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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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%{\large June 2004} |
%{\large May 2001} |
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%\end{center} |
%\end{center} |
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\subsection{Introduction} |
\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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\begin{rawhtml} |
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This section illustrates an example of MITgcm simulating a laboratory |
<!-- CMIREDIR:eg-tank: --> |
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experiment on much smaller scales than those common to geophysical |
\end{rawhtml} |
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This section illustrates an example of MITgcm simulating a laboratory |
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experiment on much smaller scales than those commonly considered in |
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geophysical |
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fluid dynamics. |
fluid dynamics. |
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\subsection{Overview} |
\subsection{Overview} |
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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 configuration demonstrates using the MITgcm to simulate |
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a laboratory experiment with a rotating tank of water with an ice |
a laboratory demonstration using a rotating tank of water with an ice |
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bucket in the center. The simulation is configured for a laboratory |
bucket in the center. The simulation is configured for a laboratory |
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scale on a 3^{\circ} \times 20cm cyclindrical grid with twenty-nine vertical |
scale on a |
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levels. |
$3^{\circ}$ $\times$ 20cm |
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cyclindrical grid with twenty-nine vertical |
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levels. |
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example illustration from GFD lab here |
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The model is forced with climatological wind stress data and surface |
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flux data from DaSilva \cite{DaSilva94}. Climatological data |
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from Levitus \cite{Levitus94} is used to initialize the model hydrography. |
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Levitus seasonal climatology data is also used throughout the calculation |
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to provide additional air-sea fluxes. |
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These fluxes are combined with the DaSilva climatological estimates of |
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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}. |
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Altogether, this yields the following forcing applied |
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in the model surface layer. |
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\noindent where ${\cal F}_{u}$, ${\cal F}_{v}$, ${\cal F}_{\theta}$, |
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${\cal F}_{s}$ are the forcing terms in the zonal and meridional |
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momentum and in the potential temperature and salinity |
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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. |
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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 |
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reference salinity, $S_{0}$ (here set to 35~ppt), |
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and a specific heat capacity, $C_{p}$ (here set to |
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$4000~{\rm J}~^{\circ}{\rm C}^{-1}~{\rm kg}^{-1}$), to convert |
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input dataset values into time tendencies of |
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potential temperature (with units of $^{\circ}{\rm C}~{\rm s}^{-1}$), |
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salinity (with units ${\rm ppt}~s^{-1}$) and |
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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 $\tau_{x}$, $\tau_{y}$, $\theta^{\ast}$, $S^{\ast}$, |
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$\cal{Q}$ and $\cal{E}-\cal{P}-\cal{R}$. The wind stress fields ($\tau_x$, $\tau_y$) |
