## 2 Materials and Methods
### Methodology
#### 2.2.2 Statistical Models  
For the monthly dam inflow forecasts with a 3-month lead time, multiple linear regression model (MLR), support vector machines (SVM) and artificial neural networks (ANN) methods were \begin{table}
\begin{tabular}{c c} \hline \hline
**Abbreviation** & **Definition** \\ \hline AAO & Antarctic Oscillation is the first leading mode from the EOF analysis of monthly mean height anomalies at 700-hPa. \\ AMM & Atlantic Meridional Mode is the atmosphere-ocean variability in the tropical Pacific and tropical Atlantic. \\ AMO & Atlantic Multidecadal Oscillation is an index of the North Atlantic temperature. \\ AO & Arctic Oscillation is a pattern of atmospheric pressures of the Arctic and North Atlantic oceans. \\ EA & East Atlantic Pattern is associated with surface temperatures in Europe and US. \\ EAWR & Eastern Asia/Western Russia index is the second prominent mode of low-frequency variability over the North Atlantic. \\ ERSST & Extended Reconstructed Sea Surface Temperature is a global grid monthly sea surface temperature. \\ MEI & Multivariate ENSO Index is related to sea-level pressure, surface wind, sea surface temperature, surface air temperature and total cloudiness fraction of the sky. \\ NAO & North Atlantic Oscillation is a dominant teleconnection patterns ranging from North America to Europe and North Asia. \\ NINA3 & NINA3 is the average of sea surface temperature anomalies over the region from 5N to 5S and 150W to 90W. \\ PDO & Pacific Decadal Oscillation is associated with monthly SSTs across the North Pacific. \\ SOI & Southern Oscillation Index is the development and intensity of El Nino or La Nina events in the Pacific Ocean. \\ TNA & Tropical Northern Atlantic Index is the anomaly of the average of the monthly SST from 5.5N to 23.5N and 15W to 57.5W. \\ WP & Western Pacific Index is a primary mode of low-frequency variability over the North Pacific in all months. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of teleconnection indices used in this study. applied, which are very popular approaches well identified as mainstream in a recent review [31] of streamflow forecasting using data-driven models and powerful statistical techniques that have found many applications in this field [17; 29; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. However, thorough the comparison of models was not the main focus of our work. The MLR method is a multivariate technique that determines a linear relationship between multiple independent variables (predictors) and a dependent variable [43]. The chosen climatic indices are the independent variables and monthly reservoir inflow is the dependent variable. The formula for the multiple linear model used is shown below in Equation (2):  
\[y=C+D_{1}x_{1}+D_{2}x_{2}+\cdots+D_{n}x_{n} \tag{2}\]  
where \(y\) is the output variable; \(x_{i}\) represent the climatic indices; \(D_{i}\) is the regression coefficients and \(C\) is the intercept. SVM is a useful tool for data classification and pattern recognition in the field of data mining [44; 45]. It has shown to provide excellent performances in regression and time series prediction. The general framework of SVM involves (1) separating data into training and test sets, (2) producing a model with training data set and (3) predicting the target value based on test data set. Support vector regression has the same concepts as the SVM for classification. The main goal of support vector regression is to find a function \(f(x)\) that has at most \(\varepsilon\) deviation from the target variable y as described in Equations (3)-(5). \[f(x)= \langle\omega,x\rangle+b \tag{3}\]  
\[\textit{Minimize}\ P(f)=\frac{1}{2}\|\omega\|^{2}+c\sum_{i=1}^{l}(\xi_{i}+ \xi_{i}{}^{*}) \tag{4}\]  
\[\textit{Subject}\ \textit{to}\left\{ \begin{array}{l}y_{i}-\langle\omega, \chi_{i}\rangle-b\leq\varepsilon+\xi_{i}\\ \langle\omega,\chi_{i}\rangle+b-y_{i}\leq\varepsilon+\xi_{i}{}^{*}\\ \xi_{i},\xi_{i}{}^{*}\geq 0\end{array} \right.