Error Evolution in Multi-Step Ahead Streamflow Forecasting for the Operation of Hydropower Reservoirs

Abstract

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.

Large-scale assessment of Prophet for multi-step ahead forecasting of monthly streamflow

“…We observe that each of the algorithms may perform better or worse compared to the rest depending on the examined case study. This figure is particularly interesting, especially when viewed in comparison to several studies presenting new techniques and reporting on their superior performance to others based on case studies, while it also confirms in an illustrative way the related to the "no free lunch theorem" findings of Papacharalampous et al (2017bPapacharalampous et al ( , 2018a. According to the no free lunch theorem, there is not a model which will always perform better than other models (Wolpert, 1996).…”

“…In fact, the selection of appropriate exogenous variables is far identified in the forecasting literature as a target and challenging at the same time problem to be solved (see, for example, Hong and Fan, 2016), while several approaches not relying on exogenous information are mostly of the same usefulness, especially in geosciences, for which small differences in the forecasting performance of the algorithms do not have any practical effect on decision-making (see also Papacharalampous et al, 2018a). This conclusion can be drawn based on the large-scale results of Tyralis and Papacharalampous (2017) and Papacharalampous et al (2017aPapacharalampous et al ( , 2018a. Here as well, the differences in the results obtained using the various forecasting algorithms are mostly small, while Naïve 1 and SES are in average the worst performing.…”

“…On the contrary, Hong and Fan (2016) emphasize that the use of appropriate exogenous predictor variables could considerably improve the forecasts. The exogenous predictor variables to be utilized for solving a specific forecasting problem could result through large-scale comparisons (since the results may vary significantly depending on the case study; Papacharalampous et al, 2017b) that precede the application of interest. Such comparisons are known to facilitate benchmarking and model assessment, and require large datasets.…”

“…There are several studies approaching this specific problem without utilizing exogenous predictor variables (e.g. Ballini et al, 2001;Koutsoyiannis et al, 2008;Papacharalampous et al, 2017a), while examples of case studies adopting the alternative approach can be found in Callegari et al (2015) and Yang et al (2017). The results of such studies are usually presented in terms of point forecasts (hereafter forecasts) rather than in a probabilistic way, as in Tyralis and Koutsoyiannis (2014).…”

“…We use a more recent dataset, i.e. the CAMELS dataset (Addor et al, 2017a, b;Newman et al, 2014Newman et al, , 2015, which is also larger than the MOPEX one. We implement Prophet, a forecasting model introduced by Taylor and Letham (2018) that provides the possibility of incorporating exogenous predictor variables.…”