The Adequacy of the Hydrostatic Assumption in Sea Breeze Modeling over Flat Terrain

Abstract

Using a linear analytic model and a nonlinear numerical model, the adequacy of the hydrostatic model is investigated for use in the simulation of sea and land breezes over flat terrain. Among the results it is found that for a given horizontal scale of heating, the hydrostatic assumption becomes less valid as the intensity of surface heating increases, and as the synoptic temperature lapse rate becomes less stable. The spatial scale at which the hydrostatic assumption fails is substantially smaller than suggested by Orlanski (1981). For sufficiently stable large-scale thermodynamic stratifications, for instance, aspect ratios of order unity can still produce nearly identical solutions, regardless of whether or not the hydrostatic assumption is used. The difference in the conclusions between our study and that of Orlanski is attributed to Orlanksi's analyses of the characteristic wave equations in the free atmosphere, whereas in a sea-breeze simulation the requirement that vertical velocity at the ground is zero limits the magnitude of the vertical acceleration.