Abstract
The interpretation of satellite-observed radiances to derive cloud optical depth and effective particle size requires radiative transfer calculations relating these parameters to the reflectance, transmittance, and emittance of the cloud. Such computations can be extremely time consuming when used in an operational mode to analyze routine satellite data. Adding–doubling (AD) radiative transfer models are used here to compute reflectance and effective emittance at wavelengths commonly used by operational meteorological satellite imagers for droplet effective radii ranging from 2 to 32 μm and for distributions of randomly oriented hexagonal ice crystals with effective diameters varying from 6 to 135 μm. Cloud reflectance lookup tables were generated at the typical visible-channel wavelength of 0.65 μm and the solar–infrared (SI) at wavelengths of 3.75 and 3.90 μm. A combination of four-point Lagrangian and linear interpolation between the model nodal points is the most accurate and economical method for estimating reflectance as a function of particle size for any set of solar zenith, viewing zenith, and relative azimuth angles. Compared to exact AD calculations, the four-point method retrieves the reflectance to within ±3%–9% for water droplets and ice crystals, respectively. Most of the error is confined to scattering angles near distinct features in the phase functions. The errors are reduced to ∼±2% for ice when the assessment is constrained to only those angles that are actually useful in satellite retrievals. Effective emittance, which includes absorption and scattering effects, was computed at SI, infrared (IR; 10.7 and 10.8 μm), and split-window (WS; 11.9 and 12.0 μm) wavelengths for a wide range of surface and cloud temperatures using the same ice crystal and water droplet distributions. The results were parameterized with a 32-term polynomial model that depends on the clear-cloud radiating temperature difference, the clear-sky temperature, and viewing zenith angle. A four-point Lagrangian method is used to interpolate between optical depth nodes. The model reproduces the adding–doubling results with an overall accuracy better than ±2%, 0.4%, and 0.3%, respectively, for the SI, IR, and WS emittances, a substantial reduction in the error compared to earlier parameterizations. Temperatures simulated with the emittance models are within 0.6 and 1 K for water droplets and ice crystals, respectively, in the SI channels. The IR temperatures are accurate to better than ±0.05 K. During the daytime, the simulations of combined reflectance and emittance for the SI channels are as accurate as the emittance models alone except at particular scattering angles. The magnitudes of the errors depend on the angle, particle size, and solar zenith angle. Examples are given showing the parameterizations applied to satellite data. Computational time exceeds that of previous models but the accuracy gain should yield emittances that are more reliable for retrieval of global cloud microphysical properties.
Corresponding author address: Dr. Patrick Minnis, MS 420, NASA/Langley Research Center, Hampton, VA 23681-0001.
Email: p.minnis@larc.nasa.gov
