/[MITgcm]/manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex
ViewVC logotype

Diff of /manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.21 by jmc, Thu Apr 21 21:27:16 2011 UTC revision 1.24 by jmc, Wed May 15 22:47:12 2013 UTC
# Line 13  Line 13 
13    
14  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
15    
16  \noindent {\bf WARNING: the description of this experiment is not up-to-date.  \noindent {\bf WARNING: the description of this experiment is not complete.
17   In particular, most of the parameters description corresponds to an older   In particular, many parameters are not yet described.}\\
  version of {\it verification/exp2} instead of the current tutorial}\\  
18    
19  %\begin{center}  %\begin{center}
20  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation  %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation
21  %At Four Degree Resolution with Asynchronous Time Stepping}  %At Four Degree Resolution with Asynchronous Time Stepping}
22  %  %
# Line 27  Line 26 
26  %{\large May 2001}  %{\large May 2001}
27  %\end{center}  %\end{center}
28    
29    This example experiment demonstrates using the MITgcm to simulate the
30  This example experiment demonstrates using the MITgcm to simulate  planetary ocean circulation. The simulation is configured with
31  the planetary ocean circulation. The simulation is configured  realistic geography and bathymetry on a $4^{\circ} \times 4^{\circ}$
32  with realistic geography and bathymetry on a  spherical polar grid. The files for this experiment are in the
33  $4^{\circ} \times 4^{\circ}$ spherical polar grid.  verification directory under tutorial\_global\_oce\_latlon. Fifteen
34  The files for this experiment are in the verification directory  levels are used in the vertical, ranging in thickness from $50\,{\rm
35  under tutorial\_global\_oce\_latlon.    m}$ at the surface to $690\,{\rm m}$ at depth, giving a maximum
36  Twenty levels are used in the vertical, ranging in thickness  model depth of $5200\,{\rm m}$.
37  from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,  Different time-steps are used to accelerate the convergence to
38  giving a maximum model depth of $6\,{\rm km}$.  equilibrium \cite[]{bryan:84} so that, at this resolution,
39  At this resolution, the configuration  the configuration can be integrated forward for thousands of years
40  can be integrated forward for thousands of years on a single  on a single processor desktop computer.
 processor desktop computer.  
41  \\  \\
42  \subsection{Overview}  \subsection{Overview}
43  %\label{www:tutorials}  %\label{www:tutorials}
44    
45  The model is forced with climatological wind stress data and surface  The model is forced with climatological wind stress data from
46  flux data from DaSilva \cite{DaSilva94}. Climatological data  \citet{trenberth90} and NCEP surface flux data from
47  from Levitus \cite{Levitus94} is used to initialize the model hydrography.  \citet{kalnay96}. Climatological data \citep{Levitus94} is
48  Levitus seasonal climatology data is also used throughout the calculation  used to initialize the model hydrography. \citeauthor{Levitus94} seasonal
49  to provide additional air-sea fluxes.  climatology data is also used throughout the calculation to provide
50  These fluxes are combined with the DaSilva climatological estimates of  additional air-sea fluxes.  These fluxes are combined with the NCEP
51  surface heat flux and fresh water, resulting in a mixed boundary  climatological estimates of surface heat flux, resulting in a mixed
52  condition of the style described in Haney \cite{Haney}.  boundary condition of the style described in \citet{Haney}.
53  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied in the model
54  in the model surface layer.  surface layer.
