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revision 1.2 by cnh, Mon Oct 22 11:55:48 2001 UTC revision 1.22 by mlosch, Mon May 2 10:46:28 2011 UTC
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1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: 4$^\circ$ Global Climatological Ocean Simulation}  \section[Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution}
5    %\label{www:tutorials}
6  \label{sec:eg-global}  \label{sec:eg-global}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-global: -->
9    \end{rawhtml}
10    \begin{center}
11    (in directory: {\it verification/tutorial\_global\_oce\_latlon/})
12    \end{center}
13    
14  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
15    
16    \noindent {\bf WARNING: the description of this experiment is not complete.
17     In particular, many parameters are not yet described.}\\
18    
19  %\begin{center}  %\begin{center}
20  %{\Large \bf Using MITgcm to Simulate Global Climatalogical 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  %  %
23  %\vspace*{4mm}  %\vspace*{4mm}
# Line 16  Line 26 
26  %{\large May 2001}  %{\large May 2001}
27  %\end{center}  %\end{center}
28    
 \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.  
29    
30    This example experiment demonstrates using the MITgcm to simulate the
31    planetary ocean circulation. The simulation is configured with
32    realistic geography and bathymetry on a $4^{\circ} \times 4^{\circ}$
33    spherical polar grid. The files for this experiment are in the
34    verification directory under tutorial\_global\_oce\_latlon. Fifteen
35    levels are used in the vertical, ranging in thickness from $50\,{\rm
36      m}$ at the surface to $690\,{\rm m}$ at depth, giving a maximum
37    model depth of $5200\,{\rm m}$.  At this resolution, the configuration
38    can be integrated forward for thousands of years on a single processor
39    desktop computer.
40    \\
41  \subsection{Overview}  \subsection{Overview}
42    %\label{www:tutorials}
43    
44  This example experiment demonstrates using the MITgcm to simulate  The model is forced with climatological wind stress data from
45  the planetary ocean circulation. The simulation is configured  \citet{trenberth90} and NCEP surface flux data from
46  with realistic geography and bathymetry on a  \citet{kalnay96}. Climatological data \citep{Levitus94} is
47  $4^{\circ} \times 4^{\circ}$ spherical polar grid.  used to initialize the model hydrography. \citeauthor{Levitus94} seasonal
48  Twenty levels are used in the vertical, ranging in thickness  climatology data is also used throughout the calculation to provide
49  from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth,  additional air-sea fluxes.  These fluxes are combined with the NCEP
50  giving a maximum model depth of $6\,{\rm km}$.  climatological estimates of surface heat flux, resulting in a mixed
51  At this resolution, the configuration  boundary condition of the style described in \citet{Haney}.
52  can be integrated forward for thousands of years on a single  Altogether, this yields the following forcing applied in the model
53  processor desktop computer.  surface layer.
 \\  
   
