Orography strongly affects spatial patterns of precipitation in many monsoon regions. Yet, changes in tropical orographic rainfall with warming are not well constrained, and the underlying physical processes are poorly resolved by climate models. Well-established theories exist for the dynamics of mountain flows in convectively stable atmospheres, but they poorly describe tropical regions, where latent heating from convection strongly influences the dynamics. We present a theory that elucidates the coupling between moist convection and the mean flow around orography. The flow is modeled as a linear Boussinesq system, forced by both topography and convective heating. Convection responds to temperature and moisture perturbations carried by the coupled flow; vertically resolved profiles of convective heating are obtained by means of a linear response function (LRF). The system effectively represents convectively coupled orographic stationary waves. The solutions provide estimates of the flow and precipitation distribution as a function of the mountain shape, basic-state wind, static stability, moisture profile, and the LRF.

The theory is used to quantify the sensitivity of tropical orographic rainfall to changes in basic-state wind and the thermodynamic environment, such as those that occur in climate warming. With fixed horizontal wind, increases in static stability and moisture stratification in a warmer state have opposite influences on orographic rainfall amounts. Changes in the sensitivity of convection to thermodynamic perturbations (through the LRF) further influence the precipitation response. Theoretical predictions are compared against long integrations of cloud resolving simulations of orographic precipitation, that predict a surprising decrease in upstream orographic rain maxima in a warmer basic state.