## 2 Materials and Methods
### Model Development and Input  
This study investigated the simulation and forecasting of river runoff at a daily scale in a selected basin. To simulate the runoff, a hydrological model and three ML models were applied. The input data for the hydrological model were the TRMM precipitation data. The parameters for the HEC-HMS model were selected by trial and error in the calibration phase for the deficit and constant loss methods based on the Snyder unit hydrograph as a transfer method. Table 1 lists the parameter values for the best evaluation indices. Three ML models, the ELM, SVR, and LSTM models, were used to simulate the streamflow at daily scales in the selected basin. To achieve higher accuracy in the ML model simulation, the antecedent values of \(TRMM\) and \(Tmean\) were used as input variables. Therefore, in addition to the input variables, a 1-day lag to a 20-day lag was applied for all input variables. The best combination of variables was chosen using the SVM-RFE approach. From Equation (4), nineteen variables were selected for the input structure in the Voshmgrir basin.  
\[Q_{l=f}\left(\begin{array}{c}{Tmean,\,TRMM_{t-1},\,TRMM_{t-3},TRMM_{t-5},} \\ {TRMM_{t-11},\,TRMM_{t-12},\,TRMM_{t-18},\,TRMM_{t-20},}\\ {Tmean_{t-1},\,Tmean_{t-2},\,Tmean_{t-3},\,Tmean_{t-4},}\\ {Tmean_{t-5},\,Tmean_{t-6}\,\,Tmean_{t-7},\,Tmean_{t-8},}\\ {Tmean_{t-11},\,Tmean_{t-12},\,Tmean_{t-15}}\end{array}\right) \tag{4}\]  
To forecast the river runoff, three ML models and their coupled models with the HEC-HMS model were used. In the current study, \(TRMM\) precipitation at days \(t\) and \(t-1\) and observed discharge at \(t\) and \(t-1\) were applied as input variables of the ML models to calculate the river runoff on day \(t+1\). Moreover, the simulated runoff values of the HEC-HMS model from the simulation were used as additional input variables for the three coupled models: HEC-HMS-ELM, HEC-HMS-SVR, and HEC-HMS-LSTM. Equation (5) shows the selected input variables for the coupled models.  
\[Q_{t+1}=f(TRMM_{t},\,TRMM_{t-1},\,Q_{t},Q_{t-1},\,Q_{HEC-HMSt+1}) \tag{5}\]  
The runoff data was the target variable. Data from January 2002 to December 2004 were applied to calibrate the models, and data from January 2005 to October 2007 were applied  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Snyder Hydrograph**} & \multicolumn{3}{c}{**Deficit and Constant**} \\
**Standard Lag** & **Peaking** & **Constant Rate** & **Maximum** & **Initial Loss** \\
**(h)** & **Coefficient** & **(mm/h) * & **Storage (mm)** & **(mm)** \\ \hline
5.94 & 0.48 & 0 & 25 & 20 \\ \hline \hline \end{tabular}
* mm: millimeter, h: hour.  
\end{table}
Table 1: Selected parameters of the HEC-HMS model.  
to test the models. [PERSON] and [PERSON] [50] recommended normalization of input data for the artificial neural network-back propagation (ANN-BP). They found that normalization of the input data was important to achieve better results and accelerate the calculation. Therefore, the normalization described by Equation (6) was applied to all input data of the ML models and coupled models.  
\[normalized\ x=\frac{x-\mu}{\sigma}, \tag{6}\]  
where \(x\) is the input variable, \(\mu\) is the mean variable, and \(\sigma\) is standard deviation.