Treatment of the layer temperature-gradient problem in band-model emission codes

An approximate method for rapid and reasonably accurate sublayer integration in band-model-based radiative transfer codes is described. The method is based on a five-parameter, second-order Padé approximation to the molecular equivalent width that is a function of a single variable, the molecular weak-line optical depth τ(m). Three of the parameters are determined by boundary conditions at τ(m) = 0 and τ(m) = ∞ The other two parameters are obtained with an error-minimization fit to the molecular equivalent width at two points along the curve of growth. This process can be applied sequentially to all adjacent pairs of points along the entire curve of growth to yield the total path radiance. Sample calculations are performed for representative curves of growth: exponential, Lorentz, and Doppler. It is shown that for atmospheric radiative flux and cooling-rate calculations this approach will yield results to within approximately 0.2% of fully converged calculations.