Probabilistic Hydrological Post-Processing at Scale: Why and How to Apply Machine-Learning Quantile Regression Algorithms

Abstract

We conduct a large-scale benchmark experiment aiming to advance the use of machine-learning quantile regression algorithms for probabilistic hydrological post-processing “at scale” within operational contexts. The experiment is set up using 34-year-long daily time series of precipitation, temperature, evapotranspiration and streamflow for 511 catchments over the contiguous United States. Point hydrological predictions are obtained using the Génie Rural à 4 paramètres Journalier (GR4J) hydrological model and exploited as predictor variables within quantile regression settings. Six machine-learning quantile regression algorithms and their equal-weight combiner are applied to predict conditional quantiles of the hydrological model errors. The individual algorithms are quantile regression, generalized random forests for quantile regression, generalized random forests for quantile regression emulating quantile regression forests, gradient boosting machine, model-based boosting with linear models as base learners and quantile regression neural networks. The conditional quantiles of the hydrological model errors are transformed to conditional quantiles of daily streamflow, which are finally assessed using proper performance scores and benchmarking. The assessment concerns various levels of predictive quantiles and central prediction intervals, while it is made both independently of the flow magnitude and conditional upon this magnitude. Key aspects of the developed methodological framework are highlighted, and practical recommendations are formulated. In technical hydro-meteorological applications, the algorithms should be applied preferably in a way that maximizes the benefits and reduces the risks from their use. This can be achieved by (i) combining algorithms (e.g., by averaging their predictions) and (ii) integrating algorithms within systematic frameworks (i.e., by using the algorithms according to their identified skills), as our large-scale results point out.

Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: A large-sample experiment at monthly timescale

“…Therefore, this methodology does not have any particular relationship with Bayesian methods by construction, as it also applies to its precursor. A statistical learning regression model that is suitable for predicting quantiles (see e.g., the models exploited in Papacharalampous et al 2019b) is then used to obtain information about the hydrological model's error. This information is used to convert the sister predictions into probabilistic predictions, which are finally combined in simple fashion to obtain the output probabilistic predictions.…”

“…can be used in the application of the error model. This point may be important for maximizing predictive performance for timescales finer than the monthly one (see e.g., the findings in Papacharalampous et al 2019b).…”

“…This choice is implied by the fact that the co-assessment regarding reliability and sharpness provided, for instance, by the interval score is of the most practical relevance in technical applications; for a justification see Papacharalampous et al (2019c); see also Gneiting and Katzfuss (2014). In spite of the placed emphasis and keeping pace with studies, such as those of Renard et al (2010Renard et al ( , 2011, Evin et al (2013Evin et al ( , 2014, Papacharalampous et al (2019b) and Tyralis et al (2019a), we subsequently summarize some information purely related to reliability assessment and sharpness assessment to facilitate interpretability and understanding of what follows.…”

“…As also emphasized in Papacharalampous et al (2019c), the overall trade-off to be considered when someone has to choose between the working methodology and a basic two-stage post-processing methodology allowing the utilization of the same type of flexible error models (see e.g., López López et al 2014;Dogulu et al 2015;Papacharalampous et al 2019b) is the one between (a) the larger robustness in performance offered by the former methodology (demonstrated in Figures 12, S.3, S.5, S.7, S.9 and S.11, and…”

“…o Any statistical learning regression model that is suitable for predicting quantiles (e.g., the error models exploited in Papacharalampous et al 2019b) can be selected as error model. This point may be particularly important for maximizing predictive performance (see also the key remarks in Section 4).…”