Uncertainty estimation of regionalised depth–duration–frequency curves in Germany

Abstract. The estimation of rainfall depth-duration-frequency (DDF) curves is necessary for the design of several water systems and protection works. These curves are typically estimated from observed locations, but due to different sources of uncertainties, the risk may be underestimated. Therefore, it becomes crucial to quantify the uncertainty ranges of such curves. For this purpose, the propagation of different uncertainty sources in the regionalisation of the DDF curves for Germany is investigated. Annual extremes are extracted at each location for different durations (from 5mins up to 7days), and local extreme value analysis is performed according to Koutsoyiannis et al. (1998). Following this analysis, five parameters are obtained for each station, from which four are interpolated using external drift kriging, while one is kept constant over the whole region. Finally, quantiles are derived for each location, duration and given return period. Through a non-parametric bootstrap and geostatistical spatial simulations, the uncertainty is estimated in terms of precision (width of 95 % confidence interval) and accuracy (expected error) for three different components of the regionalisation: i) local estimation of parameters, ii) variogram estimation and iii) spatial estimation of parameters. First two methods were tested for their suitability in generating multiple equiprobable spatial simulations: sequential Gaussian simulations (SGS) and simulated annealing (SA) simulations. Between the two, SGS proved to be more accurate and was chosen for the uncertainty estimation from spatial simulations. Next, 100 realisations were run at each component of the regionalisation procedure to investigate their impact on the final regionalisation of parameters and DDFs curves, and later combined simulations were performed to propagate the uncertainty from the main components to the final DDFs curves. It was found that spatial estimation is the major uncertainty component in the chosen regionalisation procedure, followed by the local estimation of rainfall extremes. In particular, the variogram uncertainty had very little effect in the overall estimation of DDFs curves. We conclude that the best way to estimate the total uncertainty consisted of a combination between local resampling and spatial simulations, which resulted in more precise estimation at long observation locations, and a decline in precision at un-observed locations according to the distance and density of the observations in the vicinity. Through this combination, the total uncertainty was simulated by 10,000 runs in Germany, and indicated, that depending on the location and duration level, tolerance ranges from ±10–30 % for low return periods (lower than 10 years), and from ±15–60 % for high return periods (higher than 10 years) should be expected, with the very short durations (5min) being more uncertain than long durations.