An Accurate and Efficient Radiation Algorithm for Middle Atmosphere Models

Abstract

An accurate, efficient, and user-friendly radiation algorithm is developed for calculating net radiative heating rate in middle atmosphere models. The Curtis matrix interpolation scheme originally developed by Zhu is adopted with explicit temperature dependence for the calculation of the CO₂ 15-μm band atmospheric cooling rate. The O₃ 9.6-μm band cooling rate is calculated by a Curtis matrix interpolation and includes variations of temperature and ozone mixing ratio. The water vapor cooling rate by the rotational band and the 6.3-μm vibrational band is calculated by interpolation to the H₂O mixing ratio variation. All Curtis matrices are referenced to a basic state and calculated by correlated k distributions derived from line-by-line integrations. The solar heating rate by O₃ and O2 is based on Strobel's parameterization and updated with solar fluxes and absorption cross-sectional data. A 6-point Gaussian quadrature is used to compute the diurnal average of the solar heating rate for two-dimensional models. The algorithm produces errors of less than 5% in cooling rate and less than 3% in beating rate in the region of 35–65 km where the radiative processes play a major role. Yet the computation time required for this algorithm is comparable to a scale-dependent Newtonian cooling parameterization. In addition, a unified overview of the relation among the exact line-by-line integration, the correlated k distribution, and the classical random band models is given, and the great superiority of the correlated k method over the classical random band models for nonhomogeneous atmospheres is demonstrated. The author also suggests least-squares fitting band model parameters to a line-by-line integrated k distribution.