A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description

Many two-moment bulk schemes use a three-parameter gamma distribution of the form N(D) = N(0)D(alpha)e(-lambda D) to describe the size spectrum of a given hydrometeor category. These schemes predict changes to the mass content and the total number concentration thereby allowing N-0 and lambda to vary as prognostic parameters while fixing the shape parameter, alpha. As was shown in Part I of this study, the shape parameter, which represents the relative dispersion of the hydrometeor size spectrum, plays an important role in the computation of sedimentation and instantaneous growth rates in bulk microphysics schemes. Significant improvement was shown by allowing a to vary as a diagnostic function of the predicted moments rather than using a fixed-value approach. Ideally, however, a should be an independent prognostic parameter. In this paper, a closure formulation is developed for calculating the source and sink terms of a third moment of the size distribution-the radar reffectivity. With predictive equations for the mass content, total number concentration, and radar reffectivity, a becomes a fully prognostic variable and a three-moment parameterization becomes feasible. A new bulk microphysics scheme is presented and described. The full version of the scheme predicts three moments for all precipitating hydrometeor categories. Simulations of an idealized hailstorm in the context of a 1D kinematic cloud model employing the one-moment, two-moment, and three-moment versions of the scheme are compared. The vertical distribution of the hydrometeor mass contents using the two-moment version with diagnostic-a relations are much closer to the three-moment than the one-moment simulation. However, the evolution of the surface precipitation rate is notably different between the three-moment and two-moment schemes.