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A new  k -distribution scheme without the assumption of the correlation between the absorption coefficients at different pressures is developed for solar heating due to water vapor and CO 2 . Grouping of spectral points is based on the observation that radiation at spectral points with a large absorption coefficient is quickly absorbed to heat the stratosphere, and the heating below is attributable to the absorption of the solar radiation at the remaining spectral points. By grouping the spectral points with a large absorption coefficient at low pressures, the range of the absorption coefficient of the remaining spectral points is narrowed, and the  k -distribution approximation can be accurately applied to compute solar heating in both the stratosphere and troposphere. Grouping of the spectral points is based on the absorption coefficient at a couple of reference pressures where heating is significant. With a total number of 52 spectral groups in the water vapor and CO 2  bands, fluxes and heating rates were calculated for various solar zenith angles in some typical and sampled atmospheres in diverse climatic regimes and seasons. The maximum heating rate difference between the  k -distribution and line-by-line calculations is &lt; 0.09 K day -1  for water vapor, and &lt; 0.2 K day -1  for CO 2 . The difference in the surface radiation is ~ 1.4 W m -2  for water vapor and 0.6 W m -2  for CO 2 , while it could increase to 2.6 W m -2  due to overlapping absorption. These results can be improved by increasing the number of spectral groups at the expense of computational economy.

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