In order to establish the model, the partition ratio of the data must first be selected. In the literature, there is no definite information about the rate of training and testing used in modeling AI techniques. However, in studies in general, the value is between 70 and 90% of the entire data length for education (Partal & Cigizoglu 2008). In this study, 75% of the data for the training of the AI model and the rest was reserved as tests. 1970–1999 and 2000–2009 were used for training and testing, respectively. The inputs were divided into various sub-series to select the most suitable models, and various membership functions and iterations were tried. Establishing the W-ANFIS model, the lagged streamflow data were divided into sub-series by DWT. In the design of the ANFIS model, eleven different scenarios were planned according to autocorrelation and partial autocorrelation (Figure 3). These scenarios consist of various combinations of streamflow data with a delay between 1 and 11 days (Table 1). While developing W-ANFIS models, db10 wavelets and three decomposition levels were used according to Equation (3). It was chosen according to the correlation values of the stream flows separated into sub-signals by the WT to determine the input combinations of the W-ANFIS model (Table 2). Correlation values greater than 0.2 (Partal 2007), greater than 0.1 (Tiwari & Chatterjee 2011), and greater than 0.3 were used as the limit value for selecting effective subcomponents. According to the literature, the sum of the D1, D2, D3, and A1 components with the highest correlation was presented as an input to the W-ANFIS model. In the selection of the inputs, the sum of the subcomponents with a correlation coefficient above 0.1 with the output according to the literature was included in the model.
Table 1

Comparison of designed ANFIS scenarios

ModelInputOutputIterationSub-setsMembership functionTraining RMSETest RMSETraining R2Test R2
Qt-1 Qt 1,000 Gauss2mf 15.03 12.97 0.48 0.40 
Qt-1, Qt-2 Qt 2,000 7-7 Gauss2mf 10.87 10.91 0.73 0.62 
Qt-1, Qt-2, Qt-3 Qt 100 4-4-4 Gaussmf 12.34 10.11 0.65 0.67 
4 Qt-1, Qt-2, Qt-3, Qt-4 Qt 5,000 2-2-2-2 Trimf 12.01 10.07 0.67 0.68 
Qt-1, Qt-2, Qt-3, Qt-4, Qt-5 Qt 100 3-3-3-3-3 Gbellmf 11.90 11.23 0.68 0.60 
Qt-1, Qt-2, Qt-3, Qt-4, Qt-5, Qt-6 Qt 2,000 All 2 Trimf 11.82 10.64 0.68 0.64 
Qt-1, Qt-2, …, Qt-7 Qt 300 All 2 Trimf 10,94 10.80 0.73 0.65 
Qt-1, Qt-2, …., Qt-8 Qt 50 All 2 Trimf 10.95 12.19 0.76 0.58 
Qt-1, Qt-2, …, Qt-9 Qt 50 All 2 Trimf 9.52 12.64 0.79 0.58 
10 Qt-1, Qt-2, …, Qt-10 Qt 10 All 2 Gaussmf 10.85 11.21 0.73 0.62 
11 Qt-1, Qt-2, …, Qt-11 Qt 20 All 2 Trimf 6.38 12.59 0.90 0.57 
ModelInputOutputIterationSub-setsMembership functionTraining RMSETest RMSETraining R2Test R2
Qt-1 Qt 1,000 Gauss2mf 15.03 12.97 0.48 0.40 
Qt-1, Qt-2 Qt 2,000 7-7 Gauss2mf 10.87 10.91 0.73 0.62 
Qt-1, Qt-2, Qt-3 Qt 100 4-4-4 Gaussmf 12.34 10.11 0.65 0.67 
4 Qt-1, Qt-2, Qt-3, Qt-4 Qt 5,000 2-2-2-2 Trimf 12.01 10.07 0.67 0.68 
Qt-1, Qt-2, Qt-3, Qt-4, Qt-5 Qt 100 3-3-3-3-3 Gbellmf 11.90 11.23 0.68 0.60 
Qt-1, Qt-2, Qt-3, Qt-4, Qt-5, Qt-6 Qt 2,000 All 2 Trimf 11.82 10.64 0.68 0.64 
Qt-1, Qt-2, …, Qt-7 Qt 300 All 2 Trimf 10,94 10.80 0.73 0.65 
Qt-1, Qt-2, …., Qt-8 Qt 50 All 2 Trimf 10.95 12.19 0.76 0.58 
Qt-1, Qt-2, …, Qt-9 Qt 50 All 2 Trimf 9.52 12.64 0.79 0.58 
10 Qt-1, Qt-2, …, Qt-10 Qt 10 All 2 Gaussmf 10.85 11.21 0.73 0.62 
11 Qt-1, Qt-2, …, Qt-11 Qt 20 All 2 Trimf 6.38 12.59 0.90 0.57 

Note: Bold characters indicate the most successful ANFIS model.

Table 2

Correlation coefficients of sub-series

Sub-seriesD1D2D3A3
Qt-1 −0.17 0.16 0.64 0.35 
Qt-2 0.21 0.34 0.42 0.32 
Qt-3 0.10 0.41 0.02 0.27 
Qt-4 0.15 0.17 0.37 0.30 
Qt-5 0.08 0.25 0.61 0.16 
Qt-6 0.12 0.35 0.70 0.11 
Qt-7 0.04 0.10 0.60 0.07 
Qt-8 0.14 0.18 0.32 0.03 
Qt-9 0.00 0.28 0.01 0.02 
Qt-10 0.17 0.08 0.29 0.01 
Qt-11 0.03 0.20 0.56 0.01 
Sub-seriesD1D2D3A3
Qt-1 −0.17 0.16 0.64 0.35 
Qt-2 0.21 0.34 0.42 0.32 
Qt-3 0.10 0.41 0.02 0.27 
Qt-4 0.15 0.17 0.37 0.30 
Qt-5 0.08 0.25 0.61 0.16 
Qt-6 0.12 0.35 0.70 0.11 
Qt-7 0.04 0.10 0.60 0.07 
Qt-8 0.14 0.18 0.32 0.03 
Qt-9 0.00 0.28 0.01 0.02 
Qt-10 0.17 0.08 0.29 0.01 
Qt-11 0.03 0.20 0.56 0.01 

Note: Bold characters indicate the sub-signals selected as input to the model.

Figure 3

Autocorrelation and partial autocorrelation functions of streamflow values.

Figure 3

Autocorrelation and partial autocorrelation functions of streamflow values.

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