G. Papacharalampous, H. Tyralis, D. Koutsoyiannis, and A. Montanari, Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: A large-sample experiment at monthly timescale, *Advances in Water Resources*, 136, 103470, doi:10.1016/j.advwatres.2019.103470, 2020.

[doc_id=2018]

[English]

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.

Full text is only available to the NTUA network due to copyright restrictions

**Additional material:**

- Preprint (5396 KB)
- Supplementary material (1191 KB)

**Our works referenced by this work:**

1. | D. Koutsoyiannis, and A. Montanari, Statistical analysis of hydroclimatic time series: Uncertainty and insights, Water Resources Research, 43 (5), W05429, doi:10.1029/2006WR005592, 2007. |

2. | D. Koutsoyiannis, C. Makropoulos, A. Langousis, S. Baki, A. Efstratiadis, A. Christofides, G. Karavokiros, and N. Mamassis, Climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability, Hydrology and Earth System Sciences, 13, 247–257, doi:10.5194/hess-13-247-2009, 2009. |

3. | D. Koutsoyiannis, A random walk on water, Hydrology and Earth System Sciences, 14, 585–601, doi:10.5194/hess-14-585-2010, 2010. |

4. | A. Efstratiadis, and D. Koutsoyiannis, One decade of multiobjective calibration approaches in hydrological modelling: a review, Hydrological Sciences Journal, 55 (1), 58–78, doi:10.1080/02626660903526292, 2010. |

5. | D. Koutsoyiannis, Hurst-Kolmogorov dynamics and uncertainty, Journal of the American Water Resources Association, 47 (3), 481–495, doi:10.1111/j.1752-1688.2011.00543.x, 2011. |

6. | A. Montanari, and D. Koutsoyiannis, A blueprint for process-based modeling of uncertain hydrological systems, Water Resources Research, 48, W09555, doi:10.1029/2011WR011412, 2012. |

7. | S.M. Papalexiou, and D. Koutsoyiannis, Battle of extreme value distributions: A global survey on extreme daily rainfall, Water Resources Research, 49 (1), 187–201, doi:10.1029/2012WR012557, 2013. |

8. | A. Montanari, and D. Koutsoyiannis, Modeling and mitigating natural hazards: Stationarity is immortal!, Water Resources Research, 50 (12), 9748–9756, doi:10.1002/2014WR016092, 2014. |

9. | D. Koutsoyiannis, and A. Montanari, Negligent killing of scientific concepts: the stationarity case, Hydrological Sciences Journal, 60 (7-8), 1174–1183, doi:10.1080/02626667.2014.959959, 2015. |

10. | H. Tyralis, and D. Koutsoyiannis, On the prediction of persistent processes using the output of deterministic models, Hydrological Sciences Journal, 62 (13), 2083–2102, doi:10.1080/02626667.2017.1361535, 2017. |

11. | H. Tyralis, and G. Papacharalampous, Variable selection in time series forecasting using random forests, Algorithms, 10, 114, doi:10.3390/a10040114, 2017. |

12. | H. Tyralis, P. Dimitriadis, D. Koutsoyiannis, P.E. O’Connell, K. Tzouka, and T. Iliopoulou, On the long-range dependence properties of annual precipitation using a global network of instrumental measurements, Advances in Water Resources, 111, 301–318, doi:10.1016/j.advwatres.2017.11.010, 2018. |

13. | G. Papacharalampous, H. Tyralis, and D. Koutsoyiannis, One-step ahead forecasting of geophysical processes within a purely statistical framework, Geoscience Letters, 5, 12, doi:10.1186/s40562-018-0111-1, 2018. |

14. | G. Papacharalampous, H. Tyralis, and D. Koutsoyiannis, Predictability of monthly temperature and precipitation using automatic time series forecasting methods, Acta Geophysica, 66 (4), 807–831, doi:10.1007/s11600-018-0120-7, 2018. |

15. | G. Papacharalampous, H. Tyralis, and D. Koutsoyiannis, Univariate time series forecasting of temperature and precipitation with a focus on machine learning algorithms: a multiple-case study from Greece, Water Resources Management, 32 (15), 5207–5239, doi:10.1007/s11269-018-2155-6, 2018. |

16. | G. Papacharalampous, H. Tyralis, and D. Koutsoyiannis, Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes, Stochastic Environmental Research & Risk Assessment, doi:10.1007/s00477-018-1638-6, 2019. |

17. | G. Papacharalampous, H. Tyralis, A. Langousis, A. W. Jayawardena, B. Sivakumar, N. Mamassis, A. Montanari, and D. Koutsoyiannis, Probabilistic hydrological post-processing at scale: Why and how to apply machine-learning quantile regression algorithms, Water, doi:10.3390/w11102126, 2019. |

18. | G. Papacharalampous, D. Koutsoyiannis, and A. Montanari, Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: Methodology development and investigation using toy models, Advances in Water Resources, 136, 103471, doi:10.1016/j.advwatres.2019.103471, 2020. |

**Our works that reference this work:**

1. | G. Papacharalampous, D. Koutsoyiannis, and A. Montanari, Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: Methodology development and investigation using toy models, Advances in Water Resources, 136, 103471, doi:10.1016/j.advwatres.2019.103471, 2020. |

2. | D. Koutsoyiannis, An open letter to the Editor of Frontiers, doi:10.13140/RG.2.2.34248.39689, December 2021. |

3. | D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 2, ISBN: 978-618-85370-0-2, 346 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2022. |

4. | D. Koutsoyiannis, and A. Montanari, Bluecat: A local uncertainty estimator for deterministic simulations and predictions, Water Resources Research, 58 (1), e2021WR031215, doi:10.1029/2021WR031215, 2022. |

5. | D. Koutsoyiannis, and A. Montanari, Climate extrapolations in hydrology: The expanded Bluecat methodology, Hydrology, 9, 86, doi:10.3390/hydrology9050086, 2022. |

**
Works that cite this document:
**
View on
Google Scholar
or
ResearchGate