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\section{Simulating a Rotating Tank in Cylindrical Coordinates} |
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\label{www:tutorials} |
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\label{sect:eg-tank} |
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%\begin{center} |
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%{\Large \bf Simulating a Rotating Tank in Cylindrical Coordinates} |
%{\Large \bf Using MITgcm to Simulate a Rotating Tank in Cylindrical |
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%Coordinates} |
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%\vspace*{3mm} |
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%{\large June 2004} |
%{\large May 2001} |
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%\end{center} |
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\subsection{Introduction} |
This is the first in a series of tutorials describing |
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\label{www:tutorials} |
example MITgcm numerical experiments. The example experiments |
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include both straightforward examples of idealized geophysical |
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This section illustrates an example of MITgcm simulating a laboratory |
fluid simulations and more involved cases encompassing |
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experiment on much smaller scales than those common to geophysical |
large scale modeling and |
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fluid dynamics. |
automatic differentiation. Both hydrostatic and non-hydrostatic |
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experiments are presented, as well as experiments employing |
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Cartesian, spherical-polar and cube-sphere coordinate systems. |
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These ``case study'' documents include information describing |
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the experimental configuration and detailed information on how to |
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configure the MITgcm code and input files for each experiment. |
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\subsection{Overview} |
\section{A Rotating Tank in Cylindrical Coordinates} |
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\label{sect:eg-tank} |
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\label{www:tutorials} |
\label{www:tutorials} |
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This example experiment demonstrates using the MITgcm to simulate |
This example experiment demonstrates using the MITgcm to simulate |
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a laboratory experiment with a rotating tank of water with an ice |
a Barotropic, wind-forced, ocean gyre circulation. The experiment |
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bucket in the center. The simulation is configured for a laboratory |
is a numerical rendition of the gyre circulation problem similar |
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scale on a 3^{\circ} \times 20cm cyclindrical grid with twenty-nine vertical |
to the problems described analytically by Stommel in 1966 |
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levels. |
\cite{Stommel66} and numerically in Holland et. al \cite{Holland75}. |
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In this experiment the model |
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The model is forced with climatological wind stress data and surface |
is configured to represent a rectangular enclosed box of fluid, |
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flux data from DaSilva \cite{DaSilva94}. Climatological data |
$1200 \times 1200 $~km in lateral extent. The fluid is $5$~km deep and is forced |
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from Levitus \cite{Levitus94} is used to initialize the model hydrography. |
by a constant in time zonal wind stress, $\tau_x$, that varies sinusoidally |
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Levitus seasonal climatology data is also used throughout the calculation |
in the ``north-south'' direction. Topologically the grid is Cartesian and |
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to provide additional air-sea fluxes. |
the coriolis parameter $f$ is defined according to a mid-latitude beta-plane |
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These fluxes are combined with the DaSilva climatological estimates of |
equation |
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surface heat flux and fresh water, resulting in a mixed boundary |
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condition of the style described in Haney \cite{Haney}. |
\begin{equation} |
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Altogether, this yields the following forcing applied |
\label{EQ:eg-baro-fcori} |
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in the model surface layer. |
f(y) = f_{0}+\beta y |
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\end{equation} |
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\noindent where ${\cal F}_{u}$, ${\cal F}_{v}$, ${\cal F}_{\theta}$, |
\noindent where $y$ is the distance along the ``north-south'' axis of the |
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${\cal F}_{s}$ are the forcing terms in the zonal and meridional |
simulated domain. For this experiment $f_{0}$ is set to $10^{-4}s^{-1}$ in |
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momentum and in the potential temperature and salinity |
(\ref{EQ:eg-baro-fcori}) and $\beta = 10^{-11}s^{-1}m^{-1}$. |
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equations respectively. |
\\ |
