A new k-distribution scheme for clear-sky radiative transfer calculations in earth's atmosphere. Part I: Thermal infrared (longwave) radiation

Abstract

A new k-distribution scheme of longwave radiation without the correlated-k-distribution assumption is developed. Grouping of spectral points is based on the line-by-line (LBL)-calculated absorption coefficient k at a few sets of reference pressure prand temperature θr, where the cooling rate is substantial in a spectral band. In this new scheme, the range of k(pr, θr) of a band is divided into a number of equal intervals, or g groups, in log10(kr). A spectral point at the wavenumber ν is identified with one of the g groups according to its kν(pr, θr). For each g group, a Planck-weighted k-distribution function Hgand a nonlinearly averaged absorption coefficient kg(p, θ) are derived. The function Hgand the absorption coefficient kg(p, θ) constitute the new k-distribution scheme. In this k-distribution scheme, a spectral point can only be identified with a g group regardless of pressure and temperature, which is different from the correlated-k distribution scheme. The k-distribution scheme is applied to the H2O, CO2, O3, N2O, and CH4absorption bands, and results are compared with LBL calculations. To balance between the accuracy and the computational economy, the number of g groups in a band of a given gas is chosen such that 1) the difference in cooling rate is <0.1 K day-1in the troposphere and <1.0 K day-1in the stratosphere and 2) the difference in fluxes is <0.5 W m-2at both the top of the atmosphere and the surface. These differences are attained with 130 g groups, which is the sum of the g groups of all five gases.