The clear-sky downwelling long-wave radiation at the surface in current and future climates

Downwelling long-wave radiation is a crucial component of the energy balance of the land and ocean surface. Here we develop a semi-analytic model for the downwelling long-wave dependent on five governing parameters: the near-surface air temperature, the near-surface specific humidity, the surface air pressure, the e-folding height-scale of water vapour, and the CO (Formula presented.) concentration. The model predicts the hourly clear-sky long-wave in the ERA5 reanalysis product with a global mean error of 8.2 W (Formula presented.) m (Formula presented.), and on average captures 97% of the temporal variation at individual locations. We show that the model may be used to calculate clear-sky downwelling long-wave from only surface observations of temperature and humidity by using the time-mean water vapour height-scale from the ERA5, interpolated to the location of the observation. Using this method replicates sub-hourly observations from individual sites having a range of climates with errors of 12–25 W (Formula presented.) m (Formula presented.). Furthermore, the inclusion of CO (Formula presented.) allows the model to be used to study changes in downwelling long-wave at the surface as CO (Formula presented.) concentrations vary. We validate the model's representation of CO (Formula presented.) by comparison with five CMIP5 climate models. Our model thus provides a simple yet accurate framework to understand the key parameters controlling downwelling long-wave and its variability in the current and future climates.