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revision 1.2 by cnh, Mon Oct 22 11:55:48 2001 UTC revision 1.8 by cnh, Thu Feb 28 19:32:19 2002 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}  \section{Global Ocean Simulation at 4$^\circ$ Resolution}
5  \label{sec:eg-global}  \label{sect:eg-global}
6    
7  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
8    
9  %\begin{center}  %\begin{center}
10  %{\Large \bf Using MITgcm to Simulate Global Climatalogical Ocean Circulation  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
11  %At Four Degree Resolution with Asynchronous Time Stepping}  %At Four Degree Resolution with Asynchronous Time Stepping}
12  %  %
13  %\vspace*{4mm}  %\vspace*{4mm}
# Line 16  Line 16 
16  %{\large May 2001}  %{\large May 2001}
17  %\end{center}  %\end{center}
18    
 \subsection{Introduction}  
   
 This document describes the third example MITgcm experiment. The first  
 two examples illustrated how to configure the code for hydrostatic idealised  
 geophysical fluids simulations. This example iilustrates the use of  
 the MITgcm for large scale ocean circulation simulation.  
   
 \subsection{Overview}  
19    
20  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
21  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
# Line 36  At this resolution, the configuration Line 28  At this resolution, the configuration
28  can be integrated forward for thousands of years on a single  can be integrated forward for thousands of years on a single
29  processor desktop computer.  processor desktop computer.
30  \\  \\
31    \subsection{Overview}
32    
33  The model is forced with climatalogical wind stress data and surface  The model is forced with climatological wind stress data and surface
34  flux data from DaSilva \cite{DaSilva94}. Climatalogical data  flux data from DaSilva \cite{DaSilva94}. Climatological data
35  from Levitus \cite{Levitus94} is used to initialise the model hydrography.  from Levitus \cite{Levitus94} is used to initialize the model hydrography.
36  Levitus seasonal clmatology data is also used throughout the calculation  Levitus seasonal climatology data is also used throughout the calculation
37  to provide additional air-sea fluxes.  to provide additional air-sea fluxes.
38  These fluxes are combined with the DaSilva climatalogical estimates of  These fluxes are combined with the DaSilva climatological estimates of
39  surface heat flux and fresh water, resulting in a mixed boundary  surface heat flux and fresh water, resulting in a mixed boundary
40  condition of the style decribed in Haney \cite{Haney}.  condition of the style described in Haney \cite{Haney}.
41  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied
42  in the model surface layer.  in the model surface layer.
43    
44  \begin{eqnarray}  \begin{eqnarray}
45  \label{EQ:global_forcing}  \label{EQ:eg-global-global_forcing}
46  \label{EQ:global_forcing_fu}  \label{EQ:eg-global-global_forcing_fu}
47  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
48  \\  \\
49  \label{EQ:global_forcing_fv}  \label{EQ:eg-global-global_forcing_fv}
50  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
51  \\  \\
52  \label{EQ:global_forcing_ft}  \label{EQ:eg-global-global_forcing_ft}
53  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
54   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
55  \\  \\
56  \label{EQ:global_forcing_fs}  \label{EQ:eg-global-global_forcing_fs}
57  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
58   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
59  \end{eqnarray}  \end{eqnarray}
# Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 80  have units of ${\rm N}~{\rm m}^{-2}$. Th
80  ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$  ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$
81  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
82  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
83  respectively.  respectively. The source files and procedures for ingesting this data into the
84  \\  simulation are described in the experiment configuration discussion in section
85    \ref{SEC:eg-global-clim_ocn_examp_exp_config}.
   
 Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the  
 relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,  
 the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)  
 and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used  
 in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures  
 also indicate the lateral extent and coastline used in the experiment.  
 Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model  
 domain.  
86    
87    
88  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
# Line 109  a uniform grid spacing in latitude and l Line 93  a uniform grid spacing in latitude and l
93   $\Delta \phi=\Delta \lambda=4^{\circ}$, so   $\Delta \phi=\Delta \lambda=4^{\circ}$, so
94  that there are ninety grid cells in the zonal and forty in the  that there are ninety grid cells in the zonal and forty in the
95  meridional direction. The internal model coordinate variables  meridional direction. The internal model coordinate variables
96  $x$ and $y$ are initialised according to  $x$ and $y$ are initialized according to
97  \begin{eqnarray}  \begin{eqnarray}
98  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
99  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
100  \end{eqnarray}  \end{eqnarray}
101    
102  Arctic polar regions are not  Arctic polar regions are not
# Line 146  $ Line 130  $
130   \Delta z_{18}=725\,{\rm m},\,   \Delta z_{18}=725\,{\rm m},\,
131   \Delta z_{19}=775\,{\rm m},\,   \Delta z_{19}=775\,{\rm m},\,
132   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
133  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$) to
134    give a total depth, $H$, of $-5450{\rm m}$.
