A Comparative Study of Bulk Parameterization Schemes for Estimating Cloudy-Sky Surface Downward Longwave Radiation

Parameterization schemes (bulk formulae) are widely used to estimate all-sky surface downward longwave radiation (SDLR) due to the simple, readily available inputs and acceptable accuracy from local to regional scales. Seven widely used bulk formulae are evaluated using the ground measurements collected from 44 globally distributed flux measurement sites of five networks. The Bayesian model averaging (BMA) method is introduced to integrate multiple bulk formulae to obtain an estimate of cloudy-sky SDLR for the first time. The second multiple linear regression model of Carmona et al. (2014) performs the best, with BIAS, RMSE, and R2 of zero, 20.13 W·m−2 and 0.87, respectively. The BMA method can achieve balanced results that are close to the accuracy of the second multiple linear regression model of Carmona et al. (2014) and better than the average accuracy of seven bulk formulae, with BIAS, RMSE, and R2 of −1.08 W·m−2, 21.99 W·m−2 and 0.87, respectively. In addition, the bulk formula of Crawford and Duchon (1999) is preferred if there is insufficient data to calibrate the bulk formulae because it does not need local calibration and has an acceptable accuracy, with BIAS, RMSE, and R2 of 0.96 W·m−2, 26.58 W·m−2 and 0.82, respectively. The effects of climate type, land cover type, and surface elevation are also investigated to fully assess the applicability of each bulk formula and BMA. In general, there is no cloudy-sky bulk parametrization scheme that can be successfully applied everywhere.