An Analytic Longwave Radiation Formula for Liquid Layer Clouds

Abstract

Many Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) intercomparisons of boundary layer clouds have used a convenient but idealized longwave radiation formula for clouds in their large-eddy simulations (LESs). Under what conditions is this formula justified? Can it be extended to midlevel layer clouds? This note 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. Here, the focus is primarily on midlevel, altostratocumulus layers. The results here show that the GCSS formula can be successfully extended to liquid (ice free), midlevel 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.