135  The implicit free surface form of the pressure equation described in Marshall et. al  The implicit free surface form of the pressure equation described in Marshall et. al
136  \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
137  dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
138    
139  Wind-stress forcing is added to the momentum equations for both  Wind-stress forcing is added to the momentum equations in (\ref{EQ:eg-global-model_equations})
140  the zonal flow, $u$ and the merdional flow $v$, according to equations  for both the zonal flow, $u$ and the meridional flow $v$, according to equations
141  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:eg-global-global_forcing_fu}) and (\ref{EQ:eg-global-global_forcing_fv}).
142  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations
143    in (\ref{EQ:eg-global-model_equations}) for
144  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
145  (\ref{EQ:global_forcing_ft}) and (\ref{EQ:global_forcing_fs}).  (\ref{EQ:eg-global-global_forcing_ft}) and (\ref{EQ:eg-global-global_forcing_fs}).
146  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
147    
148  \begin{eqnarray}  \begin{eqnarray}
149  \label{EQ:model_equations}  \label{EQ:eg-global-model_equations}
150  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
151    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
152    \nabla_{h}\cdot A_{h}\nabla_{h}u -    \nabla_{h}\cdot A_{h}\nabla_{h}u -
# Line 210  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d Line 196  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
196  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
197  are the zonal and meridional components of the  are the zonal and meridional components of the
198  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
199  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
200  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
201  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
202  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
# Line 218  elevation $\eta$ and the hydrostatic pre Line 204  elevation $\eta$ and the hydrostatic pre
204    
205  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
206    
207  The laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$.
208  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},  This value is chosen to yield a Munk layer width \cite{adcroft:95},
209  \begin{eqnarray}  \begin{eqnarray}
210  \label{EQ:munk_layer}  \label{EQ:eg-global-munk_layer}
211  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
212  \end{eqnarray}  \end{eqnarray}
213    
# Line 233  boundary layer is adequately resolved. Line 219  boundary layer is adequately resolved.
219  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
220  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
221  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
222  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
223  \begin{eqnarray}  \begin{eqnarray}
224  \label{EQ:laplacian_stability}  \label{EQ:eg-global-laplacian_stability}
225  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
226  \end{eqnarray}  \end{eqnarray}
227    
# Line 247  $\phi=80^{\circ}$ where $\Delta x=r\cos( Line 233  $\phi=80^{\circ}$ where $\Delta x=r\cos(
233  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
234  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
235  \begin{eqnarray}  \begin{eqnarray}
236  \label{EQ:laplacian_stability_z}  \label{EQ:eg-global-laplacian_stability_z}
237  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
238  \end{eqnarray}  \end{eqnarray}
239    
240  \noindent evaluates to $0.015$ for the smallest model  \noindent evaluates to $0.015$ for the smallest model
241  level spcing ($\Delta z_{1}=50{\rm m}$) which is again well below  level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below
242  the upper stability limit.  the upper stability limit.
243  \\  \\
244    
# Line 262  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s} Line 248  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}
248  related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.  related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$.
249  Here the stability parameter  Here the stability parameter
250  \begin{eqnarray}  \begin{eqnarray}
251  \label{EQ:laplacian_stability_xtheta}  \label{EQ:eg-global-laplacian_stability_xtheta}
252  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
253  \end{eqnarray}  \end{eqnarray}
254  evaluates to $0.07$, well below the stabilit limit of $S_{l} \approx 0.5$. The  evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The
255  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
256  \begin{eqnarray}  \begin{eqnarray}
257  \label{EQ:laplacian_stability_ztheta}  \label{EQ:eg-global-laplacian_stability_ztheta}
258  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
259  \end{eqnarray}  \end{eqnarray}
260  evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit  evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit
# Line 276  of $S_{l} \approx 0.5$. Line 262  of $S_{l} \approx 0.5$.
262  \\  \\
263    
264  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
265  \cite{Adcroft_thesis}  \cite{adcroft:95}
266    
267  \begin{eqnarray}  \begin{eqnarray}
268  \label{EQ:inertial_stability}  \label{EQ:eg-global-inertial_stability}
269  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
270  \end{eqnarray}  \end{eqnarray}
271    
# Line 287  S_{i} = f^{2} {\delta t_v}^2 Line 273  S_{i} = f^{2} {\delta t_v}^2
273  the $S_{i} < 1$ upper limit for stability.  the $S_{i} < 1$ upper limit for stability.
274  \\  \\
275    
276  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
277  horizontal flow  horizontal flow
278  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
279    
280  \begin{eqnarray}  \begin{eqnarray}
281  \label{EQ:cfl_stability}  \label{EQ:eg-global-cfl_stability}
282  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
283  \end{eqnarray}  \end{eqnarray}
284    
# Line 300  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ Line 286  S_{a} = \frac{| \vec{u} | \delta t_{v}}{
286  limit of 0.5.  limit of 0.5.
