This contribution hints at a serious problem in modelling the vertical profile of rain water concentration, which evolves under the effect of sedimentation, when cloud microphysical processes are represented in terms of a familiar one-variable parameterization. If the parameterized precipitation flux increases faster than linearly with rain water concentration, as e.g. in the original Kessler-concept, then the prognostic equation for this concentration takes the form of a quasi-linear advection equation. The analytic solution is a transient 'signal' that ultimately breaks at some time and location and the solution becomes multivalued, that is physically meaningless. If, however, the problem is treated according to shock waves in nonlinear wave dynamics, a weak solution can be constructed. In that case, the multivalued solution is replaced by a discontinuous one. ¿ 2000 American Geophysical Union |