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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 ${\rm W}~{\rm m}^{-2}$ |
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respectively. The salinity forcing fields ($S^{\ast}$ and |
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$\cal{E}-\cal{P}-\cal{R}$) have units of ${\rm ppt}$ and ${\rm m}~{\rm s}^{-1}$ |
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respectively. |
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\\ |
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Figures (\ref{FIG:sim_config_tclim}-\ref{FIG:sim_config_empmr}) show the |
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relaxation temperature ($\theta^{\ast}$) and salinity ($S^{\ast}$) fields, |
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the wind stress components ($\tau_x$ and $\tau_y$), the heat flux ($Q$) |
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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 |
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also indicate the lateral extent and coastline used in the experiment. |
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Figure ({\ref{FIG:model_bathymetry}) shows the depth contours of the model |
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domain. |
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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 domain is discretised with |
\subsection{Discrete Numerical Configuration} |
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a uniform grid spacing in latitude and longitude on the sphere |
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$\Delta \phi=\Delta \lambda=4^{\circ}$, so |
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that there are ninety grid cells in the zonal and forty in the |
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meridional direction. The internal model coordinate variables |
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$x$ and $y$ are initialized according to |
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\begin{eqnarray} |
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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} |
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\label{EQ:eg-hs-model_equations} |
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\frac{Du}{Dt} - fv + |
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\frac{1}{\rho}\frac{\partial p^{'}}{\partial x} - |
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\nabla_{h}\cdot A_{h}\nabla_{h}u - |
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\frac{\partial}{\partial z}A_{z}\frac{\partial u}{\partial z} |
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& = & |
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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 + |
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\frac{1}{\rho}\frac{\partial p^{'}}{\partial y} - |
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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} |
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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} |
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&=& |
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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} |
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\noindent where $u=\frac{Dx}{Dt}=r \cos(\phi)\frac{D \lambda}{Dt}$ and |
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$v=\frac{Dy}{Dt}=r \frac{D \phi}{Dt}$ |
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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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\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 domain is discretised with |
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This value is chosen to yield a Munk layer width \cite{adcroft:95}, |
a uniform cylindrical grid spacing in the horizontal set to |
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\begin{eqnarray} |
$\Delta a=1$~cm and $\Delta \phi=3^{\circ}$, so |
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\label{EQ:eg-hs-munk_layer} |
that there are 120 grid cells in the azimuthal direction and thirty-one grid cells in the radial. Vertically the |
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M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}} |
model is configured with twenty-nine layers of uniform 0.5cm thickness. |
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\end{eqnarray} |
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\noindent of $\approx 600$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 |
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boundary layer is adequately resolved. |
