Simulating monthly streamflow using a hybrid feature selection approach integrated with an intelligence model

Figures & data

Figure 1. Workflow of the proposed method.

Table 1. Statistical characteristics of the input and output data.

Station	Variable
	Statistical characteristic	Precipitation (mm)	Temperature (ºC)	Streamflow (m^3 s^−1)
Sira (S1)	Minimum	0	-	2.7
	Maximum	269.5	-	69.8
	Average	49.7	-	12.7
Nesa (S2)	Minimum	0	−9.1	-
	Maximum	280.5	22.2	-
	Average	57.5	8.2	-
Shahrestanak (S3)	Minimum	0	-	-
	Maximum	233	-	-
	Average	54.6	-	-
Amirkabir Dam (S4)	Minimum	0	−3.8	-
	Maximum	217.2	26.3	-
	Average	35	13.6	-

Figure 2. Location of Sira station on the Karaj River in Iran.

Figure 3. Observed monthly streamflow at Sira station on Karaj River for the period 1988–2012.

Table 2. Original and generated features in the study area. See Table 1 for abbreviations of stations.

Original features	Generated features	Observation station
Streamflow, Q (m^3 s^−1)		S1
Precipitation, P (mm)		S1, S2, S3 and S4
Temperature, T (^oC)	,	S2, S4
	P × T	S2, S4
	P × P	S1, S2, S3 and S4

Table 3. Values of the parameters used for the PSO algorithm.

No. of particles	Max. no. of iterations	c1	c2	ωmin–ωmax
40	200	0.5	0.5	0.05–1

Table 4. Selected features by feature selection method.

Method	Selected features
LASSO
PSO-ANN

Table 5. Values of the parameters used for the GOA.

Parameter	Lower bound	Upper bound	No. of search agents	Max iteration
	0.01	0.3	100	200
	1	10000

Table 6. Statistical performance evaluation of the applied models in the testing phase. R2: determination coefficient; MAE: mean absolute error; RMSE: root mean squared error; NS: Nash-Sutcliffe efficiency criterion.

Model	R^2	MAE	RMSE	NS
Selected features by LASSO+PCA+Morlet	0.92	2.40	2.79	0.91
Selected features by LASSO+PCA+Mexican hat	0.90	2.41	3.19	0.89
Selected features by PSO-ANN+PCA+Morlet	0.86	2.87	3.74	0.88
Selected features by PSO-ANN+PCA+Mexican hat	0.85	3.01	3.89	0.86
Original features+Morlet	0.65	5.06	6.23	0.76
Original features+Morlet+Q(t-1)	0.72	4.54	5.54	0.83

Table 7. Number of support vectors and optimal parameters obtained for SVR.

Method	No. of support vectors	ε	C	σ
LASSO+PCA+Morlet	228	0.041	6088	0.017
LASSO+PCA+Mexican hat	172	0.002	7512	0.035
PSO-ANN+PCA+Morlet	238	0.07	9736	0.102
PSO-ANN+PCA+Mexican hat	185	0.003	9819	0.001
Original features+Morlet	234	0.011	7646	0.023
Original features+Morlet+Q(t-1)	163	0.024	9981	0.010

Figure 4. Observed vs simulated streamflow (m³ s⁻¹) using various models on the test data: (a) LASSO and Morlet wavelet, (b) LASSO and Mexican hat wavelet, (c) PSO-ANN and Morlet wavelet and (d) PSO-ANN and Mexican hat wavelet.

Figure 5. Observed vs simulated streamflow (m³ s⁻¹) using the Lasso-Morlet model as the most accurate model with (a) original features and (b) original features and one lagged discharge.

Figure 6. Observed vs simulated streamflow for the test data using the Lasso-Morlet model.

Figure 7. Observed vs. simulated streamflow (m³ s⁻¹) using (a) LASSO-Morlet with optimized SVR parameters and (b) LASSO-Morlet with not optimized (pre-assumed) SVR parameters.