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

Ming-Dah Chou Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland

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William L. Ridgway Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland

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Michael M-H. Yan Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland

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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.

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.

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