/[MITgcm]/manual/s_examples/tracer_adjsens/co2sens.tex

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-revision 1.1 by adcroft,
Wed Aug  8 16:16:16 2001 UTC
+revision 1.10 by molod,
Tue Jun 27 19:08:22 2006 UTC
 Line 1
  % $Header$
  % $Name$
- \section{Example: Centenial Time Scale Sensitivities}
+ \section{Centennial Time Scale Tracer Injection}
+ \label{www:tutorials}
+ \label{sect:eg-simple-tracer}
+ \begin{rawhtml}
+ <!-- CMIREDIR:eg-simple-tracer: -->
+ \end{rawhtml}
  \bodytext{bgcolor="#FFFFFFFF"}
  %\begin{center}
- %{\Large \bf Using MITgcm to Look at Centenial Time Scale
+ %{\Large \bf Using MITgcm to Look at Centennial Time Scale
  %Sensitivities}
  %
  %\vspace*{4mm}
-Line 16
+Line 21
  %\end{center}
  \subsection{Introduction}
+ \label{www:tutorials}
- This document describes the fourth example MITgcm experiment.
+ This example illustrates the use of
- This example iilustrates the use of
+ the MITgcm to perform sensitivity analysis in a
- the MITgcm to perform sentivity analysis in a
  large scale ocean circulation simulation.
+ The files for this experiment can be found in the
+ verification directory under tutorial\_tracer\_adjsens.
  \subsection{Overview}
+ \label{www:tutorials}
  This example experiment demonstrates using the MITgcm to simulate
  the planetary ocean circulation. The simulation is configured
-Line 36 
 can be integrated forward for thousands
+Line 44 
 can be integrated forward for thousands
  processor desktop computer.
  \\
- The model is forced with climatalogical wind stress data and surface
+ The model is forced with climatological wind stress data and surface
- flux data from Da Silva \cite{DaSilva94}. Climatalogical data
+ flux data from Da Silva \cite{DaSilva94}. Climatological data
- from Levitus \cite{Levitus94} is used to initialise the model hydrography.
+ from Levitus \cite{Levitus94} is used to initialize the model hydrography.
  Levitus data is also used throughout the calculation
  to derive air-sea fluxes of heat at the ocean surface.
- These fluxes are combined with climatalogical estimates of
+ These fluxes are combined with climatological estimates of
  surface heat flux and fresh water, resulting in a mixed boundary
- condition of the style decribed in Haney \cite{Haney}.
+ condition of the style described in Haney \cite{Haney}.
  Altogether, this yields the following forcing applied
  in the model surface layer.
  \begin{eqnarray}
- \label{EQ:global_forcing}
+ \label{EQ:eg-simple-tracer-global_forcing}
- \label{EQ:global_forcing_fu}
+ \label{EQ:eg-simple-tracer-global_forcing_fu}
  {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}}
  \\
- \label{EQ:global_forcing_fv}
+ \label{EQ:eg-simple-tracer-global_forcing_fv}
  {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}}
  \\
- \label{EQ:global_forcing_ft}
+ \label{EQ:eg-simple-tracer-global_forcing_ft}
  {\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} )
   - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q}
  \\
- \label{EQ:global_forcing_fs}
+ \label{EQ:eg-simple-tracer-global_forcing_fs}
  {\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} )
   + \frac{S_{0}}{\Delta z_{s}}({\cal E} - {\cal P} - {\cal R})
  \end{eqnarray}
-Line 81 
 The configuration is illustrated in figu
+Line 89 
 The configuration is illustrated in figu
  \subsection{Discrete Numerical Configuration}
+ \label{www:tutorials}
   The model is configured in hydrostatic form.  The domain is discretised with
-Line 118 
 $
+Line 127 
 $
   \Delta z_{20}=815\,{\rm m}
  $ (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
+ \cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous
- dissipation. Thermal and haline diffusion is also represented by a laplacian operator.
+ dissipation. Thermal and haline diffusion is also represented by a Laplacian operator.
  \\
  Wind-stress momentum inputs are added to the momentum equations for both
- the zonal flow, $u$ and the merdional flow $v$, according to equations
+ the zonal flow, $u$ and the meridional flow $v$, according to equations
- (\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}).
  Thermodynamic forcing inputs are added to the equations for
  potential temperature, $\theta$, and salinity, $S$, according to equations
- (\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}).
  This produces a set of equations solved in this configuration as follows:
  % {\fracktur}
  \begin{eqnarray}
- \label{EQ:model_equations}
+ \label{EQ:eg-simple-tracer-model_equations}
  \frac{Du}{Dt} - fv +
    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
    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 176 
 g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} d
  \noindent where $u$ and $v$ are the $x$ and $y$ components of the
  flow vector $\vec{u}$. The suffices ${s},{i}$ indicate surface and
  interior model levels respectively. As described in
- MITgcm Numerical Solution Procedure \cite{MITgcm_Numerical_Scheme}, the time
+ MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time
  evolution of potential temperature, $\theta$, equation is solved prognostically.
