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

arXiv: https://arxiv.org/abs/1909.00247 · HTML: https://mlsanity.com/paper/1909.00247/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2019.

## Built on by (most cited first, 3 of 3)

- [A review of machine learning concepts and methods for addressing challenges in probabilistic hydrological post-processing and forecasting](https://mlsanity.com/paper/2206.08998/) (2022)
- [Deep Huber quantile regression networks](https://mlsanity.com/paper/2306.10306/) (2023)
- [Probabilistic water demand forecasting using quantile regression algorithms](https://mlsanity.com/paper/2104.07985/) (2021)

## Abstract (arXiv)

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 post-processing 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.