55    
56  \begin{eqnarray}  \begin{eqnarray}
57  \label{eq:eg-global-global_forcing}  \label{eq:eg-global-global_forcing}
# Line 64  in the model surface layer. Line 62  in the model surface layer.
62  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
63  \\  \\
64  \label{eq:eg-global-global_forcing_ft}  \label{eq:eg-global-global_forcing_ft}
65  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
66   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
67  \\  \\
68  \label{eq:eg-global-global_forcing_fs}  \label{eq:eg-global-global_forcing_fs}
69  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
70   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
71  \end{eqnarray}  \end{eqnarray}
72    
# Line 92  experiment are $\tau_{x}$, $\tau_{y}$, $ Line 90  experiment are $\tau_{x}$, $\tau_{y}$, $
90  $\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$)  $\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$)
91  have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields  have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields
92  ($\theta^{\ast}$ 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 ${\rm W}~{\rm m}^{-2}$
93  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
94  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
95  respectively. The source files and procedures for ingesting this data into the  respectively. The source files and procedures for ingesting this data into the
96  simulation are described in the experiment configuration discussion in section  simulation are described in the experiment configuration discussion in section
# Line 103  simulation are described in the experime Line 101  simulation are described in the experime
101  %\label{www:tutorials}  %\label{www:tutorials}
102    
103    
104   The model is configured in hydrostatic form.  The domain is discretised with  The model is configured in hydrostatic form.  The domain is
105  a uniform grid spacing in latitude and longitude on the sphere  discretised with a uniform grid spacing in latitude and longitude on
106   $\Delta \phi=\Delta \lambda=4^{\circ}$, so  the sphere $\Delta \phi=\Delta \lambda=4^{\circ}$, so that there are
107  that there are ninety grid cells in the zonal and forty in the  ninety grid cells in the zonal and forty in the meridional
108  meridional direction. The internal model coordinate variables  direction. The internal model coordinate variables $x$ and $y$ are
109  $x$ and $y$ are initialized according to  initialized according to
110  \begin{eqnarray}  \begin{eqnarray}
111  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
112  y=r\lambda,~\Delta y &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
113  \end{eqnarray}  \end{eqnarray}
114    
115  Arctic polar regions are not  Arctic polar regions are not
116  included in this experiment. Meridionally the model extends from  included in this experiment. Meridionally the model extends from
117  $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.  $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
118  Vertically the model is configured with twenty layers with the  Vertically the model is configured with fifteen layers with the
119  following thicknesses  following thicknesses:
120  $\Delta z_{1} = 50\,{\rm m},\,  $\Delta z_{1} = 50\,{\rm m},$\\
121   \Delta z_{2} = 50\,{\rm m},\,  $\Delta z_{2} = 70\,{\rm m},\,
122   \Delta z_{3} = 55\,{\rm m},\,   \Delta z_{3} = 100\,{\rm m},\,
123   \Delta z_{4} = 60\,{\rm m},\,   \Delta z_{4} = 140\,{\rm m},\,
124   \Delta z_{5} = 65\,{\rm m},\,   \Delta z_{5} = 190\,{\rm m},\,
125  $   \Delta z_{6} = 240\,{\rm m},\,
126  $   \Delta z_{7} = 290\,{\rm m},\,
127   \Delta z_{6}~=~70\,{\rm m},\,   \Delta z_{8} = 340\,{\rm m},$\\
128   \Delta z_{7}~=~80\,{\rm m},\,  $\Delta z_{9} = 390\,{\rm m},\,
129   \Delta z_{8}~=95\,{\rm m},\,   \Delta z_{10}= 440\,{\rm m},\,
130   \Delta z_{9}=120\,{\rm m},\,   \Delta z_{11}= 490\,{\rm m},\,
131   \Delta z_{10}=155\,{\rm m},\,   \Delta z_{12}= 540\,{\rm m},\,
132  $   \Delta z_{13}= 590\,{\rm m},\,
133  $   \Delta z_{14}= 640\,{\rm m},\,
134   \Delta z_{11}=200\,{\rm m},\,   \Delta z_{15}= 690\,{\rm m}$\\
135   \Delta z_{12}=260\,{\rm m},\,  (here the numeric subscript indicates the model level index number, ${\tt k}$) to
136   \Delta z_{13}=320\,{\rm m},\,  give a total depth, $H$, of $-5200{\rm m}$.
137   \Delta z_{14}=400\,{\rm m},\,  The implicit free surface form of the pressure equation described in
138   \Delta z_{15}=480\,{\rm m},\,  \citet{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
 $  
 $  
  \Delta z_{16}=570\,{\rm m},\,  
  \Delta z_{17}=655\,{\rm m},\,  
  \Delta z_{18}=725\,{\rm m},\,  
  \Delta z_{19}=775\,{\rm m},\,  
  \Delta z_{20}=815\,{\rm m}  
 $ (here the numeric subscript indicates the model level index number, ${\tt k}$) to  
 give a total depth, $H$, of $-5450{\rm m}$.  
 The implicit free surface form of the pressure equation described in Marshall et. al  
 \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous  
139  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
140    
141  Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations})  Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations})
142  for both 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
143  (\ref{eq:eg-global-global_forcing_fu}) and (\ref{eq:eg-global-global_forcing_fv}).  (\ref{eq:eg-global-global_forcing_fu}) and (\ref{eq:eg-global-global_forcing_fv}).
