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Table 8

Statistical indices using the applied soft computing and empirical models for predicting the secondary flow depth of hydraulic jump (h₂) in the testing phase

Method	Statistical parameters
Method	RMSE (m)	R²	MAE (m)	NSE	IA	RMSE improvement %	RMSE improvement %
ANFIS-FA	0.0053	0.975	0.0016	0.971	0.993	0.871	30.263
ANFIS-GA	0.006	0.967	0.0018	0.962	0.991	0.854	21.053
ANFIS-PSO	0.0063	0.962	0.002	0.959	0.99	0.846	17.105
ANFIS	0.0076	0.944	0.0026	0.94	0.985	0.815	Base
ANFIS-WOA	0.0079	0.938	0.0027	0.934	0.984	0.807	−3.947
ANFIS-MFO	0.0084	0.931	0.0028	0.926	0.982	0.795	−10.526
Carollo & Ferro (2004)	0.0242	0.626	0.007	0.388	0.865	0.41	–
Pagliara & Palermo (2015)	0.0339	0.632	0.0116	−0.203	0.785	0.173	–
Govinda Rao & Ramaprasad (1996)	0.035	0.573	0.012	−0.316	0.768	0.146	–
Leutheusser & Kartha (1972)	0.041	0.576	0.014	−0.794	0.722	Base	–

Method	Statistical parameters
Method	RMSE (m)	R²	MAE (m)	NSE	IA	RMSE improvement %	RMSE improvement %
ANFIS-FA	0.0053	0.975	0.0016	0.971	0.993	0.871	30.263
ANFIS-GA	0.006	0.967	0.0018	0.962	0.991	0.854	21.053
ANFIS-PSO	0.0063	0.962	0.002	0.959	0.99	0.846	17.105
ANFIS	0.0076	0.944	0.0026	0.94	0.985	0.815	Base
ANFIS-WOA	0.0079	0.938	0.0027	0.934	0.984	0.807	−3.947
ANFIS-MFO	0.0084	0.931	0.0028	0.926	0.982	0.795	−10.526
Carollo & Ferro (2004)	0.0242	0.626	0.007	0.388	0.865	0.41	–
Pagliara & Palermo (2015)	0.0339	0.632	0.0116	−0.203	0.785	0.173	–
Govinda Rao & Ramaprasad (1996)	0.035	0.573	0.012	−0.316	0.768	0.146	–
Leutheusser & Kartha (1972)	0.041	0.576	0.014	−0.794	0.722	Base	–