--- manual/s_examples/baroclinic_gyre/fourlayer.tex 2001/08/08 16:15:41 1.1
+++ manual/s_examples/baroclinic_gyre/fourlayer.tex 2002/05/16 15:54:37 1.13
@@ -1,7 +1,9 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.1 2001/08/08 16:15:41 adcroft Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.13 2002/05/16 15:54:37 adcroft Exp $
% $Name: $
-\section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}
+\section{Four Layer Baroclinic Ocean Gyre In Spherical Coordinates}
+\label{www:tutorials}
+\label{sect:eg-fourlayer}
\bodytext{bgcolor="#FFFFFFFF"}
@@ -15,19 +17,21 @@
%{\large May 2001}
%\end{center}
-\subsection{Introduction}
-
-This document describes the second example MITgcm experiment. The first
-example experiment ilustrated how to configure the code for a single layer
-simulation in a cartesian grid. In this example a similar physical problem
+This document describes an example experiment using MITgcm
+to simulate a baroclinic ocean gyre in spherical
+polar coordinates. The barotropic
+example experiment in section \ref{sect:eg-baro}
+illustrated how to configure the code for a single layer
+simulation in a Cartesian grid. In this example a similar physical problem
is simulated, but the code is now configured
for four layers and in a spherical polar coordinate system.
\subsection{Overview}
+\label{www:tutorials}
This example experiment demonstrates using the MITgcm to simulate
a baroclinic, wind-forced, ocean gyre circulation. The experiment
-is a numerical rendition of the gyre circulation problem simliar
+is a numerical rendition of the gyre circulation problem similar
to the problems described analytically by Stommel in 1966
\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}.
\\
@@ -35,14 +39,14 @@
In this experiment the model is configured to represent a mid-latitude
enclosed sector of fluid on a sphere, $60^{\circ} \times 60^{\circ}$ in
lateral extent. The fluid is $2$~km deep and is forced
-by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally
-in the north-south direction. Topologically the simulated
+by a constant in time zonal wind stress, $\tau_{\lambda}$, that varies
+sinusoidally in the north-south direction. Topologically the simulated
domain is a sector on a sphere and the coriolis parameter, $f$, is defined
-according to latitude, $\phi$
+according to latitude, $\varphi$
\begin{equation}
-\label{EQ:fcori}
-f(\phi) = 2 \Omega \sin( \phi )
+\label{EQ:eg-fourlayer-fcori}
+f(\varphi) = 2 \Omega \sin( \varphi )
\end{equation}
\noindent with the rotation rate, $\Omega$ set to $\frac{2 \pi}{86400s}$.
@@ -52,20 +56,22 @@
\begin{equation}
\label{EQ:taux}
-\tau_x(\phi) = \tau_{0}\sin(\pi \frac{\phi}{L_{\phi}})
+\tau_{\lambda}(\varphi) = \tau_{0}\sin(\pi \frac{\varphi}{L_{\varphi}})
\end{equation}
-\noindent where $L_{\phi}$ is the lateral domain extent ($60^{\circ}$) and
+\noindent where $L_{\varphi}$ is the lateral domain extent ($60^{\circ}$) and
$\tau_0$ is set to $0.1N m^{-2}$.
\\
-Figure \ref{FIG:simulation_config}
-summarises the configuration simulated.
-In contrast to example (1) \cite{baro_gyre_case_study}, the current
-experiment simulates a spherical polar domain. However, as indicated
+Figure \ref{FIG:eg-fourlayer-simulation_config}
+summarizes the configuration simulated.
+In contrast to the example in section \ref{sect:eg-baro}, the
+current experiment simulates a spherical polar domain. As indicated
by the axes in the lower left of the figure the model code works internally
-in a locally orthoganal coordinate $(x,y,z)$. In the remainder of this
-document the local coordinate $(x,y,z)$ will be adopted.