144  Thermodynamic forcing inputs are added to the equations  Thermodynamic forcing inputs are added to the equations
145  in (\ref{eq:eg-global-model_equations}) for  in (\ref{eq:eg-global-model_equations}) for
146  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
147  (\ref{eq:eg-global-global_forcing_ft}) and (\ref{eq:eg-global-global_forcing_fs}).  (\ref{eq:eg-global-global_forcing_ft}) and (\ref{eq:eg-global-global_forcing_fs}).
148  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
149    
150  \begin{eqnarray}  \begin{eqnarray}
151  \label{eq:eg-global-model_equations}  \label{eq:eg-global-model_equations}
152  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
153    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
154    \nabla_{h}\cdot A_{h}\nabla_{h}u -    \nabla_{h}\cdot A_{h}\nabla_{h}u -
155    \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}    \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z}
156   & = &   & = &
157  \begin{cases}  \begin{cases}
158  {\cal F}_u & \text{(surface)} \\  {\cal F}_u & \text{(surface)} \\
159  0 & \text{(interior)}  0 & \text{(interior)}
160  \end{cases}  \end{cases}
161  \\  \\
162  \frac{Dv}{Dt} + fu +  \frac{Dv}{Dt} + fu +
163    \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} -
164    \nabla_{h}\cdot A_{h}\nabla_{h}v -    \nabla_{h}\cdot A_{h}\nabla_{h}v -
165    \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}    \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z}
166  & = &  & = &
167  \begin{cases}  \begin{cases}
168  {\cal F}_v & \text{(surface)} \\  {\cal F}_v & \text{(surface)} \\
# Line 188  This produces a set of equations solved Line 175  This produces a set of equations solved
175  \\  \\
176  \frac{D\theta}{Dt} -  \frac{D\theta}{Dt} -
177   \nabla_{h}\cdot K_{h}\nabla_{h}\theta   \nabla_{h}\cdot K_{h}\nabla_{h}\theta
178   - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}   - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z}
179  & = &  & = &
180  \begin{cases}  \begin{cases}
181  {\cal F}_\theta & \text{(surface)} \\  {\cal F}_\theta & \text{(surface)} \\
# Line 197  This produces a set of equations solved Line 184  This produces a set of equations solved
184  \\  \\
185  \frac{D s}{Dt} -  \frac{D s}{Dt} -
186   \nabla_{h}\cdot K_{h}\nabla_{h}s   \nabla_{h}\cdot K_{h}\nabla_{h}s
187   - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}   - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z}
188  & = &  & = &
189  \begin{cases}  \begin{cases}
190  {\cal F}_s & \text{(surface)} \\  {\cal F}_s & \text{(surface)} \\
# Line 207  This produces a set of equations solved Line 194  This produces a set of equations solved
194  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'}
195  \end{eqnarray}  \end{eqnarray}
196    
197  \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and  \noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and
198  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
199  are the zonal and meridional components of the  are the zonal and meridional components of the
200  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
201  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
202  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
203  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
204  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
205  \\  \\
206    
# Line 221  elevation $\eta$ and the hydrostatic pre Line 208  elevation $\eta$ and the hydrostatic pre
208  %\label{www:tutorials}  %\label{www:tutorials}
209    
210  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 $5 \times 10^5 m s^{-1}$.
211  This value is chosen to yield a Munk layer width \cite{adcroft:95},  This value is chosen to yield a Munk layer width \citep{adcroft:95},
212  \begin{eqnarray}  \begin{eqnarray}
213  \label{eq:eg-global-munk_layer}  \label{eq:eg-global-munk_layer}
214  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
215  \end{eqnarray}  \end{eqnarray}
216    
217  \noindent  of $\approx 600$km. This is greater than the model  \noindent  of $\approx 600$km. This is greater than the model
218  resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional  resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional
219  boundary layer is adequately resolved.  boundary layer is adequately resolved.
220  \\  \\
221    
222  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a time step $\Delta
223  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  t_{\theta}=24~{\rm hours}$ for thermodynamic variables and $\Delta
224  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  t_{v}=30~{\rm minutes}$ for momentum terms. With this time step,
225  parameter to the horizontal Laplacian friction \cite{adcroft:95}  the stability parameter to the horizontal Laplacian friction
226    \citep{adcroft:95}
227  \begin{eqnarray}  \begin{eqnarray}
228  \label{eq:eg-global-laplacian_stability}  \label{eq:eg-global-laplacian_stability}
229  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \Delta t_{v}}{{\Delta x}^2}
230  \end{eqnarray}  \end{eqnarray}
231    
232  \noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the  \noindent evaluates to 0.6 at a latitude of $\phi=80^{\circ}$, which
233  0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at  is above the 0.3 upper limit for stability, but the zonal grid spacing
234  $\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.  $\Delta x$ is smallest at $\phi=80^{\circ}$ where $\Delta
235  \\  x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$ and the stability
236    criterion is already met 1 grid cell equatorwards (at $\phi=76^{\circ}$).
