Abstract
Abstract. Recent research on the bivariate flood peak/volume frequency analysis has mainly focused on the statistical aspects of the use of various copula models. The interplay of climatic and catchment processes in discriminating among these models has attracted less interest. In the paper we analyse the influence of climatic and hydrological controls on flood peak and volume relationships and their models, which are based on the concept of comparative hydrology in the catchments of a selected region in Austria. Independent flood events have been isolated and assigned to one of the three types of flood processes: synoptic floods, flash floods and snowmelt floods. First, empirical copulas are regionally compared in order to verify whether any flood processes are discernible in terms of the corresponding bivariate flood-peak relationships. Next the types of copulas, which are frequently used in hydrology are fitted, and their goodness-of-fit is examined in a regional scope. The spatial similarity of copulas and their rejection rate, depending on the flood type, region, and sample size are examined, too. In particular, the most remarkable difference is observed between flash floods and the other two types of flood. It is concluded that treating flood processes separately in such an analysis is beneficial, both hydrologically and statistically, since flood processes and the relationships associated with them are discernible both locally and regionally in the pilot region. However, uncertainties inherent in the copula-based bivariate frequency analysis itself (caused, among others, also by the relatively small sample sizes for consistent copula model selection, upper tail dependence characterization and reliable predictions) may not be overcome in the scope of such a regional comparative analysis.
Highlights
Bivariate distributions of flood peaks and flood event volumes may be needed for solving a range of practical problems, including, e.g., the design of retention basins and identifying the extent and duration of flooding in flood hazard zones
The relatively small number of events for such type of analysis in general and the differing number of events in the respective flood types in particular, may play a role in the fact, that the analysis has not brought really conclusive results. These are objective factors, which cannot be overcome in the framework of comparative hydrology, when using only data available in practice
Not much attention has been paid so far to directing a multivariate analysis of floods toward the selection of models for specific runoff generation processes. This issue was addressed in a regional context by the differentiation of the flood types into three categories
Summary
Bivariate distributions of flood peaks and flood event volumes may be needed for solving a range of practical problems, including, e.g., the design of retention basins and identifying the extent and duration of flooding in flood hazard zones. The use of copula-based multivariate models has become widespread. These allow for separate studies of the marginal distributions of the component variables and the correlation/dependence structure between them. Numerous studies have been published on this topic (e.g., Shiau, 2003; De Michele et al, 2005; Chowdhary et al, 2011; Requena et al, 2013), including recommendations how to select appropriate copula models (e.g., Favre et al, 2004; Genest and Favre, 2007). As mentioned by Chowdhary et al (2011), the use of copula-based multivariate distributions for hydrological design still cannot be regarded as having been satisfactorily resolved.
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