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The term $\Delta z_{s}$ represents the top ocean layer thickness in |
\\ |
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meters. |
The sinusoidal wind-stress variations are defined according to |
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It is used in conjunction with a reference density, $\rho_{0}$ |
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(here set to $999.8\,{\rm kg\,m^{-3}}$), a |
\begin{equation} |
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reference salinity, $S_{0}$ (here set to 35~ppt), |
\label{EQ:eg-baro-taux} |
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and a specific heat capacity, $C_{p}$ (here set to |
\tau_x(y) = \tau_{0}\sin(\pi \frac{y}{L_y}) |
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$4000~{\rm J}~^{\circ}{\rm C}^{-1}~{\rm kg}^{-1}$), to convert |
\end{equation} |
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input dataset values into time tendencies of |
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potential temperature (with units of $^{\circ}{\rm C}~{\rm s}^{-1}$), |
\noindent where $L_{y}$ is the lateral domain extent ($1200$~km) and |
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salinity (with units ${\rm ppt}~s^{-1}$) and |
$\tau_0$ is set to $0.1N m^{-2}$. |
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velocity (with units ${\rm m}~{\rm s}^{-2}$). |
\\ |
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The externally supplied forcing fields used in this |
\\ |
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experiment are $\tau_{x}$, $\tau_{y}$, $\theta^{\ast}$, $S^{\ast}$, |
Figure \ref{FIG:eg-baro-simulation_config} |
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$\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$) |
summarizes the configuration simulated. |
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have units of ${\rm N}~{\rm m}^{-2}$. The temperature forcing fields |
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($\theta^{\ast}$ and $Q$) have units of $^{\circ}{\rm C}$ and ${\rm W}~{\rm m}^{-2}$ |
%% === eh3 === |
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respectively. The salinity forcing fields ($S^{\ast}$ and |
\begin{figure} |
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$\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$ |
%% \begin{center} |
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respectively. |
%% \resizebox{7.5in}{5.5in}{ |
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\\ |
%% \includegraphics*[0.2in,0.7in][10.5in,10.5in] |
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%% {part3/case_studies/barotropic_gyre/simulation_config.eps} } |
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%% \end{center} |
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Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the |
\centerline{ |
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relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields, |
\scalefig{.95} |
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the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$) |
\epsfbox{part3/case_studies/barotropic_gyre/simulation_config.eps} |
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and the net fresh water flux (${\cal E} - {\cal P} - {\cal R}$) used |
} |
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in equations \ref{EQ:eg-hs-global_forcing_fu}-\ref{EQ:eg-hs-global_forcing_fs}. The figures |
\caption{Schematic of simulation domain and wind-stress forcing function |
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also indicate the lateral extent and coastline used in the experiment. |
for barotropic gyre numerical experiment. The domain is enclosed bu solid |
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Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model |
walls at $x=$~0,1200km and at $y=$~0,1200km.} |
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domain. |
\label{FIG:eg-baro-simulation_config} |
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\end{figure} |
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\subsection{Discrete Numerical Configuration} |
\subsection{Equations Solved} |
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\label{www:tutorials} |
\label{www:tutorials} |
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The model is configured in hydrostatic form. The implicit free surface form of the |
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pressure equation described in Marshall et. al \cite{marshall:97a} is |
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The model is configured in hydrostatic form. The domain is discretised with |
employed. |
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a uniform grid spacing in latitude and longitude on the sphere |
A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous |
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$\Delta \phi=\Delta \lambda=4^{\circ}$, so |
dissipation. The wind-stress momentum input is added to the momentum equation |
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that there are ninety grid cells in the zonal and forty in the |
for the ``zonal flow'', $u$. Other terms in the model |
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meridional direction. The internal model coordinate variables |
are explicitly switched off for this experiment configuration (see section |
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$x$ and $y$ are initialized according to |
\ref{SEC:code_config} ), yielding an active set of equations solved in this |
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\begin{eqnarray} |
configuration as follows |
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x=r\cos(\phi),~\Delta x & = &r\cos(\Delta \phi) \\ |
