A Parameterization of the Effective Layer Emission for Infrared Radiation Calculations

Abstract

The impact of the vertical integration of radiative transfer on cooling rate calculations is studied for different numerical schemes. One involves the effective emitting temperature of a layer (scheme A), and the other involves temperatures at the interface between layers (scheme B). It is found that when there are large variations of temperature and humidity in the lower troposphere, the cooling rate profiles computed with the different schemes exhibit little resemblance. When the mean layer temperature is used for the effective emitting temperature (scheme A2), the cooling rate oscillates greatly from one layer to the next. On the other hand, the cooling rate computed with scheme B varies very little with height even for the case with large vertical variations of temperature and humidity. The reason for the large cooling rate oscillation in scheme A2 is due to the use of a single effective emitting temperature for both upward and downward fluxes, which is true only for an isothermal layer. The overly smoothed cooling profile for scheme B is caused by the interpolation of level temperatures from layer temperatures. The interpolation has a smoothing effect on the vertical distribution of temperature and, hence, cooling rate. The transmission function averaged over a spectral band decreases exponentially with the square root of absorber amount. Based on this relationship, the effective emitting temperature of a layer is parameterized separately for computing upward and downward fluxes (scheme A1). Using the parameterization, the large oscillation of the cooling rate profile of scheme A2 is substantially reduced, while the problem of overly smoothing when using scheme B is eliminated. In addition, to be more accurate, the speed of computation using scheme A2 is higher than that using scheme B.