--- manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex 2008/01/15 20:04:06 1.16 +++ manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex 2015/11/25 10:57:41 1.25 @@ -1,9 +1,9 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex,v 1.16 2008/01/15 20:04:06 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/global_oce_latlon/climatalogical_ogcm.tex,v 1.25 2015/11/25 10:57:41 mlosch Exp $ % $Name: $ -\section[Global Ocean MITgcm Exmaple]{Global Ocean Simulation at $4^\circ$ Resolution} -\label{www:tutorials} -\label{sect:eg-global} +\section[Global Ocean MITgcm Example]{Global Ocean Simulation at $4^\circ$ Resolution} +%\label{www:tutorials} +\label{sec:eg-global} \begin{rawhtml} \end{rawhtml} @@ -13,7 +13,10 @@ \bodytext{bgcolor="#FFFFFFFF"} -%\begin{center} +\noindent {\bf WARNING: the description of this experiment is not complete. + In particular, many parameters are not yet described.}\\ + +%\begin{center} %{\Large \bf Using MITgcm to Simulate Global Climatological Ocean Circulation %At Four Degree Resolution with Asynchronous Time Stepping} % @@ -23,48 +26,47 @@ %{\large May 2001} %\end{center} - -This example experiment demonstrates using the MITgcm to simulate -the planetary ocean circulation. The simulation is configured -with realistic geography and bathymetry on a -$4^{\circ} \times 4^{\circ}$ spherical polar grid. -The files for this experiment are in the verification directory -under tutorial\_global\_oce\_latlon. -Twenty levels are used in the vertical, ranging in thickness -from $50\,{\rm m}$ at the surface to $815\,{\rm m}$ at depth, -giving a maximum model depth of $6\,{\rm km}$. -At this resolution, the configuration -can be integrated forward for thousands of years on a single -processor desktop computer. +This example experiment demonstrates using the MITgcm to simulate the +planetary ocean circulation. The simulation is configured with +realistic geography and bathymetry on a $4^{\circ} \times 4^{\circ}$ +spherical polar grid. The files for this experiment are in the +verification directory under tutorial\_global\_oce\_latlon. Fifteen +levels are used in the vertical, ranging in thickness from $50\,{\rm + m}$ at the surface to $690\,{\rm m}$ at depth, giving a maximum +model depth of $5200\,{\rm m}$. +Different time-steps are used to accelerate the convergence to +equilibrium \cite[]{bryan:84} so that, at this resolution, +the configuration can be integrated forward for thousands of years +on a single processor desktop computer. \\ \subsection{Overview} -\label{www:tutorials} +%\label{www:tutorials} -The model is forced with climatological wind stress data and surface -flux data from DaSilva \cite{DaSilva94}. Climatological data -from Levitus \cite{Levitus94} is used to initialize the model hydrography. -Levitus seasonal climatology data is also used throughout the calculation -to provide additional air-sea fluxes. -These fluxes are combined with the DaSilva climatological estimates of -surface heat flux and fresh water, resulting in a mixed boundary -condition of the style described in Haney \cite{Haney}. -Altogether, this yields the following forcing applied -in the model surface layer. +The model is forced with climatological wind stress data from +\citet{trenberth90} and NCEP surface flux data from +\citet{kalnay96}. Climatological data \citep{Levitus94} is +used to initialize the model hydrography. \citeauthor{Levitus94} seasonal +climatology data is also used throughout the calculation to provide +additional air-sea fluxes. These fluxes are combined with the NCEP +climatological estimates of surface heat flux, resulting in a mixed +boundary condition of the style described in \citet{Haney}. +Altogether, this yields the following forcing applied in the model +surface layer. \begin{eqnarray} -\label{EQ:eg-global-global_forcing} -\label{EQ:eg-global-global_forcing_fu} +\label{eq:eg-global-global_forcing} +\label{eq:eg-global-global_forcing_fu} {\cal F}_{u} & = & \frac{\tau_{x}}{\rho_{0} \Delta z_{s}} \\ -\label{EQ:eg-global-global_forcing_fv} +\label{eq:eg-global-global_forcing_fv} {\cal F}_{v} & = & \frac{\tau_{y}}{\rho_{0} \Delta z_{s}} \\ -\label{EQ:eg-global-global_forcing_ft} -{\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} ) +\label{eq:eg-global-global_forcing_ft} +{\cal