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 (R_ld). It is influenced by radiative properties of the atmospheric column, in particular by greenhouse gases, water vapour, 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 spatio-temporal climatological variations in R_ld. 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 agreement with r² ranging from 0.87 to 0.99 across the datasets for clear-sky and all-sky conditions. We then used the equations to show that diurnal and seasonal variations in R_ld are predominantly controlled by changes in atmospheric heat storage. Variations in the emissivity of the atmosphere form a secondary contribution to the variation in R_ld, and are mainly controlled by anomalies in cloud cover. We also found that as aridity increases, the contributions from changes in emissivity and atmospheric heat storage tend to offset each other (−40 W m⁻² and 20−30 W m⁻², respectively), explaining the relatively small decrease in R_ld with aridity (−(10−20) W/m⁻²). These equations thus provide a solid physical basis for understanding the spatio-temporal variability of surface downwelling longwave radiation. This should help to better understand and interpret climatological changes, such as those associated with extreme events and global warming.