*2.2. Methodology*

The theoretical aspects and research methodology used in the current study to identify the best neural network model to perform the rainfall and runoff modeling for the Yerli subcatchment have been discussed in this section. Figures 2 and 3 depict the methodological flowchart of NNTOOL and NNSTART respectively.

**Figure 2.** Flow chart of NNTOOL.

**Figure 3.** Flow chart of NNSTART.

2.2.1. Following Steps Should Be Performed for Developing an ANN Model Using NNTOOL


2.2.2. Following Steps Should Be Performed for Developing an ANN Model Using NNSTART


*2.3. Model Evaluation Criteria*

> The findings of the ANN model applied in this study were evaluated by means of:

• Mean Square Error (MSE):

$$\text{MSE} = \frac{1}{n} \sum\_{i=1}^{n} \left( Q\_p - Q\_o \right)^2 \tag{1}$$

• Root Mean Square Error (RMSE):

$$\text{RMSE} = \left[ \frac{\sum\_{i=1}^{n} \left( Q(i) - \hat{Q}(i) \right)^{2}}{n} \right]^{0.5} \tag{2}$$

• Regression Coefficient (R): Using Regression Plot between predicted and observed runoff.

where *Qp* is the value of predicted runoff; *Qo* is the value of observed runoff; *Q* ˆ (*i*) is the *n* estimated runoff value; and *Q*(*i*) is the *n* observed runoff value.

### **3. Results and Discussion**

*3.1. NNTOOL*

The multilayer FFBPNN and CFBPNN algorithms with Levenberg–Marquardt (LM) are utilized to optimize the learning approach in this study. Two different models were developed, i.e., (FFBPNN) and (CFBPNN) with three different architectures (6-2-1, 6-3-1 and 6-4-1) using several combinations of transfer functions, i.e., (transig, logsig, and purelin) along with two sets of neurons, 10 and 20, and then compared for their capability to estimate the flow for the period 1981–2016.

3.1.1. Feed Forward Back Propagation Neural Network (FFBPNN)

FFBPN, while considering 6-2-1, 6-3-1, and 6-4-1 architectures, the transig function provides the best value for performance. The most effective model architecture for the Transig function is 6-4-1, which has a value of MSE 0.4982, the value of RMSE 0.7056, and the value of R 0.96213. Table S1 contains the inclusive outcomes. However, in comparison to other transfer functions, the transig transfer function with architecture 6-4-1 yielded better results in the current study. Figure 4 depicts the best regression plot.

**Figure 4.** Regression plot for FFBPNN 6-4-1 model.

3.1.2. Cascade Forward Back Propagation Neural Network (CFBPNN)

Similarly, for CFBPNN, while considering 6-2-1, 6-3-1, and 6-4-1 architectures, the transig function provides the best value for performance. The most effective model architecture for the transig function is 6-4-1, which has MSE values of 0.8813, the value of RMSE 0.9387, and the value of R 0.96096. Table S2 contains the inclusive outcomes [17]. However, in comparison to other transfer functions comparison to other, the transig transfer function with architecture 6-4-1 yields better results. Figure 5 depicts the best regression plot.

**Figure 5.** Regression plot for CFBPNN 6-4-1 model.
