Research within the field of hydrology often focuses on comparing stochastic to machine learning (ML) forecasting methods. The comparisons performed are all based on case studies, while an extensive study aiming to provide generalized results on the subject is missing. Herein, we compare 11 stochastic and 9 ML methods regarding their multi-step ahead forecasting properties by conducting 12 large-scale computational experiments based on simulations. Each of these experiments uses 2 000 time series generated by linear stationary stochastic processes. We conduct each simulation experiment twice; the first time using time series of 100 values and the second time using time series of 300 values. Additionally, we conduct a real-world experiment using 405 mean annual river discharge time series of 100 values. We quantify the performance of the methods using 18 metrics. The results indicate that stochastic and ML methods perform equally well.

The finding of important explanatory variables for the location parameter and the scale parameter of the generalized extreme value (GEV) distribution, when the latter is used for the modelling of annual streamflow maxima, is known to have reduced the uncertainties in inferences, as estimated through regional flood frequency analysis frameworks. However, important explanatory variables have not been found for the GEV shape parameter, despite its critical significance, which stems from the fact that it determines the behaviour of the upper tail of the distribution. Here we examine the nature of the shape parameter by revealing its relationships with basin attributes. We use a dataset that comprises information about daily streamflow and forcing, climatic indices, topographic, land cover, soil and geological characteristics of 591 basins with minimal human influence in the contiguous United States. We propose a framework that uses random forests and linear models to find (a) important predictor variables of the shape parameter and (b) an interpretable model with high predictive performance. The process of study comprises of assessing the predictive performance of the models, selecting a parsimonious predicting model and interpreting the results in an ad-hoc manner. The findings suggest that the shape parameter mostly depends on climatic indices, while the selected prediction model results in more than 20% higher accuracy in terms of RMSE compared to a naïve approach. The implications are important, since incorporating the regression model into regional flood frequency analysis frameworks can considerably reduce the predictive uncertainties.

Multi-step ahead streamflow forecasting is of practical interest for the operation of hydropower reservoirs. We provide generalized results on the error evolution in multi-step ahead forecasting by conducting several large-scale experiments based on simulations. We also present a multiple-case study using monthly time series of streamflow. Our findings suggest that some forecasting methods are more useful than others. However, the errors computed at each time step of a forecast horizon within a specific case study strongly depend on the case examined and can be either small or large, regardless of the forecasting method used and the time step of interest.