Notes on the exact solution of moist updraught equations

TitleNotes on the exact solution of moist updraught equations
Publication TypeTechnical memorandum
Date Published07/2007
Secondary TitleECMWF Technical Memoranda
AuthorsJanssen, PAEM, Köhler, M

The entraining plume model is at the center of most convection parametrizations in global climate and weather prediction models. Entrainment can be formulated in terms of a relaxation time scale which makes it inversely dependent on the parcel vertical velocity. The result is a rather complex system of equations with a singularity for zero vertical velocity and infinite entrainment. This makes it impossible to numerically solve the coupled equations. The determination of the top of convection or the boundary layer will therefore be highly inaccurate. Here the system of equations is solved for dry, moist and cloudy situations.

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