  The total pressure, $p$, is diagnosed by summing pressure due to surface
  elevation $\eta$ and the hydrostatic pressure.
  \\
  \subsubsection{Numerical Stability Criteria}
+ \label{www:tutorials}
- The laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
+ The Laplacian dissipation coefficient, $A_{h}$, is set to $400 m s^{-1}$.
- 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},
  \begin{eqnarray}
- \label{EQ:munk_layer}
+ \label{EQ:eg-simple-tracer-munk_layer}
  M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}
  \end{eqnarray}
-Line 190 
 boundary layer is well resolved.
+Line 200 
 boundary layer is well resolved.
  \noindent The model is stepped forward with a
  time step $\delta t=1200$secs. With this time step the stability
- parameter to the horizontal laplacian friction \cite{Adcroft_thesis}
+ parameter to the horizontal Laplacian friction \cite{adcroft:95}
  \begin{eqnarray}
- \label{EQ:laplacian_stability}
+ \label{EQ:eg-simple-tracer-laplacian_stability}
  S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}
  \end{eqnarray}
-Line 205 
 for stability.
+Line 215 
 for stability.
  $1\times10^{-2} {\rm m}^2{\rm s}^{-1}$. The associated stability limit
  \begin{eqnarray}
- \label{EQ:laplacian_stability_z}
+ \label{EQ:eg-simple-tracer-laplacian_stability_z}
  S_{l} = 4 \frac{A_{z} \delta t}{{\Delta z}^2}
  \end{eqnarray}
-Line 216 
 and vertical ($K_{z}$) diffusion coeffic
+Line 226 
 and vertical ($K_{z}$) diffusion coeffic
  \\
  \noindent The numerical stability for inertial oscillations
- \cite{Adcroft_thesis}
+ \cite{adcroft:95}
  \begin{eqnarray}
- \label{EQ:inertial_stability}
+ \label{EQ:eg-simple-tracer-inertial_stability}
  S_{i} = f^{2} {\delta t}^2
  \end{eqnarray}
-Line 227 
 S_{i} = f^{2} {\delta t}^2
+Line 237 
 S_{i} = f^{2} {\delta t}^2
  limit for stability.
  \\
- \noindent The advective CFL \cite{Adcroft_thesis} for a extreme maximum
+ \noindent The advective CFL \cite{adcroft:95} for a extreme maximum
  horizontal flow
  speed of $ | \vec{u} | = 2 ms^{-1}$
  \begin{eqnarray}
- \label{EQ:cfl_stability}
+ \label{EQ:eg-simple-tracer-cfl_stability}
  S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x}
  \end{eqnarray}
-Line 240 
 S_{a} = \frac{| \vec{u} | \delta t}{ \De
+Line 250 
 S_{a} = \frac{| \vec{u} | \delta t}{ \De
  limit of 0.5.
  \\
- \noindent The stbility parameter for internal gravity waves
+ \noindent The stability parameter for internal gravity waves
- \cite{Adcroft_thesis}
+ \cite{adcroft:95}
  \begin{eqnarray}
- \label{EQ:cfl_stability}
+ \label{EQ:eg-simple-tracer-igw_stability}
  S_{c} = \frac{c_{g} \delta t}{ \Delta x}
  \end{eqnarray}
-Line 252 
 S_{c} = \frac{c_{g} \delta t}{ \Delta x}
+Line 262 
 S_{c} = \frac{c_{g} \delta t}{ \Delta x}
  stability limit of 0.25.
  \subsection{Code Configuration}
+ \label{www:tutorials}
  \label{SEC:code_config}
  The model configuration for this experiment resides under the
-Line 266 
 directory {\it verification/exp1/}.  The
+Line 277 
 directory {\it verification/exp1/}.  The
  \item {\it code/CPP\_OPTIONS.h},
  \item {\it code/SIZE.h}.
  \end{itemize}
- contain the code customisations and parameter settings for this
+ contain the code customizations and parameter settings for this
- experiements. Below we describe the customisations
+ experiments. Below we describe the customizations
  to these files associated with this experiment.
  \subsubsection{File {\it input/data}}
+ \label{www:tutorials}
  This file, reproduced completely below, specifies the main parameters
  for the experiment. The parameters that are significant for this configuration
-Line 282 
 are
+Line 294 
 are
  \begin{verbatim} tRef=20.,10.,8.,6., \end{verbatim}
  this line sets
  the initial and reference values of potential temperature at each model
- level in units of $^{\circ}$C.
+ level in units of $^{\circ}\mathrm{C}$.
  The entries are ordered from surface to depth. For each
- depth level the inital and reference profiles will be uniform in
+ depth level the initial and reference profiles will be uniform in
  $x$ and $y$.
