A FORMULA FOR THE CONCENTRATION OF TRAJECTORIES OF PRECIPITATION PARTICLES AT THE GROUND

An idealized precipitation process in a 3-dimensional unsteady mesosca le flow with a Boussinesq ap proximation is considered. The process is assumed as follows: Immediately after precipitation particles are gen erated, they attain such an equilibrium that they fall with a constant terminal vertical velocity relative to the flow, and their horizontal velocity is equal to that of the flow. The ground is in general not h at, and other forcings (e.g., thermal) mag be included in order to ind uce the vertical flow velocity. Based on these assumptions, a simple f ormula describing the concentration of trajectories of precipitation p articles at the ground is derived. In particular, in the case of a ste ady flow, the concentration (scattering) of trajectories occurs when w (0) is positive (negative). Here w(0) is the vertical flow velocity at the generation point of particles. In the case of an unsteady flow, t he unsteadiness may suppress or enhance the concentration (scattering) of trajectories.