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revision 1.1.1.1 by adcroft, Wed Aug 8 16:16:16 2001 UTC revision 1.12 by jmc, Tue Jan 15 20:00:38 2008 UTC
# Line 1  Line 1 
1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4  \section{Example: Centenial Time Scale Sensitivities}  \section{Centennial Time Scale Tracer Injection}
5    \label{www:tutorials}
6    \label{sect:eg-simple-tracer}
7    \begin{rawhtml}
8    <!-- CMIREDIR:eg-simple-tracer: -->
9    \end{rawhtml}
10    \begin{center}
11    (in directory: {\it verification/tutorial\_tracer\_adjsens/})
12    \end{center}
13    
14  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
15    
16  %\begin{center}  %\begin{center}
17  %{\Large \bf Using MITgcm to Look at Centenial Time Scale  %{\Large \bf Using MITgcm to Look at Centennial Time Scale
18  %Sensitivities}  %Sensitivities}
19  %  %
20  %\vspace*{4mm}  %\vspace*{4mm}
# Line 16  Line 24 
24  %\end{center}  %\end{center}
25    
26  \subsection{Introduction}  \subsection{Introduction}
27    \label{www:tutorials}
28    
29  This document describes the fourth example MITgcm experiment.  This example illustrates the use of
30  This example iilustrates the use of  the MITgcm to perform sensitivity analysis in a
 the MITgcm to perform sentivity analysis in a  
31  large scale ocean circulation simulation.  large scale ocean circulation simulation.
32    The files for this experiment can be found in the
33    verification directory under tutorial\_tracer\_adjsens.
34    
35  \subsection{Overview}  \subsection{Overview}
36    \label{www:tutorials}
37    
38  This example experiment demonstrates using the MITgcm to simulate  This example experiment demonstrates using the MITgcm to simulate
39  the planetary ocean circulation. The simulation is configured  the planetary ocean circulation. The simulation is configured
# Line 36  can be integrated forward for thousands Line 47  can be integrated forward for thousands
47  processor desktop computer.  processor desktop computer.
48  \\  \\
49    
50  The model is forced with climatalogical wind stress data and surface  The model is forced with climatological wind stress data and surface
51  flux data from Da Silva \cite{DaSilva94}. Climatalogical data  flux data from Da Silva \cite{DaSilva94}. Climatological data
52  from Levitus \cite{Levitus94} is used to initialise the model hydrography.  from Levitus \cite{Levitus94} is used to initialize the model hydrography.
53  Levitus data is also used throughout the calculation  Levitus data is also used throughout the calculation
54  to derive air-sea fluxes of heat at the ocean surface.  to derive air-sea fluxes of heat at the ocean surface.
55  These fluxes are combined with climatalogical estimates of  These fluxes are combined with climatological estimates of
56  surface heat flux and fresh water, resulting in a mixed boundary  surface heat flux and fresh water, resulting in a mixed boundary
57  condition of the style decribed in Haney \cite{Haney}.  condition of the style described in Haney \cite{Haney}.
58  Altogether, this yields the following forcing applied  Altogether, this yields the following forcing applied
59  in the model surface layer.  in the model surface layer.
60    
61  \begin{eqnarray}  \begin{eqnarray}
62  \label{EQ:global_forcing}  \label{EQ:eg-simple-tracer-global_forcing}
63  \label{EQ:global_forcing_fu}  \label{EQ:eg-simple-tracer-global_forcing_fu}
64  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
65  \\  \\
66  \label{EQ:global_forcing_fv}  \label{EQ:eg-simple-tracer-global_forcing_fv}
67  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
68  \\  \\
69  \label{EQ:global_forcing_ft}  \label{EQ:eg-simple-tracer-global_forcing_ft}
70  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
71   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
72  \\  \\
73  \label{EQ:global_forcing_fs}  \label{EQ:eg-simple-tracer-global_forcing_fs}
74  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
75   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
76  \end{eqnarray}  \end{eqnarray}
# Line 81  The configuration is illustrated in figu Line 92  The configuration is illustrated in figu
92    
93    
94  \subsection{Discrete Numerical Configuration}  \subsection{Discrete Numerical Configuration}
95    \label{www:tutorials}
96    
97    
98   The model is configured in hydrostatic form.  The domain is discretised with   The model is configured in hydrostatic form.  The domain is discretised with
# Line 118  $ Line 130  $
130   \Delta z_{20}=815\,{\rm m}   \Delta z_{20}=815\,{\rm m}
131  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).  $ (here the numeric subscript indicates the model level index number, ${\tt k}$).
