The Effect of Stochastic Cloud Structure on the Icing Process

Abstract

Current understanding of the icing process through collisions between a surface and supercooled cloud droplets is based upon two factors. First, for a given temperature, when the cloud liquid water content, W, exceeds a critical value, wc (the Schumann–Ludlam limit), the ice that collects, whether on the surface of a hailstone or on the wing of an aircraft, changes from lower densities to values close to that of water. Second, it is assumed that cloud droplets are dispersed in space as uniformly as randomness allows (“Poissonian” clouds). It is now becoming well established, however, that clouds are not Poissonian. Rather, the droplets are “clustered” so that clouds consist of interspersed regions both rich and deficient in droplets. This is significant because it leads to a much broader probability distribution (pdf) of droplet counts than would be the case for a Poissonian cloud. That is, the ratio of the variance to the mean is much greater than unity (the Poissonian value). As a consequence, droplet clustering also produces a bunching or clustering of W as well as leading to “patchy” clouds. This paper explores the effect of this patchiness on the icing process. Results show that clustering is important for at least three reasons. First, it produces a broadening of the pdf of W. Second, this broadening means that W > wc by significant amounts over significant distances even when a Poissonian cloud would exclude such a possibility for the same average water content. Third, these spatial inhomogeneities introduce a “memory” into the icing process that is lacking in Poissonian clouds.