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y=r\lambda,~\Delta x &= &r\Delta \lambda |
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\end{eqnarray} |
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Arctic polar regions are not |
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included in this experiment. Meridionally the model extends from |
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$80^{\circ}{\rm S}$ to $80^{\circ}{\rm N}$. |
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Vertically the model is configured with twenty layers with the |
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following thicknesses |
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$\Delta z_{1} = 50\,{\rm m},\, |
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\Delta z_{2} = 50\,{\rm m},\, |
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\Delta z_{3} = 55\,{\rm m},\, |
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\Delta z_{4} = 60\,{\rm m},\, |
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\Delta z_{5} = 65\,{\rm m},\, |
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$ |
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$ |
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\Delta z_{6}~=~70\,{\rm m},\, |
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\Delta z_{7}~=~80\,{\rm m},\, |
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\Delta z_{8}~=95\,{\rm m},\, |
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\Delta z_{9}=120\,{\rm m},\, |
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\Delta z_{10}=155\,{\rm m},\, |
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$ |
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$ |
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\Delta z_{11}=200\,{\rm m},\, |
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\Delta z_{12}=260\,{\rm m},\, |
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\Delta z_{13}=320\,{\rm m},\, |
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\Delta z_{14}=400\,{\rm m},\, |
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\Delta z_{15}=480\,{\rm m},\, |
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$ |
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$ |
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\Delta z_{16}=570\,{\rm m},\, |
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\Delta z_{17}=655\,{\rm m},\, |
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\Delta z_{18}=725\,{\rm m},\, |
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\Delta z_{19}=775\,{\rm m},\, |
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\Delta z_{20}=815\,{\rm m} |
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$ (here the numeric subscript indicates the model level index number, ${\tt k}$). |
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The implicit free surface form of the pressure equation described in Marshall et. al |
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\cite{marshall:97a} is employed. A Laplacian operator, $\nabla^2$, provides viscous |
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dissipation. Thermal and haline diffusion is also represented by a Laplacian operator. |
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Wind-stress forcing is added to the momentum equations for both |
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the zonal flow, $u$ and the meridional flow $v$, according to equations |
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(\ref{EQ:eg-hs-global_forcing_fu}) and (\ref{EQ:eg-hs-global_forcing_fv}). |
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Thermodynamic forcing inputs are added to the equations for |
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potential temperature, $\theta$, and salinity, $S$, according to equations |
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(\ref{EQ:eg-hs-global_forcing_ft}) and (\ref{EQ:eg-hs-global_forcing_fs}). |
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This produces a set of equations solved in this configuration as follows: |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-hs-model_equations} |
\label{EQ:eg-baro-model_equations} |
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\frac{Du}{Dt} - fv + |
\frac{Du}{Dt} - fv + |
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\frac{1}{\rho}\frac{\partial p^{'}}{\partial x} - |
g\frac{\partial \eta}{\partial x} - |
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\nabla_{h}\cdot A_{h}\nabla_{h}u - |
A_{h}\nabla_{h}^2u |
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\frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z} |
& = & |
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& = & |
\frac{\tau_{x}}{\rho_{0}\Delta z} |
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\begin{cases} |
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{\cal F}_u & \text{(surface)} \\ |
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0 & \text{(interior)} |
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\end{cases} |
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\\ |
\\ |
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\frac{Dv}{Dt} + fu + |
\frac{Dv}{Dt} + fu + g\frac{\partial \eta}{\partial y} - |
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\frac{1}{\rho}\frac{\partial p^{'}}{\partial y} - |
A_{h}\nabla_{h}^2v |
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\nabla_{h}\cdot A_{h}\nabla_{h}v - |
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\frac{\partial}{\partial z}A_{z}\frac{\partial v}{\partial z} |
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& = & |
& = & |
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\begin{cases} |
0 |
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{\cal F}_v & \text{(surface)} \\ |
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0 & \text{(interior)} |
