Hydrostatic and Non-Hydrostatic Simulations of Moist Convection

Applicability of the Hydrostatic Approximation to a High-Resolution Model

Abstract

Comparative experiments of moist convection using hydrostatic and non-hydrostatic models are performed to study the suitability of the hydrostatic approximation for a high-resolution model when the grid size falls below 20km. The moist convection in the models is treated by the use of an explicit warm-rain process predicting cloud water and rainwater as well as by a semi-explicit scheme consisting of the warm-rain process and moist convective adjustment. The differences between the experiments with and without hydrostatic water loading are also examined and quantitatively compared with those between the hydrostatic and non-hydrostatic simulations.
When the prognostic explicit scheme is used, the hydrostatic simulation overdevelops moist convection, overestimates the total amount of precipitation, and overexpands the area of precipitation as the grid size decreases. This overdevelopment alters substantially the structure of moist convection and precipitation patterns. The absence of hydrostatic water loading also alters the total amount and structure of precipitation. Hydrostatic water loading exerts more significant influences on simulated precipitation than the hydrostatic approximation. In the 20-km simulations, the hydrostatic simulation with hydrostatic water loading produces results that are comparable to the non-hydrostatic counterpart.
The difference in the total amount of precipitation between the hydrostatic and non-hydrostatic simulations was not as large as that of the convective development. This can be explained by considering the total water budget, which includes simulated precipitation and water vapor flux through the lateral boundaries, i. e., the water-vapor flux in the hydrostatic simulation corresponds to that in the non-hydrostatic one.
Although moist convective adjustment removes conditional instability and does not produce strong updrafts, the characteristics of the results in the comparative experiments of moist convection using hydro-static and non-hydrostatic models were hardly changed by the incorporation of moist convective adjustment (the semi-explicit scheme). On the other hand, hydrostatic water loading exerts more significant influences on simulated precipitation with the semi-explicit scheme than that with the prognostic explicit scheme. Therefore, in developing 10-20km numerical weather prediction models, hydrostatic water loading should be evaluated in preference to adopting non-hydrostatic models.