In climate studies, longwave radiation fluxes and heating rate are usually calculated as the weighted average of clear and overcast values, i.e.,
where, F is downwelling flux of radiant energy at the surface; subscripts clear and overcast denote fluxes for those conditions. N is the absolute cloud fraction, usually assumed to be the fractional coverage of the vertical projections of plane-parallel clouds. However, real cloud fields are non-uniform in both morphological and microphysical senses. The error due to neglecting the 3D effects can be climatically significant. (Harshvardhan and Weinman 1982; Ellingson 1982; Heidinger and Cox 1996; Han and Ellingson 1999; Takara and Ellingson 2000)
Three characteristics of 3D clouds have been found to be important for longwave radiative transfer. They are: (1) the 3D geometrical structure of the cloud fields (Geometrical effect), (2) the horizontal variation of cloud optical depth (Variable optical depth effect), and (3) the vertical variation of cloud temperature (Non-isothermal cloud effect). At zenith angles ϑ > 0, vertically extended clouds project greater areas than the PPH clouds. This is denoted as the geometrical effect. By neglecting the geometrical effect the PPH approximation will underestimate the downwelling longwave flux.
One way to incorporate the 3D geometrical effect in climate studies is through the use of an effective cloud fraction (Ellingson 1982; Han and Ellingson 1999). That is,
The effective cloud fraction, Ne, is the plane-parallel cloud fraction that generates the same flux as the detailed models for a given broken cloud field after taking into account the effects of geometric shapes, size, spatial distribution and absolute amount (N) of clouds. These effects may be integrated into Ne through a single cloud field property the Probability of Clear Line Of Sight (PCLOS). The PCLOS also plays an important role in accounting for longwave 3D effects caused by variable cloud optical depth and vertical change of cloud temperature. In this study we use a variety of data from the Atmospheric Radiation Measurement (ARM; Stokes and Schwartz 1994) program to test several different PCLOS models.