with four layers with constant depth,
212  $\Delta z$, of $500$~m. The internal, locally orthogonal, model coordinate  $\Delta z$, of $500$~m. The internal, locally orthogonal, model coordinate
213  variables $x$ and $y$ are initialised from the values of  variables $x$ and $y$ are initialized from the values of
214  $\lambda$, $\varphi$, $\Delta \lambda$ and $\Delta \varphi$ in  $\lambda$, $\varphi$, $\Delta \lambda$ and $\Delta \varphi$ in
215  radians according to  radians according to
216    
# Line 195  y=r\varphi,~\Delta y &= &r\Delta \varphi Line 221  y=r\varphi,~\Delta y &= &r\Delta \varphi
221    
222  The procedure for generating a set of internal grid variables from a  The procedure for generating a set of internal grid variables from a
223  spherical polar grid specification is discussed in section  spherical polar grid specification is discussed in section
224  \ref{sec:spatial_discrete_horizontal_grid}.  \ref{sect:spatial_discrete_horizontal_grid}.
225    
226  \noindent\fbox{ \begin{minipage}{5.5in}  \noindent\fbox{ \begin{minipage}{5.5in}
227  {\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em  {\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em
# Line 216  $\Delta x_v$, $\Delta y_u$: {\bf DXv}, { Line 242  $\Delta x_v$, $\Delta y_u$: {\bf DXv}, {
242    
243    
244    
245  As described in \ref{sec:tracer_equations}, the time evolution of potential  As described in \ref{sect:tracer_equations}, the time evolution of potential
246  temperature,  temperature,
247  $\theta$, equation is solved prognostically.  $\theta$, (equation \ref{eq:eg_fourl_theta})
248    is evaluated prognostically. The centered second-order scheme with
249    Adams-Bashforth time stepping described in section
250    \ref{sect:tracer_equations_abII} is used to step forward the temperature
251    equation. Prognostic terms in
252    the momentum equations are solved using flux form as
253    described in section \ref{sect:flux-form_momentum_eqautions}.
254  The pressure forces that drive the fluid motions, (  The pressure forces that drive the fluid motions, (
255  $\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface  $\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface
256  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure. The hydrostatic part of the
257    pressure is diagnosed explicitly by integrating density. The sea-surface
258    height, $\eta$, is diagnosed using an implicit scheme. The pressure
259    field solution method is described in sections
260    \ref{sect:pressure-method-linear-backward} and
261    \ref{sect:finding_the_pressure_field}.
262    
263  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
264    
265  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
266  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},  This value is chosen to yield a Munk layer width,
267    
268  \begin{eqnarray}  \begin{eqnarray}
269  \label{EQ:munk_layer}  \label{EQ:munk_layer}
# Line 234  M_{w} = \pi ( \frac { A_{h} }{ \beta } ) Line 271  M_{w} = \pi ( \frac { A_{h} }{ \beta } )
271  \end{eqnarray}  \end{eqnarray}
272    
273  \noindent  of $\approx 100$km. This is greater than the model  \noindent  of $\approx 100$km. This is greater than the model
274  resolution in mid-latitudes $\Delta x$, ensuring that the frictional  resolution in mid-latitudes
275    $\Delta x=r \cos(\varphi) \Delta \lambda \approx 80~{\rm km}$ at
276    $\varphi=45^{\circ}$, ensuring that the frictional
277  boundary layer is well resolved.  boundary layer is well resolved.
278  \\  \\
279    
280  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
281  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
282  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction
283    
284  \begin{eqnarray}  \begin{eqnarray}
285  \label{EQ:laplacian_stability}  \label{EQ:laplacian_stability}
# Line 248  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta Line 287  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta
287  \end{eqnarray}  \end{eqnarray}
288    
289  \noindent evaluates to 0.012, which is well below the 0.3 upper limit  \noindent evaluates to 0.012, which is well below the 0.3 upper limit
290  for stability.  for stability for this term under ABII time-stepping.
291  \\  \\
292    
293  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
# Line 266  and vertical ($K_{z}$) diffusion coeffic Line 305  and vertical ($K_{z}$) diffusion coeffic
305  \\  \\
306    
307  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
 \cite{Adcroft_thesis}  
308    
309  \begin{eqnarray}  \begin{eqnarray}
310  \label{EQ:inertial_stability}  \label{EQ:inertial_stability}
# Line 277  S_{i} = f^{2} {\delta t}^2 Line 315  S_{i} = f^{2} {\delta t}^2
315  limit for stability.  limit for stability.
