The formulation lends more confidence in the use of the already empirically known relations providing them a theoretical basis, and affords more flexibility to the estimation techniques by supplying new equations.
Quoted from:Jain P C . Model for Diffuse and Global Irradiation on Horizontal Surface. 1984.
http://streaming.ictp.it/preprints/P/84/006.pdf
The intensity of the direct radiation and the diffuse radiation at any time on a horizontal surface are each expressed as fractions of the intensity of the extraterrestrial radiation. Using these and assuming a random distribution of the bright sunshine hours and not too wide variations in the values of the transmission coefficients, a number of relations for estimating the global and the diffuse irradiation are derived. Two of the relations derived are already known empirically. The formulation lends more confidence in the use of the already empirically known relations providing them a theoretical basis, and affords more flexibility to the estimation techniques by supplying new equations. The study identifies three independent basic parameters and the constants appearing in the various equations as simple functions of these three basic parameters. Experimental data for the diffuse irradiation, the global irradiation and the bright sunshine duration for Macerata (Italy), Salisbury and Bulawayo (Zimbabwe) is found to show good correlation for the linear equations, and the nature and the interrelationships of the constants are found to be as predicted by the theory.
INTRODUCTION
In this paper an attempt is made to develope a theory starting from some simple expressions. Two of the known empirical relations, including the Angstrom's modified relation, are then derived in a simple and natural way. Some new relations are also obtained which may be useful in the future work on the estimation of solar irradiation. The model also brings the important realization that there are only three independent basic parameters and all the constants in different equations are simple functions of these three basic parameters. The theory has enabled a deeper study and understanding of the nature of the constants and the interrelationships amongst them. Finally, from the data for the simultaneous measurement of the diffuse irradiation, the global irradiation and the sunshine duration for Macerata in Italy and Salisbury and Bulawayo in Zimbabwe, it is shown that the new equations derived in this paper do give a good correlation and that the relationaships among the different constants and their nature is indeed as predicted by the model.
SUMMARY AND CONCLUSION
This study provides a theoretical basis to some of the known empirical relations and therefore lends more confidence in their use. The study has also established five new correlations for estimating the diffuse irradiation, thus providing more flexibility and novelty to the future attempts at estimating the diffuse irradiation.
The other important finding of the study is that there are only three basic parameters; all the constants appearing in different equations are simple functions of these three basic parameters. This has enabled to understand and predict qualitative nature of the constants in different equations and their interrelationships. The experimental data for the irradiation and the sunshine duration for three Dlaces - Macerata in Italy and Salisbury and Bulawayo in Zimbabwe - is used to show that the new equations provide a good correlation and that the interrelationships of the constants is in agreement with those predicted by the model.
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