A Cloud Physical Parameterization Method Using Movable Basis Functions: Stochastic Coalescence Parcel Calculations

Abstract

Numerical simulations of stochastic coalescence in a parcel framework are presented using a series of distribution functions. The equations governing the distribution parameter tendencies are derived using a variational approach with constraints. Solutions with two and three log-normal distribution functions are compared with a conventional benchmark model and the distribution model is shown to produce accurate solutions. Although only coalescence is considered within this paper, the procedures for including further physical processes is discussed. All of the simulations presented use the log-normal distribution although the method is general enough that it could be adapted to use other distributions such as the gamma distribution. A decrease in the number of dependent variables by as much as by a factor of 10 as well as an equivalent reduction in computation time required for the treatment of the coalescence equation makes the distribution model attractive for multi-dimensional cloud model simulations. Further research in the direction of extending the distribution model for such purposes is currently in progress.