Precipitation fronts and the reflection and transmission of tropical disturbances

This paper investigates the interactions between precipitation and the circulation in an idealized model for the tropical atmosphere where convection is represented by a quasi-equilibrium closure. When studying large-scale circulation in the Tropics, the governing equations can be further simplified by making the strict quasi-equilibrium assumption which considers that convection acts to instantaneously adjust the atmospheric temperature profile to a moist adiabatic lapse rate. It is shown here that, under this assumption, the interface between the precipitating and non-precipitating regions exhibits a discontinuity in the precipitation rate and vertical velocity. Furthermore, this interface, referred to as a precipitation front, moves at a velocity distinct from the propagation speed of dry and moist disturbances. The theory predicts the existence of three types of precipitation fronts: drying fronts, slow moistening fronts and fast moistening fronts. In previous studies, numerical simulations have demonstrated the existence of the three types of front, and have also confinned that the precipitation front theory offers a good approximation for the behaviour of the interface between dry and moist regions for finite value of the convective adjustment time. A new framework is proposed here in which the encounter of an atmospheric disturbance and the edge of a precipitation region is recast as a Riemann problem. It is shown that, for any precipitation fronts, there are three incident characteristics but only two outgoing characteristics. This makes it possible to solve simultaneously for the intensity of the outgoing invariants and the propagation speed of the front. This also implies that atmospheric disturbances will be partially transmitted and partially reflected when encountering a precipitation front. For small perturbations, linear reflection and transmission coefficients can be computed analytically. These results also indicate that that disturbances can be amplified through over-transmission or over-reflection. These theoretical results are confirmed in numerical simulations of an idealized Walker circulation. A solution that includes a stationary precipitation front is perturbed by adding a small-amplitude gravity wave, convectively coupled gravity wave, or moisture disturbance. All numerical simulations exhibit reflection and transmission of the incoming signal, and one simulation shows a case of over-transmission of the incoming disturbance.