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

Abstract

We introduce an ensemble learning post-processing methodology for probabilistic hydrological modelling. This methodology generates numerous point predictions by applying a single hydrological model, yet with different parameter values drawn from the respective simulated posterior distribution. We call these predictions "sister predictions". Each sister prediction extending in the period of interest is converted into a probabilistic prediction using information about the hydrological model's errors. This information is obtained from a preceding period for which observations are available, and is exploited using a flexible quantile regression model.All probabilistic predictions are finally combined via simple quantile averaging to produce the output probabilistic prediction. The idea is inspired by the ensemble learning methods originating from the machine learning literature. The proposed methodology offers larger robustness in performance than basic post-processing methodologies using a single hydrological point prediction. It is also empirically proven to "harness the wisdom of the crowd" in terms of average interval score, i.e., the obtained quantile predictions score no worse -usually better− than the average score of the combined individual predictions. This proof is provided within toy examples, which can be used for gaining insight on how the methodology works and under which conditions it can optimally convert point hydrological predictions to probabilistic ones.A large-scale hydrological application is made in a companion paper.

A review of modelling methodologies for flood source area (FSA) identification

“…While there are other methods capable of FSA identification such as remote sensing, soil moisture analysis, and field observations (Islam and Sado 2000;Foody et al 2004;Chormanski et al 2011;Mengistu and Spence 2016), this review concentrates on studies that are reliant on flood models. This is because flood models are a crucial tool within research and industry when investigating flood processes and influencing FRM decisions globally (Mason et al 2003;Priya 2019;Papacharalampous et al 2020). FSA identification methods have been categorised based on their modelling intent; first, those that directly apply a framework to identify FSAs, referred to as unit flood response (UFR) driven approaches.…”

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

“…To further reduce uncertainty, one has to optimize the statistical modelling part of the probabilistic methodology, which is commonly related to the modelling of the hydrological model errors (see, e.g., references [6,45,61,62,64,65,69]). These errors are known to be heteroscedastic and correlated (see, e.g., references [6,10,87]).…”

“…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.…”

“…Preliminary works on the above can be found in Papacharalampous et al [79], while Papacharalampous et al [45,69] (studies built on the work by Montanari and Koutsoyiannis [6]) and Tyralis et al [46] focus on ensemble learning probabilistic hydrological post-processing methodologies that can accommodate the algorithms assessed herein. Ensemble learning methods combining the predictions obtained by multiple learning algorithms (e.g., the equal-weight combiner tested herein) are increasingly adopted in many engineering and applied science fields, since they frequently provide improved predictive performance with respect to each of the individual learning algorithms (see, e.g., the review by Sagi and Rokach [29]).…”

Susceptibility Prediction of Groundwater Hardness Using Ensemble Machine Learning Models

“…Although ensemble models in the hydrological modeling often outperform regular machine learning models [41], their performance in groundwater quality modeling has not been explored. Ensemble learning algorithms parallelly employ learning machines to deliver higher performance than could be achieved from a single one [42,43].…”