Using Brutsaert’s Equation to Understand the Spatiotemporal Variations of Downwelling Longwave Radiation

Downwelling longwave radiation (R_ld) is a dominant term in the surface energy balance and is central to global warming. It is influenced by the radiative properties in the whole atmospheric column, particularly greenhouse gases, water vapor, clouds, and atmospheric heat storage. To reveal the leading terms responsible for the spatiotemporal climatological variations in R_ld, we use the semi-empirical equation derived by Brutsaert (1975, “B75”), which only needs near-surface observations of air temperature and humidity. We first evaluated B75 and its extension by Crawford and Duchon (1999, "C&D99") with FLUXNET observations, NASA-CERES satellite data, and ERA5 reanalysis. We found a strong agreement, with R² being 0.87, 0.97, and 0.99, respectively. 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 atmospheric emissivity form a secondary contribution to the variation of R_ld, and are mostly controlled by anomalies in cloud cover. We also found that with increased aridity, the contributions by changes in atmospheric heat storage and emissivity acted to compensate each other (20~30 W/m² and ~-40 W/m², respectively), thus explaining the relatively little variation in R_ld with aridity (-20~-10 W/m²). The equations further indicate that under global warming, the amplification of water vapor is stronger in arid regions because clear-sky conditions are more sensitive to an increase in greenhouse gases. These equations thus provide a firm, physical basis to understand the spatiotemporal variability of downwelling longwave radiation at the surface. This should be helpful to better understand and interpret climatological changes, for instance those associated with global warming and extreme events.