237    
238    
239  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
240  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
241  \begin{eqnarray}  \begin{eqnarray}
242  \label{eq:eg-global-laplacian_stability_z}  \label{eq:eg-global-laplacian_stability_z}
243  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  && S_{l} = 4 \frac{A_{z} \Delta t_{v}}{{\Delta z}^2}
244  \end{eqnarray}  \end{eqnarray}
245    
246  \noindent evaluates to $0.015$ for the smallest model  \noindent evaluates to $0.0029$ for the smallest model
247  level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below  level spacing ($\Delta z_{1}=50{\rm m}$) which is well below
248  the upper stability limit.  the upper stability limit.
249  \\  \\
250    
251  The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients  % The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients
252  for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$  % for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
253  and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit  % and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit
254  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 $\Delta x \approx 77 {\rm km}$.
255  Here the stability parameter  % Here the stability parameter
256  \begin{eqnarray}  % \begin{eqnarray}
257  \label{eq:eg-global-laplacian_stability_xtheta}  % \label{eq:eg-global-laplacian_stability_xtheta}
258  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  % S_{l} = \frac{4 K_{h} \Delta t_{\theta}}{{\Delta x}^2}
259  \end{eqnarray}  % \end{eqnarray}
260  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
261  stability parameter related to $K_{z}$  % stability parameter related to $K_{z}$
262  \begin{eqnarray}  % \begin{eqnarray}
263  \label{eq:eg-global-laplacian_stability_ztheta}  % \label{eq:eg-global-laplacian_stability_ztheta}
264  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  % S_{l} = \frac{4 K_{z} \Delta t_{\theta}}{{\Delta z}^2}
265  \end{eqnarray}  % \end{eqnarray}
266  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
267  of $S_{l} \approx 0.5$.  % of $S_{l} \approx 0.5$.
268  \\  % \\
269    
270  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
271  \cite{adcroft:95}  \citep{adcroft:95}
272    
273  \begin{eqnarray}  \begin{eqnarray}
274  \label{eq:eg-global-inertial_stability}  \label{eq:eg-global-inertial_stability}
275  S_{i} = f^{2} {\delta t_v}^2  && S_{i} = f^{2} {\Delta t_v}^2
276  \end{eqnarray}  \end{eqnarray}
277    
278  \noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to  \noindent evaluates to $0.07$ for
279  the $S_{i} < 1$ upper limit for stability.  $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is
280    below the $S_{i} < 1$ upper limit for stability.
281  \\  \\
282    
283  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum  \noindent The advective CFL \citep{adcroft:95} for a extreme maximum
284  horizontal flow  horizontal flow
285  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
286    
287  \begin{eqnarray}  \begin{eqnarray}
288  \label{eq:eg-global-cfl_stability}  \label{eq:eg-global-cfl_stability}
289  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  && S_{a} = \frac{| \vec{u} | \Delta t_{v}}{ \Delta x}
290  \end{eqnarray}  \end{eqnarray}
291    
292  \noindent evaluates to $6 \times 10^{-2}$. This is well below the stability  \noindent evaluates to $5 \times 10^{-2}$. This is well below the stability
293  limit of 0.5.  limit of 0.5.
294  \\  \\
295    
296  \noindent The stability parameter for internal gravity waves propagating  \noindent The stability parameter for internal gravity waves propagating
297  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$   with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
298  \cite{adcroft:95}  \citep{adcroft:95}
299    
300  \begin{eqnarray}  \begin{eqnarray}
301  \label{eq:eg-global-gfl_stability}  \label{eq:eg-global-gfl_stability}
302  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  && S_{c} = \frac{c_{g} \Delta t_{v}}{ \Delta x}
303  \end{eqnarray}  \end{eqnarray}
304    
305  \noindent evaluates to $3 \times 10^{-1}$. This is close to the linear  \noindent evaluates to $2.3 \times 10^{-1}$. This is close to the linear
306  stability limit of 0.5.  stability limit of 0.5.
