Comparing uncertainty propagation of different methods for regionalized IDF curves in Germany
Authors: Shehu Bora , Haberlandt Uwe 
Published: February 2023

Design extreme rainfall maps are essential for the construction of many water systems and works, and are typically achieved by regionalizing extreme rainfall statistics from ground-based observations. Different methods are used for such task, where the most popular are kriging and index-based regionalization. In a previous study conducted in Germany, Shehu et al. (2022) revealed that kriging with external drift performed better than index-based regionalization in terms of accuracy (smaller error obtained from cross-validation), however it is still unclear which of the method is superior in terms of precision (wideness of prediction intervals). As the risk may be underestimated due to different sources of uncertainty, a more certain method (in terms of narrower prediction intervals) is preferable (while maintaining a good accuracy). Therefore, the objective of this study is to investigate the propagation of different uncertainty sources for both kriging and index-based regionalization and compare these two in terms of precision and accuracy. To conduct this study, around 1200 ground-based observations at fine temporal scales (5min) from the German Weather Service (DWD) for whole Germany are employed. For each ground-based observation the annual maximum volumes at different durations (from 5mins up to 7days) are extracted, and local IDF curves are estimated according to Koutsoyiannis et al. (1998). For spatial uncertainty evaluation in the kriging system sequential Gaussian simulation (sGs) together will local sample bootstrapping are employed as shown in Shehu and Haberlandt (2022). On the other hand, the uncertainty in index-based regionalization is evaluated based on a combination of regional sample bootstrapping and spatial simulations of the index. The precision of IDF curves from both methods in terms of 95% confidence interval width is compared on a cross-validation procedure at the locations with more than 40 years of observation. &#160;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 and index-based regionalization. The comparison of the uncertainty in terms of precision sheds light on which method can produce narrower prediction intervals and hence is more precise in regionalizing IDF curves. Additionally, the accuracy of both methods is advised in order to discuss the advantages and disadvantages of each method for generating spatial IDF curves.References:&#160;Koutsoyiannis, D., Kozonis, D. and Manetas, A.: A mathematical framework for studying rainfall intensity-duration-frequency relationships, J. Hydrol., 206(1&#8211;2), 118&#8211;135, doi:10.1016/S0022-1694(98)00097-3, 1998.Shehu, B., Willems, W., Stockel, H., Thiele, L., and Haberlandt, U.: Regionalisation of Rainfall Depth-Duration-Frequency curves in Germany, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2022-118, in review, 2022.Shehu, B. and Haberlandt, U.: Uncertainty estimation of regionalised depth&#8211;duration&#8211;frequency curves in Germany, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2022-254, in review, 2022.