+in a locally orthogonal coordinate $(x,y,z)$. For this experiment description
+the local orthogonal model coordinate $(x,y,z)$ is synonymous
+with the coordinates $(\lambda,\varphi,r)$ shown in figure
+\ref{fig:spherical-polar-coord}
\\
The experiment has four levels in the vertical, each of equal thickness,
@@ -78,131 +84,222 @@
linear
\begin{equation}
-\label{EQ:linear1_eos}
+\label{EQ:eg-fourlayer-linear1_eos}
\rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
\end{equation}
\noindent which is implemented in the model as a density anomaly equation
\begin{equation}
-\label{EQ:linear1_eos_pert}
+\label{EQ:eg-fourlayer-linear1_eos_pert}
\rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
\end{equation}
\noindent with $\rho_{0}=999.8\,{\rm kg\,m}^{-3}$ and
$\alpha_{\theta}=2\times10^{-4}\,{\rm degrees}^{-1} $. Integrated forward in
-this configuration the model state variable {\bf theta} is synonomous with
+this configuration the model state variable {\bf theta} is equivalent to
either in-situ temperature, $T$, or potential temperature, $\theta$. For
consistency with later examples, in which the equation of state is
non-linear, we use $\theta$ to represent temperature here. This is
the quantity that is carried in the model core equations.
\begin{figure}
-\centerline{
+\begin{center}
\resizebox{7.5in}{5.5in}{
\includegraphics*[0.2in,0.7in][10.5in,10.5in]
{part3/case_studies/fourlayer_gyre/simulation_config.eps} }
-}
+\end{center}
\caption{Schematic of simulation domain and wind-stress forcing function
for the four-layer gyre numerical experiment. The domain is enclosed by solid
walls at $0^{\circ}$~E, $60^{\circ}$~E, $0^{\circ}$~N and $60^{\circ}$~N.
-In the four-layer case an initial temperature stratification is
+An initial stratification is
imposed by setting the potential temperature, $\theta$, in each layer.
The vertical spacing, $\Delta z$, is constant and equal to $500$m.
}
-\label{FIG:simulation_config}
+\label{FIG:eg-fourlayer-simulation_config}
\end{figure}
-\subsection{Discrete Numerical Configuration}
-
- The model is configured in hydrostatic form. The domain is discretised with
-a uniform grid spacing in latitude and longitude
- $\Delta x=\Delta y=1^{\circ}$, so
-that there are sixty grid cells in the $x$ and $y$ directions. Vertically the
-model is configured with a four layers with constant depth,
-$\Delta z$, of $500$~m.
-The implicit free surface form of the
-pressure equation described in Marshall et. al \cite{Marshall97a} is
-employed.
-A horizontal laplacian operator $\nabla_{h}^2$ provides viscous
-dissipation. The wind-stress momentum input is added to the momentum equation
-for the ``zonal flow'', $u$. Other terms in the model
-are explicitly switched off for this experiement configuration (see section
-\ref{SEC:code_config} ), yielding an active set of equations solved in this
-configuration as follows
+\subsection{Equations solved}
+\label{www:tutorials}
+For this problem
+the implicit free surface, {\bf HPE} (see section \ref{sect:hydrostatic_and_quasi-hydrostatic_forms}) form of the
+equations described in Marshall et. al \cite{marshall:97a} are
+employed. The flow is three-dimensional with just temperature, $\theta$, as
+an active tracer. The equation of state is linear.
+A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
+dissipation and provides a diffusive sub-grid scale closure for the
+temperature equation. A wind-stress momentum forcing is added to the momentum
+equation for the zonal flow, $u$. Other terms in the model
+are explicitly switched off for this experiment configuration (see section
+\ref{SEC:eg_fourl_code_config} ). This yields an active set of equations
+solved in this configuration, written in spherical polar coordinates as
+follows
\begin{eqnarray}
-\label{EQ:model_equations}
+\label{EQ:eg-fourlayer-model_equations}
\frac{Du}{Dt} - fv +
- \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
+ \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} -
A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}
& = &
-\cal{F}
+\cal{F}_{\lambda}
\\
\frac{Dv}{Dt} + fu +
- \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
+ \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \varphi} -
A_{h}\nabla_{h}^2v - A_{z}\frac{\partial^{2}v}{\partial z^{2}}
& = &
0
\\
-\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u}
+\frac{\partial \eta}{\partial t} + \frac{\partial H \widehat{u}}{\partial \lambda} +
+\frac{\partial H \widehat{v}}{\partial \varphi}
&=&
0
+\label{eq:fourl_example_continuity}
\\
\frac{D\theta}{Dt} -
K_{h}\nabla_{h}^2\theta - K_{z}\frac{\partial^{2}\theta}{\partial z^{2}}
& = &
0
+\label{eq:eg_fourl_theta}
\\
-g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
+p^{\prime} & = &
+g\rho_{0} \eta + \int^{0}_{-z}\rho^{\prime} dz
\\
-{\cal F} |_{s} & = & \frac{\tau_{x}}{\rho_{0}\Delta z_{s}}
+\rho^{\prime} & = &- \alpha_{\theta}\rho_{0}\theta^{\prime}
\\
-{\cal F} |_{i} & = & 0
+{\cal F}_{\lambda} |_{s} & = & \frac{\tau_{\lambda}}{\rho_{0}\Delta z_{s}}
+\\
+{\cal F}_{\lambda} |_{i} & = & 0
\end{eqnarray}
-\noindent where $u$ and $v$ are the $x$ and $y$ components of the
-flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and
-interior model levels respectively. As described in
-MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time
-evolution of potential temperature, $\theta$, equation is solved prognostically.