307      
308  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
309  %\label{www:tutorials}  %\label{www:tutorials}
310  \label{sec:eg-global-clim_ocn_examp_exp_config}  \label{sec:eg-global-clim_ocn_examp_exp_config}
311    
312  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
313  directory {\it tutorial\_examples/global\_ocean\_circulation/}.    directory {\it tutorial\_global\_oce\_latlon/}. The experiment files
 The experiment files  
314    
315  \begin{itemize}  \begin{itemize}
316  \item {\it input/data}  \item {\it input/data}
317  \item {\it input/data.pkg}  \item {\it input/data.pkg}
318  \item {\it input/eedata},  \item {\it input/eedata},
319  \item {\it input/windx.bin},  \item {\it input/trenberth\_taux.bin},
320  \item {\it input/windy.bin},  \item {\it input/trenberth\_tauy.bin},
321  \item {\it input/salt.bin},  \item {\it input/lev\_s.bin},
322  \item {\it input/theta.bin},  \item {\it input/lev\_t.bin},
323  \item {\it input/SSS.bin},  \item {\it input/lev\_sss.bin},
324  \item {\it input/SST.bin},  \item {\it input/lev\_sst.bin},
325  \item {\it input/topog.bin},  \item {\it input/bathymetry.bin},
326  \item {\it code/CPP\_EEOPTIONS.h}  %\item {\it code/CPP\_EEOPTIONS.h}
327  \item {\it code/CPP\_OPTIONS.h},  %\item {\it code/CPP\_OPTIONS.h},
328  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
329  \end{itemize}  \end{itemize}
330  contain the code customizations and parameter settings for these  contain the code customizations and parameter settings for these
331  experiments. Below we describe the customizations  experiments. Below we describe the customizations
# Line 344  to these files associated with this expe Line 334  to these files associated with this expe
334  \subsubsection{Driving Datasets}  \subsubsection{Driving Datasets}
335  %\label{www:tutorials}  %\label{www:tutorials}
336    
337  Figures ({\it --- missing figures ---})  %% New figures are included before
338    %% Relaxation temperature
339    %\begin{figure}
340    %\centering
341    %\includegraphics[]{relax_temperature.eps}
342    %\caption{Relaxation temperature for January}
343    %\label{fig:relax_temperature}
344    %\end{figure}
345    
346    %% Relaxation salinity
347    %\begin{figure}
348    %\centering
349    %\includegraphics[]{relax_salinity.eps}
350    %\caption{Relaxation salinity for January}
351    %\label{fig:relax_salinity}
352    %\end{figure}
353    
354    %% tau_x
355    %\begin{figure}
356    %\centering
357    %\includegraphics[]{tau_x.eps}
358    %\caption{zonal wind stress for January}
359    %\label{fig:tau_x}
360    %\end{figure}
361    
362    %% tau_y
363    %\begin{figure}
364    %\centering
365    %\includegraphics[]{tau_y.eps}
366    %\caption{meridional wind stress for January}
367    %\label{fig:tau_y}
368    %\end{figure}
369    
370    %% Qnet
371    %\begin{figure}
372    %\centering
373    %\includegraphics[]{qnet.eps}
374    %\caption{Heat flux for January}
375    %\label{fig:qnet}
376    %\end{figure}
377    
378    %% EmPmR
379    %\begin{figure}
380    %\centering
381    %\includegraphics[]{empmr.eps}
382    %\caption{Fresh water flux for January}
383    %\label{fig:empmr}
384    %\end{figure}
385    
386    %% Bathymetry
387    %\begin{figure}
388    %\centering
389    %\includegraphics[]{bathymetry.eps}
390    %\caption{Bathymetry}
391    %\label{fig:bathymetry}
392    %\end{figure}
393    
394    
395    Figures (\ref{fig:sim_config_tclim_pcoord}-\ref{fig:sim_config_empmr_pcoord})
396  %(\ref{fig:sim_config_tclim}-\ref{fig:sim_config_empmr})  %(\ref{fig:sim_config_tclim}-\ref{fig:sim_config_empmr})
397  show the relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$)  show the relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$)
398  fields, the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)  fields, the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
399  and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used  and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
400  in equations  in equations
401  (\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}).  (\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}).
402  The figures also indicate the lateral extent and coastline used in the  The figures also indicate the lateral extent and coastline used in the
403  experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})  experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})
404  shows the depth contours of the model domain.  shows the depth contours of the model domain.
