## 4 Results  
The Figures 6 and 7 present the daily streamflow forecasting performance on the test set for the five employed AutoML models, five feature sets, and three different forecasting time-lags. Both the figures report the test set forecasting performance through five separate subplots, each corresponding to a different performance metric, previously described in Section 3.4. Specifically, Figure 6 shows the forecasting performance gained by AutoML models for each selected metric over all the employed features. On the other hand, Figure 7 displays the forecasting performance gained for each metric when each selected feature was used as input over all the employed AutoML models. Both Figures 6 and 7 display results by providing summary statistics in each subplot through box plots, color-coded with three different colors, each representing a different time-lag. Regarding the results shown in Figure 6, proper statistical tests were applied to understand: (1) if there were any statistically significant differences among the employed AutoML models regarding the test set performance; (2) If the answer to the first point was positive, which specific AutoML models showed statistically significantly different performance with respect to other ones. Among the most common statistical tests to assess the first point, we may find the Analysis of Variance (ANOVA) [61]. However, the application of ANOVA requires that several assumptions be met to obtain reliable findings, such as normality (groups should be approximately normally distributed), homogeneity of variances (variances among groups should be approximately equal), and independence (observations must be independent of each other). Even if independence may be reasonably assumed in the present study, normality and homogeneity of variances were not guaranteed by the analyzed results. Indeed, the Shapiro-Wilk test [62] and the Fligner-Killeen test [63] were computed over results to check the latter two properties, with test groups defined by grouping the obtained model results by AutoML model and performance metric. First, the Shapiro-Wilk test was applied. The null hypothesis of the Shapiro-Wilk test assumes that the data follow a Normal distribution, and if the \(p\)-value obtained from the test is less than the chosen significance level \(\alpha\) (commonly set to \(\alpha=0.05\)), the null hypothesis is rejected and there is sufficient evidence to conclude that the data do not follow a Normal distribution. The tested AutoML models showed a \(p\)-value greater than \(\alpha=0.05\), except for TPOT in MAE (\(p=0.008\)), AutoKeras in RMSE (\(p=0.015\)), MLBox (\(p=0.009\)) and TPOT (\(p=0.029\)) in BIAS, and finally TPOT in NSEI (\(p=0.04\)). As a result, normality was not guaranteed within five out of twenty-five (the 20%) of the defined groups. Next, the Fligner-Killeen test was applied to check the homogeneity of variances among groups. The null hypothesis of the latter test set all the group variances to be equal, and with a \(p\)-value less than the chosen significance level \(\alpha\) (typically \(\alpha=0.05\)), the null hypothesis is rejected. In particular, a different Fligner-Killeen test was performed for each performance metric to compare the AutoML model's performance variances on the same metric scale. As a result, the performed tests showed statistically significant differences in variances for all the metrics, as all the computed \(p\)-values were less than \(\alpha=0.05\). In particular, the \(p\)-values found by the executed Fligner-Killeen tests ranged within \(0.000\leq p\leq 0.009\). Figure 6: The figure reports the forecasting performance gained by AutoML models for each selected metric, over all the employed features. The figure reports the test set forecasting performance through five separate subplots, each corresponding to a different performance metric, previously described in Section 3.4.