Analysis of inter-gauge dependence by Kendall’s τK, upper tail dependence coefficient, and 2-copulas with application to rainfall fields

Original Paper


The spatial dependence of rainfall is usually studied considering pairs of rain gauges and analysing the behaviour of Pearson’s correlation coefficient with respect to the distance between the two devices. However, this measure of linear dependence involves the underlying hypothesis that the data follow a bivariate normal distribution. When the data are skewed, as in the case of rainfall, a preliminary transformation is often performed in an attempt to obtain the required bivariate normality. This approach does not always guarantee satisfactory results, resulting in correlation estimator that exhibits bias and high variance. In this work, the inter-gauge dependence is studied by applying the alternative non-parametric Kendall’s rank correlation coefficient and the upper tail dependence coefficient. Exploiting the link between these two indices with copulas allows building an exploratory graphical method useful to drive the definition of a regional 2-copula suitable for the description of the data. Then, this copula is used to generalize the Shimizu’s bivariate mixed model, providing some freedom in the choice of the dependence structure and marginals. The analysis is performed on seven years of rainfall observations with 30-min time resolution collected by 35 gauges located in Central Italy. The effect of zero-measurements and several aggregation time scales are considered as well. Results of this study support some conclusions previously appeared in literature; mainly that only positive contemporaneous pairs of rainfall observations correctly describe the inter-site dependence.


Spatial dependence Zero values Upper tail dependence coefficient Kendall’s τK 2-copula 



The author whishes to thank S. Grimaldi. The reviewers and G. Villarini are acknowledged for their revisions, which greatly helped in improving the manuscript. Finally, the CNR-IRPI and the Umbria Regional Hydrometeorological Service are aknowledged for kindly providing the data.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dipartimento di Idraulica Trasporti e Strade“Sapienza” Università di RomaRomeItaly
  2. 2.H2CU - Honors Center of Italian Universities“Sapienza” Università di RomaRomeItaly

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