-The total pressure, $p$, is diagnosed by summing pressure due to surface
-elevation $\eta$ and the hydrostatic pressure.
-\\
+\noindent where $u$ and $v$ are the components of the horizontal
+flow vector $\vec{u}$ on the sphere ($u=\dot{\lambda},v=\dot{\varphi}$).
+The terms $H\widehat{u}$ and $H\widehat{v}$ are the components of the vertical
+integral term given in equation \ref{eq:free-surface} and
+explained in more detail in section \ref{sect:pressure-method-linear-backward}.
+However, for the problem presented here, the continuity relation (equation
+\ref{eq:fourl_example_continuity}) differs from the general form given
+in section \ref{sect:pressure-method-linear-backward},
+equation \ref{eq:linear-free-surface=P-E+R}, because the source terms
+${\cal P}-{\cal E}+{\cal R}$
+are all $0$.
+
+The pressure field, $p^{\prime}$, is separated into a barotropic part
+due to variations in sea-surface height, $\eta$, and a hydrostatic
+part due to variations in density, $\rho^{\prime}$, integrated
+through the water column.
+
+The suffices ${s},{i}$ indicate surface layer and the interior of the domain.
+The windstress forcing, ${\cal F}_{\lambda}$, is applied in the surface layer
+by a source term in the zonal momentum equation. In the ocean interior
+this term is zero.
+
+In the momentum equations
+lateral and vertical boundary conditions for the $\nabla_{h}^{2}$
+and $\frac{\partial^{2}}{\partial z^{2}}$ operators are specified
+when the numerical simulation is run - see section
+\ref{SEC:eg_fourl_code_config}. For temperature
+the boundary condition is ``zero-flux''
+e.g. $\frac{\partial \theta}{\partial \varphi}=
+\frac{\partial \theta}{\partial \lambda}=\frac{\partial \theta}{\partial z}=0$.
+
+
+
+\subsection{Discrete Numerical Configuration}
+\label{www:tutorials}
+
+ The domain is discretised with
+a uniform grid spacing in latitude and longitude
+ $\Delta \lambda=\Delta \varphi=1^{\circ}$, so
+that there are sixty grid cells in the zonal and meridional directions.
+Vertically the
+model is configured with four layers with constant depth,
+$\Delta z$, of $500$~m. The internal, locally orthogonal, model coordinate
+variables $x$ and $y$ are initialized from the values of
+$\lambda$, $\varphi$, $\Delta \lambda$ and $\Delta \varphi$ in
+radians according to
+
+\begin{eqnarray}
+x=r\cos(\varphi)\lambda,~\Delta x & = &r\cos(\varphi)\Delta \lambda \\
+y=r\varphi,~\Delta y &= &r\Delta \varphi
+\end{eqnarray}
+
+The procedure for generating a set of internal grid variables from a
+spherical polar grid specification is discussed in section
+\ref{sect:spatial_discrete_horizontal_grid}.