  \fbox{
-Line 296 
 $x$ and $y$.
+Line 308 
 $x$ and $y$.
  \item Line 6,
  \begin{verbatim} viscAz=1.E-2, \end{verbatim}
- this line sets the vertical laplacian dissipation coefficient to
+ this line sets the vertical Laplacian dissipation coefficient to
  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
  for this operator are specified later. This variable is copied into
  model general vertical coordinate variable {\bf viscAr}.
-Line 311 
 model general vertical coordinate variab
+Line 323 
 model general vertical coordinate variab
  \begin{verbatim}
  viscAh=4.E2,
  \end{verbatim}
- this line sets the horizontal laplacian frictional dissipation coefficient to
+ this line sets the horizontal Laplacian frictional dissipation coefficient to
  $1 \times 10^{-2} {\rm m^{2}s^{-1}}$. Boundary conditions
  for this operator are specified later.
-Line 320 
 for this operator are specified later.
+Line 332 
 for this operator are specified later.
  no_slip_sides=.FALSE.
  \end{verbatim}
  this line selects a free-slip lateral boundary condition for
- the horizontal laplacian friction operator
+ the horizontal Laplacian friction operator
  e.g. $\frac{\partial u}{\partial y}$=0 along boundaries in $y$ and
  $\frac{\partial v}{\partial x}$=0 along boundaries in $x$.
-Line 329 
 $\frac{\partial v}{\partial x}$=0 along
+Line 341 
 $\frac{\partial v}{\partial x}$=0 along
  no_slip_bottom=.TRUE.
  \end{verbatim}
  this line selects a no-slip boundary condition for bottom
- boundary condition in the vertical laplacian friction operator
+ boundary condition in the vertical Laplacian friction operator
  e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain.
  \item Line 10,
-Line 382 
 usingSphericalPolarGrid=.TRUE.,
+Line 394 
 usingSphericalPolarGrid=.TRUE.,
  \end{verbatim}
  This line requests that the simulation be performed in a
  spherical polar coordinate system. It affects the interpretation of
- grid inoput parameters, for exampl {\bf delX} and {\bf delY} and
+ grid input parameters, for example {\bf delX} and {\bf delY} and
- causes the grid generation routines to initialise an internal grid based
+ causes the grid generation routines to initialize an internal grid based
  on spherical polar geometry.
  \fbox{
-Line 399 
 phiMin=0.,
+Line 411 
 phiMin=0.,
  This line sets the southern boundary of the modeled
  domain to $0^{\circ}$ latitude. This value affects both the
  generation of the locally orthogonal grid that the model
- uses internally and affects the initialisation of the coriolis force.
+ uses internally and affects the initialization of the coriolis force.
  Note - it is not required to set
  a longitude boundary, since the absolute longitude does
  not alter the kernel equation discretisation.
-Line 473 
 notes.
+Line 485 
 notes.
  \end{small}
  \subsubsection{File {\it input/data.pkg}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
- customisations for this experiment.
+ customizations for this experiment.
  \subsubsection{File {\it input/eedata}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
- customisations for this experiment.
+ customizations for this experiment.
  \subsubsection{File {\it input/windx.sin\_y}}
+ \label{www:tutorials}
  The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$)
  map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$.
-Line 493 
 in MITgcm. The included matlab program {
+Line 508 
 in MITgcm. The included matlab program {
  code for creating the {\it input/windx.sin\_y} file.
  \subsubsection{File {\it input/topog.box}}
+ \label{www:tutorials}
  The {\it input/topog.box} file specifies a two-dimensional ($x,y$)
-Line 504 
 The included matlab program {\it input/g
+Line 520 
 The included matlab program {\it input/g
  code for creating the {\it input/topog.box} file.
  \subsubsection{File {\it code/SIZE.h}}
+ \label{www:tutorials}
  Two lines are customized in this file for the current experiment
-Line 530 
 the vertical domain extent in grid point
+Line 547 
 the vertical domain extent in grid point
  \end{small}
  \subsubsection{File {\it code/CPP\_OPTIONS.h}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
- customisations for this experiment.
+ customizations for this experiment.
  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
- customisations for this experiment.
+ customizations for this experiment.
  \subsubsection{Other Files }
+ \label{www:tutorials}
  Other files relevant to this experiment are
  \begin{itemize}
-Line 550 
 coriolis variables {\bf fCorU}.
+Line 570 
 coriolis variables {\bf fCorU}.
  \item {\it model/src/ini\_parms.F},
  \item {\it input/windx.sin\_y},
  \end{itemize}
- contain the code customisations and parameter settings for this
+ contain the code customizations and parameter settings for this
- experiements. Below we describe the customisations
+ experiments. Below we describe the customizations
  to these files associated with this experiment.

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