Group-based regionalization in flood frequency analysis considering heterogeneity

This dissertation deals with the problem of estimating the recurrence time of rare flood events, especially in the case of short data records. In such scenarios regional flood frequency analysis is used, a multi-step procedure with the goal of improving quantile estimates by pooling information across different gauging stations. Different aspects of regional flood frequency analysis using the Index Flood model are analysed, and improvements for parts of the procedure are proposed. In group-based regional flood frequency analysis sets of stations are built from which a similar flood distribution is assumed. In the Index Flood model, this means that the flood distributions of all stations are the same except for a site-specific scaling factor. Because the validity of this assumption is of crucial importance for the benefits of regionalization, it is commonly checked using homogeneity tests. After possible reassignments of stations to the groups, the information of records within a group is pooled and quantile estimates can be calculated by combination of a site-specific factor and a regional curve. Each of the main chapters of this dissertation focuses attention on specific steps of this procedure. The first main chapter investigates the known drawbacks of the commonly used homogeneity testing procedure of Hosking and Wallis based on L-moments. A new generalized procedure is proposed that uses copulas to model the intersite dependence and trimmed L-moments as a more robust replacement of L-moments. With these changes an improved detection rate in situations of medium to high skewness and in the case of cross-correlated data can be achieved. Another benefit is an increased robustness against outliers or extreme events. The second main chapter is more technical. The asymptotic distribution of sample probability-weighted moments is described in a setting of multiple sites of different record lengths. This theory is then extended to sample TL-moments and GEV parameter and quantile estimators based on them. An estimator for the limiting covariance matrix is given and analysed. The applicability of the theory is illustrated by the construction of a homogeneity test. This test works well when used with trimmed L-moments, but it needs a record length of at least 100 observations at each site to give acceptable error rates. The last main chapter deals with penalized Maximum-Likelihood estimation in flood frequency analysis as an alternative data pooling scheme. Under the assumption of generalized extreme value distributed data, the Index Flood model is translated to restrictions on the parameter space. The penalty term of the optimization problem is then chosen to reflect those restrictions and its influence can be controlled by a hyperparameter. The hyperparameter choice can be automated by a cross-validation which leads to a procedure that automatically finds a compromise between local and regional estimation. This is especially useful in situations in which homogeneity is unclear. A~simulation study indicates that this approach works nearly as good as pure regional methods if the homogeneity assumption is completely true and better than its competitors if the assumption does not hold. Overall, this dissertation presents different approaches and improvements to steps of a group-based regionalization procedure. A special interest is the assessment of the homogeneity of a given group that is analysed with two different approaches. However, due to short record lengths or limitations in the homogeneity testing procedures, heterogeneous groups are often still hard to detect. In such situations the presented penalized Maximum-Likelihood estimator can be applied that gives comparatively good results both in homogeneous and heterogeneous scenarios. However, application of this estimator does not supersede the group building steps, since the benefit of regionalization is highest if the homogeneity assumption is fulfilled