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\end{cases} |
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\\ |
\\ |
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\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u} |
\frac{\partial \eta}{\partial t} + \nabla_{h}\cdot \vec{u} |
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&=& |
&=& |
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0 |
0 |
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\\ |
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\frac{D\theta}{Dt} - |
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\nabla_{h}\cdot K_{h}\nabla_{h}\theta |
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- \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial\theta}{\partial z} |
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& = & |
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\begin{cases} |
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{\cal F}_\theta & \text{(surface)} \\ |
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0 & \text{(interior)} |
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\end{cases} |
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\\ |
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\frac{D s}{Dt} - |
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\nabla_{h}\cdot K_{h}\nabla_{h}s |
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- \frac{\partial}{\partial z}\Gamma(K_{z})\frac{\partial s}{\partial z} |
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& = & |
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\begin{cases} |
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{\cal F}_s & \text{(surface)} \\ |
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0 & \text{(interior)} |
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\end{cases} |
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\\ |
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g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz & = & p^{'} |
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\end{eqnarray} |
\end{eqnarray} |
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\noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and |
\noindent where $u$ and $v$ and the $x$ and $y$ components of the |
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$v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$ |
flow vector $\vec{u}$. |
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are the zonal and meridional components of the |
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flow vector, $\vec{u}$, on the sphere. As described in |
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MITgcm Numerical Solution Procedure \ref{chap:discretization}, the time |
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evolution of potential temperature, $\theta$, equation is solved prognostically. |
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The total pressure, $p$, is diagnosed by summing pressure due to surface |
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elevation $\eta$ and the hydrostatic pressure. |
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\\ |
\\ |
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\subsection{Discrete Numerical Configuration} |
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\label{www:tutorials} |
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The domain is discretised with |
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a uniform grid spacing in the horizontal set to |
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$\Delta x=\Delta y=20$~km, so |
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that there are sixty grid cells in the $x$ and $y$ directions. Vertically the |
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model is configured with a single layer with depth, $\Delta z$, of $5000$~m. |
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\subsubsection{Numerical Stability Criteria} |
\subsubsection{Numerical Stability Criteria} |
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\label{www:tutorials} |
\label{www:tutorials} |
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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 $400 m s^{-1}$. |
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This value is chosen to yield a Munk layer width \cite{adcroft:95}, |
This value is chosen to yield a Munk layer width \cite{adcroft:95}, |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-hs-munk_layer} |
\label{EQ:eg-baro-munk_layer} |
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M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} |
M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} |
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\end{eqnarray} |
\end{eqnarray} |
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\noindent of $\approx 600$km. This is greater than the model |
\noindent of $\approx 100$km. This is greater than the model |
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resolution in low-latitudes, $\Delta x \approx 400{\rm km}$, ensuring that the frictional |
resolution $\Delta x$, ensuring that the frictional boundary |
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boundary layer is adequately resolved. |
layer is well resolved. |
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\\ |
\\ |
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\noindent The model is stepped forward with a |
\noindent The model is stepped forward with a |
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time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and |
time step $\delta t=1200$secs. With this time step the stability |
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$\delta t_{v}=40~{\rm minutes}$ for momentum terms. With this time step, the stability |
