A process-based analysis of the suitability of copula types for peak-volume flood relationships

Abstract. The work aims at analyzing the bivariate relationship between flood peaks and flood volumes, with a particular focus on the type and seasonality of flood generation processes. Instead of the usual approach that deals with an analysis of the annual maxima of flood events, the current analysis includes all independent flood events in a catchment. Flood events are considered independent when they originate from distinguishably different synoptic/meteorological situations. The target region is located in the northern part of Austria, and consists of 72 small and mid-sized catchments. On the basis of the discharge measurements with a time resolution of 1 h from the period 1976–2007, independent flood events were identified and were assigned to one of the three following flood generation type categories: synoptic floods, flash floods and snowmelt floods. These were subsequently divided into two seasons, thereby separating predominantly rainfall-fed and snowmelt-fed floods. Nine frequently-used copula types were locally fitted to the samples of the flood type and seasonal data. Their goodness-of-fit was examined locally as well as analyzed in a regional scope. It was concluded that (i) treating flood processes separately is beneficial for the statistical analysis; (ii) suitability patterns of acceptable copula types are distinguishably different for the seasons/flood types considered, (iii) the Clayton and Joe copulas shows an unacceptable performance for all the seasons/flood types in the region; (iv) the rejection rate of the other copula types depends on the season/flood type and also on the sample size; (v) given that usually more than one statistically suitable dependence model exists, an uncertainty analysis of the design values in the engineering studies resulting from the choice of model seems unavoidable; (vi) reducing uncertainty in the choice of model could be attempted by a deeper hydrological analysis of the dependence structure between flood peaks and volumes in order to give hydrological support to the decision on model's suitability in specific regions and for typical flood generation mechanisms.