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ABSTRACT An intensive observation period was conducted in September 2017 in the central Namib, Namibia, as part of the project Namib Fog Life Cycle Analysis (NaFoLiCA). The purpose of the [...]

In the present paper a new method is introduced for the numerical solution of the stochastic collection equation in cloud models dealing with two-dimensional cloud microphysics. The method is based on the assumption that the probability for the collision of two cloud drops only depends on the water mass of each and not on the mass of the aerosol nuclei. With this assumption it is possible to reduce the two-dimensional solution of the stochastic collection equation to a one-dimensional approach. First, the two-dimensional particle spectrum is integrated over the aerosol mass yielding a one-dimensional drop spectrum in the water mass grid. For this intermediate drop distribution the stochastic collection equation is solved. The resulting new drop spectrum is redistributed into the two-dimensional aerosol-water grid. Numerical sensitivity studies are presented demonstrating that the flux method yields very good results. In the two-dimensional aerosol-water grid the drop distributions move from initially small aerosol and water masses toward larger values whereby the drops remain more or less concentrated along a straight line. In several calculations the numerical diffusivity of the method is investigated. The corresponding results show that in these investigations the artificial broadening of the drop distribution remains tolerably low.

A new mass conservative flux method is presented for the numerical solution of the stochastic collection equation. The method consists of a two-step procedure. In the first step the mass distribution of drops with mass x[prime] that have been newly formed in a collision process is entirely added to grid box k of the numerical grid mesh with [x.sub.k] [less than or equal to] x[prime] [less than or equal to] [x.sub.k+1]. In the second step a certain fraction of the water mass in grid box k is transported to k + 1. This transport is done by means of an advection procedure. Different numerical test runs are presented in which the proposed method is compared with the Berry-Reinhardt scheme. These tests show a very good agreement between the two approaches. In various sensitivity studies it is demonstrated that the flux method remains numerically stable for different choices of the grid mesh and the integration time step. Since a time step of 10 s may be used without significant loss of accuracy, the flux method is numerically very efficient in comparison to the Berry-Reinhardt scheme.