 The model is forced with climatalogical wind stress data and surface  
 flux data from DaSilva \cite{DaSilva94}. Climatalogical data  
 from Levitus \cite{Levitus94} is used to initialise the model hydrography.  
 Levitus seasonal clmatology data is also used throughout the calculation  
 to provide additional air-sea fluxes.  
 These fluxes are combined with the DaSilva climatalogical estimates of  
 surface heat flux and fresh water, resulting in a mixed boundary  
 condition of the style decribed in Haney \cite{Haney}.  
 Altogether, this yields the following forcing applied  
 in the model surface layer.  
54    
55  \begin{eqnarray}  \begin{eqnarray}
56  \label{EQ:global_forcing}  \label{eq:eg-global-global_forcing}
57  \label{EQ:global_forcing_fu}  \label{eq:eg-global-global_forcing_fu}
58  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
59  \\  \\
60  \label{EQ:global_forcing_fv}  \label{eq:eg-global-global_forcing_fv}
61  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
62  \\  \\
63  \label{EQ:global_forcing_ft}  \label{eq:eg-global-global_forcing_ft}
64  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
65   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
66  \\  \\
67  \label{EQ:global_forcing_fs}  \label{eq:eg-global-global_forcing_fs}
68  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
69   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
70  \end{eqnarray}  \end{eqnarray}
# Line 87  have units of ${\rm N}~{\rm m}^{-2}$. Th Line 91  have units of ${\rm N}~{\rm m}^{-2}$. Th
91  ($\theta^{\ast}$ 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 ${\rm W}~{\rm m}^{-2}$
92  respectively. The salinity forcing fields ($S^{\ast}$ and  respectively. The salinity forcing fields ($S^{\ast}$ and
93  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$  $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$
94  respectively.  respectively. The source files and procedures for ingesting this data into the
95  \\  simulation are described in the experiment configuration discussion in section
96    \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.  
97    
98    
99  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
100    %\label{www:tutorials}
101    
102    
103   The model is configured in hydrostatic form.  The domain is discretised with  The model is configured in hydrostatic form.  The domain is
104  a uniform grid spacing in latitude and longitude on the sphere  discretised with a uniform grid spacing in latitude and longitude on
105   $\Delta \phi=\Delta \lambda=4^{\circ}$, so  the sphere $\Delta \phi=\Delta \lambda=4^{\circ}$, so that there are
106  that there are ninety grid cells in the zonal and forty in the  ninety grid cells in the zonal and forty in the meridional
107  meridional direction. The internal model coordinate variables  direction. The internal model coordinate variables $x$ and $y$ are
108  $x$ and $y$ are initialised according to  initialized according to
109  \begin{eqnarray}  \begin{eqnarray}
110  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\  x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\
111  y=r\lambda,~\Delta x &= &r\Delta \lambda  y=r\lambda,~\Delta y &= &r\Delta \lambda
112  \end{eqnarray}  \end{eqnarray}
113    
114  Arctic polar regions are not  Arctic polar regions are not
115  included in this experiment. Meridionally the model extends from  included in this experiment. Meridionally the model extends from
116  $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.  $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$.
117  Vertically the model is configured with twenty layers with the  Vertically the model is configured with fifteen layers with the
118  following thicknesses  following thicknesses
119  $\Delta z_{1} = 50\,{\rm m},\,  $\Delta z_{1} = 50\,{\rm m},\,
120   \Delta z_{2} = 50\,{\rm m},\,   \Delta z_{2} = 70\,{\rm m},\,
121   \Delta z_{3} = 55\,{\rm m},\,   \Delta z_{3} = 100\,{\rm m},\,
122   \Delta z_{4} = 60\,{\rm m},\,   \Delta z_{4} = 140\,{\rm m},\,
123   \Delta z_{5} = 65\,{\rm m},\,   \Delta z_{5} = 190\,{\rm m},\,
124  $   \Delta z_{6}~=~240\,{\rm m},\,
125  $   \Delta z_{7}~=~290\,{\rm m},\,
126   \Delta z_{6}~=~70\,{\rm m},\,   \Delta z_{8}~=340\,{\rm m},\,
127   \Delta z_{7}~=~80\,{\rm m},\,   \Delta z_{9}=390\,{\rm m},\,
128   \Delta z_{8}~=95\,{\rm m},\,   \Delta z_{10}=440\,{\rm m},\,
129   \Delta z_{9}=120\,{\rm m},\,   \Delta z_{11}=490\,{\rm m},\,
130   \Delta z_{10}=155\,{\rm m},\,   \Delta z_{12}=540\,{\rm m},\,
131  $   \Delta z_{13}=590\,{\rm m},\,
132  $   \Delta z_{14}=640\,{\rm m},\,
133   \Delta z_{11}=200\,{\rm m},\,   \Delta z_{15}=690\,{\rm m}
134   \Delta z_{12}=260\,{\rm m},\,  $ (here the numeric subscript indicates the model level index number, ${\tt k}$) to
135   \Delta z_{13}=320\,{\rm m},\,  give a total depth, $H$, of $-5200{\rm m}$.
136   \Delta z_{14}=400\,{\rm m},\,  The implicit free surface form of the pressure equation described in
137   \Delta z_{15}=480\,{\rm m},\,  \citet{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
138  $  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
139  $  
140   \Delta z_{16}=570\,{\rm m},\,  Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations})
141   \Delta z_{17}=655\,{\rm m},\,  for both the zonal flow, $u$ and the meridional flow $v$, according to equations
142   \Delta z_{18}=725\,{\rm m},\,  (\ref{eq:eg-global-global_forcing_fu}) and (\ref{eq:eg-global-global_forcing_fv}).
143   \Delta z_{19}=775\,{\rm m},\,  Thermodynamic forcing inputs are added to the equations
144   \Delta z_{20}=815\,{\rm m}  in (\ref{eq:eg-global-model_equations}) for
 $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  
 The implicit free surface form of the pressure equation described in Marshall et. al  
 \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  
 dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  
   
