Next Article in Journal
Network Capacity Assessment and Increase in Systems with Intermittent Water Supply
Next Article in Special Issue
Predictive Uncertainty Estimation on a Precipitation and Temperature Reanalysis Ensemble for Shigar Basin, Central Karakoram
Previous Article in Journal
Decline in Performance of Biochemical Reactors for Sulphate Removal from Mine-Influenced Water is Accompanied by Changes in Organic Matter Characteristics and Microbial Population Composition
Previous Article in Special Issue
Post-Processing of Stream Flows in Switzerland with an Emphasis on Low Flows and Floods
Article Menu

Export Article

Open AccessArticle
Water 2016, 8(4), 125; doi:10.3390/w8040125

Predictive Uncertainty Estimation of Hydrological Multi-Model Ensembles Using Pair-Copula Construction

1
Department M2—Water Balance, Forecasting and Predictions, Federal Institute of Hydrology (BfG), Am Mainzer Tor 1, Koblenz 56068, Germany
2
Fraunhofer Institute for Intelligent Analysis and Information Systems IAIS, Schloss Birlinghoven, Sankt Augustin 53757, Germany
3
Department of Civil Engineering, University of Siegen, Paul-Bonatz-Str. 9-11, Siegen 57068, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Karl-Erich Lindenschmidt
Received: 21 December 2015 / Revised: 4 March 2016 / Accepted: 22 March 2016 / Published: 31 March 2016
(This article belongs to the Special Issue Uncertainty Analysis and Modeling in Hydrological Forecasting)
View Full-Text   |   Download PDF [3764 KB, uploaded 31 March 2016]   |  

Abstract

Predictive uncertainty (PU) is defined as the probability of occurrence of an observed variable of interest, conditional on all available information. In this context, hydrological model predictions and forecasts are considered to be accessible but yet uncertain information. To estimate the PU of hydrological multi-model ensembles, we apply a method based on the use of copulas which enables modelling the dependency structures between variates independently of their marginal distributions. Given that the option to employ copula functions imposes certain limitations in the multivariate case, we model the multivariate distribution as a cascade of bivariate copulas by using the pair-copula construction. We apply a mixture of probability distributions to estimate the marginal densities and distributions of daily flow rates for various meteorological and hydrological situations. The proposed method is applied to a multi-model ensemble involving two hydrological and one statistical flow models at two gauge stations in the Moselle river basin. Verification and inter-comparison with other PU assessment methods show that copulas are well-suited for this scope and constitute a valid approach for predictive uncertainty estimation of hydrological multi-model predictions. View Full-Text
Keywords: predictive uncertainty; pair-copula construction; C-Vine; quantile regression; Bayesian model averaging; multivariate truncated normal distribution; mixture probability distribution predictive uncertainty; pair-copula construction; C-Vine; quantile regression; Bayesian model averaging; multivariate truncated normal distribution; mixture probability distribution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Klein, B.; Meissner, D.; Kobialka, H.-U.; Reggiani, P. Predictive Uncertainty Estimation of Hydrological Multi-Model Ensembles Using Pair-Copula Construction. Water 2016, 8, 125.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Water EISSN 2073-4441 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top