What Sets the Relative Humidity of the Tropical Troposphere?

Abstract:

In global climate models, relative humidity is found to remain roughly constant with warming, but no rigorous argument has been given as to why. We can attempt to address this gap by developing an analytical (i.e., pencil-and-paper) model for the relative humidity of a tropical atmosphere in radiative-convective equilibrium. Given a few inputs (the pressure, temperature, and the convective entrainment and detrainment rates), the equations predict the RH and the temperature lapse rate analytically. RH turns out to be a simple ratio involving the fractional detrainment rate and the water-vapor lapse rate. The theory explains the magnitude of RH and the "C" shape of the tropospheric RH profile. It also predicts that RH is an invariant function of temperature as the atmosphere warms, and this behavior matches what has been seen in global climate models and what is demonstrated here with cloud-resolving simulations varied over a 30-K SST range. Extending the theory to include the evaporation of hydrometeors, a lower bound is derived for the precipitation efficiency (PE) at each height: PE > 1-RH. In a cloud-resolving simulation, this constraint is obeyed with the PE profile taking the shape of an inverted "C".