An Efficient Numerical Approach to Radiative–Convective Equilibrium

Abstract

An efficient method for computing the radiative?convective equilibrium temperature profile of a vertical?column atmospheric model is described. The equations which specify the equilibrium conditions are linearized to form a matrix equation in which the net radiative heating at levels within regions of radiative equilibrium and the net radiative flux at the tops of regions undergoing convective adjustment are linearly proportional to the differences between initial guess temperatures and equilibrium temperatures at all levels. Because the original equations am nonlinear in the temperature profile, the matrix elements of the linearized equation also depend on the temperature profile. As a result, the equilibrium temperature profile is obtained by sequentially solving the matrix equation. Sample calculations indicate that successive solutions of the matrix equation converge rapidly to the equilibrium temperature profile, and the equilibrium conditions are typically satisfied after four inversions.