 Wind-stress forcing is added to the momentum equations for both  
 the zonal flow, $u$ and the merdional flow $v$, according to equations  
 (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  
 Thermodynamic forcing inputs are added to the equations for  
145  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
146  (\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}).
147  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
148    
149  \begin{eqnarray}  \begin{eqnarray}
150  \label{EQ:model_equations}  \label{eq:eg-global-model_equations}
151  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
152    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
153    \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 197  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
197  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$  $v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$
198  are the zonal and meridional components of the  are the zonal and meridional components of the
199  flow vector, $\vec{u}$, on the sphere. As described in  flow vector, $\vec{u}$, on the sphere. As described in
200  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
201  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
202  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
203  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
204  \\  \\
205    
206  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
207    %\label{www:tutorials}
208    
209  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 $5 \times 10^5 m s^{-1}$.
210  This value is chosen to yield a Munk layer width \cite{Adcroft_thesis},  This value is chosen to yield a Munk layer width \citep{adcroft:95},
211  \begin{eqnarray}  \begin{eqnarray}
212  \label{EQ:munk_layer}  \label{eq:eg-global-munk_layer}
213  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
214  \end{eqnarray}  \end{eqnarray}
215    
216  \noindent  of $\approx 600$km. This is greater than the model  \noindent  of $\approx 600$km. This is greater than the model
# Line 230  resolution in low-latitudes, $\Delta x \ Line 218  resolution in low-latitudes, $\Delta x \
218  boundary layer is adequately resolved.  boundary layer is adequately resolved.
219  \\  \\
220    
221  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a time step $\delta
222  time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and  t_{\theta}=24~{\rm hours}$ for thermodynamic variables and $\delta
223  $\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability  t_{v}=30~{\rm minutes}$ for momentum terms. With this time step, the
224  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  stability parameter to the horizontal Laplacian friction
225    \citep{adcroft:95}
226  \begin{eqnarray}  \begin{eqnarray}
227  \label{EQ:laplacian_stability}  \label{eq:eg-global-laplacian_stability}
228  S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}  && S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2}
229  \end{eqnarray}  \end{eqnarray}
230    
231  \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
232  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
233  $\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$.  $\Delta x$ is smallest at $\phi=80^{\circ}$ where $\Delta
234  \\  x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$ and the stability
235    criterion is already met 1 grid cell equatorwards (at $\phi=76^{\circ}$).
236    
237    
238  \noindent The vertical dissipation coefficient, $A_{z}$, is set to  \noindent The vertical dissipation coefficient, $A_{z}$, is set to
239  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
240  \begin{eqnarray}  \begin{eqnarray}
241  \label{EQ:laplacian_stability_z}  \label{eq:eg-global-laplacian_stability_z}
242  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2}
243  \end{eqnarray}  \end{eqnarray}
244    
245  \noindent evaluates to $0.015$ for the smallest model  \noindent evaluates to $0.0029$ for the smallest model
246  level spcing ($\Delta z_{1}=50{\rm m}$) which is again well below  level spacing ($\Delta z_{1}=50{\rm m}$) which is well below
247  the upper stability limit.  the upper stability limit.
248  \\  \\
249    
250  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
251  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 $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$
252  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
253  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 $\Delta x \approx 77 {\rm km}$.
