--- manual/s_examples/rotating_tank/tank.tex 2004/06/22 15:07:37 1.1 +++ manual/s_examples/rotating_tank/tank.tex 2004/06/22 16:56:31 1.2 @@ -1,11 +1,15 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.1 2004/06/22 15:07:37 afe Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/rotating_tank/tank.tex,v 1.2 2004/06/22 16:56:31 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 Using MITgcm to Simulate a Rotating Tank in Cylindrical -%Coordinates} +%{\Large \bf Simulating a Rotating Tank in Cylindrical Coordinates} +% % %\vspace*{4mm} % @@ -13,59 +17,307 @@ %{\large June 2004} %\end{center} -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. - -\section{Barotropic Ocean Gyre In Cartesian Coordinates} -\label{sect:eg-baro} +\subsection{Introduction} \label{www:tutorials} - - -\subsection{Equations Solved} -\label{www:tutorials} -The model is configured in hydrostatic form. The implicit free surface form of the +This section illustrates an example of MITgcm simulating a laboratory +experiment on much smaller scales than those common to geophysical +fluid dynamics. + +\subsection{Overview} +\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 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. + + 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: + +\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} +\\ +\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)} \\ +0 & \text{(interior)} +\end{cases} +\\ +\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. +\\ \subsubsection{Numerical Stability Criteria} \label{www:tutorials} - -\subsection{Code Configuration} +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}, +\begin{eqnarray} +\label{EQ:eg-hs-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 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} +\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} +\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. +\\ + +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 +\cite{adcroft:95} + +\begin{eqnarray} +\label{EQ:eg-hs-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 The advective CFL \cite{adcroft:95} for a 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} +\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} + +\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} \label{www:tutorials} -\label{SEC:eg-baro-code_config} +\label{SEC:eg-hs_examp_exp_config} The model configuration for this experiment resides under the -directory {\it verification/exp0/}. The experiment files +directory {\it verification/hs94.128x64x5}. The experiment files \begin{itemize} \item {\it input/data} \item {\it input/data.pkg} \item {\it input/eedata}, -\item {\it input/windx.sin\_y}, -\item {\it input/topog.box}, +\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}. \end{itemize} -contain the code customizations and parameter settings for this +contain the code customizations and parameter settings for these experiments. Below we describe the customizations to these files associated with this experiment. @@ -78,74 +330,250 @@ \begin{itemize} -\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 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 27, \begin{verbatim} -startTime=0, +gravity=9.81, \end{verbatim} -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. +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 29, +\item Line 28-29, \begin{verbatim} -endTime=12000, +rigidLid=.FALSE., +implicitFreeSurface=.TRUE., \end{verbatim} -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. +Selects the barotropic pressure equation to be the implicit free surface +formulation. \item Line 30, \begin{verbatim} -deltaTmom=1200, +eosType='POLY3', \end{verbatim} -This line sets the momentum equation timestep to $1200s$. +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 39, +\item Line 31, \begin{verbatim} -usingCartesianGrid=.TRUE., +readBinaryPrec=32, \end{verbatim} -This line requests that the simulation be performed in a -Cartesian coordinate system. +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 41, +\item Line 36, \begin{verbatim} -delX=60*20E3, +cg2dMaxIters=1000, \end{verbatim} -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). +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} +} \item Line 42, \begin{verbatim} -delY=60*20E3, +startTime=0, \end{verbatim} -This line sets the horizontal grid spacing between each y-coordinate line -in the discrete grid to $20 \times 10^{3}m$ ($20$~km). +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} -delZ=5000, +endTime=2808000., \end{verbatim} -This line sets the vertical grid spacing between each z-coordinate line -in the discrete grid to $5000m$ ($5$~km). +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 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 @@ -156,12 +584,12 @@ 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 $-5000m$ indicates open ocean. The matlab program +of $-2000m$ indicates open ocean. The matlab program {\it input/gendata.m} shows an example of how to generate a bathymetry file. -\item Line 49, +\item Line 50, \begin{verbatim} zonalWindFile='windx.sin_y' \end{verbatim} @@ -169,7 +597,9 @@ 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} @@ -177,21 +607,21 @@ that are described in the MITgcm Getting Started and MITgcm Parameters notes. -%%\begin{small} -%%\input{part3/case_studies/barotropic_gyre/input/data} -%%\end{small} +\begin{small} +\input{part3/case_studies/climatalogical_ogcm/input/data} +\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. +customisations 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. +customisations for this experiment. \subsubsection{File {\it input/windx.sin\_y}} \label{www:tutorials} @@ -210,7 +640,7 @@ The {\it input/topog.box} file specifies a two-dimensional ($x,y$) map of depth values. For this experiment values are either -$0m$ or {\bf -delZ}m, corresponding respectively to a wall or to deep +$0m$ 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 @@ -233,22 +663,40 @@ 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/barotropic_gyre/code/SIZE.h} +\input{part3/case_studies/climatalogical_ogcm/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 -customizations for this experiment. +customisations 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. +customisations 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.