132  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
133  \cite{Marshall97a} is employed. A laplacian operator, $\nabla^2$, provides viscous  \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
134  dissipation. Thermal and haline diffusion is also represented by a laplacian operator.  dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
135  \\  \\
136    
137  Wind-stress momentum inputs are added to the momentum equations for both  Wind-stress momentum inputs are added to the momentum equations for both
138  the zonal flow, $u$ and the merdional flow $v$, according to equations  the zonal flow, $u$ and the meridional flow $v$, according to equations
139  (\ref{EQ:global_forcing_fu}) and (\ref{EQ:global_forcing_fv}).  (\ref{EQ:eg-simple-tracer-global_forcing_fu}) and (\ref{EQ:eg-simple-tracer-global_forcing_fv}).
140  Thermodynamic forcing inputs are added to the equations for  Thermodynamic forcing inputs are added to the equations for
141  potential temperature, $\theta$, and salinity, $S$, according to equations  potential temperature, $\theta$, and salinity, $S$, according to equations
142  (\ref{EQ:global_forcing_ft}) and (\ref{EQ:global_forcing_fs}).  (\ref{EQ:eg-simple-tracer-global_forcing_ft}) and (\ref{EQ:eg-simple-tracer-global_forcing_fs}).
143  This produces a set of equations solved in this configuration as follows:  This produces a set of equations solved in this configuration as follows:
144  % {\fracktur}  % {\fracktur}
145    
146    
147  \begin{eqnarray}  \begin{eqnarray}
148  \label{EQ:model_equations}  \label{EQ:eg-simple-tracer-model_equations}
149  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
150    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
151    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}    A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}}
# Line 167  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d Line 179  g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
179  \noindent where $u$ and $v$ are the $x$ and $y$ components of the  \noindent where $u$ and $v$ are the $x$ and $y$ components of the
180  flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and  flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and
181  interior model levels respectively. As described in  interior model levels respectively. As described in
182  MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time  MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
183  evolution of potential temperature, $\theta$, equation is solved prognostically.  evolution of potential temperature, $\theta$, equation is solved prognostically.
184  The total pressure, $p$, is diagnosed by summing pressure due to surface  The total pressure, $p$, is diagnosed by summing pressure due to surface
185  elevation $\eta$ and the hydrostatic pressure.  elevation $\eta$ and the hydrostatic pressure.
186  \\  \\
187    
188  \subsubsection{Numerical Stability Criteria}  \subsubsection{Numerical Stability Criteria}
189    \label{www:tutorials}
190    
191  The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.  The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
192  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},
193    
194  \begin{eqnarray}  \begin{eqnarray}
195  \label{EQ:munk_layer}  \label{EQ:eg-simple-tracer-munk_layer}
196  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
197  \end{eqnarray}  \end{eqnarray}
198    
# Line 190  boundary layer is well resolved. Line 203  boundary layer is well resolved.
203    
204  \noindent The model is stepped forward with a  \noindent The model is stepped forward with a
205  time step $\delta t=1200$secs. With this time step the stability  time step $\delta t=1200$secs. With this time step the stability
206  parameter to the horizontal laplacian friction \cite{Adcroft_thesis}  parameter to the horizontal Laplacian friction \cite{adcroft:95}
207    
208  \begin{eqnarray}  \begin{eqnarray}
209  \label{EQ:laplacian_stability}  \label{EQ:eg-simple-tracer-laplacian_stability}
210  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
211  \end{eqnarray}  \end{eqnarray}
212    
# Line 205  for stability. Line 218  for stability.
218  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
219    
220  \begin{eqnarray}  \begin{eqnarray}
221  \label{EQ:laplacian_stability_z}  \label{EQ:eg-simple-tracer-laplacian_stability_z}
222  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
223  \end{eqnarray}  \end{eqnarray}
224    
# Line 216  and vertical ($K_{z}$) diffusion coeffic Line 229  and vertical ($K_{z}$) diffusion coeffic
229  \\  \\
230    
231  \noindent The numerical stability for inertial oscillations  \noindent The numerical stability for inertial oscillations
232  \cite{Adcroft_thesis}  \cite{adcroft:95}
233    
234  \begin{eqnarray}  \begin{eqnarray}
235  \label{EQ:inertial_stability}  \label{EQ:eg-simple-tracer-inertial_stability}
236  S_{i} = f^{2} {\delta t}^2  S_{i} = f^{2} {\delta t}^2
237  \end{eqnarray}  \end{eqnarray}
238    
# Line 227  S_{i} = f^{2} {\delta t}^2 Line 240  S_{i} = f^{2} {\delta t}^2
240  limit for stability.  limit for stability.
