One-Parameter Scaling and Exponential-Sum Fitting for Water Vapor and CO2 Infrared Transmission Functions

Abstract

A medium-sized band model for water vapor and CO2 absorption is developed using the one-parameter scaling approximation. The infrared spectrum is divided into 10 bands. The Planck-weighted diffuse transmittance is reduced to a function dependent only upon the scaled absorber amount and fit by an exponential sum. By selecting specific sets of absorption coefficients for exponential-sum fitting, computations of fluxes and cooling rate are made very fast. Compared to a broadband model, the accuracy, speed, and versatility are all enhanced. With absorption due to water vapor line, continuum, CO2 as well as O3 included, the parameterization introduces an error of < 1.5 W m?2 in fluxes and <0.15°C day?1 in the tropospheric and lower stratospheric cooling rates.