Forecasting streamflow by combination of a genetic input selection algorithm and wavelet transforms using ANFIS models

Figures & data

Figure 1. Flowchart of input selection method.

Figure 2. Lighvan and Ajichai sub-basins in the Urmia Lake basin, Iran.

Table 1. Forecasting accuracy criteria.

Criterion	Formula	Definitions
Coefficient of determination (R^2)		Qobs: observed
		Qpred: predicted
Root mean square error (RMSE)		: mean observed
		: mean predicted
Nash-Sutcliffe model efficiency (NSE)

N: number of data; Parameter ranges: 0 ≤ R² ≤ 1; 0 ≤ RMSE ≤ ∞; −∞ ≤ NSE ≤ 1.

Table 2. The values of key parameters.

Model	Type	Lighvan		Ajichai
		No. of cluster	Radius	No. of cluster	Radius
Sub-ANFIS	Basic	_	0.6	_	0.6
	GA based	_	0.6	_	0.75
FCM-ANFIS	Basic	7	_	9	_
	GA based	6	_	7	_

Table 3. Comparison of model performance during test period.

Basin	Model	Sub-ANFIS			FCM-ANFIS
		R^2	RMSE	NSE	R^2	RMSE	NSE
Lighvan	Basic	0.7	0.076	0.67	0.74	0.068	0.74
	GA based	0.81	0.058	0.80	0.86	0.053	0.85
Ajichai	Basic	0.67	0.055	0.67	0.66	0.055	0.66
	GA based	0.83	0.045	0.83	0.82	0.047	0.82

Figure 3. Comparison of the basic and GA based FCM-ANFIS model output for test period—Lighvan.

Figure 4. Comparison of the basic and GA based Sub-ANFIS model output for test period—Ajichai.

Figure 5. Comparison of scatter plots of different ANFIS models for test period—Lighvan.

Figure 6. Comparison of scatter plots of different ANFIS models for test period—Ajichai.

Table 4. Available data in Ajichai and Lighvan basins and optimal selection by GA*.

Basin	Data type
	Precipitation	Temperature	Discharge
Ajichai	Ghurigul	Sohzab	Vanyar
	Ghushchi	Mirkuh
	Nahand	Ghurigul
	Saeedabad
	Sarab
	Sbaghran
	Sohzab
	Vanyar
	Bostanabad
Lighvan**	Ghermezigul	Lighvan	Heravi
	Zinjenab
	Tabriz

*Optimal selections by GA in both basins are shown as bold and underlined.

** For Lighvan only lag 1 of data in all stations is selected.

Table 5. Tuning of FCM-ANFIS-GA model for Lighvan.

Number of clusters	Train			Test
	R^2	RMSE	NSE	R^2	RMSE	NSE
6	0.86	0.050	0.86	0.86	0.053	0.85
7	0.81	0.056	0.81	0.81	0.057	0.81
8	0.84	0.054	0.84	0.83	0.053	0.83
9	0.83	0.054	0.83	0.83	0.054	0.81

Table 6. Tuning of Sub-ANFIS-GA model for Lighvan.

Radius	Train			Test
	R^2	RMSE	NSE	R^2	RMSE	NSE
0.55	0.81	0.057	0.81	0.80	0.060	0.79
0.6	0.81	0.057	0.81	0.81	0.058	0.80
0.65	0.77	0.063	0.77	0.77	0.063	0.77
0.7	0.80	0.060	0.80	0.79	0.061	0.78

Figure 7. Mother wavelets: (a) Haar, (b) db4, (c) sym2, (d) sym3, (e) coif1.

Figure 8. Comparison of NSE values for different mother wavelets and decomposition levels using Sub-WANFIS for test period of Lighvan data.

Table 7. Comparison of Sub-WANFIS models.

Basin	Radius	Method	Train			Test
			R^2	RMSE	NSE	R^2	RMSE	NSE
Lighvan	0.7	Basic-wave	0.91	0.04	0.91	0.87	0.048	0.86
	0.85	GA-wave	0.97	0.024	0.97	0.95	0.028	0.95
Ajichai	0.8	Basic-wave	0.94	0.035	0.93	0.85	0.061	0.85
	0.9	GA-wave	0.96	0.021	0.96	0.95	0.022	0.95

Figure 9. Comparison of Sub-ANFIS model output for the test period—Ajichai.

Figure 10. Comparison of scatter plots of Sub-ANFIS models for the test period—Ajichai.

Figure 11. Comparison of NSE values for different mother wavelets and decomposition levels using FCM-WANFIS for test period of Lighvan data.

Table 8. Results of FCM-WANFIS models.

Basin	No. of clusters	Method	Train			Test
			R^2	RMSE	NSE	R^2	RMSE	NSE
Lighvan	7	Basic-wave	0.93	0.036	0.92	0.88	0.042	0.88
	7	GA-wave	0.97	0.024	0.97	0.97	0.026	0.97
Ajichai	8	Basic-wave	0.92	0.031	0.92	0.86	0.060	0.85
	7	GA-wave	0.95	0.028	0.95	0.94	0.028	0.94

Figure 12. Comparison of FCM-ANFIS models output for the test period—Lighvan.

Figure 13. Comparison of scatter plots for FCM-ANFIS models for the test period—Lighvan.

Table 9. Summary of comparison of models during test period.

Basin	Type of model	Model		Statistical parameter
				R^2	RMSE	NSE
Lighvan	Classic	Sub-ANFIS	Basic	0.70	0.076	0.67
			GA based	0.81	0.058	0.80
		FCM-ANFIS	Basic	0.74	0.068	0.74
			GA based	0.86	0.053	0.85
		Sub-WANFIS	Basic-wave	0.87	0.048	0.86
	Hybrid		GA-wave	0.95	0.028	0.95
		FCM-WANFIS	Basic-wave	0.88	0.042	0.88
			GA-wave	0.97	0.026	0.97
Ajichai	Classic	Sub-ANFIS	Basic	0.67	0.055	0.67
			GA based	0.83	0.045	0.83
		FCM-ANFIS	Basic	0.66	0.055	0.66
			GA based	0.82	0.047	0.82
		Sub-WANFIS	Basic-wave	0.85	0.061	0.85
	Hybrid		GA-wave	0.95	0.022	0.95
		FCM-WANFIS	Basic-wave	0.86	0.060	0.85
			GA-wave	0.94	0.028	0.94