F}_{\theta} & = & - \lambda_{\theta} ( \theta - \theta^{\ast} ) - \frac{1}{C_{p} \rho_{0} \Delta z_{s}}{\cal Q} \\ -\label{EQ:eg-global-global_forcing_fs} -{\cal F}_{s} & = & - \lambda_{s} ( S - S^{\ast} ) +\label{eq:eg-global-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} @@ -88,90 +90,79 @@ $\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$) have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields ($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$ -respectively. The salinity forcing fields ($S^{\ast}$ and +respectively. The salinity forcing fields ($S^{\ast}$ and $\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$ respectively. The source files and procedures for ingesting this data into the simulation are described in the experiment configuration discussion in section -\ref{SEC:eg-global-clim_ocn_examp_exp_config}. +\ref{sec:eg-global-clim_ocn_examp_exp_config}. \subsection{Discrete Numerical Configuration} -\label{www:tutorials} +%\label{www:tutorials} - The model is configured in hydrostatic form. The domain is discretised with -a uniform grid spacing in latitude and longitude on the sphere - $\Delta \phi=\Delta \lambda=4^{\circ}$, so -that there are ninety grid cells in the zonal and forty in the -meridional direction. The internal model coordinate variables -$x$ and $y$ are initialized according to +The model is configured in hydrostatic form. The domain is +discretised with a uniform grid spacing in latitude and longitude on +the sphere $\Delta \phi=\Delta \lambda=4^{\circ}$, so that there are +ninety grid cells in the zonal and forty in the meridional +direction. The internal model coordinate variables $x$ and $y$ are +initialized according to \begin{eqnarray} x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\ -y=r\lambda,~\Delta y &= &r\Delta \lambda +y=r\lambda,~\Delta y &= &r\Delta \lambda \end{eqnarray} Arctic polar regions are not included in this experiment. Meridionally the model extends from $80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$. -Vertically the model is configured with twenty layers with the -following thicknesses -$\Delta z_{1} = 50\,{\rm m},\, - \Delta z_{2} = 50\,{\rm m},\, - \Delta z_{3} = 55\,{\rm m},\, - \Delta z_{4} = 60\,{\rm m},\, - \Delta z_{5} = 65\,{\rm m},\, -$ -$ - \Delta z_{6}~=~70\,{\rm m},\, - \Delta z_{7}~=~80\,{\rm m},\, - \Delta z_{8}~=95\,{\rm m},\, - \Delta z_{9}=120\,{\rm m},\, - \Delta z_{10}=155\,{\rm m},\, -$ -$ - \Delta z_{11}=200\,{\rm m},\, - \Delta z_{12}=260\,{\rm m},\, - \Delta z_{13}=320\,{\rm m},\, - \Delta z_{14}=400\,{\rm m},\, - \Delta z_{15}=480\,{\rm m},\, -$ -$ - \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 +Vertically the model is configured with fifteen layers with the +following thicknesses: +$\Delta z_{1} = 50\,{\rm m},$\\ +$\Delta z_{2} = 70\,{\rm m},\, + \Delta z_{3} = 100\,{\rm m},\, + \Delta z_{4} = 140\,{\rm m},\, + \Delta z_{5} = 190\,{\rm m},\, + \Delta z_{6} = 240\,{\rm m},\, + \Delta z_{7} = 290\,{\rm m},\, + \Delta z_{8} = 340\,{\rm m},$\\ +$\Delta z_{9} = 390\,{\rm m},\, + \Delta z_{10}= 440\,{\rm m},\, + \Delta z_{11}= 490\,{\rm m},\, + \Delta z_{12}= 540\,{\rm m},\, + \Delta z_{13}= 590\,{\rm m},\, + \Delta z_{14}= 640\,{\rm m},\, + \Delta z_{15}= 690\,{\rm m}$\\ +(here the numeric subscript indicates the model level index number, ${\tt k}$) to +give a total depth, $H$, of $-5200{\rm m}$. +The implicit free surface form of the pressure equation described in +\citet{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 forcing is added to the momentum equations in (\ref{EQ:eg-global-model_equations}) -for both the zonal flow, $u$ and the meridional flow $v$, according to equations -(\ref{EQ:eg-global-global_forcing_fu}) and (\ref{EQ:eg-global-global_forcing_fv}). -Thermodynamic forcing inputs are added to the equations -in (\ref{EQ:eg-global-model_equations}) for -potential temperature, $\theta$, and salinity, $S$, according to equations -(\ref{EQ:eg-global-global_forcing_ft}) and (\ref{EQ:eg-global-global_forcing_fs}). +Wind-stress forcing is added to the momentum equations in (\ref{eq:eg-global-model_equations}) +for both the zonal flow, $u$ and the meridional flow $v$, according to equations +(\ref{eq:eg-global-global_forcing_fu}) and (\ref{eq:eg-global-global_forcing_fv}). +Thermodynamic forcing inputs are added to the