Statistical models for bivariate extremal analysis of a spatial process

In the present paper different dependence measures are examined to investigate the structure of a spatial process of storm surges in the Dutch part of the North Sea. Four different dependence measures are implemented to the data: (1) the correlation coefficient as well as the Spearman (rank) correlation of the sample, (2) the transformation of the variables to determine the marginal distributions, (3) the dependence measures (chi, (chi) over bar) and (4) the coefficient of tail dependence eta. Two different approaches for modelling the threshold exceedances are examined, namely the implementation of bivariate extreme value models and the use of more general point process characterizations of extremal dependence. The strength of dependence appears to vary with the location as well as with the separation distance. It is also observed that the point process approach estimates are in general lower than those using the bivariate threshold exceedance models.