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An analytic study on the evolution of the vertical profile of rain water concentration
Author(s) -
Wacker Ulrike
Publication year - 2000
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/1999gl006088
Subject(s) - advection , parameterized complexity , precipitation , variable (mathematics) , nonlinear system , transient (computer programming) , shock wave , flux (metallurgy) , environmental science , sedimentation , meteorology , mathematics , physics , mathematical analysis , mechanics , geology , thermodynamics , computer science , materials science , paleontology , combinatorics , quantum mechanics , sediment , metallurgy , operating system
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.