241  \\  \\
242    
243  \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum  \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
244  horizontal flow  horizontal flow
245  speed of $ | \vec{u} | = 2 ms^{-1}$  speed of $ | \vec{u} | = 2 ms^{-1}$
246    
247  \begin{eqnarray}  \begin{eqnarray}
248  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-cfl_stability}
249  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
250  \end{eqnarray}  \end{eqnarray}
251    
# Line 240  S_{a} = \frac{| \vec{u} | \delta t}{ \De Line 253  S_{a} = \frac{| \vec{u} | \delta t}{ \De
253  limit of 0.5.  limit of 0.5.
254  \\  \\
255    
256  \noindent The stbility parameter for internal gravity waves  \noindent The stability parameter for internal gravity waves
257  \cite{Adcroft_thesis}  \cite{adcroft:95}
258    
259  \begin{eqnarray}  \begin{eqnarray}
260  \label{EQ:cfl_stability}  \label{EQ:eg-simple-tracer-igw_stability}
261  S_{c} = \frac{c_{g} \delta t}{ \Delta x}  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
262  \end{eqnarray}  \end{eqnarray}
263    
# Line 252  S_{c} = \frac{c_{g} \delta t}{ \Delta x} Line 265  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
265  stability limit of 0.25.  stability limit of 0.25.
266        
267  \subsection{Code Configuration}  \subsection{Code Configuration}
268    \label{www:tutorials}
269  \label{SEC:code_config}  \label{SEC:code_config}
270    
271  The model configuration for this experiment resides under the  The model configuration for this experiment resides under the
# Line 266  directory {\it verification/exp1/}.  The Line 280  directory {\it verification/exp1/}.  The
280  \item {\it code/CPP\_OPTIONS.h},  \item {\it code/CPP\_OPTIONS.h},
281  \item {\it code/SIZE.h}.  \item {\it code/SIZE.h}.
282  \end{itemize}  \end{itemize}
283  contain the code customisations and parameter settings for this  contain the code customizations and parameter settings for this
284  experiements. Below we describe the customisations  experiments. Below we describe the customizations
285  to these files associated with this experiment.  to these files associated with this experiment.
286    
287  \subsubsection{File {\it input/data}}  \subsubsection{File {\it input/data}}
288    \label{www:tutorials}
289    
290  This file, reproduced completely below, specifies the main parameters  This file, reproduced completely below, specifies the main parameters
291  for the experiment. The parameters that are significant for this configuration  for the experiment. The parameters that are significant for this configuration
# Line 282  are Line 297  are
297  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}
298  this line sets  this line sets
299  the initial and reference values of potential temperature at each model  the initial and reference values of potential temperature at each model
300  level in units of $^{\circ}$C.  level in units of $^{\circ}\mathrm{C}$.
301  The entries are ordered from surface to depth. For each  The entries are ordered from surface to depth. For each
302  depth level the inital and reference profiles will be uniform in  depth level the initial and reference profiles will be uniform in
303  $x$ and $y$.  $x$ and $y$.
304    
305  \fbox{  \fbox{
# Line 296  $x$ and $y$. Line 311  $x$ and $y$.
311    
312  \item Line 6,  \item Line 6,
313  \begin{verbatim} viscAz=1.E-2, \end{verbatim}  \begin{verbatim} viscAz=1.E-2, \end{verbatim}
314  this line sets the vertical laplacian dissipation coefficient to  this line sets the vertical Laplacian dissipation coefficient to
315  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
316  for this operator are specified later. This variable is copied into  for this operator are specified later. This variable is copied into
317  model general vertical coordinate variable {\bf viscAr}.  model general vertical coordinate variable {\bf viscAr}.
# Line 311  model general vertical coordinate variab Line 326  model general vertical coordinate variab
326  \begin{verbatim}  \begin{verbatim}
327  viscAh=4.E2,  viscAh=4.E2,
328  \end{verbatim}  \end{verbatim}
329  this line sets the horizontal laplacian frictional dissipation coefficient to  this line sets the horizontal Laplacian frictional dissipation coefficient to
330  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
331  for this operator are specified later.  for this operator are specified later.
332    
# Line 320  for this operator are specified later. Line 335  for this operator are specified later.
335  no_slip_sides=.FALSE.  no_slip_sides=.FALSE.
336  \end{verbatim}  \end{verbatim}
337  this line selects a free-slip lateral boundary condition for  this line selects a free-slip lateral boundary condition for
338  the horizontal laplacian friction operator  the horizontal Laplacian friction operator
339  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
340  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
341    
# Line 329  $\frac{\partial v}{\partial x}$=0 along Line 344  $\frac{\partial v}{\partial x}$=0 along
344  no_slip_bottom=.TRUE.  no_slip_bottom=.TRUE.
