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

Abstract

Predictive hydrological uncertainty can be quantified by using ensemble methods. If properly formulated, these methods can offer improved predictive performance by combining multiple predictions. In this work, we use 50-year-long monthly time series observed in 270 catchments in the United States to explore the performances provided by an ensemble learning post-processing methodology for issuing probabilistic hydrological predictions. This methodology allows the utilization of flexible quantile regression models for exploiting information about the hydrological model's error. Its key differences with respect to basic two-stage hydrological postprocessing methodologies using the same type of regression models are that: (a) instead of a single point hydrological prediction it generates a large number of "sister predictions" (yet using a single hydrological model), and that (b) it relies on the concept of combining probabilistic predictions via simple quantile averaging. A major hydrological modelling challenge is obtaining probabilistic predictions that are simultaneously reliable and associated to prediction bands that are as narrow as possible; therefore, we assess both these desired properties of the predictions by computing their coverage probabilities, average widths and average interval scores. The results confirm the usefulness of the proposed methodology and its larger robustness with respect to basic two-stage post-processing methodologies. Finally, this methodology is empirically proven to harness the "wisdom of the crowd" in terms of average interval score, i.e., the average of the individual predictions combined by this methodology scores no worse -usually better− than the average of the scores of the individual predictions.

Explanation and Probabilistic Prediction of Hydrological Signatures with Statistical Boosting Algorithms

“…Therefore, some concessions should be accepted, since there is no free lunch in modelling [64], so that one obtains a model that provides acceptable predictions and is interpretable simultaneously. For instance, one could combine multiple models and obtain more accurate points [65,66] or probabilistic [67,68] pre- To understand Figure 6, we note that attributes in the vertical axis are reported with regards to their type, i.e., topographic characteristics, climatic indices, land cover characteristics, soil characteristics and geological characteristics (from lower to upper). In general, topographic characteristics and climatic indices seem to be most important when predicting hydrological signatures.…”

“…Therefore, some concessions should be accepted, since there is no free lunch in modelling [64], so that one obtains a model that provides acceptable predictions and is interpretable simultaneously. For instance, one could combine multiple models and obtain more accurate points [65,66] or probabilistic [67,68] predictions. However, in this case, interpretability would be lost for the sake of generalization.…”

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

“…We are explicitly interested in probabilistic hydrological post-processing methodologies whose models are estimated sequentially in more than one stage (see also Section 2.1; hereafter referred to as "multi-stage probabilistic hydrological post-processing methodologies") and machine-learning quantile regression algorithms, since the former can accommodate the latter naturally and effectively. The effectiveness of this accommodation has already been proven, for example, with the large-scale results by Papacharalampous et al [45] and Tyralis et al [46] for the monthly and daily timescales, respectively. Aiming at combining the advantages from both the above-outlined "streams of thought" in predictive hydrological modelling, these studies and a few earlier ones (to the best of our knowledge, those mentioned in Table 1) have integrated process-based hydrological models and data-driven algorithmic approaches (spanning from conditional distribution modelling approaches to regression algorithms) within multi-stage probabilistic hydrological post-processing methodologies for predictive uncertainty quantification purposes.…”

“…Advancing the implementation of machine-learning regression algorithms by conducting large-sample (and in-depth) hydrological investigations has been gaining prominence recently (see, e.g., references [42][43][44][45][46]), perhaps following a more general tendency for embracing large-scale hydrological analyses and model evaluations (see, e.g., references [47][48][49][50][51]). The key significance of such studies in improving the modelling of hydrological phenomena, especially when the modelling is data-driven, has been emphasized by several experts in the field (see, e.g., references [16,[52][53][54][55]).…”

“…In the present study, we exploit a large dataset for advancing the use of machine-learning algorithms within broader methodological approaches for quantifying the predictive uncertainty in hydrology. The hydrological modelling and hydro-meteorological forecasting literatures include a large variety of such methodologies (see, e.g., references [45,46,[56][57][58][59][60][61][62][63][64][65][66][67][68][69]), reviewed in detail by Montanari [9] and Li et al [70]. Deterministic "process-based" hydrological models are usually and preferably a core ingredient of probabilistic approaches of this family.…”