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parameter to the horizontal Laplacian friction \cite{adcroft:95} |
parameter to the horizontal Laplacian friction \cite{adcroft:95} |
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\begin{eqnarray} |
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\label{EQ:eg-hs-laplacian_stability} |
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S_{l} = 4 \frac{A_{h} \delta t_{v}}{{\Delta x}^2} |
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\end{eqnarray} |
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\noindent evaluates to 0.16 at a latitude of $\phi=80^{\circ}$, which is below the |
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0.3 upper limit for stability. The zonal grid spacing $\Delta x$ is smallest at |
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$\phi=80^{\circ}$ where $\Delta x=r\cos(\phi)\Delta \phi\approx 77{\rm km}$. |
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\\ |
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\noindent The vertical dissipation coefficient, $A_{z}$, is set to |
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$1\times10^{-3} {\rm m}^2{\rm s}^{-1}$. The associated stability limit |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-hs-laplacian_stability_z} |
\label{EQ:eg-baro-laplacian_stability} |
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S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2} |
S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2} |
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\end{eqnarray} |
\end{eqnarray} |
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\noindent evaluates to $0.015$ for the smallest model |
\noindent evaluates to 0.012, which is well below the 0.3 upper limit |
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level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below |
for stability. |
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the upper stability limit. |
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\\ |
\\ |
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The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients |
\noindent The numerical stability for inertial oscillations |
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for both temperature and salinity are set to $1 \times 10^{3}~{\rm m}^{2}{\rm s}^{-1}$ |
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and $3 \times 10^{-5}~{\rm m}^{2}{\rm s}^{-1}$ respectively. The stability limit |
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related to $K_{h}$ will be at $\phi=80^{\circ}$ where $\Delta x \approx 77 {\rm km}$. |
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Here the stability parameter |
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\begin{eqnarray} |
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\label{EQ:eg-hs-laplacian_stability_xtheta} |
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S_{l} = \frac{4 K_{h} \delta t_{\theta}}{{\Delta x}^2} |
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\end{eqnarray} |
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evaluates to $0.07$, well below the stability limit of $S_{l} \approx 0.5$. The |
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stability parameter related to $K_{z}$ |
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\begin{eqnarray} |
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\label{EQ:eg-hs-laplacian_stability_ztheta} |
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S_{l} = \frac{4 K_{z} \delta t_{\theta}}{{\Delta z}^2} |
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\end{eqnarray} |
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evaluates to $0.005$ for $\min(\Delta z)=50{\rm m}$, well below the stability limit |
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of $S_{l} \approx 0.5$. |
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\\ |
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\noindent The numerical stability for inertial oscillations |
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\cite{adcroft:95} |
\cite{adcroft:95} |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-hs-inertial_stability} |
\label{EQ:eg-baro-inertial_stability} |
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S_{i} = f^{2} {\delta t_v}^2 |
S_{i} = f^{2} {\delta t}^2 |
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\end{eqnarray} |
\end{eqnarray} |
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\noindent evaluates to $0.24$ for $f=2\omega\sin(80^{\circ})=1.43\times10^{-4}~{\rm s}^{-1}$, which is close to |
\noindent evaluates to $0.0144$, which is well below the $0.5$ upper |
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the $S_{i} < 1$ upper limit for stability. |
limit for stability. |
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\\ |
\\ |
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\noindent The advective CFL \cite{adcroft:95} for a extreme maximum |
\noindent The advective CFL \cite{adcroft:95} for an extreme maximum |
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horizontal flow |
horizontal flow speed of $ | \vec{u} | = 2 ms^{-1}$ |
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speed of $ | \vec{u} | = 2 ms^{-1}$ |
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\begin{eqnarray} |
\begin{eqnarray} |
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\label{EQ:eg-hs-cfl_stability} |
\label{EQ:eg-baro-cfl_stability} |
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S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x} |
S_{a} = \frac{| \vec{u} | \delta t}{ \Delta x} |
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\end{eqnarray} |
\end{eqnarray} |
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\noindent evaluates to $6 \times 10^{-2}$. This is well below the stability |
