Performance improvement of empirical models for estimation of global solar radiation in India: A k-fold cross-validation approach

In this work, global solar radiation is estimated based on sunshine duration. Solar radiation measurements have been collected from the Indian Meteorological Department (Pune, India) for the period 1986-2000. 25 model forms were selected from the literature which correlates the clearness index with sunshine duration. The coefficients of models are extracted from the data. k-fold cross-validation is then employed to improve the performance of the models. Data is split into k-groups with each group containing the same amount of data. (k-1) groups are utilized for the development of models and the rest one group is utilized for the testing of models performance. The procedure is repeated k-times and those coefficients are selected which produces the least error. Models are evaluated and compared with the help of statistical errors. Further, the statistical errors were scaled and Global Performance Indicator (GPI) was evaluated. Using GPI, models were given rank in order of suitability of estimates produced. The GPI value lies between -9.4269 and 0.4695. It has been observed that the quartic model (M-04) exhibited the best performance with MBE = 0.0259, RMSE = 1.7927, MPE = 0.1495, RRMSE = 0.0352, erMAX = 0.9072, MARE = 0.0812, MAE = 1.3843, U-95 = 6.3100, t-stats = 0.2397 and R = 0.8597 resulting in the highest GPI amongst all the models which were proposed.