Exploring the asymmetric dependence in hydrologic extremes

The issue of dependence and causality is fundamental for the study of compound events. Dependence measures are largely exploited in literature to study the interconnections among hazards and drivers. Classical dependence measures are symmetric, dependence in one direction is considered equal as the dependence in the other direction. Nevertheless, there are many situations in which there can exists a directionality on dependence. Considering the extremes in river network case study, there exists a physical link between upstream and downstream river sites, and this must be reflected in their dependence relationships. Upstream influences downstream more that in the other direction. In this work, we want to explore the concept of asymmetric dependence considering the extremes and the possible existing link with causality effects. A conditional version of the Kendall’s tau has been proposed and investigated to give some information about the directionality of the dependence.

As case study we use the UK river network considering daily discharge data and a POT analysis approach. Exploring the issue of asymmetry in the statistical pairwise dependence, it could provide a new tool/perspective to address the joint statistical behaviour of dependent variables.