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Table 2

Results of single AI-based models for both case studies for four seasons

Case study	Season	Model	Model structure^a	DC		RMSE^b		AIC
Case study	Season	Model	Model structure^a	Calibration	Verification	Calibration	Verification	AIC
Tabriz	Spring	SVR	0.268-0.125-20	0.901	0.797	0.069	0.091	−0.804
		FFNN	6-8-1	0.876	0.755	0.081	0.098	−0.677
		ANFIS	Gaussian-3	0.853	0.729	0.113	0.123	−0.549
	Summer	SVR	0.250-0.112-15	0.875	0.783	0.073	0.101	−0.663
		FFNN	6-9-1	0.845	0.737	0.089	0.103	−0.643
		ANFIS	Gaussian-3	0.802	0.721	0.114	0.126	−0.527
	Autumn	SVR	0.200-0.125-20	0.868	0.781	0.075	0.104	−0.672
		FFNN	6-8-1	0.844	0.723	0.093	0.107	−0.630
		ANFIS	Gaussian-3	0.789	0.718	0.115	0.129	−0.464
	Winter	SVR	0.5-0.380-25	0.814	0.701	0.092	0.108	−0.605
		FFNN	6-12-1	0.787	0.673	0.101	0.114	−0.589
		ANFIS	Gaussian-2	0.766	0.662	0.117	0.132	−0.507
Rasht	Spring	SVR	0.310-0.145-15	0.838	0.769	0.075	0.096	−0.312
		FFNN	6-10-1	0.814	0.740	0.098	0.115	−0.257
		ANFIS	Gaussian-3	0.800	0.661	0.103	0.130	−0.225
	Summer	SVR	0.400-0.130-10	0.816	0.757	0.086	0.103	−0.209
		FFNN	6-12-1	0.788	0.727	0.107	0.123	−0.186
		ANFIS	Gaussian-3	0.731	0.682	0.126	0.136	−0.064
	Autumn	SVR	0.450-0.136-10	0.803	0.741	0.089	0.107	−0200
		FFNN	6-10-1	0.781	0.719	0.118	0.129	−0.186
		ANFIS	Gaussian-3	0.724	0.663	0.128	0.138	−0.092
	Winter	SVR	0.40-0.300-20	0.745	0.696	0.101	0.122	−0.146
		FFNN	6-14-1	0.714	0.639	0.122	0.133	−0.139
		ANFIS	Gaussian-2	0.693	0.604	0.131	0.144	−0.075

Case study	Season	Model	Model structure^a	DC		RMSE^b		AIC
Case study	Season	Model	Model structure^a	Calibration	Verification	Calibration	Verification	AIC
Tabriz	Spring	SVR	0.268-0.125-20	0.901	0.797	0.069	0.091	−0.804
		FFNN	6-8-1	0.876	0.755	0.081	0.098	−0.677
		ANFIS	Gaussian-3	0.853	0.729	0.113	0.123	−0.549
	Summer	SVR	0.250-0.112-15	0.875	0.783	0.073	0.101	−0.663
		FFNN	6-9-1	0.845	0.737	0.089	0.103	−0.643
		ANFIS	Gaussian-3	0.802	0.721	0.114	0.126	−0.527
	Autumn	SVR	0.200-0.125-20	0.868	0.781	0.075	0.104	−0.672
		FFNN	6-8-1	0.844	0.723	0.093	0.107	−0.630
		ANFIS	Gaussian-3	0.789	0.718	0.115	0.129	−0.464
	Winter	SVR	0.5-0.380-25	0.814	0.701	0.092	0.108	−0.605
		FFNN	6-12-1	0.787	0.673	0.101	0.114	−0.589
		ANFIS	Gaussian-2	0.766	0.662	0.117	0.132	−0.507
Rasht	Spring	SVR	0.310-0.145-15	0.838	0.769	0.075	0.096	−0.312
		FFNN	6-10-1	0.814	0.740	0.098	0.115	−0.257
		ANFIS	Gaussian-3	0.800	0.661	0.103	0.130	−0.225
	Summer	SVR	0.400-0.130-10	0.816	0.757	0.086	0.103	−0.209
		FFNN	6-12-1	0.788	0.727	0.107	0.123	−0.186
		ANFIS	Gaussian-3	0.731	0.682	0.126	0.136	−0.064
	Autumn	SVR	0.450-0.136-10	0.803	0.741	0.089	0.107	−0200
		FFNN	6-10-1	0.781	0.719	0.118	0.129	−0.186
		ANFIS	Gaussian-3	0.724	0.663	0.128	0.138	−0.092
	Winter	SVR	0.40-0.300-20	0.745	0.696	0.101	0.122	−0.146
		FFNN	6-14-1	0.714	0.639	0.122	0.133	−0.139
		ANFIS	Gaussian-2	0.693	0.604	0.131	0.144	−0.075

^aNumbering of a-b-c in SVR structure represents γ, ε, c. The numbering of a-b-c in the structure of the neural network illustrates the number of the input layer, hidden layer, and output layer neurons. In ANFIS structure, MF-a denotes the used membership function and number of membership functions, respectively.

^bSince all data are normalized, the RMSE has no dimension.

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