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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 …