Choice of a Vertical Grid in Incorporating Condensation Heating into an Isentropic Vertical Coordinate Model

Abstract

Advantages of using an isentropic vertical coordinate in atmospheric models are well recognized. In particular, the use of an isentropic coordinate virtually eliminates discretization errors for vertical advection since isentropic surfaces are material surfaces under dry-adiabatic processes. This is also advantageous for predicting moist-adiabatic condensation processes because their occurrence and maintenance largely depend on the converging moisture transport through the surrounding unsaturated regions. In this paper, a basic problem in incorporating condensation heating into an isentropic coordinate model is discussed: that is, the problem of choosing a proper vertical grid for predicting moisture and computing condensation amount and condensation heating. Two different vertical grids are described, one of which predicts moisture for each model layer (M grid) and the other predicts it at each interface separating the model layers (N grid). The models based on these two vertical grids become identical without condensation. To illustrate the different impacts of these grids on dynamics, simulations of horizontally standing oscillations with two models based on these grids are presented. Results indicate that the model based on the M grid has difficulty in correctly recognizing the reduction of effective static stability due to condensation heating, while the model based on the N grid does 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 based on an isentropic vertical coordinate. The vertically discrete moisture continuity equation and a method to calculate condensation amount and heating on the N grid are presented.