Most available verification metrics for ensemble forecasts focus on univariate quantities. That is, they assess whether the ensemble provides an adequate representation of the forecast uncertainty about the quantity of interest at a particular location and time. For spatially indexed ensemble forecasts, however, it is also important that forecast fields reproduce the spatial structure of the observed field and represent the uncertainty about spatial properties such as the size of the area for which heavy precipitation, high winds, critical fire weather conditions, etc., are expected. In this article we study the properties of the fraction of threshold exceedance (FTE) histogram, a new diagnostic tool designed for spatially indexed ensemble forecast fields. Defined as the fraction of grid points where a prescribed threshold is exceeded, the FTE is calculated for the verification field and separately for each ensemble member. It yields a projection of a – possibly high-dimensional – multivariate quantity onto a univariate quantity that can be studied with standard tools like verification rank histograms. This projection is appealing since it reflects a spatial property that is intuitive and directly relevant in applications, though it is not obvious whether the FTE is sufficiently sensitive to misrepresentation of spatial structure in the ensemble. In a comprehensive simulation study we find that departures from uniformity of the FTE histograms can indeed be related to forecast ensembles with biased spatial variability and that these histograms detect shortcomings in the spatial structure of ensemble forecast fields that are not obvious by eye. For demonstration, FTE histograms are applied in the context of spatially downscaled ensemble precipitation forecast fields from NOAA's Global Ensemble Forecast System.

中文翻译：

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超越单变量校准：验证预报场集合中的空间结构

集成预测的大多数可用验证指标都集中在单变量数量上。也就是说，他们评估整体是否能在特定位置和时间提供足够的表示不确定性的预测不确定性。但是，对于以空间为索引的集合预报，预报字段重现观察到的字段的空间结构并表示有关空间特性的不确定性也很重要，例如不确定的区域，如暴雨，强风，重大火灾天气情况，等。在本文中，我们研究阈值超出（FTE）直方图的分数的特性，该特性是为空间索引的整体预报字段设计的一种新的诊断工具。定义为超出规定阈值的网格点的分数，FTE是针对验证字段计算的，并且是针对每个集合成员分别计算的。它产生了一个（可能是高维的）多元数量到单变量上的投影，可以使用标准工具（如验证等级直方图）进行研究。该投影很吸引人，因为它反映了在应用中直观且直接相关的空间属性，尽管尚不清楚FTE是否对集合中的空间结构的错误表示足够敏感。在全面的模拟研究中，我们发现偏离FTE直方图的均匀性确实与具有偏差的空间变异性的预报集合有关，并且这些直方图可以检测出肉眼看不到的整体预报场的空间结构缺陷。为了示范