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A model of a cumulus cloud field, parameterized as right circular cylinders, has been used to estimate the uncertainties in longwave radiation calculations of irradiances and heating rates caused by neglecting the dimensions of the clouds. The results show that the irradiances and heating rates are nonlinear functions of the absolute cloud amount, height to radius ratio, and the cloud base and top altitudes. Cylindrically shaped clouds result in more downward irradiance at the surface (1–4%) and less escaping the atmosphere (up to 8%) than from flat plate clouds. The subcloud layer experiences as much as 20% more beating from cylindrical clouds than from flat plates, whereas the tropospheric column may experience up to 10% greater radiative cooling. Although the cloud parameters result in nonlinear effects, these effects may he taken into account with the use of easily calculable functions.
Robert G. Ellingson (Thu,) studied this question.