Model of precipitation and vertical air currents

Time-dependent moist columnar convection is numerically modeled; a version of Priestley's 1953 study of dry elements in a turbulent environment is combined with Kessler's 1969 treatment of the distribution of water substance in atmospheric circulations. Solutions are given of simultaneous equations for the vertical velocity, buoyancy, and cloud and precipitation content, in an air column moving under buoyancy and subject to rainout and continuous mixing of heat, momentum and moisture with ambient air. The velocity regime of the model depends on parameters of environmental lapse rate, moisture content, and the size and amplitude of an initiating disturbance. The model admits damped Brunt-Vaisala oscillations, condensation oscillations, and steady state updrafts of three kinds. Great changes of the solutions from one type to another occur as parameters cross thresholds determined by values of other parameters. Relationships among coupled periodic variations and steady state values of condensed water, precipitation rate, buoyancy and vertical velocity of air are analyzed in depth and with reference to microphysical processes. In the model, a definite horizontal size and perturbation buoyancy must be exceeded for sustained moist convection to accompany a given conditionally unstable lapse rate and ambient moisture condition. This leads to consideration of boundary-layer properties related to the geographical and diurnal variability of thunderstorms. It is proposed that strong static instability within the boundary layer tends to inhibit thunderstorm development because an unstable layer does not sustain large wave disturbances which may be essential to initiate deep convection and because the small scale convection promoted by strong boundary layer instability dissipates some of the energy that would otherwise remain available for deep convection. A number of other storm characteristics find plausible explanations within the framework of the theory, and some studies are suggested for its evaluation and improvement.