Accounting for Unresolved Clouds in a 1D Infrared Radiative Transfer Model. Part II: Horizontal Variability of Cloud Water Path

A 1D infrared radiative transfer model that handles clouds with subgrid-scale horizontal variability is developed and tested. It assumes that fluctuations in cloud absorptance optical depth κ across layers (and collections of layers) can be described by gamma distributions. Unlike homogeneous clouds, flux incident at a level inside a horizontally inhomogeneous cloud requires explicit computation of transmittance to all other levels in the cloud. Consequently, in addition to estimates of variability for each layer, variability between any two levels must be specified too. Scattering by hydrometeors and a general treatment of cloud overlap are included in this model. Solutions for isothermal and nonisothermal Planck source functions are presented. For the synthetic cloudy atmospheres used here, the new model produces errors for outgoing longwave radiation (OLR) and cloud cooling rates that are typically more than an order of magnitude smaller than those associated with the conventional homogeneous cloud model (as used in all GCMs at present). It is shown that up- and downwelling fluxes and cloud cooling rates can depend much on subgrid-scale variability. For high overcast clouds with realistic variability, OLR can be up to 20 W m−2 more than that predicted by a conventional homogeneous model using the same mean κ. At the same time, cooling rate errors at cloud top and cloud base due to the homogeneous assumption can be up to ±25%; the sign depending primarily on mean κ and magnitude of variability. For lower, thicker clouds, the homogeneous assumption leads primarily to errors in cloud-top cooling. The new code usually remedies these errors greatly. This model, and its solar counterpart, are used currently in the Canadian Centre for Climate Modelling and Analysis GCM.