Temporal Evolution of Drop Spectra to Collisional Equilibrium in Steady and Pulsating Rain

Abstract

The evolution of raindrop spectra by collisional breakup is examined analytically and modelled in box and 1-dimensional shaft models, using the parameterization of Low and List. The significant analytical result shows that equilibrium drop size distributions occur in families that are multiples of one another: f(D,R) = Rψ(D) where D is the drop diameter, R is the rainfall rate, f(D,R) the number density distribution in terms of D and R and ψ is a shape function. For the Low-List breakup scheme the shapes are trimodal, with peaks in the number distributions at diameters of 264, 790, and 1760 μm. Similar structures were found by Valdez and Young, and Brown for box models. These peaks are expected to exist wherever spectra approach equilibrium, independently of the rainfall rate. In this paper the development of these peaks from non-equilibrium spectra is examined, together with the effect of periodically varying rainfall rates. In box and one-dimensional shaft models, nonequilibrium spectra quickly develop features similar to those at equilibrium, but times and/or heights to reach true equilibrium are in excess of 30 minutes, or 3 km for all but the very heaviest rainfall rates. The peaks, however, should be identifiable in a matter of minutes, thus encouraging field verification under favorable conditions. In the absence of evaporation, spectral evolution below a cloud is dominated by the large drops, which produce the accompanying small drops by breakup. Evaporation, while basically affecting the smallest drops, is quickly spread over the whole spectrum by the collision process and reduces the total liquid water content The drop spectrum shape however, remains unchanged.