254  Here the stability parameter  % Here the stability parameter
255  \begin{eqnarray}  % \begin{eqnarray}
256  \label{EQ:laplacian_stability_xtheta}  % \label{eq:eg-global-laplacian_stability_xtheta}
257  S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}  % S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2}
258  \end{eqnarray}  % \end{eqnarray}
259  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
260  stability parameter related to $K_{z}$  % stability parameter related to $K_{z}$
261  \begin{eqnarray}  % \begin{eqnarray}
262  \label{EQ:laplacian_stability_ztheta}  % \label{eq:eg-global-laplacian_stability_ztheta}
263  S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}  % S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2}
264  \end{eqnarray}  % \end{eqnarray}
265  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
266  of $S_{l} \approx 0.5$.  % of $S_{l} \approx 0.5$.
267  \\  % \\
268    
269  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
270  \cite{Adcroft_thesis}  \citep{adcroft:95}
271    
272  \begin{eqnarray}  \begin{eqnarray}
273  \label{EQ:inertial_stability}  \label{eq:eg-global-inertial_stability}
274  S_{i} = f^{2} {\delta t_v}^2  S_{i} = f^{2} {\delta t_v}^2
275  \end{eqnarray}  \end{eqnarray}
276    
277  \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
278  the $S_{i} < 1$ upper limit for stability.  $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is
279    below the $S_{i} < 1$ upper limit for stability.
280  \\  \\
281    
282  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \citep{adcroft:95} for a extreme maximum
283  horizontal flow  horizontal flow
284  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
285    
286  \begin{eqnarray}  \begin{eqnarray}
287  \label{EQ:cfl_stability}  \label{eq:eg-global-cfl_stability}
288  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x}
289  \end{eqnarray}  \end{eqnarray}
290    
291  \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
292  limit of 0.5.  limit of 0.5.
293  \\  \\
294    
295  \noindent The stability parameter for internal gravity waves propogating  \noindent The stability parameter for internal gravity waves propagating
296  with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$   with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$
297  \cite{Adcroft_thesis}  \citep{adcroft:95}
298    
299  \begin{eqnarray}  \begin{eqnarray}
300  \label{EQ:cfl_stability}  \label{eq:eg-global-gfl_stability}
301  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}  S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x}
302  \end{eqnarray}  \end{eqnarray}
303    
304  \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
305  stability limit of 0.5.  stability limit of 0.5.
306        
307  \subsection{Experiment Configuration}  \subsection{Experiment Configuration}
308  \label{SEC:clim_ocn_examp_exp_config}  %\label{www:tutorials}
309    \label{sec:eg-global-clim_ocn_examp_exp_config}
310    
311    The model configuration for this experiment resides under the
312    directory {\it tutorial\_global\_oce\_latlon/}. The experiment files
313    
 The model configuration for this experiment resides under the  
 directory {\it verification/exp2/}.  The experiment files  
314  \begin{itemize}  \begin{itemize}
315  \item {\it input/data}  \item {\it input/data}
316  \item {\it input/data.pkg}  \item {\it input/data.pkg}
317  \item {\it input/eedata},  \item {\it input/eedata},
318  \item {\it input/windx.bin},  \item {\it input/trenberth\_taux.bin},
319  \item {\it input/windy.bin},  \item {\it input/trenberth\_tauy.bin},
320  \item {\it input/salt.bin},  \item {\it input/lev\_s.bin},
321  \item {\it input/theta.bin},  \item {\it input/lev\_t.bin},
322  \item {\it input/SSS.bin},  \item {\it input/lev\_sss.bin},
323  \item {\it input/SST.bin},  \item {\it input/lev\_sst.bin},
324  \item {\it input/topog.bin},  \item {\it input/bathymetry.bin},
325  \item {\it code/CPP\_EEOPTIONS.h}  \item {\it code/CPP\_EEOPTIONS.h}
326  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
327  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
328  \end{itemize}  \end{itemize}
329  contain the code customisations and parameter settings for these  contain the code customizations and parameter settings for these
330  experiements. Below we describe the customisations  experiments. Below we describe the customizations
331  to these files associated with this experiment.  to these files associated with this experiment.
332    
333  \subsubsection{File {\it input/data}}  \subsubsection{Driving Datasets}
