Uncertainty analysis of regionalized intensity-duration-frequency curves in Germany

Rainfall intensity-duration-frequency (IDF) curves are required for the design of several water systems and protection works. Typically, long (more than 40 years) station data are employed first to generate annual extremes (AMS) for different durations and then to fit a GEV probability distribution. Since station data are only point measurements, regionalization techniques are applied to estimate IDF curves at ungauged locations.  Prior results revealed that the best way to obtain IDF maps for Germany was kriging interpolation of parameters from very long stations with the parameters of the short stations acting as an external drift. However, how certain the obtained IDFs values are, and how to derive the uncertainty range at each location, remain still unanswered. Therefore, it is the objective of this study, to investigate the propagation of uncertainty in the regionalization of the IDF curves for Germany.

For this purpose, the available station data from the German Weather Service (DWD) for whole Germany are employed, which includes; 1100 sub-hourly (5min) recordings with observations period shorter than 20 years, and 89 sub-hourly (5min) recordings with 60-70 years of observations. Annual extremes are extracted at each location for different durations (from 5mins up to 7days), and local IDF curves are estimated according to Koutsoyiannis et al. (1998). The parameters of the obtained IDF functions are then interpolated using external drift kriging. Finally, quantiles are derived for each location, duration and given return period (Ta=2, 10, 20, 50 and 100 years). Through a non-parametric bootstrap, the uncertainty is estimated for three different components of the regionalization: i) local estimation of parameters, ii) variogram estimation and iii) spatial sampling distribution.  Simulated annealing is employed to ensure that the spatial resampling of locations represents the obtained variograms. The final uncertainty range is then considered as the 95% confidence interval of the obtained IDF curve for each location, duration and return period.      

The results of this study reveal how the uncertainty of annual rainfall extremes propagates from local estimation to the regionalization of IDF curves based on kriging theory. The comparison of the three components will shed light to the following questions: Which is the contribution of each component to the final uncertainty range of IDFs curve? How is the uncertainty range changing based on different durations and return periods? Are there any spatial trends in Germany regarding the uncertainty range of IDFs curves?