| 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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