Derivation and tests of the GCSS analytic longwave radiation formula

Many GCSS intercomparisons of boundary layer clouds have used a convenient but idealized longwave radiation formula for clouds in their large-eddy simulations (LES). Under what conditions is this formula justified? Can it be extended to mid-level layer clouds?

This paper first derives the GCSS formula using an alternative method to effective emissivity. A key simplifying assumption is that the cloud is isothermal in the vertical and horizontal. However, this assumption does not turn out to be overly restrictive in practice. Then the GCSS formula is compared with a detailed numerical code, BugsRad. Sensitivity studies are performed in which cloud properties, cloud altitude, and thermodynamic profiles are modified. Our focus is primarily on mid-level, altostratocumulus layers.

Our results show that the GCSS formula can be successfully extended to liquid (ice-free), mid-level clouds. The GCSS formula produces remarkably accurate radiative profiles if the parameters are adjusted on a case-by-case basis. However, the formula needs to be calibrated using a more general radiative transfer code.