A New Representation of Collision-Induced Breakup of Raindrops and Its Implications for the Shapes of Raindrop Size Distributions

Using results of laboratory experiments on collision-induced raindrop breakup, Low and List (LL) developed a parameterization describing the fragment size distribution (FSD) produced by collisions of raindrops. An equilibrium raindrop size distribution (ED) is approached when this parameterization is used in numerical models of steady rain. Since scant observational evidence of such EDs exists, the need for a careful examination of the parameterization's foundation is evident. Using LL's experimental observations, an alternate parameterization is developed that alleviates three shortcomings of the original scheme, namely, ensuring mass conservation, the use of adequate uncertainty analysis, and the use of a more physical basis for deriving parameterized relationships. FSDs generated by raindrop collisions are represented by combinations of lognormal, Gaussian, and modified delta distributions for each of the three breakup types (filament, sheet, and disk) observed. The mode, width, and height of these distributions are calculated for the 10 colliding drop size combinations used in the LL experiments; uncertainty estimates for these parameters are determined using a bootstrap method, a technique that randomly chooses results of individual collisions. Relations giving the mode, width, and height in terms of the diameters of arbitrary large and small colliding raindrops are then determined so that the FSD from any raindrop collision can be predicted.