345  \end{verbatim}  \end{verbatim}
346  this line selects a no-slip boundary condition for bottom  this line selects a no-slip boundary condition for bottom
347  boundary condition in the vertical laplacian friction operator  boundary condition in the vertical Laplacian friction operator
348  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.
349    
350  \item Line 10,  \item Line 10,
# Line 382  usingSphericalPolarGrid=.TRUE., Line 397  usingSphericalPolarGrid=.TRUE.,
397  \end{verbatim}  \end{verbatim}
398  This line requests that the simulation be performed in a  This line requests that the simulation be performed in a
399  spherical polar coordinate system. It affects the interpretation of  spherical polar coordinate system. It affects the interpretation of
400  grid inoput parameters, for exampl {\bf delX} and {\bf delY} and  grid input parameters, for example {\bf delX} and {\bf delY} and
401  causes the grid generation routines to initialise an internal grid based  causes the grid generation routines to initialize an internal grid based
402  on spherical polar geometry.  on spherical polar geometry.
403    
404  \fbox{  \fbox{
# Line 399  phiMin=0., Line 414  phiMin=0.,
414  This line sets the southern boundary of the modeled  This line sets the southern boundary of the modeled
415  domain to $0^{\circ}$ latitude. This value affects both the  domain to $0^{\circ}$ latitude. This value affects both the
416  generation of the locally orthogonal grid that the model  generation of the locally orthogonal grid that the model
417  uses internally and affects the initialisation of the coriolis force.  uses internally and affects the initialization of the coriolis force.
418  Note - it is not required to set  Note - it is not required to set
419  a longitude boundary, since the absolute longitude does  a longitude boundary, since the absolute longitude does
420  not alter the kernel equation discretisation.  not alter the kernel equation discretisation.
# Line 473  notes. Line 488  notes.
488  \end{small}  \end{small}
489    
490  \subsubsection{File {\it input/data.pkg}}  \subsubsection{File {\it input/data.pkg}}
491    \label{www:tutorials}
492    
493  This file uses standard default values and does not contain  This file uses standard default values and does not contain
494  customisations for this experiment.  customizations for this experiment.
495    
496  \subsubsection{File {\it input/eedata}}  \subsubsection{File {\it input/eedata}}
497    \label{www:tutorials}
498    
499  This file uses standard default values and does not contain  This file uses standard default values and does not contain
500  customisations for this experiment.  customizations for this experiment.
501    
502  \subsubsection{File {\it input/windx.sin\_y}}  \subsubsection{File {\it input/windx.sin\_y}}
503    \label{www:tutorials}
504    
505  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
506  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
# Line 493  in MITgcm. The included matlab program { Line 511  in MITgcm. The included matlab program {
511  code for creating the {\it input/windx.sin\_y} file.  code for creating the {\it input/windx.sin\_y} file.
512    
513  \subsubsection{File {\it input/topog.box}}  \subsubsection{File {\it input/topog.box}}
514    \label{www:tutorials}
515    
516    
517  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
# Line 504  The included matlab program {\it input/g Line 523  The included matlab program {\it input/g
523  code for creating the {\it input/topog.box} file.  code for creating the {\it input/topog.box} file.
524    
525  \subsubsection{File {\it code/SIZE.h}}  \subsubsection{File {\it code/SIZE.h}}
526    \label{www:tutorials}
527    
528  Two lines are customized in this file for the current experiment  Two lines are customized in this file for the current experiment
529    
# Line 530  the vertical domain extent in grid point Line 550  the vertical domain extent in grid point
550  \end{small}  \end{small}
551    
552  \subsubsection{File {\it code/CPP\_OPTIONS.h}}  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
553    \label{www:tutorials}
554    
555  This file uses standard default values and does not contain  This file uses standard default values and does not contain
556  customisations for this experiment.  customizations for this experiment.
557    
558    
559  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
560    \label{www:tutorials}
561    
562  This file uses standard default values and does not contain  This file uses standard default values and does not contain
563  customisations for this experiment.  customizations for this experiment.
564    
565  \subsubsection{Other Files }  \subsubsection{Other Files }
566    \label{www:tutorials}
567    
568  Other files relevant to this experiment are  Other files relevant to this experiment are
569  \begin{itemize}  \begin{itemize}
# Line 550  coriolis variables {\bf fCorU}. Line 573  coriolis variables {\bf fCorU}.
573  \item {\it model/src/ini\_parms.F},  \item {\it model/src/ini\_parms.F},
574  \item {\it input/windx.sin\_y},  \item {\it input/windx.sin\_y},
575  \end{itemize}  \end{itemize}
576  contain the code customisations and parameter settings for this  contain the code customizations and parameter settings for this
577  experiements. Below we describe the customisations  experiments. Below we describe the customizations
578  to these files associated with this experiment.  to these files associated with this experiment.
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