Comparison of support vector machine and copula-based nonlinear quantile regression for estimating the daily diffuse solar radiation: A case study in China

Abstract In this paper, three kinds of models, including support vector machine-firefly algorithm (SVM-FFA), copula-base nonlinear quantile regression (CNQR) and empirical models were developed for daily diffuse radiation ( H d ) estimation. The meteorological data during 1981–2000 and 2001–2010 of Lhasa, Urumqi, Beijing and Wuhan in China were used for model training and validation, respectively. Five combinations of meteorological data: (a) clearness index ( K t ); (b) sunshine ratio ( S ); (c) K t and S ; (d) K t , S and average temperature ( T a ); (e) K t , S , T a and average relative humidity, were considered for simulation. The results showed that for the training phases, SVM-FFA outperformed the corresponding models while empirical models performed slightly better than corresponding CNQR models. For validation phases, CNQR and SVM-FFA models performed much better than empirical models. Compared CNQR and SVM-FFA, SVM-FFA performed slightly better than CNQR models with average MABE decreased by 0.67% (0.01 MJm −2 d −1 ) and average R 2 increased by 0.43% (0.004). For the training time, SVM-FFA (1.68 s) showed less computational costs than CNQR (6.68 s); but the parameter optimization time of SVM-FFA (4.9 × 10 5 ) were 10 5 times as much as CNQR. Thus, the overall computational costs of SVM-FFA during training phases were much higher than CNQR. Considering the trade-off between accuracy and computational costs, CNQR were highly recommended for the daily H d estimation.