Estimation of joint return periods of compound precipitation-discharge extremes for small catchments

Abstract. Compound hydro-meteorological extreme events represent a simultaneous occurrence of extremes or one extreme triggering another. These events do not necessarily require extremes in any of the components, but their combination could lead to an extreme. This study brings insights on compound extremes from the watershed scale perspective by applying a multivariate distribution approach to estimate return periods of compound precipitation-discharge extremes. Main research question concerned the degree of the agreement between extremes in terms of joint return periods (JRP). Additionally, impacts of spatial generalization for copula functions (best-per-area) and outstanding extreme events were investigated and finally an attempt to correlate JRP with catchment characteristics was performed.

The study was elaborated using data of small catchments from 5 to 675 km² (with median value of 103 km²) in Saxony (Germany) interpolated on a 1 × 1 km grid. A specially designed block-maxima subset was defined to account for cases when the annual daily discharge and the annual daily precipitation maxima do not occur on the same day. 20 copulas were tested to find the one, which fits best-per-grid. Afterwards, the most frequent copula (best-per-area) was chosen to estimate JRP for compound extreme events. Additionally, a pool of the most frequent copulas for the study area was used to create an ensemble and calculate various quantiles of JRP. All chosen copulas have undergone two goodness-of-fit tests to account for the legitimacy of the approach, which result in very low percentage of rejection for both statistics.

Overall, the approach shows a good agreement between precipitation-discharge extremes and a high potential for a probabilistic instead of a deterministic analysis of JRP. For the investigated catchments, compound precipitation-discharge extremes are highly correlated. Large uncertainty in the estimation of the JRP was revealed by comparing different copulas. This uncertainty increases with larger non-exceedance probability of the compound event. Few spatial patterns with either very low or high anomalies of JRP were identified. A best-per-area distribution can be detected based on a frequency analysis of the best-per-grid distributions. Nevertheless, in case of time-series shortage it could be more compelling and reliable to create an ensemble of the most frequent copulas since it allows already a probabilistic instead of a deterministic estimation of JRP. It is concluded that outstanding extreme events, which occurred in 2002 and 2013 have a significant effect on the compound extreme statistics. Finally, the catchment response seems to be largely independent of size and mean elevation of the catchment, as no clear correlations between those and the corresponding JRP were found.