316  \\  \\
317    
318  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL for a extreme maximum
319  horizontal flow  horizontal flow
320  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
321    
322  \begin{eqnarray}  \begin{eqnarray}
323  \label{EQ:cfl_stability}  \label{EQ:cfl_stability}
324  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
325  \end{eqnarray}  \end{eqnarray}
326    
327  \noindent evaluates to $5 \times 10^{-2}$. This is well below the stability  \noindent evaluates to $5 \times 10^{-2}$. This is well below the stability
328  limit of 0.5.  limit of 0.5.
329  \\  \\
330    
331  \noindent The stability parameter for internal gravity waves  \noindent The stability parameter for internal gravity waves
332  \cite{Adcroft_thesis}  propagating at $2~{\rm m}~{\rm s}^{-1}$
333    
334  \begin{eqnarray}  \begin{eqnarray}
335  \label{EQ:igw_stability}  \label{EQ:igw_stability}
336  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
337  \end{eqnarray}  \end{eqnarray}
338    
339  \noindent evaluates to $5 \times 10^{-2}$. This is well below the linear  \noindent evaluates to $\approx 5 \times 10^{-2}$. This is well below the linear
340  stability limit of 0.25.  stability limit of 0.25.
341        
342  \subsection{Code Configuration}  \subsection{Code Configuration}
343  \label{SEC:code_config}  \label{SEC:eg_fourl_code_config}
344    
345  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
346  directory {\it verification/exp1/}.  The experiment files  directory {\it verification/exp2/}.  The experiment files
347  \begin{itemize}  \begin{itemize}
348  \item {\it input/data}  \item {\it input/data}
349  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 317  directory {\it verification/exp1/}.  The Line 355  directory {\it verification/exp1/}.  The
355  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
356  \end{itemize}  \end{itemize}
357  contain the code customisations and parameter settings for this  contain the code customisations and parameter settings for this
358  experiements. Below we describe the customisations  experiments. Below we describe the customisations
359  to these files associated with this experiment.  to these files associated with this experiment.
360    
361  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
# Line 334  this line sets Line 372  this line sets
372  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
373  level in units of $^{\circ}$C.  level in units of $^{\circ}$C.
374  The entries are ordered from surface to depth. For each  The entries are ordered from surface to depth. For each
375  depth level the inital and reference profiles will be uniform in  depth level the initial and reference profiles will be uniform in
376  $x$ and $y$. The values specified here are read into the  $x$ and $y$. The values specified here are read into the
377  variable  variable
378  {\bf  {\bf
# Line 380  goto code Line 418  goto code
418    
419  \item Line 6,  \item Line 6,
420  \begin{verbatim} viscAz=1.E-2, \end{verbatim}  \begin{verbatim} viscAz=1.E-2, \end{verbatim}
421  this line sets the vertical laplacian dissipation coefficient to  this line sets the vertical Laplacian dissipation coefficient to
422  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
423  for this operator are specified later.  for this operator are specified later.
424  The variable  The variable
# Line 400  and is copied into model general vertica Line 438  and is copied into model general vertica
438  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PF.htm> \end{rawhtml}
439  viscAr  viscAr
440  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
441  }.  }. At each time step, the viscous term contribution to the momentum equations
442    is calculated in routine
443    {\it S/R CALC\_DIFFUSIVITY}.
444    
445  \fbox{  \fbox{
446  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 431  is read in the routine Line 471  is read in the routine
471  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
472  INI\_PARMS  INI\_PARMS
473  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
474  }.  } and applied in routines {\it CALC\_MOM\_RHS} and {\it CALC\_GW}.
475    
476  \fbox{  \fbox{
477  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 474  is read in the routine Line 514  is read in the routine
514  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
515  INI\_PARMS  INI\_PARMS
516  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
517  }.  } and the boundary condition is evaluated in routine
518    {\it S/R CALC\_MOM\_RHS}.
519    
520    
521  \fbox{  \fbox{
# Line 506  is read in the routine Line 547  is read in the routine
547  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
548  INI\_PARMS  INI\_PARMS
549  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
550  }.  } and is applied in the routine {\it S/R CALC\_MOM\_RHS}.
551    
552  \fbox{  \fbox{
553  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 538  is read in the routine Line 579  is read in the routine
579  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
580  INI\_PARMS  INI\_PARMS
581  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
582  }.  } and used in routine {\it S/R CALC\_GT}.