equations +in (\ref{eq:eg-global-model_equations}) for +potential temperature, $\theta$, and salinity, $S$, according to equations +(\ref{eq:eg-global-global_forcing_ft}) and (\ref{eq:eg-global-global_forcing_fs}). This produces a set of equations solved in this configuration as follows: \begin{eqnarray} -\label{EQ:eg-global-model_equations} -\frac{Du}{Dt} - fv + - \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} - - \nabla_{h}\cdot A_{h}\nabla_{h}u - - \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z} +\label{eq:eg-global-model_equations} +\frac{Du}{Dt} - fv + + \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} - + \nabla_{h}\cdot A_{h}\nabla_{h}u - + \frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z} & = & \begin{cases} {\cal F}_u & \text{(surface)} \\ 0 & \text{(interior)} \end{cases} \\ -\frac{Dv}{Dt} + fu + - \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} - - \nabla_{h}\cdot A_{h}\nabla_{h}v - - \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z} +\frac{Dv}{Dt} + fu + + \frac{1}{\rho}\frac{\partial p^{'}}{\partial y} - + \nabla_{h}\cdot A_{h}\nabla_{h}v - + \frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z} & = & \begin{cases} {\cal F}_v & \text{(surface)} \\ @@ -184,7 +175,7 @@ \\ \frac{D\theta}{Dt} - \nabla_{h}\cdot K_{h}\nabla_{h}\theta - - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z} + - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z} & = & \begin{cases} {\cal F}_\theta & \text{(surface)} \\ @@ -193,7 +184,7 @@ \\ \frac{D s}{Dt} - \nabla_{h}\cdot K_{h}\nabla_{h}s - - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z} + - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z} & = & \begin{cases} {\cal F}_s & \text{(surface)} \\ @@ -203,529 +194,280 @@ g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'} \end{eqnarray} -\noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and -$v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$ +\noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and +$v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$ are the zonal and meridional components of the flow vector, $\vec{u}$, on the sphere. As described in -MITgcm Numerical Solution Procedure \ref{chap:discretization}, 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 +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} +%\label{www:tutorials} The Laplacian dissipation coefficient, $A_{h}$, is set to $5 \times 10^5 m s^{-1}$. -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}, \begin{eqnarray} -\label{EQ:eg-global-munk_layer} +\label{eq:eg-global-munk_layer} && M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} \end{eqnarray} \noindent of $\approx 600$km. This is greater than the model -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 boundary layer is adequately resolved. \\ -\noindent The model is stepped forward with a -time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and -$\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability -parameter to the horizontal Laplacian friction \cite{adcroft:95} +\noindent The model is stepped forward with a time step $\Delta +t_{\theta}=24~{\rm hours}$ for thermodynamic variables and $\Delta +t_{v}=30~{\rm minutes}$ for momentum terms. With this time step, +the stability parameter to the horizontal Laplacian friction +\citep{adcroft:95} \begin{eqnarray} -\label{EQ:eg-global-laplacian_stability} -&& S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2} +\label{eq:eg-global-laplacian_stability} +&& S_{l} = 4 \frac{A_{h} \Delta t_{v}}{{\Delta x}^2} \end{eqnarray} -\noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the -0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at -$\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$. -\\ +\noindent evaluates to 0.6 at a latitude of $\phi=80^{\circ}$, which +is above the 0.3 upper limit for stability, but the zonal grid spacing +$\Delta x$ is smallest at $\phi=80^{\circ}$ where $\Delta +x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$ and the stability +criterion is already met 1 grid cell equatorwards (at $\phi=76^{\circ}$). + -\noindent The vertical dissipation coefficient, $A_{z}$, is set to +\noindent The vertical dissipation coefficient, $A_{z}$, is set to $1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit \begin{eqnarray} -\label{EQ:eg-global-laplacian_stability_z} -S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2} +\label{eq:eg-global-laplacian_stability_z} +&& S_{l} = 4 \frac{A_{z} \Delta t_{v}}{{\Delta z}^2} \end{eqnarray} -\noindent evaluates to $0.015$ for the smallest model -level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below +\noindent evaluates to $0.0029$ for the smallest model +level spacing ($\Delta z_{1}=50{\rm m}$) which is well below the upper stability limit. \\ -The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients -for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$ -and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit -related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$. -Here the stability parameter -\begin{eqnarray} -\label{EQ:eg-global-laplacian_stability_xtheta} -S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2} -\end{eqnarray} -evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The -stability parameter related to $K_{z}$ -\begin{eqnarray} -\label{EQ:eg-global-laplacian_stability_ztheta} -S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2} -\end{eqnarray} -evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit -of $S_{l} \approx 0.5$. -\\ +% The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients +% for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$ +% and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit +% related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$. +% Here the stability parameter +% \begin{eqnarray} +% \label{eq:eg-global-laplacian_stability_xtheta} +% S_{l} = \frac{4 K_{h} \Delta t_{\theta}}{{\Delta x}^2} +% \end{eqnarray} +% evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The +% stability parameter related to $K_{z}$ +% \begin{eqnarray} +% \label{eq:eg-global-laplacian_stability_ztheta} +% S_{l} = \frac{4 K_{z} \Delta t_{\theta}}{{\Delta z}^2} +% \end{eqnarray} +% evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit +% of $S_{l} \approx 0.5$. +% \\ \noindent The numerical stability for inertial oscillations -\cite{adcroft:95} +\citep{adcroft:95} \begin{eqnarray} -\label{EQ:eg-global-inertial_stability} -S_{i} = f^{2} {\delta t_v}^2 +\label{eq:eg-global-inertial_stability} +&& S_{i} = f^{2} {\Delta t_v}^2 \end{eqnarray} -\noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to -the $S_{i} < 1$ upper limit for stability. +\noindent evaluates to $0.07$ for +$f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is +below the $S_{i} < 1$ upper limit for stability. \\ -\noindent The advective CFL \cite{adcroft:95} for a extreme maximum +\noindent The advective CFL \citep{adcroft:95} for a extreme maximum horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ \begin{eqnarray} -\label{EQ:eg-global-cfl_stability} -S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x} +\label{eq:eg-global-cfl_stability} +&& S_{a} = \frac{| \vec{u} | \Delta t_{v}}{ \Delta x} \end{eqnarray} -\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 limit of 0.5. \\ \noindent The stability parameter for internal gravity waves propagating -with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$ -\cite{adcroft:95} + with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$ +\citep{adcroft:95} \begin{eqnarray} -\label{EQ:eg-global-gfl_stability} -S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x} +\label{eq:eg-global-gfl_stability} +&& S_{c} = \frac{c_{g} \Delta t_{v}}{ \Delta x} \end{eqnarray} -\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 stability limit of 0.5. - + \subsection{Experiment Configuration} -\label{www:tutorials} -\label{SEC:eg-global-clim_ocn_examp_exp_config} +%\label{www:tutorials} +\label{sec:eg-global-clim_ocn_examp_exp_config} -The model configuration for this experiment resides under the -directory {\it tutorial\_examples/global\_ocean\_circulation/}. -The experiment files +The model configuration for this experiment resides under the +directory {\it tutorial\_global\_oce\_latlon/}. The experiment files \begin{itemize} \item {\it input/data} \item {\it input/data.pkg} \item {\it input/eedata}, -\item {\it input/windx.bin}, -\item {\it input/windy.bin}, -\item {\it input/salt.bin}, -\item {\it input/theta.bin}, -\item {\it input/SSS.bin}, -\item {\it input/SST.bin}, -\item {\it input/topog.bin}, -\item {\it