A Simple Model of Climatological Rainfall and Vertical Motion Patterns over the Tropical Oceans

Abstract

A simple model is developed that predicts climatological rainfall, vertical motion, and diabatic heating profiles over the tropical oceans given the sea surface temperature (SST), using statistical relationships deduced from the 40-yr ECMWF Re-Analysis (ERA-40). The model allows for two modes of variability in the vertical motion profiles: a shallow mode responsible for all “boundary layer” convergence between 850 hPa and the surface, and a deep mode with no boundary layer convergence. The model is based on the argument expressed in the authors’ companion paper that boundary layer convergence can be usefully viewed as a forcing on deep convection, not just a result thereof. The shallow mode is either specified from satellite observations or modeled using a simple mixed-layer model that has SST as well as 850-hPa geopotential height, winds, and temperature as boundary conditions. The deep-mode amplitude is empirically shown to be proportional to a simple measure of conditional instability in convecting regions, and is determined by the constraint that radiative cooling must balance adiabatic warming in subsidence regions. This two-mode model is tested against a reanalysis-derived dry static energy budget and in a reanalysis-independent framework based on satellite-derived surface convergence and using SST as a proxy for conditional instability. It can predict the observed annual mean and seasonal cycle of rainfall, vertical motion, and diabatic heating profiles across the tropical oceans with significantly more skill than optimized predictions using a thresholded linear relationship with SST. In most warm-ocean regions, significant rainfall only occurs in regions of monthly-mean boundary layer convergence. In such regions, deep-mode amplitude and rainfall increase linearly with SST, with an additional rainfall contribution from the shallow mode directly tied to boundary layer convergence. This second contribution is significant mainly in the east and central Pacific ITCZ, where it is responsible for that region’s “bottom-heavy” vertical-velocity, diabatic heating, and cloud profiles.