skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation

Abstract

A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. Here, this paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel–Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved tobe generally reliable and robust by many simulations under three different situations. TheGumbel–Hougaard copula with MEE can also be appliedmore » to the bivariate frequency analysis ofother extreme events in data-scarce regions.« less

Authors:
 [1]; ORCiD logo [2];  [3];  [4];  [2];  [5]
  1. National Univ. of Defense Technology, Nanjing (China). Research Center of Ocean Environment Numerical Simulation, Inst. of Meteorology and Oceanography
  2. Beijing Normal Univ., Beijing (China). Key Lab. for Water and Sediment Sciences, College of Water Sciences
  3. Yellow River Inst. of Hydraulic Research, Zhengzhou (China). Yellow River Conservancy Commission
  4. Argonne National Lab. (ANL), Argonne, IL (United States). Environmental Science Division
  5. China Inst. of water Resources and Hydropower Research, Beijing (China). State Key Lab. of Simulation and Regulation of Water Cycle in River Basin,
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
National Natural Science Foundation of China (NNSFC); USDOE
OSTI Identifier:
1466300
Grant/Contract Number:  
AC02-06CH11357; 2016YFC0402409; 2016YFC0401407
Resource Type:
Accepted Manuscript
Journal Name:
Hydrological Processes
Additional Journal Information:
Journal Volume: 32; Journal Issue: 2; Journal ID: ISSN 0885-6087
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; Gumbel distribution; Gumbel-Hougaard copula; extreme frequency analysis; insufficient data; maximum entropy estimation

Citation Formats

Qian, Longxia, Wang, Hongrui, Dang, Suzhen, Wang, Cheng, Jiao, Zhiqian, and Zhao, Yong. Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation. United States: N. p., 2017. Web. doi:10.1002/hyp.11406.
Qian, Longxia, Wang, Hongrui, Dang, Suzhen, Wang, Cheng, Jiao, Zhiqian, & Zhao, Yong. Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation. United States. doi:10.1002/hyp.11406.
Qian, Longxia, Wang, Hongrui, Dang, Suzhen, Wang, Cheng, Jiao, Zhiqian, and Zhao, Yong. Thu . "Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation". United States. doi:10.1002/hyp.11406. https://www.osti.gov/servlets/purl/1466300.
@article{osti_1466300,
title = {Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation},
author = {Qian, Longxia and Wang, Hongrui and Dang, Suzhen and Wang, Cheng and Jiao, Zhiqian and Zhao, Yong},
abstractNote = {A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. Here, this paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel–Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved tobe generally reliable and robust by many simulations under three different situations. TheGumbel–Hougaard copula with MEE can also be applied to the bivariate frequency analysis ofother extreme events in data-scarce regions.},
doi = {10.1002/hyp.11406},
journal = {Hydrological Processes},
number = 2,
volume = 32,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Multivariate hydrological frequency analysis using copulas: MULTIVARIATE FREQUENCY ANALYSIS USING COPULAS
journal, January 2004

  • Favre, Anne-Catherine; El Adlouni, Salaheddine; Perreault, Luc
  • Water Resources Research, Vol. 40, Issue 1
  • DOI: 10.1029/2003WR002456

Application of copulas for regional bivariate frequency analysis of meteorological droughts in Turkey
journal, February 2016


Trivariate Flood Frequency Analysis Using the Gumbel–Hougaard Copula
journal, July 2007


Spatial Interpolation of Annual Runoff in Ungauged Basins Based on the Improved Information Diffusion Model Using a Genetic Algorithm
journal, January 2017

  • Hong, Mei; Zhang, Ren; Wang, Dong
  • Discrete Dynamics in Nature and Society, Vol. 2017
  • DOI: 10.1155/2017/4293731

Fitting Drought Duration and Severity with Two-Dimensional Copulas
journal, June 2006


A Bayesian Joint Probability Approach for flood record augmentation
journal, June 2001


Multivariate assessment of droughts: Frequency analysis and dynamic return period: Multivariate Assessment of Droughts
journal, October 2013

  • De Michele, C.; Salvadori, G.; Vezzoli, R.
  • Water Resources Research, Vol. 49, Issue 10
  • DOI: 10.1002/wrcr.20551

Multivariate drought characteristics using trivariate Gaussian and Student t copulas: DROUGHT MODELING USING COPULAS
journal, April 2012

  • Ma, Mingwei; Song, Songbai; Ren, Liliang
  • Hydrological Processes, Vol. 27, Issue 8
  • DOI: 10.1002/hyp.8432

Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain: BAYESIAN SPATIAL EXTREMES FOR LARGE REGIONS
journal, August 2016

  • Bracken, C.; Rajagopalan, B.; Cheng, L.
  • Water Resources Research, Vol. 52, Issue 8
  • DOI: 10.1002/2016WR018768

Analysis of hydrological drought frequency for the Xijiang River Basin in South China using observed streamflow data
journal, February 2015


Smooth regional estimation of low-flow indices: physiographical space based interpolation and top-kriging
journal, January 2011

  • Castiglioni, S.; Castellarin, A.; Montanari, A.
  • Hydrology and Earth System Sciences, Vol. 15, Issue 3
  • DOI: 10.5194/hess-15-715-2011

Multivariate analysis of flood characteristics in a climate change context of the watershed of the Baskatong reservoir, Province of Québec, Canada
journal, May 2011

  • Aissia, M. -A. Ben; Chebana, F.; Ouarda, T. B. M. J.
  • Hydrological Processes, Vol. 26, Issue 1
  • DOI: 10.1002/hyp.8117

IDF Curves Using the Frank Archimedean Copula
journal, November 2007


Goodness-of-fit test for copulas
journal, September 2005


A multivariate copula-based framework for dealing with hazard scenarios and failure probabilities: MULTIVARIATE HAZARD SCENARIOS AND RISK ASSESSMENT
journal, May 2016

  • Salvadori, G.; Durante, F.; De Michele, C.
  • Water Resources Research, Vol. 52, Issue 5
  • DOI: 10.1002/2015WR017225

Understanding Relationships Using Copulas
journal, January 1998


A study on selection of probability distributions for at-site flood frequency analysis in Australia
journal, July 2013


Application of copulas for derivation of drought severity-duration-frequency curves: APPLICATION OF COPULAS FOR DERIVATION OF DROUGHT S-D-F CURVES
journal, September 2011

  • Janga Reddy, M.; Ganguli, Poulomi
  • Hydrological Processes, Vol. 26, Issue 11
  • DOI: 10.1002/hyp.8287

Copula-based flood frequency (COFF) analysis at the confluences of river systems
journal, May 2009

  • Wang, Cheng; Chang, Ni-Bin; Yeh, Gour-Tsyh
  • Hydrological Processes, Vol. 23, Issue 10
  • DOI: 10.1002/hyp.7273

The Gumbel mixed model for flood frequency analysis
journal, December 1999


Frequency analysis via copulas: Theoretical aspects and applications to hydrological events: FREQUENCY ANALYSIS VIA COPULAS
journal, December 2004

  • Salvadori, G.; De Michele, C.
  • Water Resources Research, Vol. 40, Issue 12
  • DOI: 10.1029/2004WR003133

Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data: METAELLIPTICAL COPULAS AND FREQUENCY ANALYSIS
journal, September 2007

  • Genest, C.; Favre, A. -C.; Béliveau, J.
  • Water Resources Research, Vol. 43, Issue 9
  • DOI: 10.1029/2006WR005275

Comparison and evaluation of spatial interpolation schemes for daily rainfall in data scarce regions
journal, September 2012