Process-based selection of copula types for flood peak-volume relationships in Northwest Austria: a case study

Abstract The case study aims at selecting optimal bivariate copula models of the relationships between flood peaks and flood volumes from a regional perspective with a particular focus on flood generation processes. Besides the traditional approach that deals with the annual maxima of flood events, the current analysis also includes all independent flood events. The target region is located in the northwest of Austria; it consists of 69 small and mid-sized catchments. On the basis of the hourly runoff data from the period 1976- 2007, independent flood events were identified and assigned to one of the following three types of flood categories: synoptic floods, flash floods and snowmelt floods. Flood events in the given catchment are considered independent when they originate from different synoptic situations. Nine commonly-used copula types were fitted to the flood peak - flood volume pairs at each site. In this step, two databases were used: i) a process-based selection of all the independent flood events (three data samples at each catchment) and ii) the annual maxima of the flood peaks and the respective flood volumes regardless of the flood processes (one data sample per catchment). The goodness-of-fit of the nine copula types was examined on a regional basis throughout all the catchments. It was concluded that (1) the copula models for the flood processes are discernible locally; (2) the Clayton copula provides an unacceptable performance for all three processes as well as in the case of the annual maxima; (3) the rejection of the other copula types depends on the flood type and the sample size; (4) there are differences in the copulas with the best fits: for synoptic and flash floods, the best performance is associated with the extreme value copulas; for snowmelt floods, the Frank copula fits the best; while in the case of the annual maxima, no firm conclusion could be made due to the number of copulas with similarly acceptable overall performances. The general conclusion from this case study is that treating flood processes separately is beneficial; however, the usually available sample size in such real life studies is not sufficient to give generally valid recommendations for engineering design tasks.