Scaling relations in warm-rain orographic precipitation

Abstract

Warm-rain orographic precipitation at an isolated mountain is studied by numerical experiments using the non-hydrostatic COSMO model. The simulations are analyzed to derive scaling relations for the precipitation efficiency as a function of the relevant microphysical and advective timescales and Froude numbers. For the microphysical conversion timescale a new formulation is applied based on a parameterization of the stochastic collection equation. This warm-rain microphysical timescale couples the rain formation to the forcing by condensation, i.e. updraft velocity and liquid water lapse rate, and microphysical properties like the cloud droplet number concentration. Using this microphysical timescale the scaling relations for warm-rain orographic precipitation for an isolated mountain are revisited. A simple scaling relation for the precipitation efficiency is found, but the physical explanation remains challenging due to the strong nonlinearity of the microphysical growth rates. It is hypothesised that, in addition to local variables, the dependency of cloud depth on the Froude number calculated with mountain width, U/(aN), plays an important role in determining the effective microphysical timescale.