Modeling the spatial dependence of floods using the Fisher copula

Abstract

Abstract. Floods often affect not only a single location, but also 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 to propose a simple model that on the one hand 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 of multivariate data including elliptical copulas, R-vine copulas, and max-stable models. The comparison of the dependence structures of 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 was for a medium-sized catchment found to be a suitable model for the stochastic simulation of flood event sets at multiple gauged and ungauged locations.

Understanding dominant controls on streamflow spatial variability to set up a semi-distributed hydrological model: the case study of the Thur catchment

“…The Thur catchment has been the subject of several studies in the past: Gurtz et al (1999) performed the first modelling study on the entire catchment using a semi-distributed hydrological model; Abbaspour et al (2007) modelled hydrology and water quality using the SWAT model; Fundel et al (2013) and Jorg-Hess et al (2015) focused on low flows and droughts; Jasper et al (2004) investigated the impact of climate change on the natural water budget. Other modelling studies also include Melsen et al (2014Melsen et al ( , 2016, who investigated parameter estimation in data-limited scenarios and parameter transferability across spatial and temporal scales, and Brunner et al (2019), who studied the spatial dependence of floods. The Thur also includes a small-sized experimental subcatchment (Rietholzbach, called Mosnang in this paper after the name of the gauging station) that was the subject of many field studies at the interface between process understanding and hydrological modelling (e.g.…”

Flood hazard and change impact assessments may profit from rethinking model calibration strategies

“…Flood events are identified for each of the five time series (one observed, four simulated) using a peak-over-threshold (POT) approach similar to the one used in Brunner et al (2019aBrunner et al ( , 2020b. This approach consists of two main steps and results in two data sets each, which are used for the local and spatial analysis, respectively: (1) POT events in individual catchments and 2event occurrences across all catchments.…”

Spatial Dependence of Floods Shaped by Spatiotemporal Variations in Meteorological and Land‐Surface Processes

“…Despite the importance of understanding the spatial dependence of floods when deriving regional flood estimates, it has often been overlooked in practical applications and is not well understood. While the spatial dependence of precipitation has been investigated in several studies (e.g., Davison et al, 2012;Le et al, 2018;Thibaud et al, 2013;Touma et al, 2018), the spatial dependence of floods has been addressed in only a few studies primarily focused on modeling this spatial dependence under stationary conditions (Asadi et al, 2015;Bracken et al, 2016;Brunner et al, 2019;Diederen et al, 2019;Keef et al, 2009;Neal et al, 2013;Quinn et al, 2019). Asadi et al (2015) and Brunner et al (2019) have shown that the spatial dependence of floods at different locations decreases with the increase of the distance along the river network between these stations.…”