KINEMATICAL RELATIONS BETWEEN WIND AND PRECIPITATION DISTRIBUTIONS, II

Abstract

In order to extend our understanding of the relationships between the atmospheric distributions of water substance and the wind, a two-dimensional continuity equation for water substance is studied in terms of model wind fields. Water-budget parameters are defined, and digital methods are used to develop time-dependent solutions of the continuity equation with the assumptions that the fall speed of condensate with respect to air is uniform, that condensation in rising saturated air and evaporation in subsaturated air occur instantaneously, and that the assumed wind field does not vary with time. It is shown that, for given distributions of the wind and condensation rate, the shape of the developing water distribution is determined only by the ratio of the updrafts to the fall speed of condensate. The distributions of water substance derived from the continuity equations show features analogous to radar observations of water substance in the real atmosphere. For example, when the falling speed of condensate is larger than the maximum speed of updrafts, relatively small amounts of condensed water exist aloft, and vertical profiles of condensed water content correspond to those observed by radar in widespread precipitation. When the maximum updrafts are larger, condensate occurs aloft in large amounts: in these cases, the vertical protiles display upper-level maxima similar to radar observations of thunderstorms and early stages of shower development. When fall speeds are large, nearly all the water condensed is also precipitated. However, the amount of precipitation decreases to about 35 per cent of the condensed water when fall speeds are comparatively quite small; in these cases, condensate aloft is so distributed that much of it evaporates in the downdraft part of the assumed wind field. The methods used in this study can readily be adapted to study a variety of wind fields and to incorporate less restrictive postulates regarding the physical processes of precipitation.