Solar Energy VoL 44, No. 3, pp. 149-156, 1990 0038-092X/90 $3.00 + .00 Printed in lhe U.S.A. Copyright © 1990 Pergamon Press pie DEVELOPMENT OF IMPROVED SOLAR RADIATION MODELS FOR PREDICTING BEAM TRANSMITTANCE SHELDON M. JETER and CONSTANTINOS A. BALARAS* The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A. Abstract--A pair of enhanced models are presented herein which, while relying only on global irradiation measurements, result in increased predictive power in estimating the hourly beam irradiation. The first model correlates the beam transmittance with clearness index and air mass. The second correlates the beam transmittance with the clearness index and with a new variable based on the temporal variation of the global radiation. The new variable helps describe the sky condition without the need of any further meteorological information. The models were developed using a new surface fitting technique applied to data which were collected at the Solar Total Energy Project in Shenandoah, Georgia (33.4°N, 84.7°W) over a five-year period. 1. INTRODUCTION Proper design of a solar energy system requires knowl- edge of the locally available solar energy. For example, all design methods used to size solar energy systems require radiation data. As a result of this need, the quest for accurate solar radiation data has intensified in recent years. The best data base would always be long-term mea- sured data at the site of the proposed solar energy sys- tem such as available in [ 1 ]. However, the limited cov- erage of reliable radiation measuring networks dictates the need for developing alternatives that can replace or complement observations. Dependable solar radia- tion models can successfully satisfy this need. Knowledge of the direct beam component of solar radiation is essential for modeling many solar energy systems. This is particularly critical for applications that concentrate the incident energy for high temper- ature heat engines or for high-intensity solar cells. In order to estimate the performance of such systems, accurate knowledge or prediction of the beam radiation is necessary as only this component can be concen- trated. Consequently, emphasis is often on modeling the beam component or, alternatively, on predicting the sky component with which the beam radiation can readily be computed. There are basically two categories of correlations available in the literature that predict the beam or sky radiation based on other more readily measured quan- tities, specifically a group of parametric and a group of decomposition models. The models included in the first group require de- tailed information on the atmospheric conditions. When detailed meteorological observations are avail- able, these models [ 2-8 ] make it possible to estimate the solar radiation components. Meteorological pa- rameters frequently used as predictors include the type, amount, and distribution of clouds or other observa- * Present affiliation: Senior Mechanical Engineer, Amer- ican Standards Testing Bureau, Inc., Philadelphia,PA, U.S.A. tions, such as the fractional sunshine, atmospheric tur- bidity, and moisture content. Development of correlation models that predict the beam or sky radiation using other solar radiation mea- surements is also possible. This group of models usually use information only on global radiation to predict the beam and sky components; consequently, they may be referred to as decomposition models. Such rela- tionships are usually expressed in terms of the irradia- tions which are the time integrals (i.e., over one hour) of the radiant flux or irradiance. A convenient repre- sentation is the relationship between two dimensionless numbers, the beam transmittance of the atmosphere, 7b, and the hourly or short period clearness index, kt, such that kt is used to predict 7b according to the fol- lowing functional form: rt, = f(k,), (l) where rb is defined, according to [9] and [10] as r6 = Ib,/Io,,, and Ib, = hourly or short period beam normal radiation, Io,, = corresponding extraterrestrial normal radiation, and the hourly or short period clearness index, kt, is defined as: k, = I/Io, (2) where I = hourly or short period global radiation, Io = corresponding extraterrestrial global radiation. The beam normal and global radiation are both related to the atmospheric and sky conditions. Con- sequently, one would expect that there is a correlation between 7b and kt. As is well known, several relation- ships between these two variables have been success- fully developed. Especially notable among this work are the pioneering efforts by Boes et al. [ I l ], and the 149