334    %\label{www:tutorials}
335    
336  This file, reproduced completely below, specifies the main parameters  %% New figures are included before
337  for the experiment. The parameters that are significant for this configuration  %% Relaxation temperature
338  are  %\begin{figure}
339    %\centering
340  \begin{itemize}  %\includegraphics[]{relax_temperature.eps}
341    %\caption{Relaxation temperature for January}
342  \item Lines 7-10 and 11-14  %\label{fig:relax_temperature}
343  \begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 ,  \end{verbatim}  %\end{figure}
344  $\cdots$ \\  
345  set reference values for potential  %% Relaxation salinity
346  temperature and salinity at each model level in units of $^{\circ}$C and  %\begin{figure}
347  ${\rm ppt}$. The entries are ordered from surface to depth.  %\centering
348  Density is calculated from anomalies at each level evaluated  %\includegraphics[]{relax_salinity.eps}
349  with respect to the reference values set here.\\  %\caption{Relaxation salinity for January}
350  \fbox{  %\label{fig:relax_salinity}
351  \begin{minipage}{5.0in}  %\end{figure}
352  {\it S/R INI\_THETA}({\it ini\_theta.F})  
353  \end{minipage}  %% tau_x
354  }  %\begin{figure}
355    %\centering
356    %\includegraphics[]{tau_x.eps}
357  \item Line 15,  %\caption{zonal wind stress for January}
358  \begin{verbatim} viscAz=1.E-3, \end{verbatim}  %\label{fig:tau_x}
359  this line sets the vertical laplacian dissipation coefficient to  %\end{figure}
360  $1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions  
361  for this operator are specified later. This variable is copied into  %% tau_y
362  model general vertical coordinate variable {\bf viscAr}.  %\begin{figure}
363    %\centering
364  \fbox{  %\includegraphics[]{tau_y.eps}
365  \begin{minipage}{5.0in}  %\caption{meridional wind stress for January}
366  {\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F})  %\label{fig:tau_y}
367  \end{minipage}  %\end{figure}
368  }  
369    %% Qnet
370  \item Line 16,  %\begin{figure}
371  \begin{verbatim}  %\centering
372  viscAh=5.E5,  %\includegraphics[]{qnet.eps}
373  \end{verbatim}  %\caption{Heat flux for January}
374  this line sets the horizontal laplacian frictional dissipation coefficient to  %\label{fig:qnet}
375  $5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions  %\end{figure}
376  for this operator are specified later.  
377    %% EmPmR
378  \item Lines 17,  %\begin{figure}
379  \begin{verbatim}  %\centering
380  no_slip_sides=.FALSE.  %\includegraphics[]{empmr.eps}
381  \end{verbatim}  %\caption{Fresh water flux for January}
382  this line selects a free-slip lateral boundary condition for  %\label{fig:empmr}
383  the horizontal laplacian friction operator  %\end{figure}
384  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and  
385  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  %% Bathymetry
386    %\begin{figure}
387  \item Lines 9,  %\centering
388  \begin{verbatim}  %\includegraphics[]{bathymetry.eps}
389  no_slip_bottom=.TRUE.  %\caption{Bathymetry}
390  \end{verbatim}  %\label{fig:bathymetry}
391  this line selects a no-slip boundary condition for bottom  %\end{figure}
392  boundary condition in the vertical laplacian friction operator  
393  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.  
394    Figures (\ref{fig:sim_config_tclim_pcoord}-\ref{fig:sim_config_empmr_pcoord})
395  \item Line 19,  %(\ref{fig:sim_config_tclim}-\ref{fig:sim_config_empmr})
396  \begin{verbatim}  show the relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$)
397  diffKhT=1.E3,  fields, the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$)
398  \end{verbatim}  and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used
399  this line sets the horizontal diffusion coefficient for temperature  in equations
400  to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this  (\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}).
401  operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on  The figures also indicate the lateral extent and coastline used in the
402  all boundaries.  experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry})
403    shows the depth contours of the model domain.
 \item Line 20,  
 \begin{verbatim}  
 diffKzT=3.E-5,  
 \end{verbatim}  
 this line sets the vertical diffusion coefficient for temperature  
 to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary  
 condition on this operator is $\frac{\partial}{\partial z}=0$ at both  
 the upper and lower boundaries.  
   
