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

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 (Hd) 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 (Kt); (b) sunshine ratio (S); (c) Kt and S; (d) Kt, S and average temperature (Ta); (e) Kt, S, Ta 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−2d−1) and average R2 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 × 105) were 105 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 Hd estimation.