Natural Hazards

, Volume 68, Issue 2, pp 791–807 | Cite as

Estimating storm surge intensity with Poisson bivariate maximum entropy distributions based on copulas

  • Shanshan Tao
  • Sheng Dong
  • Nannan Wang
  • C. Guedes Soares
Original Paper


This paper introduces four kinds of novel bivariate maximum entropy distributions based on bivariate normal copula, Gumbel–Hougaard copula, Clayton copula and Frank copula. These joint distributions consist of two marginal univariate maximum entropy distributions. Four types of Poisson bivariate compound maximum entropy distributions are developed, based on the occurrence frequency of typhoons, on these novel bivariate maximum entropy distributions and on bivariate compound extreme value theory. Groups of disaster-induced typhoon processes since 1949–2001 in Qingdao area are selected, and the joint distribution of extreme water level and corresponding significant wave height in the same typhoon processes are established using the above Poisson bivariate compound maximum entropy distributions. The results show that all these four distributions are good enough to fit the original data. A novel grade of disaster-induced typhoon surges intensity is established based on the joint return period of extreme water level and corresponding significant wave height, and the disaster-induced typhoons in Qingdao verify this grade criterion.


Poisson bivariate maximum entropy distribution Typhoon-induced storm surge Disaster intensity Joint period Water level Significant wave height 



Univariate maximum entropy distribution


Bivariate maximum entropy distributions


Bivariate maximum entropy distributions with normal copula


Bivariate maximum entropy distributions with Gumbel–Hougaard copula


Bivariate maximum entropy distributions with Clayton copula


Bivariate maximum entropy distributions with Frank copula


Equivalent bivariate maximum entropy distribution


Poisson bivariate compound extreme value distribution


Poisson–Gumbel mixed compound distribution


Poisson bivariate compound maximum entropy distribution


Method of moments


Empirical curve-fitting method


Maximum likelihood method


Poisson normal bivariate maximum entropy distribution


Poisson Gumbel–Hougaard bivariate maximum entropy distribution


Poisson Clayton bivariate maximum entropy distribution


Poisson Frank bivariate maximum entropy distribution



The study was partially supported by the National Natural Science Foundation of China (51279186), the National Program on Key Basic Research Project (2011CB013704) and the Program for New Century Excellent Talents in University (NCET-07-0778).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Shanshan Tao
    • 1
  • Sheng Dong
    • 1
  • Nannan Wang
    • 1
  • C. Guedes Soares
    • 2
  1. 1.College of EngineeringOcean University of ChinaQingdaoChina
  2. 2.Centre for Marine Technology and Engineering (CENTEC), Instituto Superior TécnicoTechnical University of LisbonLisbonPortugal

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