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revision 1.3 by cnh, Thu Oct 25 18:36:55 2001 UTC revision 1.8 by cnh, Thu Feb 28 19:32:19 2002 UTC
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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    
# 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 idealized  
 geophysical fluids simulations. This example illustrates 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 climatological wind stress data and surface  The model is forced with climatological wind stress data and surface
34  flux data from DaSilva \cite{DaSilva94}. Climatological data  flux data from DaSilva \cite{DaSilva94}. Climatological data
# Line 49  Altogether, this yields the following fo Line 42  Altogether, this yields the following fo
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 112  meridional direction. The internal model Line 96  meridional direction. The internal model
96  $x$ and $y$ are initialized 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 meridional 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 219  elevation $\eta$ and the hydrostatic pre Line 205  elevation $\eta$ and the hydrostatic pre
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    
# 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 stability 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 302  limit of 0.5. Line 288  limit of 0.5.
288    
289  \noindent The stability parameter for internal gravity waves propagating  \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 336  contain the code customizations and para Line 324  contain the code customizations and para
324  experiments. Below we describe the customizations  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
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