/[MITgcm]/manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex
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revision 1.2 by cnh, Mon Oct 22 11:55:48 2001 UTC revision 1.3 by cnh, Thu Oct 25 18:36:55 2001 UTC
# Line 7  Line 7 
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 19  Line 19 
19  \subsection{Introduction}  \subsection{Introduction}
20    
21  This document describes the third example MITgcm experiment. The first  This document describes the third example MITgcm experiment. The first
22  two examples illustrated how to configure the code for hydrostatic idealised  two examples illustrated how to configure the code for hydrostatic idealized
23  geophysical fluids simulations. This example iilustrates the use of  geophysical fluids simulations. This example illustrates the use of
24  the MITgcm for large scale ocean circulation simulation.  the MITgcm for large scale ocean circulation simulation.
25    
26  \subsection{Overview}  \subsection{Overview}
# Line 37  can be integrated forward for thousands Line 37  can be integrated forward for thousands
37  processor desktop computer.  processor desktop computer.
38  \\  \\
39    
40  The model is forced with climatalogical wind stress data and surface  The model is forced with climatological wind stress data and surface
41  flux data from DaSilva \cite{DaSilva94}. Climatalogical data  flux data from DaSilva \cite{DaSilva94}. Climatological data
42  from Levitus \cite{Levitus94} is used to initialise the model hydrography.  from Levitus \cite{Levitus94} is used to initialize the model hydrography.
43  Levitus seasonal clmatology data is also used throughout the calculation  Levitus seasonal climatology data is also used throughout the calculation
44  to provide additional air-sea fluxes.  to provide additional air-sea fluxes.
45  These fluxes are combined with the DaSilva climatalogical estimates of  These fluxes are combined with the DaSilva climatological estimates of
46  surface heat flux and fresh water, resulting in a mixed boundary  surface heat flux and fresh water, resulting in a mixed boundary
47  condition of the style decribed in Haney \cite{Haney}.  condition of the style described in Haney \cite{Haney}.
48  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied
49  in the model surface layer.  in the model surface layer.
50    
# Line 109  a uniform grid spacing in latitude and l Line 109  a uniform grid spacing in latitude and l
109   $\Delta \phi=\Delta \lambda=4^{\circ}$, so   $\Delta \phi=\Delta \lambda=4^{\circ}$, so
110  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
111  meridional direction. The internal model coordinate variables  meridional direction. The internal model coordinate variables
112  $x$ and $y$ are initialised according to  $x$ and $y$ are initialized according to
113  \begin{eqnarray}  \begin{eqnarray}
114  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
115  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta x &= &r\Delta \lambda
# Line 148  $ Line 148  $
148   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
149  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
150  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
151  \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  \cite{Marshall97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
152  dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
153    
154  Wind-stress forcing is added to the momentum equations for both  Wind-stress forcing is added to the momentum equations for both
155  the zonal flow, $u$ and the merdional flow $v$, according to equations  the zonal flow, $u$ and the meridional flow $v$, according to equations
156  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).
157  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations for
158  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
# Line 218  elevation $\eta$ and the hydrostatic pre Line 218  elevation $\eta$ and the hydrostatic pre
218    
219  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
220    
221  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 $5 \times 10^5 m s^{-1}$.
222  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_thesis},
223  \begin{eqnarray}  \begin{eqnarray}
224  \label{EQ:munk_layer}  \label{EQ:munk_layer}
# Line 233  boundary layer is adequately resolved. Line 233  boundary layer is adequately resolved.
233  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
234  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and
235  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability
236  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{Adcroft_thesis}
237  \begin{eqnarray}  \begin{eqnarray}
238  \label{EQ:laplacian_stability}  \label{EQ:laplacian_stability}
239  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
# Line 252  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\De Line 252  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\De
252  \end{eqnarray}  \end{eqnarray}
253    
254  \noindent evaluates to $0.015$ for the smallest model  \noindent evaluates to $0.015$ for the smallest model
255  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
256  the upper stability limit.  the upper stability limit.
257  \\  \\
258    
# Line 265  Here the stability parameter Line 265  Here the stability parameter
265  \label{EQ:laplacian_stability_xtheta}  \label{EQ:laplacian_stability_xtheta}
266  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
267  \end{eqnarray}  \end{eqnarray}
268  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
269  stability parameter related to $K_{z}$  stability parameter related to $K_{z}$
270  \begin{eqnarray}  \begin{eqnarray}
271  \label{EQ:laplacian_stability_ztheta}  \label{EQ:laplacian_stability_ztheta}
# Line 300  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ Line 300  S_{a} = \frac{| \vec{u} | \delta t_{v}}{
300  limit of 0.5.  limit of 0.5.
301  \\  \\
302    
303  \noindent The stability parameter for internal gravity waves propogating  \noindent The stability parameter for internal gravity waves propagating
304  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
305  \cite{Adcroft_thesis}  \cite{Adcroft_thesis}
306    
# Line 332  directory {\it verification/exp2/}.  The Line 332  directory {\it verification/exp2/}.  The
332  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
333  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
334  \end{itemize}  \end{itemize}
335  contain the code customisations and parameter settings for these  contain the code customizations and parameter settings for these
336  experiements. Below we describe the customisations  experiments. Below we describe the customizations
337  to these files associated with this experiment.  to these files associated with this experiment.
338    
339  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
# 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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