Abstract
Abstract. Analytic approximations of the binary collision rates of hydrometeors are derived for use in bulk microphysical parameterizations. Special attention is given to non-spherical hydrometeors like raindrops and snowflakes. The terminal fall velocity of these particles cannot be sufficiently well approximated by power-law relations which are used in most microphysical parameterizations, and therefore an improved formulation is needed. The analytic approximations of the bulk collision rates given in this paper are an alternative to look-up tables and can replace the Wisner approximation, which is used in many atmospheric models.
Highlights
The approximation of bulk collision rates is a classic problem in the formulation of cloud microphysical parameterizations for atmospheric models
The standard approach for the collision rate of two ensembles of precipitation-sized particles goes back to Wisner et al (1972), who used the ansatz that the velocity difference can be approximated by the difference of weighted means which simplifies the solution of the collision integrals
The main disadvantage of this approach is that the bulk collision rate of the Wisner approximation becomes zero, if the difference of the weighted mean sedimentation velocities is zero, while for broad size distributions as they occur in nature the bulk collision rate is always non-zero
Summary
The approximation of bulk collision rates is a classic problem in the formulation of cloud microphysical parameterizations for atmospheric models. Verlinde et al (1990) studied analytic solution of the bulk collision integrals for generalized gamma distributions and terminal fall velocities which can be approximated by powerlaw relations. They provide exact solutions for this problem, but those include the general hypergeometric function and are difficult and expensive to evaluate. A. Seifert et al.: Approximation of bulk collision rates parameterizations SB2006 limited their formulas to powerlaw relations for the terminal fall velocities. The Supplement contains auxiliary figures and further technical details on the collision interactions which are not in discussed in the main text
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