The Parameterization of Longwave Flux in Energy Balance Climate Models

Abstract

Many climate models of the energy balance type parameterize the zonally-averaged infrared flux at the top of the atmosphere in terms of the surface (or sea level) temperature T and cloud cover n in the form I = A + BT ? (C + DT)nMost recent studies have used the annual average data of Ellis and Vonder Haar (1976) to determine the coefficients of this regression relation, and it leads to tolerable parameterization errors. However, we see here that when such formulas are used to simulate the seasonal cycle, very large errors are incurred. These errors are not greatly reduced if the regression coefficients are deduced by fitting the seasonal data. The more recent and comprehensive data set Winston et al. (1979) has been used to define and evaluate regression equations for the longwave emission at the top of the atmosphere. Whatever the relative accuracy of these two sets, it is found that regressions developed on the latter are about 2?5 W m?2 (or 20?50%) more accurate for the annual mean and 6?7 W m?2 (?50%) more accurate over the seasonal cycle. A better fit over polar regions is most evident. It is found that the inclusion of the nonlinear term in the parameterization makes little change in the accuracy to which the data are fitted. However, the explicit inclusion of the effects of clouds is found to be important. The analysis also reveals that clouds exert a significant feedback mechanism on climate. When the infrared flux formula is tuned to fit the later satellite data set, the implied extent of this feedback lies within the range determined by model calculations. It is also found that the sensitivity of climate implied by the formula, as expressed through the sensitivity of the longwave to surface temperature, is somewhat greater than that presented in recent determinations.