Temperature Dependent Precipitation in Exact Nonlinear Mountain Waves

Abstract Lagrangian variables are used to develop an explicit description of nonlinear mountain waves propagating in a moist atmosphere. This Lagrangian description is used to deduce an integral representation of the atmospheric pressure distribution in terms of the temperature within the laminar flow layer. Kirchoff’s equation is used to determine a temperature dependent enthalpy which together with the Clausius-Clapeyron equation is used to obtain an explicit expression for temperature and vapour pressure profiles in a saturated atmosphere where mountain waves are prominent. Precipitation rates are computed from the first law of thermodynamics and compare favourably with meteorological field data at Feldberg, a mountain in Germany. The second law of thermodynamics is used to show that there is a subregion near the tropopause at which precipitation is prohibited within the laminar flow.