Modeling the spatial dependence of floods using the Fisher copula

Abstract

Abstract. Floods do often not only affect a single location but a whole region. Flood frequency analysis should therefore be undertaken at a regional scale which requires the considerations of the dependence of events at different locations. This dependence is often neglected even though its consideration is essential to derive reliable flood estimates. A model used in regional multivariate frequency analysis should ideally consider the dependence of events at multiple sites which might show dependence in the lower and/or upper tail of the distribution. We here seek at proposing a simple model that on the one hand 5 considers this dependence with respect to the network structure of the region and on the other hand, allows for the simulation of stochastic event sets at both gauged and ungauged locations. The new Fisher copula model is used for representing the spatial dependence of flood events in the nested Thur catchment in Switzerland. Flood event samples generated for the gauged stations using the Fisher copula are compared to samples generated by other dependence models allowing for modeling multivariate data including elliptical copulas, R-vine copulas, and max-stable models. The comparison of the dependence structures of 10 the generated samples shows that the Fisher copula is a suitable model for capturing the spatial dependence in the data. We therefore use the copula in a way such that it can be used in an interpolation context to simulate event sets comprising gauged and ungauged locations. The spatial event sets generated using the Fisher copula well capture the general dependence structure in the data and the upper tail dependence, which is of particular interest when looking at extreme flood events and when extrapolating to higher return periods. The Fisher copula is therefore a suitable model for the stochastic simulation of flood 15 event sets at multiple gauged and ungauged locations.

Copula geoadditive modelling of anaemia and malaria in young children in Kenya, Malawi, Tanzania and Uganda

“…An advantage of the copula approach to joint modelling is that the selection of the copula for modelling the dependence between the outcomes is independent of the choice of the marginal distributions [ 35 ]. Several different types of copulas exist, of which the most common are discussed in [ 36 ] and [ 37 ].…”

Dynamical systems theory sheds new light on compound climate extremes in Europe and Eastern North America

“…Statistical models thus rely heavily on extrapolation. A wide range of techniques have been proposed to study compound extremes, ranging from multivariate extreme value statistical models based on copula assumptions (e.g., Shiau, ; Bevacqua et al ., ; Lee and Joe, ; Brunner et al, ), to max‐stable models (e.g., Wang et al ., ; Oesting and Stein, ), conditional exceedance models (e.g., Keef et al ., ; ; Neal et al ., ; Zheng et al ., ; Speight et al ., ), Bayesian models (Kuczera, ; Madadgar and Moradkhani, ; Yan and Moradkhani, ; Kwon et al ., ) and the multivariate skew‐ t distribution (Ghizzoni et al ., ; ). All these approaches can provide only partial information about the chaotic and spatial behaviour of the atmosphere.…”

How Probable Is Widespread Flooding in the United States?

“…However, information on the relationship between threshold and impact is often not available, especially not at a large spatial scale. We therefore use a threshold, which is based on the annual maximum series similar to the approach used by Brunner, Furrer, & Favre, (2019) and by Brunner, Gilleland, et al (2020). We vary this threshold to extract events more extreme than annual maxima and biannual maxima.…”

“…The latter is crucial to make them useful for the analysis of widespread events and their probabilities. So far, three main modeling approaches have been proposed, which enable consideration of spatial dependencies: (1) indirect, continuous modeling approaches (corresponding to discrete‐time models in the stochastic literature) simulating continuous streamflow series by combining a stochastic weather generator with a hydrological model (Winter et al, 2019); (2) indirect, event‐based modeling approaches simulating flood events for specific rainfall events generated using spatially dependent intensity‐duration‐frequency curves allowing for extreme rainfall of different durations at different locations (Le et al, 2019); and (3) direct, event‐based approaches enabling the direct generation of flood events by employing spatial extreme value models such as the conditional exceedance model by Heffernan and Tawn (2004) (Diederen et al, 2019; Keef et al, 2013), hierarchical Bayesian models (Yan & Moradkhani, 2015), the multivariate skew‐ t distribution (Ghizzoni et al, 2010; 2012), or copula‐based approaches including pair‐copula constructions (Bevacqua et al, 2017; Schulte & Schumann, 2015), Student‐t copulas (Ghizzoni et al, 2012), dynamical conditional copulas (Serinaldi & Kilsby, 2017), or the Fisher copula (Brunner, Furrer, & Favre, 2019). All types of approaches have their advantages and disadvantages.…”