 \item Line 21,  
 \begin{verbatim}  
 diffKhS=1.E3,  
 \end{verbatim}  
 this line sets the horizontal diffusion coefficient for salinity  
 to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this  
 operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on  
 all boundaries.  
   
 \item Line 22,  
 \begin{verbatim}  
 diffKzS=3.E-5,  
 \end{verbatim}  
 this line sets the vertical diffusion coefficient for salinity  
 to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary  
 condition on this operator is $\frac{\partial}{\partial z}=0$ at both  
 the upper and lower boundaries.  
   
 \item Lines 23-26  
 \begin{verbatim}  
 beta=1.E-11,  
 \end{verbatim}  
 \vspace{-5mm}$\cdots$\\  
 These settings do not apply for this experiment.  
   
 \item Line 27,  
 \begin{verbatim}  
 gravity=9.81,  
 \end{verbatim}  
 Sets the gravitational acceleration coeeficient to $9.81{\rm m}{\rm s}^{-1}$.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\  
 {\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\  
 {\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\  
 {\it S/R INI\_PARMS}~({\it ini\_parms.F})\\  
 {\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F})  
 \end{minipage}  
 }  
   
   
 \item Line 28-29,  
 \begin{verbatim}  
 rigidLid=.FALSE.,  
 implicitFreeSurface=.TRUE.,  
 \end{verbatim}  
 Selects the barotropic pressure equation to be the implicit free surface  
 formulation.  
   
 \item Line 30,  
 \begin{verbatim}  
 eosType='POLY3',  
 \end{verbatim}  
 Selects the third order polynomial form of the equation of state.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R FIND\_RHO}~({\it find\_rho.F})\\  
 {\it S/R FIND\_ALPHA}~({\it find\_alpha.F})  
 \end{minipage}  
 }  
   
 \item Line 31,  
 \begin{verbatim}  
 readBinaryPrec=32,  
 \end{verbatim}  
 Sets format for reading binary input datasets holding model fields to  
 use 32-bit representation for floating-point numbers.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\  
 {\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F})  
 \end{minipage}  
 }  
   
 \item Line 36,  
 \begin{verbatim}  
 cg2dMaxIters=1000,  
 \end{verbatim}  
 Sets maximum number of iterations the two-dimensional, conjugate  
 gradient solver will use, {\bf irrespective of convergence  
 criteria being met}.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R CG2D}~({\it cg2d.F})  
 \end{minipage}  
 }  
   
 \item Line 37,  
 \begin{verbatim}  
 cg2dTargetResidual=1.E-13,  
 \end{verbatim}  
 Sets the tolerance which the two-dimensional, conjugate  
 gradient solver will use to test for convergence in equation  
 \ref{EQ:congrad_2d_resid} to $1 \times 10^{-13}$.  
 Solver will iterate until  
 tolerance falls below this value or until the maximum number of  
 solver iterations is reached.\\  
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R CG2D}~({\it cg2d.F})  
 \end{minipage}  
 }  
   
 \item Line 42,  
 \begin{verbatim}  
 startTime=0,  
 \end{verbatim}  
 Sets the starting time for the model internal time counter.  
 When set to non-zero this option implicitly requests a  
 checkpoint file be read for initial state.  
 By default the checkpoint file is named according to  
 the integer number of time steps in the {\bf startTime} value.  
 The internal time counter works in seconds.  
   