code/CPP\_EEOPTIONS.h} -\item {\it code/CPP\_OPTIONS.h}, -\item {\it code/SIZE.h}. +\item {\it input/trenberth\_taux.bin}, +\item {\it input/trenberth\_tauy.bin}, +\item {\it input/lev\_s.bin}, +\item {\it input/lev\_t.bin}, +\item {\it input/lev\_sss.bin}, +\item {\it input/lev\_sst.bin}, +\item {\it input/bathymetry.bin}, +%\item {\it code/CPP\_EEOPTIONS.h} +%\item {\it code/CPP\_OPTIONS.h}, +\item {\it code/SIZE.h}. \end{itemize} contain the code customizations and parameter settings for these experiments. Below we describe the customizations to these files associated with this experiment. \subsubsection{Driving Datasets} -\label{www:tutorials} +%\label{www:tutorials} -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 ($Q$) +%% New figures are included before +%% Relaxation temperature +%\begin{figure} +%\centering +%\includegraphics[]{relax_temperature.eps} +%\caption{Relaxation temperature for January} +%\label{fig:relax_temperature} +%\end{figure} + +%% Relaxation salinity +%\begin{figure} +%\centering +%\includegraphics[]{relax_salinity.eps} +%\caption{Relaxation salinity for January} +%\label{fig:relax_salinity} +%\end{figure} + +%% tau_x +%\begin{figure} +%\centering +%\includegraphics[]{tau_x.eps} +%\caption{zonal wind stress for January} +%\label{fig:tau_x} +%\end{figure} + +%% tau_y +%\begin{figure} +%\centering +%\includegraphics[]{tau_y.eps} +%\caption{meridional wind stress for January} +%\label{fig:tau_y} +%\end{figure} + +%% Qnet +%\begin{figure} +%\centering +%\includegraphics[]{qnet.eps} +%\caption{Heat flux for January} +%\label{fig:qnet} +%\end{figure} + +%% EmPmR +%\begin{figure} +%\centering +%\includegraphics[]{empmr.eps} +%\caption{Fresh water flux for January} +%\label{fig:empmr} +%\end{figure} + +%% Bathymetry +%\begin{figure} +%\centering +%\includegraphics[]{bathymetry.eps} +%\caption{Bathymetry} +%\label{fig:bathymetry} +%\end{figure} + + +Figures (\ref{fig:sim_config_tclim_pcoord}-\ref{fig:sim_config_empmr_pcoord}) +%(\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. - +in equations +(\ref{eq:eg-global-global_forcing_fu}-\ref{eq:eg-global-global_forcing_fs}). +The figures also indicate the lateral extent and coastline used in the +experiment. Figure ({\it --- missing figure --- }) %ref{fig:model_bathymetry}) +shows the depth contours of the model domain. \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 -are - -\begin{itemize} - -\item Lines 7-10 and 11-14 -\begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim} -$\cdots$ \\ -set reference values for potential -temperature and salinity at each model level in units of $^{\circ}\mathrm{C}$ and -${\rm ppt}$. The entries are ordered from surface to depth. -Density is calculated from anomalies at each level evaluated -with respect to the reference values set here.\\ -\fbox{ -\begin{minipage}{5.0in} -{\it S/R INI\_THETA}({\it ini\_theta.F}) -\end{minipage} -} - - -\item Line 15, -\begin{verbatim} viscAz=1.E-3, \end{verbatim} -this line sets the vertical Laplacian dissipation coefficient to -$1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions -for this operator are specified later. This variable is copied into -model general vertical coordinate variable {\bf viscAr}. - -\fbox{ -\begin{minipage}{5.0in} -{\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F}) -\end{minipage} -} - -\item Line 16, -\begin{verbatim} -viscAh=5.E5, -\end{verbatim} -this line sets the horizontal Laplacian frictional dissipation coefficient to -$5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions -for this operator are specified later. - -\item Lines 17, -\begin{verbatim} -no_slip_sides=.FALSE. -\end{verbatim} -this line selects a free-slip lateral boundary condition for -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 $x$. - -\item Lines 9, -\begin{verbatim} -no_slip_bottom=.TRUE. -\end{verbatim} -this line selects a no-slip boundary condition for bottom -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 19, -\begin{verbatim} -diffKhT=1.E3, -\end{verbatim} -this line sets the horizontal diffusion coefficient for temperature -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 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 coefficient 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 MOM\_FLUXFORM}({\it mom\_fluxform.