A New k-Distribution Scheme for Clear-Sky Radiative Transfer Calculations in Earth's Atmosphere. Part II: Solar (Shortwave) Heating due to H₂O and CO₂

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 p_r and temperature θ_r, where the cooling rate is substantial in a spectral band. In this new scheme, the range of k(p_r, θ_r) of a band is divided into a number of equal intervals, or g groups, in log₁₀(k_r). A spectral point at the wavenumber ν is identified with one of the g groups according to its k_ν(p_r, θ_r). For each g group, a Planck-weighted k-distribution function H_g and a nonlinearly averaged absorption coefficient ${\bar{k}}_g(p,{\theta})$ are derived. The function H_g and the absorption coefficient ${\bar{k}}_g(p,{\theta})$ 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 CH₄ absorption 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^-1 in the troposphere and <1.0 K day^-1 in the stratosphere and 2) the difference in fluxes is <0.5 W m^-2 at 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.