 \item Line 43,  
 \begin{verbatim}  
 endTime=2808000.,  
 \end{verbatim}  
 Sets the time (in seconds) at which this simulation will terminate.  
 At the end of a simulation a checkpoint file is automatically  
 written so that a numerical experiment can consist of multiple  
 stages.  
   
 \item Line 44,  
 \begin{verbatim}  
 #endTime=62208000000,  
 \end{verbatim}  
 A commented out setting for endTime for a 2000 year simulation.  
   
 \item Line 45,  
 \begin{verbatim}  
 deltaTmom=2400.0,  
 \end{verbatim}  
 Sets the timestep $\delta t_{v}$ used in the momentum equations to  
 $20~{\rm mins}$.  
 See section \ref{SEC:mom_time_stepping}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R TIMESTEP}({\it timestep.F})  
 \end{minipage}  
 }  
   
 \item Line 46,  
 \begin{verbatim}  
 tauCD=321428.,  
 \end{verbatim}  
 Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations.  
 See section \ref{SEC:cd_scheme}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R INI\_PARMS}({\it ini\_parms.F})\\  
 {\it S/R CALC\_MOM\_RHS}({\it calc\_mom\_rhs.F})  
 \end{minipage}  
 }  
   
 \item Line 47,  
 \begin{verbatim}  
 deltaTtracer=108000.,  
 \end{verbatim}  
 Sets the default timestep, $\delta t_{\theta}$, for tracer equations to  
 $30~{\rm hours}$.  
 See section \ref{SEC:tracer_time_stepping}.  
   
 \fbox{  
 \begin{minipage}{5.0in}  
 {\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F})  
 \end{minipage}  
 }  
   
 \item Line 47,  
 \begin{verbatim}  
 bathyFile='topog.box'  
 \end{verbatim}  
 This line specifies the name of the file from which the domain  
 bathymetry is read. This file is a two-dimensional ($x,y$) map of  
 depths. This file is assumed to contain 64-bit binary numbers  
 giving the depth of the model at each grid cell, ordered with the x  
 coordinate varying fastest. The points are ordered from low coordinate  
 to high coordinate for both axes. The units and orientation of the  
 depths in this file are the same as used in the MITgcm code. In this  
 experiment, a depth of $0m$ indicates a solid wall and a depth  
 of $-2000m$ indicates open ocean. The matlab program  
 {\it input/gendata.m} shows an example of how to generate a  
 bathymetry file.  
   
   
 \item Line 50,  
 \begin{verbatim}  
 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  
 ($x,y$) 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  
 {\bf zonalWindFile}  
 file.    
404    
405  \end{itemize}  \subsubsection{File {\it input/data}}
406    %\label{www:tutorials}
407    
408  \noindent other lines in the file {\it input/data} are standard values  \input{s_examples/global_oce_latlon/inp_data}
 that are described in the MITgcm Getting Started and MITgcm Parameters  
 notes.  
   
