Can we tell more than we can know? The limits of bivariate drought analyses in the United States

Original Paper


The joint occurrence of extreme hydroclimatic events, such as simultaneous precipitation deficit and high temperature, results in the so-called compound events, and has a serious impact on risk assessment and mitigation strategies. Multivariate frequency analysis (MFA) allows a probabilistic quantitative assessment of this risk under uncertainty. Analyzing precipitation and temperature records in the contiguous United States (CONUS), and focusing on the assessment of the degree of rarity of the 2014 California drought, we highlight some critical aspects of MFA that are often overlooked and should be carefully taken into account for a correct interpretation of the results. In particular, we show that an informative exploratory data analysis (EDA) devised to check the basic hypotheses of MFA, a suitable assessment of the sampling uncertainty, and a better understanding of probabilistic concepts can help to avoid misinterpretation of univariate and multivariate return periods, and incoherent conclusions concerning the risk of compound extreme hydroclimatic events. Empirical results show that the dependence between precipitation deficit and temperature across the CONUS can be positive, negative or not significant and does not exhibit significant changes in the last three decades. Focusing on the 2014 California drought as a compound event and based on the data used, the probability of occurrence strongly depends on the selected variables and how they are combined, and is affected by large uncertainty, thus preventing definite conclusions about the actual degree of rarity of this event.


Bivariate frequency analysis Joint return periods Copulas Uncertainty Joint extreme events Drought Temperature Precipitation deficit Moisture conditions 



This work was partly supported by the Willis Research Network. The data used in this study are obtained from the web site: http://www. The author wishes to thank three anonymous reviewers for their remarks and constructive criticisms, and Prof. M. Bayani Cardenas (The University of Texas at Austin, US) for his useful comments on an earlier version of this paper. The analyses were performed in R (R Core Team 2013) by using the contributed packages Cairo (Urbanek and Horner 2011), CDVine (Schepsmeier and Brechmann 2012), copula (Yan 2007; Kojadinovic and Yan 2010), hdrcde (Hyndman et al. 2012), HH (Heiberger 2012), KernSmooth (Wand 2012), and lmom (Hosking 2014). The authors and maintainers of this software are gratefully acknowledged.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

477_2015_1124_MOESM1_ESM.pdf (2.6 mb)
Supplementary material 1 (pdf 2667 KB)


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Civil Engineering and GeosciencesNewcastle UniversityNewcastle Upon TyneUK
  2. 2.Willis Research NetworkLondonUK

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