On the analytic approximation of bulk collision rates of non-spherical hydrometeors

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.