\noindent evaluates to 0.12. This is approaching the stability limit |
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limit of 0.5. |
of 0.5 and limits $\delta t$ to $1200s$. |
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\noindent The stability parameter for internal gravity waves propagating |
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with a maximum speed of $c_{g}=10~{\rm ms}^{-1}$ |
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\cite{adcroft:95} |
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\begin{eqnarray} |
\subsection{Code Configuration} |
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\label{EQ:eg-hs-gfl_stability} |
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S_{c} = \frac{c_{g} \delta t_{v}}{ \Delta x} |
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\end{eqnarray} |
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\noindent evaluates to $3 \times 10^{-1}$. This is close to the linear |
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stability limit of 0.5. |
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\subsection{Experiment Configuration} |
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\label{www:tutorials} |
\label{www:tutorials} |
| 188 |
\label{SEC:eg-hs_examp_exp_config} |
\label{SEC:eg-baro-code_config} |
| 189 |
|
|
| 190 |
The model configuration for this experiment resides under the |
The model configuration for this experiment resides under the |
| 191 |
directory {\it verification/hs94.128x64x5}. The experiment files |
directory {\it verification/exp0/}. The experiment files |
| 192 |
\begin{itemize} |
\begin{itemize} |
| 193 |
\item {\it input/data} |
\item {\it input/data} |
| 194 |
\item {\it input/data.pkg} |
\item {\it input/data.pkg} |
| 195 |
\item {\it input/eedata}, |
\item {\it input/eedata}, |
| 196 |
\item {\it input/windx.bin}, |
\item {\it input/windx.sin\_y}, |
| 197 |
\item {\it input/windy.bin}, |
\item {\it input/topog.box}, |
|
\item {\it input/salt.bin}, |
|
|
\item {\it input/theta.bin}, |
|
|
\item {\it input/SSS.bin}, |
|
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\item {\it input/SST.bin}, |
|
|
\item {\it input/topog.bin}, |
|
| 198 |
\item {\it code/CPP\_EEOPTIONS.h} |
\item {\it code/CPP\_EEOPTIONS.h} |
| 199 |
\item {\it code/CPP\_OPTIONS.h}, |
\item {\it code/CPP\_OPTIONS.h}, |
| 200 |
\item {\it code/SIZE.h}. |
\item {\it code/SIZE.h}. |
| 201 |
\end{itemize} |
\end{itemize} |
| 202 |
contain the code customizations and parameter settings for these |
contain the code customizations and parameter settings for this |
| 203 |
experiments. Below we describe the customizations |
experiments. Below we describe the customizations |
| 204 |
to these files associated with this experiment. |
to these files associated with this experiment. |
| 205 |
|
|
| 212 |
|
|
| 213 |
\begin{itemize} |
\begin{itemize} |
| 214 |
|
|
| 215 |
\item Lines 7-10 and 11-14 |
\item Line 7, \begin{verbatim} viscAh=4.E2, \end{verbatim} this line sets |
| 216 |
\begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim} |
the Laplacian friction coefficient to $400 m^2s^{-1}$ |
| 217 |
$\cdots$ \\ |
\item Line 10, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets |
| 218 |
set reference values for potential |
$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$ |
| 219 |
temperature and salinity at each model level in units of $^{\circ}$C and |
|
| 220 |
${\rm ppt}$. The entries are ordered from surface to depth. |
\item Lines 15 and 16 |
| 221 |
Density is calculated from anomalies at each level evaluated |
\begin{verbatim} |
| 222 |
with respect to the reference values set here.\\ |
rigidLid=.FALSE., |
| 223 |
\fbox{ |
implicitFreeSurface=.TRUE., |
| 224 |
\begin{minipage}{5.0in} |
\end{verbatim} |
| 225 |
{\it S/R INI\_THETA}({\it ini\_theta.F}) |
these lines suppress the rigid lid formulation of the surface |
| 226 |
\end{minipage} |
pressure inverter and activate the implicit free surface form |
| 227 |
} |
of the pressure inverter. |
|
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|
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|
|
\item Line 15, |
|
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\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 |
|
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model general vertical coordinate variable {\bf viscAr}. |
|
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|
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\fbox{ |
|
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\begin{minipage}{5.0in} |
|
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{\it S/R CALC\_DIFFUSIVITY}({\it calc\_diffusivity.F}) |
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\end{minipage} |
|
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} |
|
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\item Line 16, |
|
|
\begin{verbatim} |
|
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viscAh=5.E5, |
|
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\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. |
|
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|
|
|
\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 $x$. |
|
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|
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|
\item Lines 9, |
|
|
\begin{verbatim} |
|
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no_slip_bottom=.TRUE. |
|
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\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. |
|
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|
|
|
\item Line 19, |
|
|
\begin{verbatim} |
|
|
diffKhT=1.E3, |
|
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\end{verbatim} |
|
|
this line sets the horizontal diffusion coefficient for temperature |
|
|
to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this |
|
