An Analytic Model of Cold Air Damming and Its Applications

Abstract

It is shown that the geometric shape of the cold dome in the two-layer model of cold air damming of Xu can be described approximately by a cubic polynomial and thus a set of coupled algebraic equations can be derived to quantify the scale and intensity of cold air damming as functions of the external parameters that characterize the environmental flow. In particular, these functions are easily computed and plotted in the parameter space, showing quantitatively how the cold dome width (scaled by the Rossby radius of deformation) and mountain-parallel jet speed change with the Froude number, surface roughness, inertial aspect ratio, and incident angle of the upstream inflow. The results also show that the cold dome width and mountain-parallel jet speed are insensitive to the depth of the upper-layer cross-mountain flow if the cross-mountain flow is sufficiently deep. The surface roughness and inverse inertial aspect ratio are found to have nearly the same control on the cold dome width and mountain-parallel jet speed and, thus, can be combined into a single parameter-the normalized Ekman number. The algebraic equations are shown to be useful for diagnoses or local forecasts of cold air damming provided the external parameters are properly estimated from the operational analyses or predictions. Examples of application are given for three cases of cold air damming.