--- manual/s_examples/rotating_tank/tank.tex 2004/06/22 16:56:31 1.2 +++ manual/s_examples/rotating_tank/tank.tex 2004/07/26 16:21:15 1.3 @@ -1,323 +1,205 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.2 2004/06/22 16:56:31 afe Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.3 2004/07/26 16:21:15 afe Exp $ % $Name: $ -\section{Simulating a Rotating Tank in Cylindrical Coordinates} -\label{www:tutorials} -\label{sect:eg-tank} - \bodytext{bgcolor="#FFFFFFFF"} %\begin{center} -%{\Large \bf Simulating a Rotating Tank in Cylindrical Coordinates} -% +%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical +%Coordinates} % %\vspace*{4mm} % %\vspace*{3mm} -%{\large June 2004} +%{\large May 2001} %\end{center} -\subsection{Introduction} -\label{www:tutorials} - -This section illustrates an example of MITgcm simulating a laboratory -experiment on much smaller scales than those common to geophysical -fluid dynamics. +This is the first in a series of tutorials describing +example MITgcm numerical experiments. The example experiments +include both straightforward examples of idealized geophysical +fluid simulations and more involved cases encompassing +large scale modeling and +automatic differentiation. Both hydrostatic and non-hydrostatic +experiments are presented, as well as experiments employing +Cartesian, spherical-polar and cube-sphere coordinate systems. +These ``case study'' documents include information describing +the experimental configuration and detailed information on how to +configure the MITgcm code and input files for each experiment. -\subsection{Overview} +\section{A Rotating Tank in Cylindrical Coordinates} +\label{sect:eg-tank} \label{www:tutorials} This example experiment demonstrates using the MITgcm to simulate -a laboratory experiment with a rotating tank of water with an ice -bucket in the center. The simulation is configured for a laboratory -scale on a 3^{\circ} \times 20cm cyclindrical grid with twenty-nine vertical -levels. -\\ - -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. - - -\noindent where ${\cal F}_{u}$, ${\cal F}_{v}$, ${\cal F}_{\theta}$, -${\cal F}_{s}$ are the forcing terms in the zonal and meridional -momentum and in the potential temperature and salinity -equations respectively. -The term $\Delta z_{s}$ represents the top ocean layer thickness in -meters. -It is used in conjunction with a reference density, $\rho_{0}$ -(here set to $999.8\,{\rm kg\,m^{-3}}$), a -reference salinity, $S_{0}$ (here set to 35~ppt), -and a specific heat capacity, $C_{p}$ (here set to -$4000~{\rm J}~^{\circ}{\rm C}^{-1}~{\rm kg}^{-1}$), to convert -input dataset values into time tendencies of -potential temperature (with units of $^{\circ}{\rm C}~{\rm s}^{-1}$), -salinity (with units ${\rm ppt}~s^{-1}$) and -velocity (with units ${\rm m}~{\rm s}^{-2}$). -The externally supplied forcing fields used in this -experiment are $\tau_{x}$, $\tau_{y}$, $\theta^{\ast}$, $S^{\ast}$, -$\cal{Q}$ 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 -$\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$ -respectively. -\\ - - -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:eg-hs-global_forcing_fu}-\ref{EQ:eg-hs-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. - - -\subsection{Discrete Numerical Configuration} -\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 -\begin{eqnarray} -x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\ -y=r\lambda,~\Delta x &= &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, ${\tt k}$). -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 -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 meridional flow $v$, according to equations -(\ref{EQ:eg-hs-global_forcing_fu}) and (\ref{EQ:eg-hs-global_forcing_fv}). -Thermodynamic forcing inputs are added to the equations for -potential temperature, $\theta$, and salinity, $S$, according to equations -(\ref{EQ:eg-hs-global_forcing_ft}) and (\ref{EQ:eg-hs-global_forcing_fs}). -This produces a set of equations solved in this configuration as follows: +a Barotropic, wind-forced, ocean gyre circulation. The experiment +is a numerical rendition of the gyre circulation problem similar +to the problems described analytically by Stommel in 1966 +\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}. + +In this experiment the model +is configured to represent a rectangular enclosed box of fluid, +$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced +by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally +in the ``north-south'' direction. Topologically the grid is Cartesian and +the coriolis parameter $f$ is defined according to a mid-latitude beta-plane +equation + +\begin{equation} +\label{EQ:eg-baro-fcori} +f(y) = f_{0}+\beta y +\end{equation} + +\noindent where $y$ is the distance along the ``north-south'' axis of the +simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in +(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. +\\ +\\ + The sinusoidal wind-stress variations are defined according to + +\begin{equation} +\label{EQ:eg-baro-taux} +\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y}) +\end{equation} + +\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and +$\tau_0$ is set to $0.1N m^{-2}$. +\\ +\\ +Figure \ref{FIG:eg-baro-simulation_config} +summarizes the configuration simulated. + +%% === eh3 === +\begin{figure} +%% \begin{center} +%% \resizebox{7.5in}{5.5in}{ +%% \includegraphics*[0.2in,0.7in][10.5in,10.5in] +%% {part3/case_studies/barotropic_gyre/simulation_config.eps} } +%% \end{center} +\centerline{ + \scalefig{.95} + \epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps} +} +\caption{Schematic of simulation domain and wind-stress forcing function +for barotropic gyre numerical experiment. The domain is enclosed bu solid +walls at $x=$~0,1200km and at $y=$~0,1200km.} +\label{FIG:eg-baro-simulation_config} +\end{figure} + +\subsection{Equations Solved} +\label{www:tutorials} +The model is configured in hydrostatic form. The implicit free surface form of the +pressure equation described in Marshall et. al \cite{marshall:97a} is +employed. +A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous +dissipation. The wind-stress momentum input is added to the momentum equation +for the ``zonal flow'', $u$. Other terms in the model +are explicitly switched off for this experiment configuration (see section +\ref{SEC:code_config} ), yielding an active set of equations solved in this +configuration as follows \begin{eqnarray} -\label{EQ:eg-hs-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} +\label{EQ:eg-baro-model_equations} +\frac{Du}{Dt} - fv + + g\frac{\partial \eta}{\partial x} - + A_{h}\nabla_{h}^2u +& = & +\frac{\tau_{x}}{\rho_{0}\Delta 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} +\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} - + A_{h}\nabla_{h}^2v & = & -\begin{cases} -{\cal F}_v & \text{(surface)} \\ -0 & \text{(interior)} -\end{cases} +0 \\ \frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u} &=& 0 -\\ -\frac{D\theta}{Dt} - - \nabla_{h}\cdot K_{h}\nabla_{h}\theta - - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z} -& = & -\begin{cases} -{\cal F}_\theta & \text{(surface)} \\ -0 & \text{(interior)} -\end{cases} -\\ -\frac{D s}{Dt} - - \nabla_{h}\cdot K_{h}\nabla_{h}s - - \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z} -& = & -\begin{cases} -{\cal F}_s & \text{(surface)} \\ -0 & \text{(interior)} -\end{cases} -\\ -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 -$v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$ -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 -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. +\noindent where $u$ and $v$ and the $x$ and $y$ components of the +flow vector $\vec{u}$. \\ + +\subsection{Discrete Numerical Configuration} +\label{www:tutorials} + + The domain is discretised with +a uniform grid spacing in the horizontal set to + $\Delta x=\Delta y=20$~km, so +that there are sixty grid cells in the $x$ and $y$ directions. Vertically the +model is configured with a single layer with depth, $\Delta z$, of $5000$~m. + \subsubsection{Numerical Stability Criteria} \label{www:tutorials} -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 $400 m s^{-1}$. This value is chosen to yield a Munk layer width \cite{adcroft:95}, + \begin{eqnarray} -\label{EQ:eg-hs-munk_layer} +\label{EQ:eg-baro-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 -boundary layer is adequately resolved. +\noindent of $\approx 100$km. This is greater than the model +resolution $\Delta x$, ensuring that the frictional boundary +layer is well 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 +time step $\delta t=1200$secs. With this time step the stability parameter to the horizontal Laplacian friction \cite{adcroft:95} -\begin{eqnarray} -\label{EQ:eg-hs-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 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-hs-laplacian_stability_z} -S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2} +\label{EQ:eg-baro-laplacian_stability} +S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^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 -the upper stability limit. +\noindent evaluates to 0.012, which is well below the 0.3 upper limit +for stability. \\ -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-hs-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-hs-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 +\noindent The numerical stability for inertial oscillations \cite{adcroft:95} \begin{eqnarray} -\label{EQ:eg-hs-inertial_stability} -S_{i} = f^{2} {\delta t_v}^2 +\label{EQ:eg-baro-inertial_stability} +S_{i} = f^{2} {\delta t}^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 $0.0144$, which is well below the $0.5$ upper +limit for stability. \\ -\noindent The advective CFL \cite{adcroft:95} for a extreme maximum -horizontal flow -speed of $ | \vec{u} | = 2 ms^{-1}$ +\noindent The advective CFL \cite{adcroft:95} for an extreme maximum +horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ \begin{eqnarray} -\label{EQ:eg-hs-cfl_stability} -S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x} +\label{EQ:eg-baro-cfl_stability} +S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} \end{eqnarray} -\noindent evaluates to $6 \times 10^{-2}$. 