Flood statistics with seasonal differentiated mixed distributions

在过去的几十年里，德国通过诸如DWAM-552这样的规则，在很大程度上标准化了通过年最大流量的极值统计来估计洪水概率。然而，Gumbel在1941年已经强调的将极值统计应用于年最大值的基本条件(样本是均匀的，即样本的每个值都服从相同的分布，并且事件的原因是相同的)并不满足。观测到的洪水事件的原因复杂多样。例如，由雨雪融化引起的洪水混合在一系列年最大流量中。结果表明，冬、夏季洪水具有不同的频率，可以用不同的分布函数来描述。洪水成因的季节性差异反映在不同大小洪水事件发生的季节性变化上，是流域洪情的一个重要特征。在洪水统计分析中加入这一特征可以减少其不确定性，并改进对极其罕见的洪水事件的概率估计。作为计划工作的一部分，将分析德国不同地区洪水的季节性。这一结果将被考虑在以混合分布对极大事件进行概率评估时。假定不同来源的洪水事件的分布函数可以通过季节差异分析来确定。不同的季节将由水文指标区分，这些指标是根据对观测到的洪水事件的分析得出的。季节洪水概率可以用不同的统计方法来描述，并最终组合成年最大值的分布。将比较几种用于计算季节性差异洪水统计的数学选项。通过考虑巴伐利亚州、图林根州和萨克森州的更大数量的集水区，将展示新开发的产生混合分布的方法的普遍性。由于计划中的研究工作，洪水统计分析的结果预计会有显著的改进。这一基础性研究成果将广泛应用于实践。

In the last decades the estimation of flood probabilities by extreme value statistics for annual maximum flows was largely standardized in Germany by rules such as the DWA M -552. However the basic conditions for the application of extreme value statistics to the annual maximum values which were already emphasized by Gumbel in 1941 (the sample is homogeneous, i.e. each value of the sample is subject to the same distribution, and the causes of the events are the same) are not satisfied. The causes of the observed flood events are complex and varied. E.g. floods, caused by rain and snowmelt are mixed within series of annual maximum flows. It can be shown that winter and summer floods have different frequencies, which can be described by different distribution functions. The seasonal differences in the flood genesis, which is reflected in the seasonal variability of the occurrence of flood events of different sizes, are an important feature of the flood regime of a catchment. An inclusion of this feature in flood statistical analyzes can reduce their uncertainty and improves the estimation of probabilities for extremely rare flood events. As part of the planned work the seasonality of floods in different German regions will be analyzed. The results will be taken into account in the probabilistic assessment of extremely large events by mixed distributions. It is assumed that distribution functions of flood events, which differ in their origins can be determined with the help of seasonal differentiated analyzes. The different seasons will be separated by hydrological indicators which are derived from analyses of observed flood events. The seasonal flood probabilities can be described by different statistical approaches and finally combined to distributions of annual maximum values . Several mathematical options for calculating seasonal differentiated flood statistics will be compared. By considering a larger number of catchments in Bavaria, Thuringia and Saxony the generality of the newly developed approaches for generation of mixed distributions will be demonstrated. A significant improvement of flood statistical analyzes is expected as a result of the planned research work. The results of this basic research will be widely applicable for practice.