Extensive spatio-temporal assessment of flood events by application of pair-copulas

Abstract

Abstract. Although the consequences of floods are strongly related to their peak discharges, a statistical classification of flood events that only depends on these peaks may not be sufficient for flood risk assessments. In many cases, the flood risk depends on a number of event characteristics. In case of an extreme flood, the whole river basin may be affected instead of a single watershed, and there will be superposition of peak discharges from adjoining catchments. These peaks differ in size and timing according to the spatial distribution of precipitation and watershed-specific processes of flood formation. Thus, the spatial characteristics of flood events should be considered as stochastic processes. Hence, there is a need for a multivariate statistical approach that represents the spatial interdependencies between floods from different watersheds and their coincidences. This paper addresses the question how these spatial interdependencies can be quantified. Each flood event is not only assessed with regard to its local conditions but also according to its spatio-temporal pattern within the river basin. In this paper we characterise the coincidence of floods by trivariate Joe-copula and pair-copulas. Their ability to link the marginal distributions of the variates while maintaining their dependence structure characterizes them as an adequate method. The results indicate that the trivariate copula model is able to represent the multivariate probabilities of the occurrence of simultaneous flood peaks well. It is suggested that the approach of this paper is very useful for the risk-based design of retention basins as it accounts for the complex spatio-temporal interactions of floods.

Modeling the spatial dependence of floods using the Fisher copula

“…The R-vine copula was thanks to its flexible structure able to reproduce the general dependence structure. This is in line with findings by Schulte and Schumann (2015), who worked with pair-copula constructions and found that the use of flexible Archimedean copulas allowed representation of spatial dependence in flood event data. This is essentially due to the fact that Archimedean copulas can model asymmetric lower and upper tail dependence, but they are only available for lower dimensions.…”

“…Spatial dependence was found to be important because no single event caused the maximum flood extent at all locations and assuming perfect correlation between tributaries overestimated flood hazard (Neal et al, 2013). A multivariate approach is therefore needed which represents the spatial dependence between floods from different watersheds (Schulte and Schumann, 2015) which might be radially asymmetric and show non-null tail dependence since more extreme events might be more strongly related than less extreme events. A multivariate approach should allow for the generation of stochastic event sets at multiple stations and for the consideration of the network structure of the catchment.…”

“…The spatial dependence of flood events at several locations has been assessed using different types of approaches comprising conditional exceedance models (Keef et al, 2013;Neal et al, 2013), hierarchical Bayesian models (Yan and Moradkhani, 2015), the multivariate skew-t distribution (Ghizzoni et al, 2010(Ghizzoni et al, , 2012, max-stable models (Wang et al, 2014), and copula models such as pair-copula constructions (Bevacqua et al, 2017;Gräler, 2014;Schulte and Schumann, 2015), hierarchical Kendall copulas (Fischer et al, 2017), and factor copula models (Lee and Joe, 2017). Maxstable and copula models are two classes of approaches which are well established in multivariate extreme value modeling and have been used in other contexts than those of floods.…”

“…Max-stable distributions arise out of the study of the limiting behavior of vectors of component-wise maxima. There exist a number of parametric max-stable models (Segers, 2012). The consideration of concomitance in annual maxima, however, only informs whether maxima tend to cooccur in the same year without accounting for their timing within a year (Blanchet et al, 2018).…”

Modeling the spatial dependence of floods using the Fisher copula

“…The R-vine copula was thanks to its flexible structure able to reproduce the general dependence structure. This is in line with findings by Schulte and Schumann (2015) who worked with pair copula constructions 5 and found that the use of flexible Archimedean copulas are able to represent spatial dependence in flood event data. This is essentially due to the fact that Archimedean copulas can model asymmetric lower and upper tail dependence but they are only available for lower dimensions.…”