| 44 |
\begin{figure}[htbp] |
\begin{figure}[htbp] |
| 45 |
\vspace*{-0.4in} |
\vspace*{-0.4in} |
| 46 |
\begin{center} |
\begin{center} |
| 47 |
\includegraphics[height=2.4in]{part6/vertical.eps} |
\includegraphics[height=2.4in]{s_phys_pkgs/figs/vertical.eps} |
| 48 |
\caption{Vertical discretization for MITgcm (dark grey lines) and for the |
\caption{Vertical discretization for MITgcm (dark grey lines) and for the |
| 49 |
atmospheric physics (light grey lines). In this implementation, all MITgcm level |
atmospheric physics (light grey lines). In this implementation, all MITgcm level |
| 50 |
interfaces must coincide with atmospheric physics level interfaces.} |
interfaces must coincide with atmospheric physics level interfaces.} |
| 69 |
a second set of evolution equations for the atmospheric state variables on the modified grid. |
a second set of evolution equations for the atmospheric state variables on the modified grid. |
| 70 |
If the equation for the evolution of $U$ on $p^*$ can be expressed as: |
If the equation for the evolution of $U$ on $p^*$ can be expressed as: |
| 71 |
\[ |
\[ |
| 72 |
\left . {\partial U \over {\partial t}} \right |_{p^*}^{total} = |
\left . \frac{\partial U}{\partial t} \right |_{p^*}^{total} = |
| 73 |
\left . {\partial U \over {\partial t}} \right |_{p^*}^{dynamics} + |
\left . \frac{\partial U}{\partial t} \right |_{p^*}^{dynamics} + |
| 74 |
\left . {\partial U \over {\partial t}} \right |_{p^*}^{physics} |
\left . \frac{\partial U}{\partial t} \right |_{p^*}^{physics} |
| 75 |
\] |
\] |
| 76 |
where the physics forcing terms on $p^*$ have been mapped from the modified grid, then an additional |
where the physics forcing terms on $p^*$ have been mapped from the modified grid, then an additional |
| 77 |
equation to govern the evolution of $U$ (for example) on the modified grid is written: |
equation to govern the evolution of $U$ (for example) on the modified grid is written: |
| 78 |
\[ |
\[ |
| 79 |
\left . {\partial U \over {\partial t}} \right |_{p^{*m}}^{total} = |
\left . \frac{\partial U}{\partial t} \right |_{p^{*m}}^{total} = |
| 80 |
\left . {\partial U \over {\partial t}} \right |_{p^{*m}}^{dynamics} + |
\left . \frac{\partial U}{\partial t} \right |_{p^{*m}}^{dynamics} + |
| 81 |
\left . {\partial U \over {\partial t}} \right |_{p^{*m}}^{physics} + |
\left . \frac{\partial U}{\partial t} \right |_{p^{*m}}^{physics} + |
| 82 |
\gamma ({\left . U \right |_{p^*}} - {\left . U \right |_{p^{*m}}}) |
\gamma ({\left . U \right |_{p^*}} - {\left . U \right |_{p^{*m}}}) |
| 83 |
\] |
\] |
| 84 |
where $p^{*m}$ refers to the modified higher resolution grid, and the dynamics forcing terms have |
where $p^{*m}$ refers to the modified higher resolution grid, and the dynamics forcing terms have |
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