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\\ |
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\noindent The model is stepped forward with a |
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time step $\delta t_{\theta}=30~{\rm hours}$ for thermodynamic variables and |
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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} |
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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} |
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\label{EQ:eg-hs-laplacian_stability_z} |
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S_{l} = 4 \frac{A_{z} \delta t_{v}}{{\Delta z}^2} |
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\end{eqnarray} |
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\noindent evaluates to $0.015$ for the smallest model |
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level spacing ($\Delta z_{1}=50{\rm m}$) which is again well below |
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the upper stability limit. |
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\\ |
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something about heat flux |
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The values of the horizontal ($K_{h}$) and vertical ($K_{z}$) diffusion coefficients |
\subsection{Code Configuration} |
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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} |
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\begin{eqnarray} |
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\label{EQ:eg-hs-inertial_stability} |
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S_{i} = f^{2} {\delta t_v}^2 |
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\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 |
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the $S_{i} < 1$ upper limit for stability. |
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\\ |
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\noindent The advective CFL \cite{adcroft:95} for a extreme maximum |
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horizontal flow |
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speed of $ | \vec{u} | = 2 ms^{-1}$ |
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\begin{eqnarray} |
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\label{EQ:eg-hs-cfl_stability} |
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S_{a} = \frac{| \vec{u} | \delta t_{v}}{ \Delta x} |
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\end{eqnarray} |
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\noindent evaluates to $6 \times 10^{-2}$. This is well below the stability |
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limit of 0.5. |
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\\ |
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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} |
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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} |
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\label{SEC:eg-hs_examp_exp_config} |
\label{SEC:eg-baro-code_config} |
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The model configuration for this experiment resides under the |
The model configuration for this experiment resides under the |
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directory {\it verification/hs94.128x64x5}. The experiment files |
directory {\it verification/rotatingi\_tank/}. The experiment files |
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\begin{itemize} |
\begin{itemize} |
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\item {\it input/data} |
\item {\it input/data} |
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\item {\it input/data.pkg} |
\item {\it input/data.pkg} |
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\item {\it input/eedata}, |
\item {\it input/eedata}, |
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\item {\it input/windx.bin}, |
\item {\it input/bathyPol.bin}, |
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\item {\it input/windy.bin}, |
\item {\it input/thetaPol.bin}, |
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\item {\it input/salt.bin}, |
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\item {\it input/theta.bin}, |
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\item {\it input/SSS.bin}, |
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\item {\it input/SST.bin}, |
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\item {\it input/topog.bin}, |
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\item {\it code/CPP\_EEOPTIONS.h} |
\item {\it code/CPP\_EEOPTIONS.h} |