405    
406  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
# Line 372  customisations for this experiment. Line 420  customisations for this experiment.
420  This file uses standard default values and does not contain  This file uses standard default values and does not contain
421  customisations for this experiment.  customisations for this experiment.
422    
423  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{Files{\it input/trenberth\_taux.bin} and {\it
424      input/trenberth\_tauy.bin}}
425  %\label{www:tutorials}  %\label{www:tutorials}
426    
427  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/trenberth\_taux.bin} and {\it
428  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.    input/trenberth\_tauy.bin} files specify a three-dimensional
429  Although $\tau_{x}$ is only a function of $y$n in this experiment  ($x,y,time$) map of wind stress, $(\tau_{x},\tau_{y})$, values
430  this file must still define a complete two-dimensional map in order  \citep{trenberth90}. The units used are $Nm^{-2}$.
 to be compatible with the standard code for loading forcing fields  
 in MITgcm. The included matlab program {\it input/gendata.m} gives a complete  
 code for creating the {\it input/windx.sin\_y} file.  
431    
432  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/bathymetry.bin}}
433  %\label{www:tutorials}  %\label{www:tutorials}
434    
435    
436  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
437  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
438  $0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep  $0m$ or $-5200\,{\rm m}$, corresponding respectively to a wall or to deep
439  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
440  in the same way as standard MITgcm two-dimensional, horizontal arrays.  in the same way as standard MITgcm two-dimensional, horizontal arrays.
441  The included matlab program {\it input/gendata.m} gives a complete  The included matlab program {\it input/gendata.m} gives a complete
# Line 398  code for creating the {\it input/topog.b Line 444  code for creating the {\it input/topog.b
444  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
445  %\label{www:tutorials}  %\label{www:tutorials}
446    
447  Two lines are customized in this file for the current experiment  \input{s_examples/global_oce_latlon/cod_SIZE.h}
   
 \begin{itemize}  
   
 \item Line 39,  
 \begin{verbatim} sNx=60, \end{verbatim} this line sets  
 the lateral domain extent in grid points for the  
 axis aligned with the x-coordinate.  
   
 \item Line 40,  
 \begin{verbatim} sNy=60, \end{verbatim} this line sets  
 the lateral domain extent in grid points for the  
 axis aligned with the y-coordinate.  
   
 \item Line 49,  
 \begin{verbatim} Nr=4,   \end{verbatim} this line sets  
 the vertical domain extent in grid points.  
   
 \end{itemize}  
   
 \begin{small}  
 \input{s_examples/global_oce_latlon/code/SIZE.h}  
 \end{small}  
448    
449  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  %\subsubsection{File {\it code/CPP\_OPTIONS.h}}
450  %\label{www:tutorials}  %\label{www:tutorials}
451    
452  This file uses standard default values and does not contain  %This file uses standard default values and does not contain
453  customisations for this experiment.  %customisations for this experiment.
454    
455    
456  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  %\subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
457  %\label{www:tutorials}  %\label{www:tutorials}
458    
459  This file uses standard default values and does not contain  %This file uses standard default values and does not contain
460  customisations for this experiment.  %customisations for this experiment.
461    
462  \subsubsection{Other Files }  \subsubsection{Other Files }
463  %\label{www:tutorials}  %\label{www:tutorials}
464    
465  Other files relevant to this experiment are  % Other files relevant to this experiment are
466  \begin{itemize}  % \begin{itemize}
467  \item {\it model/src/ini\_cori.F}. This file initializes the model  % \item {\it model/src/ini\_cori.F}. This file initializes the model
468  coriolis variables {\bf fCorU}.  % coriolis variables {\bf fCorU}.
469  \item {\it model/src/ini\_spherical\_polar\_grid.F}  % \item {\it model/src/ini\_spherical\_polar\_grid.F}
470  \item {\it model/src/ini\_parms.F},  % \item {\it model/src/ini\_parms.F},
471  \item {\it input/windx.sin\_y},  % \item {\it input/windx.sin\_y},
472  \end{itemize}  % \end{itemize}
473  contain the code customisations and parameter settings for this  % contain the code customisations and parameter settings for this
474  experiments. Below we describe the customisations  % experiments. Below we describe the customisations
475  to these files associated with this experiment.  % to these files associated with this experiment.

Legend:
Removed from v.1.21  
changed lines
  Added in v.1.24

  ViewVC Help
Powered by ViewVC 1.1.22