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operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on |
|
|
all boundaries. |
|
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|
|
|
\item Line 20, |
|
|
\begin{verbatim} |
|
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diffKzT=3.E-5, |
|
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\end{verbatim} |
|
|
this line sets the vertical diffusion coefficient for temperature |
|
|
to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary |
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|
condition on this operator is $\frac{\partial}{\partial z}=0$ at both |
|
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the upper and lower boundaries. |
|
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|
|
|
\item Line 21, |
|
|
\begin{verbatim} |
|
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diffKhS=1.E3, |
|
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\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. |
|
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|
|
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\item Line 22, |
|
|
\begin{verbatim} |
|
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diffKzS=3.E-5, |
|
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\end{verbatim} |
|
|
this line sets the vertical diffusion coefficient for salinity |
|
|
to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary |
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condition on this operator is $\frac{\partial}{\partial z}=0$ at both |
|
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the upper and lower boundaries. |
|
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|
|
|
\item Lines 23-26 |
|
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\begin{verbatim} |
|
|
beta=1.E-11, |
|
|
\end{verbatim} |
|
|
\vspace{-5mm}$\cdots$\\ |
|
|
These settings do not apply for this experiment. |
|
| 228 |
|
|
| 229 |
\item Line 27, |
\item Line 27, |
| 230 |
\begin{verbatim} |
\begin{verbatim} |
| 231 |
gravity=9.81, |
startTime=0, |
| 232 |
\end{verbatim} |
\end{verbatim} |
| 233 |
Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\ |
this line indicates that the experiment should start from $t=0$ |
| 234 |
\fbox{ |
and implicitly suppresses searching for checkpoint files associated |
| 235 |
\begin{minipage}{5.0in} |
with restarting an numerical integration from a previously saved state. |
|
{\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\ |
|
|
{\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\ |
|
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{\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\ |
|
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{\it S/R INI\_PARMS}~({\it ini\_parms.F})\\ |
|
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{\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F}) |
|
|
\end{minipage} |
|
|
} |
|
| 236 |
|
|
| 237 |
|
\item Line 29, |
|
\item Line 28-29, |
|
| 238 |
\begin{verbatim} |
\begin{verbatim} |
| 239 |
rigidLid=.FALSE., |
endTime=12000, |
|
implicitFreeSurface=.TRUE., |
|
| 240 |
\end{verbatim} |
\end{verbatim} |
| 241 |
Selects the barotropic pressure equation to be the implicit free surface |
this line indicates that the experiment should start finish at $t=12000s$. |
| 242 |
formulation. |
A restart file will be written at this time that will enable the |
| 243 |
|
simulation to be continued from this point. |
| 244 |
|
|
| 245 |
\item Line 30, |
\item Line 30, |
| 246 |
\begin{verbatim} |
\begin{verbatim} |
| 247 |
eosType='POLY3', |
deltaTmom=1200, |
| 248 |
\end{verbatim} |
\end{verbatim} |
| 249 |
Selects the third order polynomial form of the equation of state.\\ |
This line sets the momentum equation timestep to $1200s$. |
|
\fbox{ |
|
|
\begin{minipage}{5.0in} |
|
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{\it S/R FIND\_RHO}~({\it find\_rho.F})\\ |
|
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{\it S/R FIND\_ALPHA}~({\it find\_alpha.F}) |
|
|
\end{minipage} |
|
|
} |
|
| 250 |
|
|
| 251 |
\item Line 31, |
\item Line 39, |
| 252 |
\begin{verbatim} |
\begin{verbatim} |
| 253 |
readBinaryPrec=32, |
usingCartesianGrid=.TRUE., |
| 254 |
\end{verbatim} |
\end{verbatim} |
| 255 |
Sets format for reading binary input datasets holding model fields to |
This line requests that the simulation be performed in a |
| 256 |
use 32-bit representation for floating-point numbers.\\ |
Cartesian coordinate system. |
|
\fbox{ |
|
|
\begin{minipage}{5.0in} |
|
|
{\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\ |
|
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{\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F}) |
|
|
\end{minipage} |
|
|
} |
|
| 257 |
|
|
| 258 |
\item Line 36, |
\item Line 41, |
| 259 |
\begin{verbatim} |
\begin{verbatim} |
| 260 |
cg2dMaxIters=1000, |
delX=60*20E3, |
| 261 |
\end{verbatim} |
\end{verbatim} |
| 262 |
Sets maximum number of iterations the two-dimensional, conjugate |
This line sets the horizontal grid spacing between each x-coordinate line |
| 263 |
gradient solver will use, {\bf irrespective of convergence |
in the discrete grid. The syntax indicates that the discrete grid |
| 264 |
criteria being met}.\\ |
should be comprise of $60$ grid lines each separated by $20 \times 10^{3}m$ |
| 265 |
\fbox{ |
($20$~km). |
|
\begin{minipage}{5.0in} |
|
|
{\it S/R CG2D}~({\it cg2d.F}) |
|
|
\end{minipage} |
|
|
} |
|
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|
|
|
\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} |
|
|
} |
|
| 266 |
|
|
| 267 |
\item Line 42, |
\item Line 42, |
| 268 |
\begin{verbatim} |
\begin{verbatim} |
| 269 |
startTime=0, |
delY=60*20E3, |
| 270 |
\end{verbatim} |
\end{verbatim} |
| 271 |
Sets the starting time for the model internal time counter. |
This line sets the horizontal grid spacing between each y-coordinate line |
| 272 |
When set to non-zero this option implicitly requests a |
