TREATMENT OF THE LAYER TEMPERATURE-GRADIENT PROBLEM IN BAND-MODEL EMISSION CODES

An approximate method for rapid and reasonably accurate sublayer integ ration in band-model-based radiative transfer codes is described, The method is based on a five-parameter, second-order Pade approximation t o the molecular equivalent width that is a function of a single variab le, the molecular weak-line optical depth tau(m). Three of the paramet ers are determined by boundary conditions at tau(m) = 0 and tau(m) = i nfinity. The other two parameters are obtained with an error-minimizat ion fit to the molecular equivalent width at two points along the curv e of growth. This process can be applied sequentially to all adjacent pairs of points along the entire curve of growth to yield the total pa th radiance. Sample calculations are performed for representative curv es 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 ca lculations.