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\item {\it code/CPP\_OPTIONS.h}, |
\item {\it code/CPP\_OPTIONS.h}, |
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\item {\it code/SIZE.h}. |
\item {\it code/SIZE.h}. |
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\end{itemize} |
\end{itemize} |
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contain the code customizations and parameter settings for these |
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contain the code customizations and parameter settings for this |
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experiments. Below we describe the customizations |
experiments. Below we describe the customizations |
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to these files associated with this experiment. |
to these files associated with this experiment. |
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\begin{itemize} |
\begin{itemize} |
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\item Lines 7-10 and 11-14 |
\item Line 10, \begin{verbatim} viscAh=5.0E-6, \end{verbatim} this line sets |
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\begin{verbatim} tRef= 16.0 , 15.2 , 14.5 , 13.9 , 13.3 , \end{verbatim} |
the Laplacian friction coefficient to $6 \times 10^{-6} m^2s^{-1}$, |
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$\cdots$ \\ |
which is ususally |
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set reference values for potential |
low because of the small scale, presumably.... qqq |
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temperature and salinity at each model level in units of $^{\circ}$C and |
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${\rm ppt}$. The entries are ordered from surface to depth. |
\item Line 19, \begin{verbatim}f0=0.5 , \end{verbatim} this line sets the |
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Density is calculated from anomalies at each level evaluated |
coriolis term, and represents a tank spinning at 2/s |
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with respect to the reference values set here.\\ |
\item Line 20, \begin{verbatim} beta=1.E-11, \end{verbatim} this line sets |
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\fbox{ |
$\beta$ (the gradient of the coriolis parameter, $f$) to $10^{-11} s^{-1}m^{-1}$ |
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\begin{minipage}{5.0in} |
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{\it S/R INI\_THETA}({\it ini\_theta.F}) |
\item Lines 27 and 28 |
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\end{minipage} |
\begin{verbatim} |
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} |
rigidLid=.TRUE., |
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implicitFreeSurface=.FALSE., |
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\end{verbatim} |
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\item Line 15, |
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\begin{verbatim} viscAz=1.E-3, \end{verbatim} |
qqq these lines do the opposite of the following: |
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this line sets the vertical Laplacian dissipation coefficient to |
suppress the rigid lid formulation of the surface |
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$1 \times 10^{-3} {\rm m^{2}s^{-1}}$. Boundary conditions |
pressure inverter and activate the implicit free surface form |
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for this operator are specified later. This variable is copied into |
of the pressure inverter. |
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model general vertical coordinate variable {\bf viscAr}. |
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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, |
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\begin{verbatim} |
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viscAh=5.E5, |
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\end{verbatim} |
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this line sets the horizontal Laplacian frictional dissipation coefficient to |
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$5 \times 10^{5} {\rm m^{2}s^{-1}}$. Boundary conditions |
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for this operator are specified later. |
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\item Lines 17, |
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\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 $x$. |
|
| 112 |
|
|
| 113 |
\item Lines 9, |
\item Line 44, |
|
\begin{verbatim} |
|
|
no_slip_bottom=.TRUE. |
|
|
\end{verbatim} |
|
|
this line selects a no-slip boundary condition for bottom |
|
|
boundary condition in the vertical Laplacian friction operator |
|
|
e.g. $u=v=0$ at $z=-H$, where $H$ is the local depth of the domain. |