287  \\  \\
288    
289  \noindent The stability parameter for internal gravity waves propogating  \noindent The stability parameter for internal gravity waves propagating
290  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
291  \cite{Adcroft_thesis}  \cite{adcroft:95}
292    
293  \begin{eqnarray}  \begin{eqnarray}
294  \label{EQ:cfl_stability}  \label{EQ:eg-global-gfl_stability}
295  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
296  \end{eqnarray}  \end{eqnarray}
297    
# Line 313  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt Line 299  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delt
299  stability limit of 0.5.  stability limit of 0.5.
300        
301  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
302  \label{SEC:clim_ocn_examp_exp_config}  \label{SEC:eg-global-clim_ocn_examp_exp_config}
303    
304  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
305  directory {\it verification/exp2/}.  The experiment files  directory {\it tutorial\_examples/global\_ocean\_circulation/}.  
306    The experiment files
307    
308  \begin{itemize}  \begin{itemize}
309  \item {\it input/data}  \item {\it input/data}
310  \item {\it input/data.pkg}  \item {\it input/data.pkg}
# Line 332  directory {\it verification/exp2/}.  The Line 320  directory {\it verification/exp2/}.  The
320  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
321  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
322  \end{itemize}  \end{itemize}
323  contain the code customisations and parameter settings for these  contain the code customizations and parameter settings for these
324  experiements. Below we describe the customisations  experiments. Below we describe the customizations
325  to these files associated with this experiment.  to these files associated with this experiment.
326    
327    \subsubsection{Driving Datasets}
328    
329    Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the
330    relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields,
331    the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
332    and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
333    in equations \ref{EQ:global_forcing_fu}-\ref{EQ:global_forcing_fs}. The figures
334    also indicate the lateral extent and coastline used in the experiment.
335    Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model
336    domain.
337    
338    
339  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
340    
341  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
# Line 361  with respect to the reference values set Line 361  with respect to the reference values set
361    
362  \item Line 15,  \item Line 15,
363  \begin{verbatim} viscAz=1.E-3, \end{verbatim}  \begin{verbatim} viscAz=1.E-3, \end{verbatim}
364  this line sets the vertical laplacian dissipation coefficient to  this line sets the vertical Laplacian dissipation coefficient to
365  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions
366  for this operator are specified later. This variable is copied into  for this operator are specified later. This variable is copied into
367  model general vertical coordinate variable {\bf viscAr}.  model general vertical coordinate variable {\bf viscAr}.
# Line 376  model general vertical coordinate variab Line 376  model general vertical coordinate variab
376  \begin{verbatim}  \begin{verbatim}
377  viscAh=5.E5,  viscAh=5.E5,
378  \end{verbatim}  \end{verbatim}
379  this line sets the horizontal laplacian frictional dissipation coefficient to  this line sets the horizontal Laplacian frictional dissipation coefficient to
380  $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions  $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions
381  for this operator are specified later.  for this operator are specified later.
382    
# Line 385  for this operator are specified later. Line 385  for this operator are specified later.
385  no_slip_sides=.FALSE.  no_slip_sides=.FALSE.
386  \end{verbatim}  \end{verbatim}
387  this line selects a free-slip lateral boundary condition for  this line selects a free-slip lateral boundary condition for
388  the horizontal laplacian friction operator  the horizontal Laplacian friction operator
389  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
390  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
391    
# Line 394  $\frac{\partial v}{\partial x}$=0 along Line 394  $\frac{\partial v}{\partial x}$=0 along
394  no_slip_bottom=.TRUE.  no_slip_bottom=.TRUE.
395  \end{verbatim}  \end{verbatim}
396  this line selects a no-slip boundary condition for bottom  this line selects a no-slip boundary condition for bottom
397  boundary condition in the vertical laplacian friction operator  boundary condition in the vertical Laplacian friction operator
398  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
399    
400  \item Line 19,  \item Line 19,
# Line 444  These settings do not apply for this exp Line 444  These settings do not apply for this exp
444  \begin{verbatim}  \begin{verbatim}
445  gravity=9.81,  gravity=9.81,
446  \end{verbatim}  \end{verbatim}
447  Sets the gravitational acceleration coeeficient to $9.81{\rm m}{\rm s}^{-1}$.\\  Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\
448  \fbox{  \fbox{
449  \begin{minipage}{5.0in}  \begin{minipage}{5.0in}
450  {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\  {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\
# Line 704  coriolis variables {\bf fCorU}. Line 704  coriolis variables {\bf fCorU}.
704  \item {\it input/windx.sin\_y},  \item {\it input/windx.sin\_y},
705  \end{itemize}  \end{itemize}
706  contain the code customisations and parameter settings for this  contain the code customisations and parameter settings for this
707  experiements. Below we describe the customisations  experiments. Below we describe the customisations
708  to these files associated with this experiment.  to these files associated with this experiment.
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