Flood risk mapping and the attendant designation of hazard zones are an important issue facing hydrologists to ensure the safety of hydrological structures, and to protect lives, property, cultural landmarks, centres of economic activity and zones of environmental significance (Directive 2007/60/EC of the European Parliament). Resolving such questions has been largely based on an analysis of measured parameters associated with extreme flooding events (e.g. peak flow/discharge and flood timing on an annual basis). Supported by long-term measurements of these parameters, statistical methods employed in flood frequency analysis (FFA) allow engineers to calculate the return faah inhibitors (in years) of a particular maximum flood discharge (Qmax,f). This knowledge can then inform the selection of design floods for water management and, in particular, flood control structures, as well as aid in the design of flood hazard and risk zones. In turn, this can help various stakeholders manage water resources in a more effective and sustainable manner (e.g. Halbe et al., 2013; Halbe et al., 2014; Kolinjivadi et al., 2014; Straith et al., 2014; Inam et al., 2015; Butler and Adamowski, 2015).
Numerous studies have investigated the question of how to select the best probability distribution for a one dimensional (1D) random variable descriptive of peak flow during the most severe flood of a given year (Singh and Wang, 2005; Ferro and Porto, 2006; Stedinger and Griffis, 2008; Ciupak, 2013). However, in many engineering applications, the description of hydrological extreme events through a single parameter remains inadequate. When designing water management structures, it is imperative to take into account the long-term impact of peak flows on the safety, effectiveness and risk of failure of hydrological structures. This requires not only historic or predicted Qmax,f values, but also other parameters describing the flooding event, including the related parameters of flood volume (Vf) and flood duration (Tf). To address more complex flood-related water management and water engineering issues requires the analysis of a greater number of flood parameters (Ozga-Zielinska and Brzeziński, 1997), which necessitates the use of mathematical methods capable of describing multidimensional variables. Developed by a number of investigators (Krstanovic and Singh, 1987; Yue, 1999; Zhang, 2005), the classical approach to handling these issues requires the description of various natural phenomena and their extreme events (such as floods) to employ a multidimensional normal probability distribution.
The current development of state-of-the-art computational facilities (Nourani et al., 2014) allows for the application of new approaches, including the use of probability distributions constructed with copula functions (Song and Singh, 2010; Ciupak, 2011; Jeong et al., 2013; Bačová Mitková and Halmová, 2014; Saad et al., 2014). When several probability distributions co-occur, Heterogeneous nuclear (hn) RNA is necessary to develop selection criteria to assess which probability distribution best describes that of the random variable being tested.
Since the copula method considers more than one joint distribution function when estimating parameters of a multidimensional probability distribution, selecting the optimal copula function is crucial and requires one or more suitable classification criteria. These should be oriented towards assessing the goodness-of-fit between theoretical and empirical distributions in the latter’s tail region, where extreme values of flood characteristics are located, and which represent conditions when the largest flooding losses occur. The large number of copula functions currently documented in the literature (Chowdhary et al., 2011; Kuchment and Demidov, 2013; Lee et al., 2013; Li et al., 2014), as well as those currently being generated, provide a significant challenge to the selection of an optimal multidimensional probability distribution by hydrologists for a given flooding situation.