A regional comparative analysis of empirical and theoretical flood peak-volume relationships

Abstract

This paper analyses the bivariate relationship between flood peaks and corresponding flood event volumes modelled by empirical and theoretical copulas in a regional context, with a focus on flood generation processes in general, the regional differentiation of these and the effect of the sample size on reliable discrimination among models. A total of 72 catchments in North-West of Austria are analysed for the period . From the hourly runoff data set, 25 697 flood events were isolated and assigned to one of three flood process types: synoptic floods (including long-and short-rain floods), flash floods or snowmelt floods (both rain-on-snow and snowmelt floods). The first step of the analysis examines whether the empirical peak-volume copulas of different flood process types are regionally statistically distinguishable, separately for each catchment and the role of the sample size on the strength of the statements. The results indicate that the empirical copulas of flash floods tend to be different from those of the synoptic and snowmelt floods. The second step examines how similar are the empirical flood peak-volume copulas between catchments for a given flood type across the region. Empirical copulas of synoptic floods are the least similar between the catchments, however with the decrease of the sample size the difference between the performances of the process types becomes small. The third step examines the goodness-of-fit of different commonly used copula types to the data samples that represent the annual maxima of flood peaks and the respective volumes both regardless of flood generating processes (the traditional engineering approach) and also considering the three process-based classes. Extreme value copulas (Galambos, Gumbel and Hüsler-Reiss) show the best performance both for synoptic and flash floods, while the Frank copula shows the best performance for snowmelt floods. It is concluded that there is merit in treating flood types separately when analysing and estimating flood peak-volume dependence copulas; however, even the enlarged dataset gained by the process-based analysis in this study does not give sufficient information for a reliable model choice for multivariate statistical analysis of flood peaks and volumes.

Flood type classification and assessment of their past changes across Europe

“…Gaál et al (2012Gaál et al ( , 2015 and Szolgay et al (2016) found similar results when they 20 analyzed durations of flood events across Austria. They found that the flood event duration consistently increases with increasing snow-to-rainfall ratio of the process leading to the event despite the diversity of the non-climate catchment characteristics that have impact on the flood generation process that affect the flood event duration.…”

A New Framework for Exploring Process Controls of Flow Duration Curves

“…where F Q f ;Q s q f ; q s is the joint CDF of fast flow and slow flow; F Q f q f is the CDF of fast flow; F Q s q s ð Þ is the CDF of slow flow; and C is a copula function which quantifies the joint CDF of fast flow and slow flow as a function of F Q f q f and F Q s q s ð Þ. Copulas have been applied for characterizing complex hydrological events such as floods through a small number of dependent variables such as flood peak, volume, and duration (Favre et al, 2004;Grimaldi & Serinaldi, 2006;Salvadori & De Michele, 2004;Szolgay et al, 2016;Zhang & Singh, 2007). Kao and Govindaraju (2008) applied a trivariate copula to characterize the temporal distribution of extreme rainfall.…”

Joint probability analysis of flood hazard at river confluences using bivariate copulas

“…Volpi and Fiori [2] used Gumbel-Hougaard copulas to model dependency between peak and volume in flood analysis; Gräler et al [1] used synthetic dataset to show difference in performance of 2D and 3D copulas for various combinations of hydrologic variables; Xu et al [5] compared four Archimedean family copulas for derivation of a design flood hydrograph; Bender et al [14] used Gumbel copula for bivariate analysis of concurrent flows at a river confluence, and Bender et al [15] continued to investigate bivariate analysis of discharges on confluences, investigating sites where floods do not occur simultaneously. Szolgay et al [16] evaluated applicability of different copula types to a peakvolume flood relationship over a large region in Austria and its sub-catchments, and also studied the influence of the data series length on bivariate copula performance. Sraj et al [17] compared three copula families for bivariate flood frequency analysis in the Sava River basin in Slovenia, and the results obtained by Ozga-Zielinski et al [18] showed that the Gumbel-Hougaard copula yields better results compared to Gaussian copula for snowmelt floods.…”