+
+\noindent\fbox{ \begin{minipage}{5.5in}
+{\em S/R INI\_SPHERICAL\_POLAR\_GRID} ({\em
+model/src/ini\_spherical\_polar\_grid.F})
+
+$A_c$, $A_\zeta$, $A_w$, $A_s$: {\bf rAc}, {\bf rAz}, {\bf rAw}, {\bf rAs}
+({\em GRID.h})
+
+$\Delta x_g$, $\Delta y_g$: {\bf DXg}, {\bf DYg} ({\em GRID.h})
+
+$\Delta x_c$, $\Delta y_c$: {\bf DXc}, {\bf DYc} ({\em GRID.h})
+
+$\Delta x_f$, $\Delta y_f$: {\bf DXf}, {\bf DYf} ({\em GRID.h})
+
+$\Delta x_v$, $\Delta y_u$: {\bf DXv}, {\bf DYu} ({\em GRID.h})
+
+\end{minipage} }\\
+
+
+
+As described in \ref{sect:tracer_equations}, the time evolution of potential
+temperature,
+$\theta$, (equation \ref{eq:eg_fourl_theta})
+is evaluated prognostically. The centered second-order scheme with
+Adams-Bashforth time stepping described in section
+\ref{sect:tracer_equations_abII} is used to step forward the temperature
+equation. Prognostic terms in
+the momentum equations are solved using flux form as
+described in section \ref{sect:flux-form_momentum_eqautions}.
+The pressure forces that drive the fluid motions, (
+$\frac{\partial p^{'}}{\partial \lambda}$ and $\frac{\partial p^{'}}{\partial \varphi}$), are found by summing pressure due to surface
+elevation $\eta$ and the hydrostatic pressure. The hydrostatic part of the
+pressure is diagnosed explicitly by integrating density. The sea-surface
+height, $\eta$, is diagnosed using an implicit scheme. The pressure
+field solution method is described in sections
+\ref{sect:pressure-method-linear-backward} and
+\ref{sect:finding_the_pressure_field}.
\subsubsection{Numerical Stability Criteria}
+\label{www:tutorials}
-The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
-This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},
+The Laplacian viscosity coefficient, $A_{h}$, is set to $400 m s^{-1}$.
+This value is chosen to yield a Munk layer width,
\begin{eqnarray}
-\label{EQ:munk_layer}
+\label{EQ:eg-fourlayer-munk_layer}
M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
\end{eqnarray}
\noindent of $\approx 100$km. This is greater than the model
-resolution in mid-latitudes $\Delta x$, ensuring that the frictional
+resolution in mid-latitudes
+$\Delta x=r \cos(\varphi) \Delta \lambda \approx 80~{\rm km}$ at
+$\varphi=45^{\circ}$, ensuring that the frictional
boundary layer is well resolved.
\\
\noindent The model is stepped forward with a
time step $\delta t=1200$secs. With this time step the stability
-parameter to the horizontal laplacian friction \cite{Adcroft_thesis}
+parameter to the horizontal Laplacian friction
\begin{eqnarray}
-\label{EQ:laplacian_stability}
+\label{EQ:eg-fourlayer-laplacian_stability}
S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
\end{eqnarray}
\noindent evaluates to 0.012, which is well below the 0.3 upper limit
-for stability.
+for stability for this term under ABII time-stepping.
\\
\noindent The vertical dissipation coefficient, $A_{z}$, is set to
$1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
\begin{eqnarray}
-\label{EQ:laplacian_stability_z}
+\label{EQ:eg-fourlayer-laplacian_stability_z}
S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
\end{eqnarray}
@@ -213,10 +310,9 @@
\\
\noindent The numerical stability for inertial oscillations
-\cite{Adcroft_thesis}
\begin{eqnarray}
-\label{EQ:inertial_stability}
+\label{EQ:eg-fourlayer-inertial_stability}
S_{i} = f^{2} {\delta t}^2
\end{eqnarray}
@@ -224,35 +320,36 @@
limit for stability.
\\
-\noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum
+\noindent The advective CFL for a extreme maximum
horizontal flow
speed of $ | \vec{u} | = 2 ms^{-1}$
\begin{eqnarray}
-\label{EQ:cfl_stability}
-S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
+\label{EQ:eg-fourlayer-cfl_stability}
+C_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
\end{eqnarray}
\noindent evaluates to $5 \times 10^{-2}$. This is well below the stability
limit of 0.5.
\\
-\noindent The stability parameter for internal gravity waves
-\cite{Adcroft_thesis}
+\noindent The stability parameter for internal gravity waves
+propagating at $2~{\rm m}~{\rm s}^{-1}$
\begin{eqnarray}
-\label{EQ:igw_stability}
+\label{EQ:eg-fourlayer-igw_stability}
S_{c} = \frac{c_{g} \delta t}{ \Delta x}
\end{eqnarray}
-\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
stability limit of 0.25.
