Radiative Constraints on the Hydrological Cycle in an Idealized Radiative–Convective Equilibrium Model

Abstract

The radiative constraints on the partitioning of the surface energy budget and, hence, on the strength of the hydrological cycle are analyzed in an idealized one-dimensional radiative?convective equilibrium model formulated in terms of the energy budgets at the top of the atmosphere, the subcloud layer, and the free atmosphere, which enables it to predict both surface relative humidity and the air?sea temperature difference. Using semigray radiative transfer, a semianalytical solution was obtained that explicitly shows how the surface latent heat flux (LHF) is related to the radiative properties of the atmosphere. This solution was also used in conjunction with a full radiative transfer code and was found to provide reasonably realistic quantitative estimates. In the model the LHF is fundamentally constrained by the net longwave flux divergence above the level of condensation by lifting (LCL) and by the atmospheric absorption of shortwave radiation, with only a weak indirect control by near-surface moisture. The latter implies that the Clausius?Clapeyron relation does not directly constrain the strength of the hydrological cycle. Under radiative perturbations, the changes in LHF are determined by the changes in the net longwave fluxes at the LCL, associated mainly with the changes in the longwave transmissivity, and by the changes in shortwave absorption by the atmosphere (e.g., by increased water vapor). Using a full radiative transfer model with interactive water vapor feedback with the semianalytical solution indicates a rate of change in LHF with greenhouse forcing of around 2 W m?2 K?1 of surface warming, which corresponds to the Planck feedback (?3.2 W m?2 K?1) multiplied by a coefficient of order one that, to first approximation, depends only on the relative magnitudes of the net longwave radiation fluxes at the LCL and the top of the atmosphere (i.e., on the shape of the vertical profile of the net longwave flux).