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.

Highlights

  • Issuing useful hydrological predictions is one of the most important challenges in hydrology

  • Other drawbacks of gradient boosting machine are: (a) that they are memory-consuming due to a large number of iterations; (b) their evaluation speed; and (c) that they are slower to learn compared to random forests

  • Three of the assessed machine-learning quantile regression algorithms, generalized regression forests, gradient boosting machine and gradient boosting with linear models as base learners, are implemented for the first time to solve the practical problem of interest

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Summary

Introduction

Issuing useful hydrological predictions (e.g., river flow predictions) is one of the most important challenges in hydrology. Machine-learning regression algorithms are regularly implemented in the data-driven hydrological literature for solving a vast amount of technical problems, and for building confidence in predictive and explanatory modelling (see, e.g., references [34,35,36,37,38,39,40]) Their potential has been realized and exploited only to a limited extent, and mostly for obtaining “point” predictions (term used here as opposed to “probabilistic”). The results of the present study advocate the value of ensemble learning for probabilistic hydrological post-processing

Multi-Stage Probabilistic Hydrological Post-Processing
Implemented Hydrological Model
Background and List
Quantile Regression
Quantile Regression Forests and Generalized Random Forests
Gradient Boosting Machine and Model-Based Boosting
Quantile Regression Neural Networks
Rainfall-Runoff Data and Time Periods
Application of the Hydrological Model
Solved Regression Problem and Assessed Configurations
Performance Assessment
Overall Assessment of the Machine-Learning Aalgorithms
Investigations
Mean absolute deviation reliabilityscores scores from their nominal values
Innovations and Highlights in Light of the Literature
Contributions and Challenges from an Uncertainty Reduction Perspective
A Culture-Integrating Approach to Probabilistic Hydrological Modelling
Value of Ensemble Learning Hydrological Post-Processing Methodologies
Grounds and Implications of the Proposed Methodological Framework
Summary and Take-Home Messages

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