A simple model of climatological rainfall over the Tropical oceans

Model construction is based on the argument that boundary layer convergence can usefully be viewed as a forcing on deep convection, not just a result. This view is developed using a linear mixed layer model (Stevens et al. 2002) which skillfully reproduces observed surface winds and convergence and which we use to diagnose the relative influence of boundary layer and free tropospheric processes on boundary layer convergence. The mixed layer model is forced is forced with 850mb horizontal winds and pressure gradients from the ERA-40 reanalysis. Results show that variability in boundary layer convergence is predominantly associated with meridional boundary layer temperature gradients and SST, not deeper tropospheric processes.

Based on these results, we construct a simple model which predicts climatological precipitation and vertical motion profiles over the tropical oceans given the sea-surface temperature (SST), using statistical relationships deduced from the ERA-40 reanalysis. The model allows for two modes of variability in vertical motion profiles, a shallow mode responsible for all `boundary-layer' convergence between 850mb and the surface, and a deep mode with no boundary-layer convergence. The shallow mode is either specified from satellite observations or modeled using a simple mixed layer model which has SST as well as 850mb 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.