583    
584  \fbox{ \begin{minipage}{5.0in}  \fbox{ \begin{minipage}{5.0in}
585  {\it S/R CALC\_GT}({\it calc\_gt.F})  {\it S/R CALC\_GT}({\it calc\_gt.F})
# Line 574  It is copied into model general vertical Line 615  It is copied into model general vertical
615  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/names/PD.htm> \end{rawhtml}
616  diffKrT  diffKrT
617  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
618  }.  } which is used in routine {\it S/R CALC\_DIFFUSIVITY}.
619    
620  \fbox{ \begin{minipage}{5.0in}  \fbox{ \begin{minipage}{5.0in}
621  {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})  {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
# Line 605  is read in the routine Line 646  is read in the routine
646  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
647  INI\_PARMS  INI\_PARMS
648  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
649  }.  }. The routine {\it S/R FIND\_RHO} makes use of {\bf tAlpha}.
650    
651  \fbox{  \fbox{
652  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 634  is read in the routine Line 675  is read in the routine
675  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
676  INI\_PARMS  INI\_PARMS
677  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
678  }.  }. The values of {\bf eosType} sets which formula in routine
679    {\it FIND\_RHO} is used to calculate density.
680    
681  \fbox{  \fbox{
682  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 655  usingSphericalPolarGrid=.TRUE., Line 697  usingSphericalPolarGrid=.TRUE.,
697  \end{verbatim}  \end{verbatim}
698  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
699  spherical polar coordinate system. It affects the interpretation of  spherical polar coordinate system. It affects the interpretation of
700  grid inoput parameters, for exampl {\bf delX} and {\bf delY} and  grid input parameters, for example {\bf delX} and {\bf delY} and
701  causes the grid generation routines to initialise an internal grid based  causes the grid generation routines to initialize an internal grid based
702  on spherical polar geometry.  on spherical polar geometry.
703  The variable  The variable
704  {\bf  {\bf
# Line 669  is read in the routine Line 711  is read in the routine
711  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
712  INI\_PARMS  INI\_PARMS
713  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
714  }.  }. When set to {\bf .TRUE.} the settings of {\bf delX} and {\bf delY} are
715    taken to be in degrees. These values are used in the
716    routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
717    
718  \fbox{  \fbox{
719  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 689  phiMin=0., Line 733  phiMin=0.,
733  This line sets the southern boundary of the modeled  This line sets the southern boundary of the modeled
734  domain to $0^{\circ}$ latitude. This value affects both the  domain to $0^{\circ}$ latitude. This value affects both the
735  generation of the locally orthogonal grid that the model  generation of the locally orthogonal grid that the model
736  uses internally and affects the initialisation of the coriolis force.  uses internally and affects the initialization of the coriolis force.
737  Note - it is not required to set  Note - it is not required to set
738  a longitude boundary, since the absolute longitude does  a longitude boundary, since the absolute longitude does
739  not alter the kernel equation discretisation.  not alter the kernel equation discretisation.
# Line 704  is read in the routine Line 748  is read in the routine
748  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
749  INI\_PARMS  INI\_PARMS
750  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
751  }.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
752    
753  \fbox{  \fbox{
754  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 734  is read in the routine Line 778  is read in the routine
778  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
779  INI\_PARMS  INI\_PARMS
780  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
781  }.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
782    
783  \fbox{  \fbox{
784  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 764  is read in the routine Line 808  is read in the routine
808  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
809  INI\_PARMS  INI\_PARMS
810  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
811  }.  } and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
812    
813  \fbox{  \fbox{
814  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 802  model coordinate variable Line 846  model coordinate variable
846  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10Y.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/names/10Y.htm> \end{rawhtml}
847  delR  delR
848  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
849  }.  } which is used in routine {\it INI\_VERTICAL\_GRID}.
850    
851  \fbox{  \fbox{
852  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 841  is read in the routine Line 885  is read in the routine
885  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
886  INI\_PARMS  INI\_PARMS
887  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
888  }.  }. The bathymetry file is read in the routine {\it INI\_DEPTHS}.