|
|
|
|
|
\item Line 19, |
|
|
\begin{verbatim} |
|
|
diffKhT=1.E3, |
|
|
\end{verbatim} |
|
|
this line sets the horizontal diffusion coefficient for temperature |
|
|
to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this |
|
|
operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on |
|
|
all boundaries. |
|
|
|
|
|
\item Line 20, |
|
|
\begin{verbatim} |
|
|
diffKzT=3.E-5, |
|
|
\end{verbatim} |
|
|
this line sets the vertical diffusion coefficient for temperature |
|
|
to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary |
|
|
condition on this operator is $\frac{\partial}{\partial z}=0$ at both |
|
|
the upper and lower boundaries. |
|
|
|
|
|
\item Line 21, |
|
|
\begin{verbatim} |
|
|
diffKhS=1.E3, |
|
|
\end{verbatim} |
|
|
this line sets the horizontal diffusion coefficient for salinity |
|
|
to $1000\,{\rm m^{2}s^{-1}}$. The boundary condition on this |
|
|
operator is $\frac{\partial}{\partial x}=\frac{\partial}{\partial y}=0$ on |
|
|
all boundaries. |
|
|
|
|
|
\item Line 22, |
|
|
\begin{verbatim} |
|
|
diffKzS=3.E-5, |
|
|
\end{verbatim} |
|
|
this line sets the vertical diffusion coefficient for salinity |
|
|
to $3 \times 10^{-5}\,{\rm m^{2}s^{-1}}$. The boundary |
|
|
condition on this operator is $\frac{\partial}{\partial z}=0$ at both |
|
|
the upper and lower boundaries. |
|
|
|
|
|
\item Lines 23-26 |
|
|
\begin{verbatim} |
|
|
beta=1.E-11, |
|
|
\end{verbatim} |
|
|
\vspace{-5mm}$\cdots$\\ |
|
|
These settings do not apply for this experiment. |
|
|
|
|
|
\item Line 27, |
|
|
\begin{verbatim} |
|
|
gravity=9.81, |
|
|
\end{verbatim} |
|
|
Sets the gravitational acceleration coefficient to $9.81{\rm m}{\rm s}^{-1}$.\\ |
|
|
\fbox{ |
|
|
\begin{minipage}{5.0in} |
|
|
{\it S/R CALC\_PHI\_HYD}~({\it calc\_phi\_hyd.F})\\ |
|
|
{\it S/R INI\_CG2D}~({\it ini\_cg2d.F})\\ |
|
|
{\it S/R INI\_CG3D}~({\it ini\_cg3d.F})\\ |
|
|
{\it S/R INI\_PARMS}~({\it ini\_parms.F})\\ |
|
|
{\it S/R SOLVE\_FOR\_PRESSURE}~({\it solve\_for\_pressure.F}) |
|
|
\end{minipage} |
|
|
} |
|
|
|
|
|
|
|
|
\item Line 28-29, |
|
|
\begin{verbatim} |
|
|
rigidLid=.FALSE., |
|
|
implicitFreeSurface=.TRUE., |
|
|
\end{verbatim} |
|
|
Selects the barotropic pressure equation to be the implicit free surface |
|
|
formulation. |
|
|
|
|
|
\item Line 30, |
|
|
\begin{verbatim} |
|
|
eosType='POLY3', |
|
|
\end{verbatim} |
|
|
Selects the third order polynomial form of the equation of state.\\ |
|
|
\fbox{ |
|
|
\begin{minipage}{5.0in} |
|
|
{\it S/R FIND\_RHO}~({\it find\_rho.F})\\ |
|
|
{\it S/R FIND\_ALPHA}~({\it find\_alpha.F}) |
|
|
\end{minipage} |
|
|
} |
|
|
|
|
|
\item Line 31, |
|
|
\begin{verbatim} |
|
|
readBinaryPrec=32, |
|
|
\end{verbatim} |
|
|
Sets format for reading binary input datasets holding model fields to |
|
|
use 32-bit representation for floating-point numbers.\\ |
|
|
\fbox{ |
|
|
\begin{minipage}{5.0in} |
|
|
{\it S/R READ\_WRITE\_FLD}~({\it read\_write\_fld.F})\\ |
|
|
{\it S/R READ\_WRITE\_REC}~({\it read\_write\_rec.F}) |
|
|
\end{minipage} |
|
|
} |
|
|
|
|
|
\item Line 36, |
|
|
\begin{verbatim} |
|
|
cg2dMaxIters=1000, |
|
|
\end{verbatim} |
|
|
Sets maximum number of iterations the two-dimensional, conjugate |
|
|
gradient solver will use, {\bf irrespective of convergence |
|
|
criteria being met}.\\ |
|
|
\fbox{ |
|
|
\begin{minipage}{5.0in} |
|
|
{\it S/R CG2D}~({\it cg2d.F}) |
|
|
\end{minipage} |
|
|
} |
|
|
|
|
|
\item Line 37, |
|
| 114 |
\begin{verbatim} |
\begin{verbatim} |
| 115 |
cg2dTargetResidual=1.E-13, |
nIter=0, |
| 116 |
\end{verbatim} |
\end{verbatim} |
| 117 |
Sets the tolerance which the two-dimensional, conjugate |
this line indicates that the experiment should start from $t=0$ |
| 118 |
gradient solver will use to test for convergence in equation |
and implicitly suppresses searching for checkpoint files associated |
| 119 |
\ref{EQ:eg-hs-congrad_2d_resid} to $1 \times 10^{-13}$. |
with restarting an numerical integration from a previously saved state. |
|
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} |
|
|
} |
|
| 120 |
|
|
| 121 |
\item Line 42, |
\item Line 47, |
| 122 |
\begin{verbatim} |
\begin{verbatim} |
| 123 |
startTime=0, |
deltaT=0.1, |
| 124 |
\end{verbatim} |
\end{verbatim} |
| 125 |
Sets the starting time for the model internal time counter. |
This line sets the integration timestep to $0.1s$. This is an unsually |
| 126 |
When set to non-zero this option implicitly requests a |
small value among the examples due to the small physical scale of the |
| 127 |
checkpoint file be read for initial state. |
experiment. |
|
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. |
|
| 128 |
|
|
| 129 |
\item Line 43, |
\item Line 58, |
| 130 |
\begin{verbatim} |
\begin{verbatim} |
| 131 |
endTime=2808000., |
usingCylindricalGrid=.TRUE., |
| 132 |
\end{verbatim} |
\end{verbatim} |