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. - -\end{itemize} +%\label{www:tutorials} -\noindent other lines in the file {\it input/data} are standard values -that are described in the MITgcm Getting Started and MITgcm Parameters -notes. - -\begin{small} -\input{part3/case_studies/climatalogical_ogcm/input/data} -\end{small} +\input{s_examples/global_oce_latlon/inp_data} \subsubsection{File {\it input/data.pkg}} -\label{www:tutorials} +%\label{www:tutorials} This file uses standard default values and does not contain customisations for this experiment. \subsubsection{File {\it input/eedata}} -\label{www:tutorials} +%\label{www:tutorials} This file uses standard default values and does not contain customisations 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 $Nm^{-2}$. -Although $\tau_{x}$ is only a function of $y$n in this experiment -this file must still define a complete two-dimensional map in order -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. - -\subsubsection{File {\it input/topog.box}} -\label{www:tutorials} - - -The {\it input/topog.box} file specifies a two-dimensional ($x,y$) -map of depth values. For this experiment values are either -$0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep -ocean. The file contains a raw binary stream of data that is enumerated -in the same way as standard MITgcm two-dimensional, horizontal arrays. -The included matlab program {\it input/gendata.m} gives a complete -code for creating the {\it input/topog.box} file. +\subsubsection{Files{\it input/trenberth\_taux.bin} and {\it + input/trenberth\_tauy.bin}} +%\label{www:tutorials} + +The {\it input/trenberth\_taux.bin} and {\it + input/trenberth\_tauy.bin} files specify a three-dimensional +($x,y,time$) map of wind stress, $(\tau_{x},\tau_{y})$, values +\citep{trenberth90}. The units used are $Nm^{-2}$. + +\subsubsection{File {\it input/bathymetry.bin}} +%\label{www:tutorials} + +The {\it input/bathymetry.bin} file specifies a two-dimensional +($x,y$) map of depth values. For this experiment values range +between~$0$ and $-5200\,{\rm m}$, and have been derived from +ETOPO5. The file contains a raw binary stream of data that is +enumerated in the same way as standard MITgcm two-dimensional, +horizontal arrays. \subsubsection{File {\it code/SIZE.h}} -\label{www:tutorials} - -Two lines are customized in this file for the current experiment - -\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} +%\label{www:tutorials} -\begin{small} -\input{part3/case_studies/climatalogical_ogcm/code/SIZE.h} -\end{small} +\input{s_examples/global_oce_latlon/cod_SIZE.h} -\subsubsection{File {\it code/CPP\_OPTIONS.h}} -\label{www:tutorials} +%\subsubsection{File {\it code/CPP\_OPTIONS.h}} +%\label{www:tutorials} -This file uses standard default values and does not contain -customisations for this experiment. +%This file uses standard default values and does not contain +%customisations for this experiment. -\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} -\label{www:tutorials} +%\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} +%\label{www:tutorials} -This file uses standard default values and does not contain -customisations for this experiment. +%This file uses standard default values and does not contain +%customisations for this experiment. \subsubsection{Other Files } -\label{www:tutorials} +%\label{www:tutorials} -Other files relevant to this experiment are -\begin{itemize} -\item {\it model/src/ini\_cori.F}. This file initializes the model -coriolis variables {\bf fCorU}. -\item {\it model/src/ini\_spherical\_polar\_grid.F} -\item {\it model/src/ini\_parms.F}, -\item {\it input/windx.sin\_y}, -\end{itemize} -contain the code customisations and parameter settings for this -experiments. Below we describe the customisations -to these files associated with this experiment. +% Other files relevant to this experiment are +% \begin{itemize} +% \item {\it model/src/ini\_cori.F}. This file initializes the model +% coriolis variables {\bf fCorU}. +% \item {\it model/src/ini\_spherical\_polar\_grid.F} +% \item {\it model/src/ini\_parms.F}, +% \item {\it input/windx.sin\_y}, +% \end{itemize} +% contain the code customisations and parameter settings for this +% experiments. Below we describe the customisations +% to these files associated with this experiment.