Propagation, reflection and transmission of precipitation fronts in the tropical atmosphere

The behavior of the interface between the precipitating and non-precipitating regions is analyzed in an idealized model for the large scale atmospheric circulation. This model uses a quasi-equilibrium relaxation closure in which convection acts to removed the convective instability. It is shown that in the strict quasiequilibrium limit, i.e. for instantaneous convective adjustment, the boundary between the dry and moist regions can exhibit a discontinuity in the precipitation rate and vertical velocity. This interface, referred here to as a precipitation front, behaves as a propagating shock. Three distinct precipitation fronts can be obtained: drying front, slow moistening front and fast moistening front. The front velocity is distinct from the propagation speed of dry and moist disturbances and must be determined by solving a Riemman problem. Stationary precipitation fronts are also found in steady solutions for idealized Walker circulations in both one and two dimensions. Dry gravity waves and coupled convective-gravity waves are partially ∗Correspondence to: Courant Institute of Mathematical Sciences, 251 Mercer street, New York, NY 10012, USA. E-mail: [email protected]. Copyright c © 2007 Royal Meteorological Society Prepared using qjrms3.cls [Version: 2007/01/05 v1.00] transmitted and partially reflected when they encounter a precipitation front. Similarly, it is also shown that advection of a water vapor perturbation into a precipitation front generates propagating waves on both sides of the front. For small perturbations, the reflection and transmission coefficients can be determined analytically. For large perturbations, the interaction with the precipitation front is highly nonlinear, and can result in a change in the direction of propagation of the front. The theory for precipitation fronts discussed here can be viewed as an extension of the Strict QuasiEquilibrium (SQE) theory for the tropical atmosphere. This theory makes it possible to solve the SQE equations when deep convection is inactive in some portion of the atmosphere, and capture the fundamental non-linearity associated with the onset of precipitation in the SQE framework.