Calibration and validation of the Angstrom–Prescott model in solar radiation estimation using optimization algorithms

The Angstrom–Prescott (A–P) model is widely suggested for estimating solar radiation (R(s)) in areas without measured or deficiency of data. The aim of this research was calibration and validation of the coefficients of the A–P model at six meteorological stations across arid and semi-arid regions of Iran. This model has improved by adding the air temperature and relative humidity terms. Besides, the coefficients of the A–P model and improved models have calibrated using some optimization algorithms including Harmony Search (HS) and Shuffled Complex Evolution (SCE). Performance indices, i.e., Root Mean Square Error (RMSE), Mean Bias Error, and coefficient of determination (R(2)) have used to analyze the models ability in estimating R(s). The results indicated that the performance of the A–P model had more precision and less error than improved models in all the stations. In addition, the best results have obtained for the A–P model with the SCE algorithm. The RMSE varies between 0.82 and 2.67 MJ m(−2) day(−1) for the A–P model with the SCE algorithm in the calibration phase. In the SCE algorithm, the values of RMSE had decreased about 4% and 7% for Mashhad and Kerman stations in the calibration phase compared to the HS algorithm, respectively.