Multivariate skew-t approach to the design of accumulation risk scenarios for the flooding hazard

The multivariate version of the skew-t distribution provides a powerful analytical description of the joint behavior of multivariate processes. It enjoys valuable properties: from the aptitude to model skewed as well as leptokurtic datasets to the availability of moments and likelihood analytical expressions. Moreover, it offers a wide range of extremal dependence strength, allowing for upper and lower tail dependence. The idea underneath this work is to employ the multivariate skew-t distribution to provide an estimation of the joint probability of flood events in a multi-site multi-basin approach. This constitutes the basis for the design and evaluation of flood hazard scenarios for large areas in terms of their intensity, extension and frequency, i.e. those information required by civil protection agencies to put in action mitigation strategies and by insurance companies to price the flooding risk and to evaluate portfolios. Performances of the skew-t distribution and the corresponding t copula function, introduced to represent the state of the art for multivariate simulations, are discussed with reference to the Tanaro Basin, North-western Italy. To enhance the characteristics of the correlation structure, three nested and non-nested gauging stations are selected with contributing areas from 1500 to 8000 km2. A dataset of 76 trivariate flood events is extracted from a mean daily discharges database available for the time period from January 1995 to December 2003. Applications include the generation of multivariate skew-t and t copula samples and models' comparison through the principle of minimum cross-entropy, here revised for the application to multivariate samples. Copula and skew-t based scenario return period estimations are provided for the November 1994 flood event, i.e. the worst on record in the 1801–2001 period. Results are encouraging: the skew-t distribution seems able to describe the joint behavior, being close to the observations. Marginal distributions derived from the skew-t multivariate fit are comparable to the observed ones, and the model is also able to describe the tail behavior.