\subsection{Code Configuration}
-\label{SEC:code_config}
+\label{www:tutorials}
+\label{SEC:eg_fourl_code_config}
The model configuration for this experiment resides under the
-directory {\it verification/exp1/}. The experiment files
+directory {\it verification/exp2/}. The experiment files
\begin{itemize}
\item {\it input/data}
\item {\it input/data.pkg}
@@ -264,10 +361,11 @@
\item {\it code/SIZE.h}.
\end{itemize}
contain the code customisations and parameter settings for this
-experiements. Below we describe the customisations
+experiments. Below we describe the customisations
to these files associated with this experiment.
\subsubsection{File {\it input/data}}
+\label{www:tutorials}
This file, reproduced completely below, specifies the main parameters
for the experiment. The parameters that are significant for this configuration
@@ -281,7 +379,7 @@
the initial and reference values of potential temperature at each model
level in units of $^{\circ}$C.
The entries are ordered from surface to depth. For each
-depth level the inital and reference profiles will be uniform in
+depth level the initial and reference profiles will be uniform in
$x$ and $y$. The values specified here are read into the
variable
{\bf
@@ -327,7 +425,7 @@
\item Line 6,
\begin{verbatim} viscAz=1.E-2, \end{verbatim}
-this line sets the vertical laplacian dissipation coefficient to
+this line sets the vertical Laplacian dissipation coefficient to
$1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
for this operator are specified later.
The variable
@@ -347,7 +445,9 @@
\begin{rawhtml} \end{rawhtml}
viscAr
\begin{rawhtml} \end{rawhtml}
-}.
+}. At each time step, the viscous term contribution to the momentum equations
+is calculated in routine
+{\it S/R CALC\_DIFFUSIVITY}.
\fbox{
\begin{minipage}{5.0in}
@@ -378,7 +478,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+} and applied in routines {\it CALC\_MOM\_RHS} and {\it CALC\_GW}.
\fbox{
\begin{minipage}{5.0in}
@@ -421,7 +521,8 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+} and the boundary condition is evaluated in routine
+{\it S/R CALC\_MOM\_RHS}.
\fbox{
@@ -453,7 +554,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+} and is applied in the routine {\it S/R CALC\_MOM\_RHS}.
\fbox{
\begin{minipage}{5.0in}
@@ -485,7 +586,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+} and used in routine {\it S/R CALC\_GT}.
\fbox{ \begin{minipage}{5.0in}
{\it S/R CALC\_GT}({\it calc\_gt.F})
@@ -521,7 +622,7 @@
\begin{rawhtml} \end{rawhtml}
diffKrT
\begin{rawhtml} \end{rawhtml}
-}.
+} which is used in routine {\it S/R CALC\_DIFFUSIVITY}.
\fbox{ \begin{minipage}{5.0in}
{\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})
@@ -552,7 +653,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+}. The routine {\it S/R FIND\_RHO} makes use of {\bf tAlpha}.
\fbox{
\begin{minipage}{5.0in}
@@ -581,7 +682,8 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+}. The values of {\bf eosType} sets which formula in routine
+{\it FIND\_RHO} is used to calculate density.
\fbox{
\begin{minipage}{5.0in}
@@ -602,8 +704,8 @@
\end{verbatim}
This line requests that the simulation be performed in a
spherical polar coordinate system. It affects the interpretation of
-grid inoput parameters, for exampl {\bf delX} and {\bf delY} and
-causes the grid generation routines to initialise an internal grid based
+grid input parameters, for example {\bf delX} and {\bf delY} and
+causes the grid generation routines to initialize an internal grid based
on spherical polar geometry.
The variable
{\bf
@@ -616,7 +718,9 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+}. When set to {\bf .TRUE.} the settings of {\bf delX} and {\bf delY} are
+taken to be in degrees. These values are used in the
+routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
\fbox{
\begin{minipage}{5.0in}
@@ -636,7 +740,7 @@
This line sets the southern boundary of the modeled
domain to $0^{\circ}$ latitude. This value affects both the
generation of the locally orthogonal grid that the model
-uses internally and affects the initialisation of the coriolis force.
+uses internally and affects the initialization of the coriolis force.
Note - it is not required to set
a longitude boundary, since the absolute longitude does
not alter the kernel equation discretisation.
@@ -651,7 +755,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+} and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
\fbox{
\begin{minipage}{5.0in}
@@ -681,7 +785,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+} and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
\fbox{
\begin{minipage}{5.0in}
@@ -711,7 +815,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+} and is used in routine {\it INI\_SPEHRICAL\_POLAR\_GRID}.
