Evaluation of the relative ability of three models, the isotropic, klucher and hay, to predict the global radiation on a tilted surface in Beer Sheva, Israel

Abstract

The purpose of this work was to test the relative ability of three widely used models, isotropic, Klucher and Hay, to predict the total radiation incident on a tilted surface. The last two models correct the isotropic model for the inherent anisotropy present in the diffuse component of global radiation. A statistical analysis of the three models, using values of measured normal incidence beam and global radiation on a horizontal surface and on a south-facing surface inclined at 40° at a semi-arid site, Beer Sheva, Israel (31°15′N, 34°48′E), gave the following conclusions: (i) on a yearly basis, the Hay model gives the most accurate prediction of total radiation on a tilted surface, i.e. an average RMSE value of 4.0% as opposed to 4.4 and 5.8% for the Klucher and isotropic models, respectively; (ii) from April to August, the accuracy of the isotropic model approaches that of the Hay model, i.e. average RMSE values of 3.6 and 3.2% for the isotropic and Hay models, respectively; (iii) from January to March and from September to December, the accuracy of the Klucher and Hay models are comparable, i.e. average RMSE values of 4.3 and 4.4% for the Klucher and Hay models, respectively, and (iv) based upon the results of the analysis, the simple isotropic model provides a very good first approximation of the total radiation incident on south-facing surfaces inclined up to an angle of 40°, i.e. an average RMSE value of 5.8%. The results for the present analysis are consistent with those reported in previous studies in that any differences in the relative predictive ability of the three models are the result of differences in either surface tilt angle or local climatic conditions.