Choice of a vertical grid in incorporating condensation heating into an isentropic vertical coordinate model

Advantages of using an isentropic vertical coordinate in atmospheric models are well recognized. In particular, the use of an isentropic coordinate vi rtually eliminates discretization errors for vertical advection since isent ropic surfaces are material surfaces under dry-adiabatic processes. This is also advantageous for predicting moistadiabatic condensation processes bec ause their occurrence and maintenance largely depend on the converging mois ture transport through the surrounding unsaturated regions. In this paper, a basic problem in incorporating condensation heating into a n isentropic coordinate model is discussed: that is, the problem of choosin g a proper vertical grid for predicting moisture and computing condensation amount and condensation heating. Two different vertical grids are describe d, one of which predicts moisture for each model layer (M grid) and the oth er predicts it at each interface separating the model layers (N grid). The models based on these two vertical grids become identical without condensat ion. To illustrate the different impacts of these grids on dynamics, simula tions of horizontally standing oscillations with two models based on these grids are presented. Results indicate that the model based on the M grid ha s difficulty in correctly recognizing the reduction of effective static sta bility due to condensation heating, while the model based on the N grid doe s not. The difficulty with the M grid is due to decoupling of condensation and heating for vertically small scales. In view of these results, it is desirable to use the N grid in a model base d on an isentropic vertical coordinate. The vertically discrete moisture co ntinuity equation and a method to calculate condensation amount and heating on the N grid are presented.