889    
890  \fbox{  \fbox{
891  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 860  goto code Line 904  goto code
904  zonalWindFile='windx.sin_y'  zonalWindFile='windx.sin_y'
905  \end{verbatim}  \end{verbatim}
906  This line specifies the name of the file from which the x-direction  This line specifies the name of the file from which the x-direction
907  surface wind stress is read. This file is also a two-dimensional  (zonal) surface wind stress is read. This file is also a two-dimensional
908  ($x,y$) map and is enumerated and formatted in the same manner as the  ($x,y$) map and is enumerated and formatted in the same manner as the
909  bathymetry file. The matlab program {\it input/gendata.m} includes example  bathymetry file. The matlab program {\it input/gendata.m} includes example
910  code to generate a valid  code to generate a valid
# Line 877  is read in the routine Line 921  is read in the routine
921  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}  \begin{rawhtml} <A href=../../../code_reference/vdb/code/94.htm> \end{rawhtml}
922  INI\_PARMS  INI\_PARMS
923  \begin{rawhtml} </A>\end{rawhtml}  \begin{rawhtml} </A>\end{rawhtml}
924  }.  }.  The wind-stress file is read in the routine
925    {\it EXTERNAL\_FIELDS\_LOAD}.
926    
927  \fbox{  \fbox{
928  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
# Line 892  goto code Line 937  goto code
937    
938  \end{itemize}  \end{itemize}
939    
940  \noindent other lines in the file {\it input/data} are standard values  \noindent other lines in the file {\it input/data} are standard values.
 that are described in the MITgcm Getting Started and MITgcm Parameters  
 notes.  
941    
942  \begin{rawhtml}<PRE>\end{rawhtml}  \begin{rawhtml}<PRE>\end{rawhtml}
943  \begin{small}  \begin{small}
# Line 915  customisations for this experiment. Line 958  customisations for this experiment.
958  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
959    
960  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
961  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the
962  Although $\tau_{x}$ is only a function of $y$n in this experiment  default for MITgcm).
963    Although $\tau_{x}$ is only a function of latitude, $y$,
964    in this experiment
965  this file must still define a complete two-dimensional map in order  this file must still define a complete two-dimensional map in order
966  to be compatible with the standard code for loading forcing fields  to be compatible with the standard code for loading forcing fields
967  in MITgcm. The included matlab program {\it input/gendata.m} gives a complete  in MITgcm (routine {\it EXTERNAL\_FIELDS\_LOAD}.
968    The included matlab program {\it input/gendata.m} gives a complete
969  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
970    
971  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
# Line 927  code for creating the {\it input/windx.s Line 973  code for creating the {\it input/windx.s
973    
974  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
975  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
976  $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep  $0~{\rm m}$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep
977  ocean. The file contains a raw binary stream of data that is enumerated  ocean. The file contains a raw binary stream of data that is enumerated
978  in the same way as standard MITgcm two-dimensional, horizontal arrays.  in the same way as standard MITgcm two-dimensional, horizontal arrays.
979  The included matlab program {\it input/gendata.m} gives a complete  The included matlab program {\it input/gendata.m} gives a complete
# Line 988  dxF, dyF, dxG, dyG, dxC, dyC}. Line 1034  dxF, dyF, dxG, dyG, dxC, dyC}.
1034  \subsubsection{Code Download}  \subsubsection{Code Download}
1035    
1036   In order to run the examples you must first download the code distribution.   In order to run the examples you must first download the code distribution.
1037  Instructions for downloading the code can be found in the Getting Started  Instructions for downloading the code can be found in section
1038  Guide \cite{MITgcm_Getting_Started}.  \ref{sect:obtainingCode}.
1039    
1040  \subsubsection{Experiment Location}  \subsubsection{Experiment Location}
1041    
1042   This example experiments is located under the release sub-directory   This example experiments is located under the release sub-directory
1043    
1044  \vspace{5mm}  \vspace{5mm}
1045  {\it verification/exp1/ }  {\it verification/exp2/ }
1046    
1047  \subsubsection{Running the Experiment}  \subsubsection{Running the Experiment}
1048    
# Line 1015  Guide \cite{MITgcm_Getting_Started}. Line 1061  Guide \cite{MITgcm_Getting_Started}.
1061  % pwd  % pwd
1062  \end{verbatim}  \end{verbatim}
1063    
1064   You shold see a response on the screen ending in   You should see a response on the screen ending in
1065    
1066  {\it verification/exp1/input }  {\it verification/exp2/input }
1067    
1068    
1069  \item Run the genmake script to create the experiment {\it Makefile}  \item Run the genmake script to create the experiment {\it Makefile}
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