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} +\noindent evaluates to 0.12. This is approaching the stability limit +of 0.5 and limits $\delta t$ to $1200s$. -\begin{eqnarray} -\label{EQ:eg-hs-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 -stability limit of 0.5. - -\subsection{Experiment Configuration} +\subsection{Code Configuration} \label{www:tutorials} -\label{SEC:eg-hs_examp_exp_config} +\label{SEC:eg-baro-code_config} The model configuration for this experiment resides under the -directory {\it verification/hs94.128x64x5}. The experiment files +directory {\it verification/exp0/}. 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 input/windx.sin\_y}, +\item {\it input/topog.box}, \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 +contain the code customizations and parameter settings for this experiments. Below we describe the customizations to these files associated with this experiment. @@ -330,250 +212,74 @@ \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 $^{\circ}$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 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets +the Laplacian friction coefficient to $400 m^2s^{-1}$ +\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets +$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$ + +\item Lines 15 and 16 +\begin{verbatim} +rigidLid=.FALSE., +implicitFreeSurface=.TRUE., +\end{verbatim} +these lines suppress the rigid lid formulation of the surface +pressure inverter and activate the implicit free surface form +of the pressure inverter. \item Line 27, \begin{verbatim} -gravity=9.81, +startTime=0, \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} -} +this line indicates that the experiment should start from $t=0$ +and implicitly suppresses searching for checkpoint files associated +with restarting an numerical integration from a previously saved state. - -\item Line 28-29, +\item Line 29, \begin{verbatim} -rigidLid=.FALSE., -implicitFreeSurface=.TRUE., +endTime=12000, \end{verbatim} -Selects the barotropic pressure equation to be the implicit free surface -formulation. +this line indicates that the experiment should start finish at $t=12000s$. +A restart file will be written at this time that will enable the +simulation to be continued from this point. \item Line 30, \begin{verbatim} -eosType='POLY3', +deltaTmom=1200, \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} -} +This line sets the momentum equation timestep to $1200s$. -\item Line 31, +\item Line 39, \begin{verbatim} -readBinaryPrec=32, +usingCartesianGrid=.TRUE., \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} -} +This line requests that the simulation be performed in a +Cartesian coordinate system. -\item Line 36, +\item Line 41, \begin{verbatim} -cg2dMaxIters=1000, +delX=60*20E3, \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:eg-hs-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} -} +This line sets the horizontal grid spacing between each x-coordinate line +in the discrete grid. The syntax indicates that the discrete grid +should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$ +($20$~km). \item Line 42, \begin{verbatim} -startTime=0, +delY=60*20E3, \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. +This line sets the horizontal grid spacing between each y-coordinate line +in the discrete grid to $20 \times 10^{3}m$ ($20$~km). \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, +delZ=5000, \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} -} +This line sets the vertical grid spacing between each z-coordinate line +in the discrete grid to $5000m$ ($5$~km). \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 @@ -584,12 +290,12 @@ 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 +of $-5000m$ indicates open ocean. The matlab program {\it input/gendata.m} shows an example of how to generate a bathymetry file. -\item Line 50, +\item Line 49, \begin{verbatim} zonalWindFile='windx.sin_y' \end{verbatim} @@ -597,9 +303,7 @@ 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. +code to generate a valid {\bf zonalWindFile} file. \end{itemize} @@ -608,20 +312,20 @@ notes. \begin{small} -\input{part3/case_studies/climatalogical_ogcm/input/data} +\input{part3/case_studies/barotropic_gyre/input/data} \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} @@ -640,7 +344,7 @@ 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 +$0m$ or {\bf -delZ}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 @@ -663,40 +367,22 @@ 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} \begin{small} -\input{part3/case_studies/climatalogical_ogcm/code/SIZE.h} +\input{part3/case_studies/barotropic_gyre/code/SIZE.h} \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} -\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.