A Investigation of the Relationship Between Beam and Global Irradiation with the Development of Numerical Solar Radiation Models.

A number of improved numerical models have been developed to predict the beam radiation from global radiation data. The analysis was based on five years of hourly radiation data collected at the Solar Total Energy Project in Shenandoah, Georgia. Previously developed empirical correlations relate hourly values of the beam transmittance, tau _{rm b}--beam normal radiation over the extraterrestrial normal radiation, to clearness index, k_{rm t} --global radiation over the extraterrestrial global radiation. The relationship of tau_{rm b}-k_{rm t} , though, is not deterministic. Some the observed variation was explained by a seasonal dependence. Improved performance was achieved by introducing a third variable, either the atmospheric air-mass (m), or the temporal variation coefficient, eta, a new dimensionless parameter used to describe the sky condition without using any meteorological information. Seasonal effects on solar radiation caused by cloudiness and air quality were found to be significant and two methods were developed to account for this phenomenon. The air-mass dependence of solar radiation was examined through a study of the relationships between (tau _{rm b}-m) and (k _{rm t}-m). A simple clear sky beam transmittance model was developed for the region, although it was shown that clearest skies are not necessarily site specific. Two improved beam radiation models were developed, relating three variables at a time--namely (k_ {rm t},m,tau_ {rm b}) and (k_{ rm t},eta, tau_{rm b}). These correlations have significantly increased the predictive powers of the beam radiation model, without compensating for additional input information. These models can predict different values of beam radiation for a given day and over the year, for the same value of global radiation which is what is observed. Several surface fitting techniques were used to generate the response surface among which are, a best RMS triangulation method, an inversely weighted fit method, and a fifth-degree polynomial fit. The work satisfies a major deficiency in solar radiation modeling by providing the most accurate up-to -date models for the southeast United States. The proposed models were validated with data from the National Observatory of Athens, Greece. The good performance of the models is reassuring of their wide applicability.