Specification of the design snow loads for gable roofs based on a consistent probabilistic approach

关于气候行动的编码的基本任务之一是根据对单个站的观测，在全区范围内规定设计值。估计值的统计稳定性很大程度上取决于系综的大小。对于每个单站的估计和地统计内插都是如此，即单站集合的观测值抽样越多，用作地统计内插的输入的站越多，结果的统计稳定性就越高。对于德国的224个站点，可以直接根据观测到的水当量进行极值统计，平均可用37年。发展的概率等效雪密度模型与使用独立事件而不是年极值的新方法相结合，产生了相当大的集合规模，平均有130个条目。通过将单站模型转换为区域模型，可以对另外525个站进行分析，这些站只提供对积雪覆盖高度的观测。进一步的改进，即减少统计不确定性，是通过引入超站来获得的，这些超站按照一致的概率策略组合来自单站的观测。然后，可以用足够的统计稳定性来识别分布的类型。该项目的目的是在积雪荷载极值统计的范围内利用观测到的积雪高度数据，并对相应的设计值进行统计优化。这需要一个一致的策略来检测非常罕见的事件中的离群值。欧洲雪负荷研究中使用的实际策略不太合适，因为太多事件没有被检测到，大量事件被错误地归类为异常值。该项目的目的是开发和应用一种改进的策略，特别是考虑到像BLUE这样的无偏估计者。因此，以概率一致的方式分析真正的异常值成为可能。屋面积雪的大小和空间分布很大程度上取决于风速。德国的雪风气候可细分为三种基本类型。I类显示了大雪载荷下几乎确定的风速值。然后，可以在一期工程开发的荷载模型上指定形状参数。第二类以散射风速为特征，这需要扩展基本的卷积积分。只有III类风暴和降雪同时发生。然后，这两种气候行为需要一致的组合规则。

One of the basic tasks of codification in regard to climatologic actions is the area-wide specification of the design values based on observations for single stations. The statistical stability of the estimated values greatly depends on the ensemble size. This is true for the estimates of each single station as well as for the geostatistical interpolation, i.e. the more observations are sampled for the single station ensembles and the more stations are used as input for the geostatistical interpolaten the higher is the statistical stability of the results. For 224 stations in Germany, extreme value statistics can be performed directly based on the observed water equivalents, which are available on average for 37 years. The developed probabilistically equivalent snow density model in combination with the new approach of using independent events instead of yearly extremes leads to considerable larger ensemble sizes with 130 entries on average. The translation of the single station model to regional models allows analysing a further 525 stations which provide only observations of the height of the snow cover. A further improvement, i.e. a reduction of the statistical uncertainties, is obtained by introducing super-stations which combine observations from single stations following a consistent probabilistic strategy. Then, the type of distribution can be identified with a sufficient statistical stability. Aim of the project is the utilization of the observed snow height data in the scope of the extreme value statistics of the snow loads and the statistical optimal specification of the corresponding design values. This requires a consistent strategy for the detection of outliers in terms of very rare events. The actual strategy used in the European snow load research is less appropriate, since too many events are not detected and a large number of events are erroneously classified as outlier. Aim of the project is the development and application of an improved strategy, which especially considers unbiased estimators like BLUE. Thus, it becomes possible to analyse true outliers in a probabilistic consistent way. The accumulation and spatial distribution of snow on roofs greatly depends on the wind speed. The snow-wind climate of Germany can be sub-divided into three basic types. Type I shows for large snow loads virtually deterministic wind speed values. Then, the shape parameters can be specified on the load model which has been developed in the first period of the project. Type II features scattering wind speeds, which requires extensions of the basic convolution integrals. Only for type III storm and snow occur simultaneously. Then, consistent combination rules are required for these two climatologic actions.