\fbox{
\begin{minipage}{5.0in}
@@ -749,7 +853,7 @@
\begin{rawhtml} \end{rawhtml}
delR
\begin{rawhtml} \end{rawhtml}
-}.
+} which is used in routine {\it INI\_VERTICAL\_GRID}.
\fbox{
\begin{minipage}{5.0in}
@@ -788,7 +892,7 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+}. The bathymetry file is read in the routine {\it INI\_DEPTHS}.
\fbox{
\begin{minipage}{5.0in}
@@ -807,7 +911,7 @@
zonalWindFile='windx.sin_y'
\end{verbatim}
This line specifies the name of the file from which the x-direction
-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
($x,y$) map and is enumerated and formatted in the same manner as the
bathymetry file. The matlab program {\it input/gendata.m} includes example
code to generate a valid
@@ -824,7 +928,8 @@
\begin{rawhtml} \end{rawhtml}
INI\_PARMS
\begin{rawhtml} \end{rawhtml}
-}.
+}. The wind-stress file is read in the routine
+{\it EXTERNAL\_FIELDS\_LOAD}.
\fbox{
\begin{minipage}{5.0in}
@@ -839,9 +944,7 @@
\end{itemize}
-\noindent other lines in the file {\it input/data} are standard values
-that are described in the MITgcm Getting Started and MITgcm Parameters
-notes.
+\noindent other lines in the file {\it input/data} are standard values.
\begin{rawhtml}\end{rawhtml}
\begin{small}
@@ -850,37 +953,45 @@
\begin{rawhtml}\end{rawhtml}
\subsubsection{File {\it input/data.pkg}}
+\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it input/eedata}}
+\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it input/windx.sin\_y}}
+\label{www:tutorials}
The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
-map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
-Although $\tau_{x}$ is only a function of $y$n in this experiment
+map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$ (the
+default for MITgcm).
+Although $\tau_{x}$ is only a function of latitude, $y$,
+in this experiment
this file must still define a complete two-dimensional map in order
to be compatible with the standard code for loading forcing fields
-in MITgcm. The included matlab program {\it input/gendata.m} gives a complete
+in MITgcm (routine {\it EXTERNAL\_FIELDS\_LOAD}.
+The included matlab program {\it input/gendata.m} gives a complete
code for creating the {\it input/windx.sin\_y} file.
\subsubsection{File {\it input/topog.box}}
+\label{www:tutorials}
The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
map of depth values. For this experiment values are either
-$0m$ 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
ocean. The file contains a raw binary stream of data that is enumerated
in the same way as standard MITgcm two-dimensional, horizontal arrays.
The included matlab program {\it input/gendata.m} gives a complete
code for creating the {\it input/topog.box} file.
\subsubsection{File {\it code/SIZE.h}}
+\label{www:tutorials}
Two lines are customized in this file for the current experiment
@@ -907,17 +1018,20 @@
\end{small}
\subsubsection{File {\it code/CPP\_OPTIONS.h}}
+\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
+\label{www:tutorials}
This file uses standard default values and does not contain
customisations for this experiment.
\subsubsection{Other Files }
+\label{www:tutorials}
Other files relevant to this experiment are
\begin{itemize}
@@ -930,22 +1044,26 @@
\end{itemize}
\subsection{Running The Example}
+\label{www:tutorials}
\label{SEC:running_the_example}
\subsubsection{Code Download}
+\label{www:tutorials}
In order to run the examples you must first download the code distribution.
-Instructions for downloading the code can be found in the Getting Started
-Guide \cite{MITgcm_Getting_Started}.
+Instructions for downloading the code can be found in section
+\ref{sect:obtainingCode}.
\subsubsection{Experiment Location}
+\label{www:tutorials}
This example experiments is located under the release sub-directory
\vspace{5mm}
-{\it verification/exp1/ }
+{\it verification/exp2/ }
\subsubsection{Running the Experiment}
+\label{www:tutorials}
To run the experiment
@@ -962,9 +1080,9 @@
% pwd
\end{verbatim}
- You shold see a response on the screen ending in
+ You should see a response on the screen ending in
-{\it verification/exp1/input }
+{\it verification/exp2/input }
\item Run the genmake script to create the experiment {\it Makefile}