Evolution of rain water profiles resulting from pure sedimentation: Spectral vs. parameterized description

The paper focuses on a comparison of solutions of the budget equations for specific moments of a hydrometeor size distribution, simplified to the prob lem of pure drop sedimentation, as following from models with a one-moment or a two-moment parameterization of microphysical processes and from a refe rence model based on spectral treatment of sedimentation. The solutions for the transient vertical profiles of liquid water content show remarkable di fferences in their spatial structure: starting from an idealized, discontin uous initial profile in form of a square wave, shock and rarefaction waves evolve in the parameterized models, while the reference solution describes a smooth distribution. These principle differences follow from the fact, th at the budget equations for the moments in the parameterized models are of the form of quasi-linear advection equations, with the decisive nonlinearit y arising from the parameterization relation for the sedimentation flux, wh ereas the reference solution follows from a linear partial differential equ ation. Hence, the quasi-linear shock effects have to be interpreted as a ma thematical artifact of the parameterization assumptions. The differing evol ution of the liquid water profiles finds expression in remarkable differenc es in the time series of surface precipitation rate for the spectral and pa rameterized models. (C) 2001 Elsevier Science B.V. All rights reserved.