Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes

Abstract

We perform an extensive comparison between 11 stochastic to 9 machine learning methods regarding their multi-step ahead forecasting properties by conducting 12 large-scale computational experiments. 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 110 values and the second time using time series of 310 values. Additionally, we conduct 92 real-world case studies using mean monthly time series of streamflow and particularly focus on one of them to reinforce the findings and highlight important facts. We quantify the performance of the methods using 18 metrics. The results indicate that the machine learning methods do not differ dramatically from the stochastic, while none of the methods under comparison is uniformly better or worse than the rest. However, there are methods that are regularly better or worse than others according to specific metrics.

Influent Forecasting for Wastewater Treatment Plants in North America

“…Comparing to these two examples, this study demonstrates that ARIMA can be considered a reliable forecasting model, especially with longer temporal resolutions. An extensive test of ARIMA and 11 other stochastic methods regarding their streamflow forecasting properties can be found in [13].…”

“…It was discovered that the seasonal ARIMA model was the most effective for monthly forecasts up to twelve months. Furthermore, larger scale studies which evaluated the performance of ARIMA can be found in [13]. Models derived from the Autoregressive Moving Average (ARMA) families and machine learning black box methods, such as Neural Networks and Random Forests, were used to forecast monthly or annual hydrological processes, such as streamflow rates.…”

Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: Methodology development and investigation using toy models

“…Examples of toy experiments from the probabilistic hydrological modelling literature are available in Krzysztofowicz (1999), Beven and Freer (2001), Stedinger et al (2008), Farmer and Vogel (2016), and Volpi et al (2017). Toy models have also been exploited for other modelling situations in geoscience (see e.g., Koutsoyiannis 2006Koutsoyiannis , 2010; see also the references in Koutsoyiannis 2006), while falling into the broader category of simulation or synthetic experiments, which are increasingly conducted within various hydrological contexts, including some more relevant to the present study (see e.g., Kavetski et al 2002;Vrugt et al 2005;Montanari 2005;Montanari and Koutsoyiannis 2012;Montanari and Di Baldassarre 2013;Papacharalampous et al 2018Papacharalampous et al , 2019aRenard et al 2010;Sadegh and Vrugt 2014;Sadegh et al 2015;Sikorska et al 2015;Schoups and Vrugt 2010;Tyralis and Papacharalampous 2017;Tyralis et al 2013;Vrugt et al 2003;Vrugt and Robinson 2007;Vrugt et al 2008;Vrugt et al 2013;Vrugt et al 2016); see also Montanari (2007) for a discussion on the significance of this type of experiments. In fact, simplified modelling situations can be useful as starting points for achieving effective real-world modelling, especially in cases where analytical solutions exist (see e.g., Volpi 2012).…”

Improving the Reliability of Probabilistic Multi-Step-Ahead Flood Forecasting by Fusing Unscented Kalman Filter with Recurrent Neural Network

“…The reliability of hydrologic forecasts can be affected by input uncertainty, meteorological uncertainty, and hydrologic uncertainty of model structure and parameters. One of the primary techniques to reflect different uncertainties in hydrologic forecasts is to create a probabilistic forecast [10,11]. Probabilistic forecasts can be made using three approaches: a probabilistic pre-processing approach plus a deterministic forecast model; a probabilistic forecast model; and a deterministic forecast model plus a probabilistic post-processing approach [12][13][14].…”

“…Bearing this in mind as motivation, for the first time, the UKF is introduced to quantify the uncertainty of multi-step-ahead flood forecasts driven by the RNN (i.e., RNN is more complicated than the static ANNs). Therefore, it is interesting to explore UKF for modeling and lowering the uncertainty appeared in RNN-driven flood forecasts.Machine-learning techniques have developed fast during the last few decades, and they have been adopted as data-driven methods to model hydrological systems [11,25,26]. For instance, the back-propagation neural network (BPNN), the radial basis function (RBF), the support vector machine, the quantile regression neural network (QRNN), the recurrent neural network (RNN), the long-short term memory (LSTM) and the non-linear auto-regressive with exogenous inputs neural network (NARX) have been widely applied to modeling hydrologic and meteorological time series [27][28][29][30][31][32][33][34][35][36][37][38].…”