Characteristic non-dimensional numbers for orographic precipitation

Several dynamical and microphysical factors determine the precipitation amount originating from a stable orographic cloud. In this study we show that the changes in precipitation efficiency can be described with a set of non-dimensional control parameters. The most important of these is an analogue to the first Damkoehler number, i.e. the ratio of advection time to the microphysical timescale of the cloud. These timescales have been investigated with a Lagrangian analysis of orographic clouds in 2D simulations. Analytical approximations are developed and it is shown that after a suitable integration of properties from a vertical stack of trajectories, a unique relation between the precipitation efficiency of orographic clouds and the bulk Damkoehler number exists. This scaling relation allows to separate "regimes" in which the precipitation output is very sensitive to aerosol perturbations and such in which the precipitation efficiency is solely controlled by the flow dynamics and the geometry of the cloud. In addition to identifying a small set of non-dimensional characteristic numbers, this approach hence allows to shed more light on the sensitivity of orographic cloud systems to aerosol perturbations in different dynamical settings.