## Materials and Methods
### Metrics for AutoML Models Evaluation  
The daily streamflow forecasting capabilities of AutoML models were assessed using the following performance metrics: Mean Absolute Error (MAE--Equation (3)), Root Mean Square Error (RMSE--Equation (4)), Bias (BIAS--Equation (5)), Nash-Sutcliffe Efficiency Index (NSEI--Equation (6)), and Kling-Gupta Efficiency Index (KGEI--Equation (7)):  
\[\text{MAE}=\frac{1}{N}\sum_{i=1}^{N}|O_{i}-P_{i}|, \tag{3}\]  
\[\text{RMSE}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(O_{i}-P_{i})^{2}}, \tag{4}\]  
\[\text{BIAS}=\frac{1}{N}\sum_{i=1}^{N}(O_{i}-P_{i}), \tag{5}\]  
\[\text{NSEI}=1-\frac{\sum_{i=1}^{N}(O_{i}-P_{i})^{2}}{\sum_{i=1}^{N}(O_{i}- \overline{O})^{2}}, \tag{6}\]  
\[\text{KGEI}=1-\sqrt{(r-1)^{2}+\left(\frac{\sigma_{e}}{\sigma_{o}}-1\right)^{2 }+(\text{BIAS}-1)^{2}}, \tag{7}\]  
where \(P_{i}\) represents the predicted streamflow (in m\({}^{3}\) s\({}^{-1}\)), \(O_{i}\) is the observed streamflow (in m\({}^{3}\) s\({}^{-1}\)), \(\overline{O}\) stands as the average of the observed streamflow (in m\({}^{3}\) s\({}^{-1}\)), \(N\) is the number of values contained in the sample, \(r\) represents the correlation coefficient between the observed and predicted data, \(\sigma_{e}\) is the standard deviation of the data predicted by the model, and \(\sigma_{o}\) is the standard deviation of the observed data.  
Regarding the NSEI and KGEI metrics, assessment of the models was carried out relying on the performance categorization proposed in past research works related to the present one [19; 60]: an NSEI value equal to 1 reported an equal match between the model  
\begin{table}
\begin{tabular}{c l c c c} \hline \hline \multirow{2}{*}{**Time-Lag (Days)**} & **Models Input Features** & \multirow{2}{*}{**Predicted Outputs**} & **Development Data** & \multirow{2}{*}{**Test Data Interval**} \\  & (\(\overline{Q}_{t}\) and \(\overline{P}_{t}\))** & & **Interval** & \\ \hline
1 & Thiessen & \(\overline{Q}_{t+1}\) & 1985–2012 & 2013–2023 \\
1 & PERSIANN & \(\overline{Q}_{t+1}\) & 2000–2016 & 2017–2023 \\
1 & PERSIANN-CCS & \(\overline{Q}_{t+1}\) & 2003–2017 & 2018–2023 \\
1 & PERSIANN-CDR & \(\overline{Q}_{t+1}\) & 1985–2010 & 2011–2020 \\
1 & PDIR-Now & \(\overline{Q}_{t+1}\) & 2000–2016 & 2017–2023 \\ \hline
2 & Thiessen & \(\overline{Q}_{t+2}\) & 1985–2012 & 2013–2023 \\
2 & PERSIANN & \(\overline{Q}_{t+2}\) & 2000–2016 & 2017–2023 \\
2 & PERSIANN-CCS & \(\overline{Q}_{t+2}\) & 2003–2017 & 2018–2023 \\
2 & PERSIANN-CDR & \(\overline{Q}_{t+2}\) & 1985–2010 & 2011–2020 \\
2 & PDIR-Now & \(\overline{Q}_{t+2}\) & 2000–2016 & 2017–2023 \\ \hline
3 & Thiessen & \(\overline{Q}_{t+3}\) & 1985–2012 & 2013–2023 \\
3 & PERSIANN & \(\overline{Q}_{t+3}\) & 2000–2016 & 2017–2023 \\
3 & PERSIANN-CCS & \(\overline{Q}_{t+3}\) & 2003–2017 & 2018–2023 \\
3 & PDIR-Now & \(\overline{Q}_{t+3}\) & 1985–2010 & 2011–2020 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Covariates related to streamflow (denoted as \(Q\)) and rainfall (denoted as \(P\)) were employed as input features to train the AutoML models. In particular, the mean time-lagged streamflow (\(\overline{Q}_{t}\)) and rainfall (\(\overline{P}_{t}\)) for the considered basin were leveraged relying on five different methods: Thiessen, PERSIANN, PERSIANN-CCS, PERSIANN-CDR, and PDIR-Now. The time-lag \(l\) for which the streamflow predictions were computed was set as \(1\leq l\leq 3\) days in the present research. The last two columns report the development and test data intervals employed for all the selected feature sets.  
predicted data and the actual data; a value greater than 0.75 implied model predictions of high quality; an NSEI value between 0.36 and 0.75 reported that the model performance was sufficient; finally, a NSEI value less than 0.36 denoted unsatisfactory predictions. The latter categorization was equally used to assess the model's performance with KGEI.