Radiative constraints on the hydrological cycle in an idealized radiative-convective equilibrium model

Ken Takahashi, 2008

Accepted by Journal of the Atmospheric Sciences (Submitted: March 27, 2008, Revised: June 17, 2008, Accepted: June 21, 2008).

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This paper is motivated by the robust result from coupled climate models that global warming is accompanied by an increase in global moisture of around 7% per degree warming, but the global evaporation/precipitation increases at most by 2%. It is believed that radiative constraints determine the latter (i.e. how much the longwave cooling increases with temperature), but a physically based theory of how this actually occurs is lacking.
In this paper I explore a highly simplified model that (I believe) captures the essential processes for this problem, analyze it in detail and produce an explicit theory for the relation between the global hydrological cycle and radiation.

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 semi-gray radiative transfer a semi-analytical 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.

The model shows that 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 semi-analytical solution indicates a rate of change in LHF with greenhouse forcing of around 2 Wm^-2 per degree of surface warming, which corresponds to the Planck feedback (~3.2 Wm^-2/K) multiplied by a coefficient 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).

June, 2008.