Understanding variations in downwelling longwave radiation using Brutsaert's equation

Abstract. A dominant term in the surface energy balance and central to global warming is downwelling longwave radiation (Rld). It is influenced by radiative properties of the atmospheric column, in particular by greenhouse gases, water vapor, clouds, and differences in atmospheric heat storage. We use the semi-empirical equation derived by Brutsaert (1975) to identify the leading terms responsible for the spatial–temporal climatological variations in Rld. This equation requires only near-surface observations of air temperature and humidity. We first evaluated this equation and its extension by Crawford and Duchon (1999) with observations from FLUXNET, the NASA-CERES dataset, and the ERA5 reanalysis. We found a strong spatiotemporal correlation between estimated Rld and the datasets above, with r2 ranging from 0.87 to 0.98 across the datasets for clear-sky and all-sky conditions. We then used the equations to show that changes in lower atmospheric heat storage explain more than 95 % and around 73 % of diurnal range and seasonal variations in Rld, respectively, with the regional contribution decreasing with latitude. Seasonal changes in the emissivity of the atmosphere play a second role, which is controlled by anomalies in cloud cover at high latitudes but dominated by water vapor changes at midlatitudes and subtropics, especially over monsoon regions. We also found that as aridity increases over the region, the contributions from changes in emissivity and lower atmospheric heat storage tend to offset each other (−40 and 20–30 W m−2, respectively), explaining the relatively small decrease in Rld with aridity (−(10–20) W m−2). These equations thus provide a solid physical basis for understanding the spatiotemporal variability of surface downwelling longwave radiation. This should help us to better understand and interpret climatological changes, such as those associated with extreme events and global warming.