A Cloud Physical Parameterization Method for the Colision-Coalescence Process using Log-normal Distributions as Basis Functions

Numerical simulations of stochastic coalescence processes are presented using a series of distribution functions to characterize the drop spectra. The method is based in (Clark, 1976) and (Clark & Hall, 1983), where the distribution parameter tendencies are calculated, along with distribution moments tendencies. A lineal combination of two log-normal distribution functions are employed as basis functions of the parameterized model, although any number of distribution functions can be introduced. The equations governing the distribution parameter tendencies are derived from a multidimensional lagrangian polynomial fitting and integration. The solutions are compared with the output of an explicit microphysical model (Bott, 1998), showing reasonable accuracy.