The Simplified Exchange Approximation: A New Method for Radiative Transfer Calculations

Abstract

A new scheme for the efficient calculation of longwave radiative heating rates is proposed. Its speed and accuracy make it attractive for use in large atmospheric circulation models. The approximation suggested iswhere q is the heating rate, qe an "emissivity" heating rate calculated using the strong-line approximation and neglecting variation of line intensity with temperature, qeCTS the heating rate calculated using the cool-to-space approximation and the emissivity assumption, and qCTS the heating rate calculated by the cool-to-space approximation. Tests using a variety of soundings indicate that for both clear sky and cloudy cases the new approximation is substantially more accurate than either the emissivity or the cool-to-space approximations alone. Deviations from exact calculations are generally under 0.05 K day−1. Errors in the calculated flux at the surface are also shown to be small especially with the inclusion of a "heat from ground" term in the approximation. Some alternate schemes using similar approximations are presented and their utility discussed.