| 133 |
Sets the time (in seconds) at which this simulation will terminate. |
This line requests that the simulation be performed in a |
| 134 |
At the end of a simulation a checkpoint file is automatically |
cylindrical coordinate system. |
|
written so that a numerical experiment can consist of multiple |
|
|
stages. |
|
| 135 |
|
|
| 136 |
\item Line 44, |
\item Line 60, |
| 137 |
\begin{verbatim} |
\begin{verbatim} |
| 138 |
#endTime=62208000000, |
dXspacing=3, |
| 139 |
\end{verbatim} |
\end{verbatim} |
| 140 |
A commented out setting for endTime for a 2000 year simulation. |
This line sets the azimuthal grid spacing between each $x$-coordinate line |
| 141 |
|
in the discrete grid. The syntax indicates that the discrete grid |
| 142 |
|
should be comprise of $120$ grid lines each separated by $3^{\circ}$. |
| 143 |
|
|
| 144 |
|
|
|
\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} |
|
|
} |
|
| 145 |
|
|
| 146 |
\item Line 46, |
\item Line 61, |
| 147 |
\begin{verbatim} |
\begin{verbatim} |
| 148 |
tauCD=321428., |
dYspacing=0.01, |
| 149 |
\end{verbatim} |
\end{verbatim} |
| 150 |
Sets the D-grid to C-grid coupling time scale $\tau_{CD}$ used in the momentum equations. |
This line sets the radial cylindrical grid spacing between each $a$-coordinate line |
| 151 |
See section \ref{SEC:cd_scheme}. |
in the discrete grid to $1cm$. |
|
|
|
|
\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} |
|
|
} |
|
| 152 |
|
|
| 153 |
\item Line 47, |
\item Line 62, |
| 154 |
\begin{verbatim} |
\begin{verbatim} |
| 155 |
deltaTtracer=108000., |
delZ=29*0.005, |
| 156 |
\end{verbatim} |
\end{verbatim} |
| 157 |
Sets the default timestep, $\delta t_{\theta}$, for tracer equations to |
This line sets the vertical grid spacing between each z-coordinate line |
| 158 |
$30~{\rm hours}$. |
in the discrete grid to $5000m$ ($5$~km). |
|
See section \ref{SEC:tracer_time_stepping}. |
|
|
|
|
|
\fbox{ |
|
|
\begin{minipage}{5.0in} |
|
|
{\it S/R TIMESTEP\_TRACER}({\it timestep\_tracer.F}) |
|
|
\end{minipage} |
|
|
} |
|
| 159 |
|
|
| 160 |
\item Line 47, |
\item Line 68, |
| 161 |
\begin{verbatim} |
\begin{verbatim} |
| 162 |
bathyFile='topog.box' |
bathyFile='bathyPol.bin', |
| 163 |
\end{verbatim} |
\end{verbatim} |
| 164 |
This line specifies the name of the file from which the domain |
This line specifies the name of the file from which the domain |
| 165 |
bathymetry is read. This file is a two-dimensional ($x,y$) map of |
``bathymetry'' (tank depth) is read. This file is a two-dimensional |
| 166 |
|
($a,\phi$) map of |
| 167 |
depths. This file is assumed to contain 64-bit binary numbers |
depths. This file is assumed to contain 64-bit binary numbers |
| 168 |
giving the depth of the model at each grid cell, ordered with the x |
giving the depth of the model at each grid cell, ordered with the $\phi$ |
| 169 |
coordinate varying fastest. The points are ordered from low coordinate |
coordinate varying fastest. The points are ordered from low coordinate |
| 170 |
to high coordinate for both axes. The units and orientation of the |
to high coordinate for both axes. The units and orientation of the |
| 171 |
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 |
| 172 |
experiment, a depth of $0m$ indicates a solid wall and a depth |
experiment, a depth of $0m$ indicates an area outside of the tank |
| 173 |
of $-2000m$ indicates open ocean. The matlab program |
and a depth |
| 174 |
{\it input/gendata.m} shows an example of how to generate a |
f $-0.145m$ indicates the tank itself. |
|
bathymetry file. |
|
| 175 |
|
|
| 176 |
|
\item Line 67, |
| 177 |
|
\begin{verbatim} |
| 178 |
|
hydrogThetaFile='thetaPol.bin', |
| 179 |
|
\end{verbatim} |
| 180 |
|
This line specifies the name of the file from which the initial values |
| 181 |
|
of temperature |
| 182 |
|
are read. This file is a three-dimensional |
| 183 |
|
($x,y,z$) map and is enumerated and formatted in the same manner as the |
| 184 |
|
bathymetry file. |
| 185 |
|
|
| 186 |
\item Line 50, |
\item Line qqq |
| 187 |
\begin{verbatim} |
\begin{verbatim} |
| 188 |
zonalWindFile='windx.sin_y' |
tCyl = 0 |
| 189 |
\end{verbatim} |
\end{verbatim} |
| 190 |
This line specifies the name of the file from which the x-direction |
This line specifies the temperature in degrees Celsius of the interior |
| 191 |
surface wind stress is read. This file is also a two-dimensional |
wall of the tank -- usually a bucket of ice water. |
| 192 |
($x,y$) 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. |
|
| 193 |
|
|
| 194 |
\end{itemize} |
\end{itemize} |
| 195 |
|
|
| 198 |
notes. |
notes. |
| 199 |
|
|
| 200 |
\begin{small} |
\begin{small} |
| 201 |
\input{part3/case_studies/climatalogical_ogcm/input/data} |
\input{part3/case_studies/rotating_tank/input/data} |
| 202 |
\end{small} |
\end{small} |
| 203 |
|
|
| 204 |
