Modeling Surface Solar Radiation: Model Formulation and Validation

A model for computing global solar radiation at the surface was formulated for use with satellite observations. A compromise in the approach was necessary, whereby the model accuracy and the inherent limitations of satellite observations were made compatible. A three-layer model atmosphere was used. The part of the solar spectrum from 0.3 to 0.7 μm was split into four equally spaced spectral intervals; the region from 0.7 to 4 μm was divided into eight nonspectral intervals. Use was made of the Delta–Eddington approximation, and parameterization was applied to the optical properties of Rayleigh scattering, water vapor absorption, aerosol absorption and scattering, and cloud absorption and scattering. Ozone absorption was also accounted for. The primary driving input of the model is the cloud optical depth, which can be inferred either from satellite observations (Experiment A) or from surface cloud observations (Experiment B). In Experiment A, the model was run for the months of May–August 1982 to produce estimates of daily cumulative insulation for Toronto, Canada. The mean value of the daily estimate was 19.61 MJ m−2. While the mean measured value was 19.72 MJ m−2. The correlation between the predicted and measured daily totals was 0.944, and the standard error of estimate was 2.47 MJ m−2, which is 12.5% of the mean observed value. Experiment B was run for the months May–August of 1981 and 1982. The standard errors of estimate were 16 and 18% of the respective means.