A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter

With increasing computer power, explicit microphysics schemes are becoming increasingly important in atmospheric models. Many schemes have followed the approach of Kessler in which one moment of the hydrometeor size distribution, proportional to the mass content, is predicted. More recently, the two-moment method has been introduced in which both the mass and the total number concentration of the hydrometeor categories are independently predicted. In bulk schemes, the size spectrum of each hydrometeor category is often described by a three-parameter gamma distribution function, N(D) = N(0)D(alpha)e(-lambda D). Two-moment schemes generally treat No and X as prognostic parameters while holding a constant. In this paper, the role of the spectral shape parameter, alpha, is investigated by examining its effects on sedimentation and microphysical growth rates. An approach is introduced for a two-moment scheme where alpha is allowed to vary diagnostically as a function of the mean-mass diameter. Comparisons are made between calculations using various bulk approaches-a one-moment, a two-moment, and a three-moment method-and an analytic bin model. It is found that the size-sorting mechanism, which exists in a bulk scheme when different fall velocities are applied to advect the different predicted moments, is significantly different amongst the schemes. The shape parameter plays an important role in determining the rate of size sorting. Likewise, instantaneous growth rates related to the moments are shown to be significantly affected by this parameter.