\subsubsection{File {\it input/data.pkg}} |
\subsubsection{File {\it input/data.pkg}} |
| 205 |
\label{www:tutorials} |
\label{www:tutorials} |
| 206 |
|
|
| 207 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 208 |
customisations for this experiment. |
customizations for this experiment. |
| 209 |
|
|
| 210 |
\subsubsection{File {\it input/eedata}} |
\subsubsection{File {\it input/eedata}} |
| 211 |
\label{www:tutorials} |
\label{www:tutorials} |
| 212 |
|
|
| 213 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 214 |
customisations for this experiment. |
customizations for this experiment. |
| 215 |
|
|
| 216 |
\subsubsection{File {\it input/windx.sin\_y}} |
\subsubsection{File {\it input/thetaPol.bin}} |
| 217 |
\label{www:tutorials} |
\label{www:tutorials} |
| 218 |
|
|
| 219 |
The {\it input/windx.sin\_y} file specifies a two-dimensional ($x,y$) |
The {\it input/thetaPol.bin} file specifies a three-dimensional ($x,y,z$) |
| 220 |
map of wind stress ,$\tau_{x}$, values. The units used are $Nm^{-2}$. |
map of initial values of $\theta$ in degrees Celsius. This particular |
| 221 |
Although $\tau_{x}$ is only a function of $y$n in this experiment |
experiment is set to random values x around 20C to provide initial |
| 222 |
this file must still define a complete two-dimensional map in order |
perturbations. |
|
to be compatible with the standard code for loading forcing fields |
|
|
in MITgcm. The included matlab program {\it input/gendata.m} gives a complete |
|
|
code for creating the {\it input/windx.sin\_y} file. |
|
| 223 |
|
|
| 224 |
\subsubsection{File {\it input/topog.box}} |
\subsubsection{File {\it input/bathyPol.bin}} |
| 225 |
\label{www:tutorials} |
\label{www:tutorials} |
| 226 |
|
|
| 227 |
|
|
| 228 |
The {\it input/topog.box} file specifies a two-dimensional ($x,y$) |
The {\it input/bathyPol.bin} file specifies a two-dimensional ($x,y$) |
| 229 |
map of depth values. For this experiment values are either |
map of depth values. For this experiment values are either |
| 230 |
$0m$ or $-2000\,{\rm m}$, corresponding respectively to a wall or to deep |
$0m$ or {\bf -delZ}m, corresponding respectively to outside or inside of |
| 231 |
ocean. The file contains a raw binary stream of data that is enumerated |
the tank. The file contains a raw binary stream of data that is enumerated |
| 232 |
in the same way as standard MITgcm two-dimensional, horizontal arrays. |
in the same way as standard MITgcm two-dimensional, horizontal arrays. |
|
The included matlab program {\it input/gendata.m} gives a complete |
|
|
code for creating the {\it input/topog.box} file. |
|
| 233 |
|
|
| 234 |
\subsubsection{File {\it code/SIZE.h}} |
\subsubsection{File {\it code/SIZE.h}} |
| 235 |
\label{www:tutorials} |
\label{www:tutorials} |
| 239 |
\begin{itemize} |
\begin{itemize} |
| 240 |
|
|
| 241 |
\item Line 39, |
\item Line 39, |
| 242 |
\begin{verbatim} sNx=60, \end{verbatim} this line sets |
\begin{verbatim} sNx=120, \end{verbatim} this line sets |
| 243 |
the lateral domain extent in grid points for the |
the lateral domain extent in grid points for the |
| 244 |
axis aligned with the x-coordinate. |
axis aligned with the x-coordinate. |
| 245 |
|
|
| 246 |
\item Line 40, |
\item Line 40, |
| 247 |
\begin{verbatim} sNy=60, \end{verbatim} this line sets |
\begin{verbatim} sNy=31, \end{verbatim} this line sets |
| 248 |
the lateral domain extent in grid points for the |
the lateral domain extent in grid points for the |
| 249 |
axis aligned with the y-coordinate. |
axis aligned with the y-coordinate. |
| 250 |
|
|
|
\item Line 49, |
|
|
\begin{verbatim} Nr=4, \end{verbatim} this line sets |
|
|
the vertical domain extent in grid points. |
|
|
|
|
| 251 |
\end{itemize} |
\end{itemize} |
| 252 |
|
|
| 253 |
\begin{small} |
\begin{small} |
| 254 |
\input{part3/case_studies/climatalogical_ogcm/code/SIZE.h} |
\input{part3/case_studies/rotating_tank/code/SIZE.h} |
| 255 |
\end{small} |
\end{small} |
| 256 |
|
|
| 257 |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
\subsubsection{File {\it code/CPP\_OPTIONS.h}} |
| 258 |
\label{www:tutorials} |
\label{www:tutorials} |
| 259 |
|
|
| 260 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 261 |
customisations for this experiment. |
customizations for this experiment. |
| 262 |
|
|
| 263 |
|
|
| 264 |
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
\subsubsection{File {\it code/CPP\_EEOPTIONS.h}} |
| 265 |
\label{www:tutorials} |
\label{www:tutorials} |
| 266 |
|
|
| 267 |
This file uses standard default values and does not contain |
This file uses standard default values and does not contain |
| 268 |
customisations for this experiment. |
customizations for this experiment. |
| 269 |
|
|
|
\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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