in the discrete grid to $20 \times 10^{3}m$ ($20$~km). |
|
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. |
|
| 273 |
|
|
| 274 |
\item Line 43, |
\item Line 43, |
| 275 |
\begin{verbatim} |
\begin{verbatim} |
| 276 |
endTime=2808000., |
delZ=5000, |
|
\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. |
|
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|
|
|
\item Line 44, |
|
|
\begin{verbatim} |
|
|
#endTime=62208000000, |
|
| 277 |
\end{verbatim} |
\end{verbatim} |
| 278 |
A commented out setting for endTime for a 2000 year simulation. |
This line sets the vertical grid spacing between each z-coordinate line |
| 279 |
|
in the discrete grid to $5000m$ ($5$~km). |
|
\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} |
|
|
} |
|
| 280 |
|
|
| 281 |
\item Line 46, |
\item Line 46, |
| 282 |
\begin{verbatim} |
\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} |
|
| 283 |
bathyFile='topog.box' |
bathyFile='topog.box' |
| 284 |
\end{verbatim} |
\end{verbatim} |
| 285 |
This line specifies the name of the file from which the domain |
This line specifies the name of the file from which the domain |
| 290 |
to high coordinate for both axes. The units and orientation of the |
to high coordinate for both axes. The units and orientation of the |
| 291 |
depths in this file are the same as used in the MITgcm code. In this |
depths in this file are the same as used in the MITgcm code. In this |
| 292 |
experiment, a depth of $0m$ indicates a solid wall and a depth |
experiment, a depth of $0m$ indicates a solid wall and a depth |
| 293 |
of $-2000m$ indicates open ocean. The matlab program |
of $-5000m$ indicates open ocean. The matlab program |
| 294 |
{\it input/gendata.m} shows an example of how to generate a |
{\it input/gendata.m} shows an example of how to generate a |
| 295 |
bathymetry file. |
bathymetry file. |
| 296 |
|
|
| 297 |
|
|
| 298 |
\item Line 50, |
\item Line 49, |
| 299 |
\begin{verbatim} |
\begin{verbatim} |
| 300 |
zonalWindFile='windx.sin_y' |
zonalWindFile='windx.sin_y' |
| 301 |
\end{verbatim} |
\end{verbatim} |
| 303 |
surface wind stress is read. This file is also a two-dimensional |
surface wind stress is read. This file is also a two-dimensional |
| 304 |
($x,y$) map and is enumerated and formatted in the same manner as the |
($x,y$) map and is enumerated and formatted in the same manner as the |
| 305 |
bathymetry file. The matlab program {\it input/gendata.m} includes example |
bathymetry file. The matlab program {\it input/gendata.m} includes example |
| 306 |
code to generate a valid |
code to generate a valid {\bf zonalWindFile} file. |
|
{\bf zonalWindFile} |
|
|
file. |
|
| 307 |
|
|
| 308 |
\end{itemize} |
\end{itemize} |
| 309 |
|
|
| 312 |
notes. |
notes. |
| 313 |
|
|
| 314 |
\begin{small} |
\begin{small} |
| 315 |
\input{part3/case_studies/climatalogical_ogcm/input/data} |
\input{part3/case_studies/barotropic_gyre/input/data} |
| 316 |
\end{small} |
\end{small} |
| 317 |
|
|
| 318 |
\subsubsection{File {\it input/data.pkg}} |
\subsubsection{File {\it input/data.pkg}} |
| 319 |
\label{www:tutorials} |
\label{www:tutorials} |
| 320 |
|
|
| 321 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 322 |
customisations for this experiment. |
customizations for this experiment. |
| 323 |
|
|
| 324 |
\subsubsection{File {\it input/eedata}} |
\subsubsection{File {\it input/eedata}} |
| 325 |
\label{www:tutorials} |
\label{www:tutorials} |
| 326 |
|
|
| 327 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 328 |
customisations for this experiment. |
customizations for this experiment. |
| 329 |
|
|
| 330 |
\subsubsection{File {\it input/windx.sin\_y}} |
\subsubsection{File {\it input/windx.sin\_y}} |
| 331 |
\label{www:tutorials} |
\label{www:tutorials} |
| 344 |
|
|
| 345 |
The {\it input/topog.box} file specifies a two-dimensional ($x,y$) |
The {\it input/topog.box} file specifies a two-dimensional ($x,y$) |
| 346 |
map of depth values. For this experiment values are either |
map of depth values. For this experiment values are either |
| 347 |
$0m$ 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 |
| 348 |
ocean. The file contains a raw binary stream of data that is enumerated |
ocean. The file contains a raw binary stream of data that is enumerated |
| 349 |
in the same way as standard MITgcm two-dimensional, horizontal arrays. |
in the same way as standard MITgcm two-dimensional, horizontal arrays. |
| 350 |
The included matlab program {\it input/gendata.m} gives a complete |
The included matlab program {\it input/gendata.m} gives a complete |
| 367 |
the lateral domain extent in grid points for the |
the lateral domain extent in grid points for the |
| 368 |
axis aligned with the y-coordinate. |
axis aligned with the y-coordinate. |
| 369 |
|
|
|
\item Line 49, |
|
|
\begin{verbatim} Nr=4, \end{verbatim} this line sets |
|
|
the vertical domain extent in grid points. |
|
|
|
|
| 370 |
\end{itemize} |
\end{itemize} |
| 371 |
|
|
| 372 |
\begin{small} |
\begin{small} |
| 373 |
\input{part3/case_studies/climatalogical_ogcm/code/SIZE.h} |
\input{part3/case_studies/barotropic_gyre/code/SIZE.h} |
| 374 |
\end{small} |
\end{small} |
| 375 |
|
|
| 376 |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
| 377 |
\label{www:tutorials} |
\label{www:tutorials} |
| 378 |
|
|
| 379 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 380 |
customisations for this experiment. |
customizations for this experiment. |
| 381 |
|
|
| 382 |
|
|
| 383 |
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
| 384 |
\label{www:tutorials} |
\label{www:tutorials} |
| 385 |
|
|
| 386 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 387 |
customisations for this experiment. |
customizations for this experiment. |
| 388 |
|
|
|
\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. |
|
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