 \begin{small}  
 \input{part3/case_studies/climatalogical_ogcm/input/data}  
 \end{small}  
409    
410  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
411    %\label{www:tutorials}
412    
413  This file uses standard default values and does not contain  This file uses standard default values and does not contain
414  customisations for this experiment.  customisations for this experiment.
415    
416  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
417    %\label{www:tutorials}
418    
419  This file uses standard default values and does not contain  This file uses standard default values and does not contain
420  customisations for this experiment.  customisations for this experiment.
421    
422  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{Files{\it input/trenberth\_taux.bin} and {\it
423      input/trenberth\_tauy.bin}}
424  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  %\label{www:tutorials}
425  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  
426  Although $\tau_{x}$ is only a function of $y$n in this experiment  The {\it input/trenberth\_taux.bin} and {\it
427  this file must still define a complete two-dimensional map in order    input/trenberth\_tauy.bin} files specify a three-dimensional
428  to be compatible with the standard code for loading forcing fields  ($x,y,time$) map of wind stress, $(\tau_{x},\tau_{y})$, values
429  in MITgcm. The included matlab program {\it input/gendata.m} gives a complete  \citep{trenberth90}. The units used are $Nm^{-2}$.
 code for creating the {\it input/windx.sin\_y} file.  
430    
431  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/bathymetry.bin}}
432    %\label{www:tutorials}
433    
434    
435  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
436  map of depth values. For this experiment values are either  map of depth values. For this experiment values are either
437  $0m$ 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
438  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
439  in the same way as standard MITgcm two-dimensional, horizontal arrays.  in the same way as standard MITgcm two-dimensional, horizontal arrays.
440  The included matlab program {\it input/gendata.m} gives a complete  The included matlab program {\it input/gendata.m} gives a complete
441  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
442    
443  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
444    %\label{www:tutorials}
445    
446  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
447    
448  \begin{itemize}  \begin{itemize}
449    
450  \item Line 39,  \item Line 39,
451  \begin{verbatim} sNx=60, \end{verbatim} this line sets  \begin{verbatim} sNx=45, \end{verbatim} this line sets
452  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
453  axis aligned with the x-coordinate.  axis aligned with the x-coordinate.
454    
455  \item Line 40,  \item Line 40,
456  \begin{verbatim} sNy=60, \end{verbatim} this line sets  \begin{verbatim} sNy=40, \end{verbatim} this line sets
457  the lateral domain extent in grid points for the  the lateral domain extent in grid points for the
458  axis aligned with the y-coordinate.  axis aligned with the y-coordinate.
459    
460  \item Line 49,  \item Line 49,
461  \begin{verbatim} Nr=4,   \end{verbatim} this line sets  \begin{verbatim}
462    Nr=15,
463    \end{verbatim} this line sets
464  the vertical domain extent in grid points.  the vertical domain extent in grid points.
465    
466  \end{itemize}  \end{itemize}
467    
468  \begin{small}  \begin{small}
469  \input{part3/case_studies/climatalogical_ogcm/code/SIZE.h}  \input{s_examples/global_oce_latlon/code/SIZE.h}
470  \end{small}  \end{small}
471    
472  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
473    %\label{www:tutorials}
474    
475  This file uses standard default values and does not contain  This file uses standard default values and does not contain
476  customisations for this experiment.  customisations for this experiment.
477    
478    
479  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
480    %\label{www:tutorials}
481    
482  This file uses standard default values and does not contain  This file uses standard default values and does not contain
483  customisations for this experiment.  customisations for this experiment.
484    
485  \subsubsection{Other Files }  \subsubsection{Other Files }
486    %\label{www:tutorials}
487    
488  Other files relevant to this experiment are  % Other files relevant to this experiment are
489  \begin{itemize}  % \begin{itemize}
490  \item {\it model/src/ini\_cori.F}. This file initializes the model  % \item {\it model/src/ini\_cori.F}. This file initializes the model
491  coriolis variables {\bf fCorU}.  % coriolis variables {\bf fCorU}.
492  \item {\it model/src/ini\_spherical\_polar\_grid.F}  % \item {\it model/src/ini\_spherical\_polar\_grid.F}
493  \item {\it model/src/ini\_parms.F},  % \item {\it model/src/ini\_parms.F},
494  \item {\it input/windx.sin\_y},  % \item {\it input/windx.sin\_y},
495  \end{itemize}  % \end{itemize}
496  contain the code customisations and parameter settings for this  % contain the code customisations and parameter settings for this
497  experiements. Below we describe the customisations  % experiments. Below we describe the customisations
498  to these files associated with this experiment.  % to these files associated with this experiment.
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