--- manual/s_phys_pkgs/text/gridalt.tex 2009/11/23 21:08:56 1.12 +++ manual/s_phys_pkgs/text/gridalt.tex 2010/08/30 23:09:21 1.14 @@ -44,7 +44,7 @@ \begin{figure}[htbp] \vspace*{-0.4in} \begin{center} -\includegraphics[height=2.4in]{part6/vertical.eps} +\includegraphics[height=2.4in]{s_phys_pkgs/figs/vertical.eps} \caption{Vertical discretization for MITgcm (dark grey lines) and for the atmospheric physics (light grey lines). In this implementation, all MITgcm level interfaces must coincide with atmospheric physics level interfaces.} @@ -69,16 +69,16 @@ a second set of evolution equations for the atmospheric state variables on the modified grid. If the equation for the evolution of $U$ on $p^*$ can be expressed as: \[ -\left . {\partial U \over {\partial t}} \right |_{p^*}^{total} = -\left . {\partial U \over {\partial t}} \right |_{p^*}^{dynamics} + -\left . {\partial U \over {\partial t}} \right |_{p^*}^{physics} +\left . \frac{\partial U}{\partial t} \right |_{p^*}^{total} = +\left . \frac{\partial U}{\partial t} \right |_{p^*}^{dynamics} + +\left . \frac{\partial U}{\partial t} \right |_{p^*}^{physics} \] where the physics forcing terms on $p^*$ have been mapped from the modified grid, then an additional equation to govern the evolution of $U$ (for example) on the modified grid is written: \[ -\left . {\partial U \over {\partial t}} \right |_{p^{*m}}^{total} = -\left . {\partial U \over {\partial t}} \right |_{p^{*m}}^{dynamics} + -\left . {\partial U \over {\partial t}} \right |_{p^{*m}}^{physics} + +\left . \frac{\partial U}{\partial t} \right |_{p^{*m}}^{total} = +\left . \frac{\partial U}{\partial t} \right |_{p^{*m}}^{dynamics} + +\left . \frac{\partial U}{\partial t} \right |_{p^{*m}}^{physics} + \gamma ({\left . U \right |_{p^*}} - {\left . U \right |_{p^{*m}}}) \] where $p^{*m}$ refers to the modified higher resolution grid, and the dynamics forcing terms have