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

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-revision 1.3 by adcroft,
Tue Nov 13 18:19:18 2001 UTC
+revision 1.11 by jmc,
Tue Jan 15 18:41:46 2008 UTC
 Line 1
  % $Header$
  % $Name$
- \section{Example: Centennial 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}
+ \begin{center}
+ (in directory: {\it verification/tutorial\_tracer\_adjsens/})
+ \end{center}
  \bodytext{bgcolor="#FFFFFFFF"}
-Line 16
+Line 24
  %\end{center}
  \subsection{Introduction}
+ \label{www:tutorials}
- This document describes the fourth example MITgcm experiment.
  This example illustrates the use of
  the MITgcm to perform sensitivity 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 48 
 Altogether, this yields the following fo
+Line 59 
 Altogether, this yields the following fo
  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 92 
 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 130 
 $
   \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.
  \\
  Wind-stress momentum inputs are added to the momentum equations for both
  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 179 
 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 $400 m s^{-1}$.
  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 193 
 time step $\delta t=1200$secs. With this
+Line 206 
 time step $\delta t=1200$secs. With this
  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 218 
 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 219 
 and vertical ($K_{z}$) diffusion coeffic
+Line 232 
 and vertical ($K_{z}$) diffusion coeffic
  \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 232 
 horizontal flow
+Line 245 
 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 244 
 limit of 0.5.
+Line 257 
 limit of 0.5.
  \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 265 
 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 271 
 experiments. Below we describe the custo
+Line 285 
 experiments. Below we describe the custo
  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 297 
 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 initial and reference profiles will be uniform in
  $x$ and $y$.
-Line 473 
 notes.
+Line 488 
 notes.
  \end{small}
  \subsubsection{File {\it input/data.pkg}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
  customizations for this experiment.
  \subsubsection{File {\it input/eedata}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
  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 511 
 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 523 
 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 550 
 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
  customizations for this experiment.
  \subsubsection{File {\it code/CPP\_EEOPTIONS.h}}
+ \label{www:tutorials}
  This file uses standard default values and does not contain
  customizations for this experiment.
  \subsubsection{Other Files }
+ \label{www:tutorials}
  Other files relevant to this experiment are
  \begin{itemize}

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