A Radiation Algorithm with Correlated-k Distribution. Part I: Local Thermal Equilibrium

Abstract A new radiation scheme is proposed that uses the correlated-k distribution (CKD) method. The definition of the k-distribution function, the transformation between frequency space and k space, and the upper limit of the absorption coefficient in cumulative probability space (CPS) are discussed. The corresponding relation between each interval in CPS and the heating rate profile provides a method for determining the width of intervals in CPS. Three schemes are discussed for handling the spectral overlap of gases. Method 1 rearranges the appropriate combination of gaseous absorption coefficients when the spectral overlap of two gases is extensive. Method 2 applies to most overlapping gases and addresses the most important aspects of each gas’s spectrum in each interval of CPS. Method 3 applies to weak gases only and seeks to adjust the main absorption coefficients in order that radiative forcing at the surface and the top of the atmosphere is correct. This model is quite efficient because 1) relatively few intervals in CPS are used (up to 1 mb, only 35 intervals for solar radiation, and 46 for infrared); 2) for some intervals with very large absorption coefficients, the radiative transfer process is simplified by ignoring scattering; 3) the water vapor continuum is dealt with efficiently by neglecting its effect in some nonimportant intervals in CPS and at high altitudes; and 4) gaseous overlap methods are simple and effective. Moreover, this model contains a proper treatment of spectral overlap between solar and infrared radiation. For both solar and infrared radiation, heating rate errors are generally less than 0.2 K day−1, and errors in flux at the surface and the top of the atmosphere are generally less than 1 W m−2.