The prediction of debris flows is relevant because this type of natural hazard can pose a threat to humans and infrastructure. Debris-flow (and landslide) early warning systems often rely on rainfall intensity–duration (ID) thresholds. Multiple competing methods exist for the determination of such ID thresholds but have not been objectively and thoroughly compared at multiple scales, and a validation and uncertainty assessment is often missing in their formulation. As a consequence, updating, interpreting, generalizing and comparing rainfall thresholds is challenging. Using a 17-year record of rainfall and 67 debris flows in a Swiss Alpine catchment (Illgraben), we determined ID thresholds and associated uncertainties as a function of record duration. Furthermore, we compared two methods for rainfall definition based on linear regression and/or true-skill-statistic maximization. The main difference between these approaches and the well-known frequentist method is that non-triggering rainfall events were also considered for obtaining ID-threshold parameters. Depending on the method applied, the ID-threshold parameters and their uncertainties differed significantly. We found that 25 debris flows are sufficient to constrain uncertainties in ID-threshold parameters to ±30 % for our study site. We further demonstrated the change in predictive performance of the two methods if a regional landslide data set with a regional rainfall product was used instead of a local one with local rainfall measurements. Hence, an important finding is that the ideal method for ID-threshold determination depends on the available landslide and rainfall data sets. Furthermore, for the local data set we tested if the ID-threshold performance can be increased by considering other rainfall properties (e.g. antecedent rainfall, maximum intensity) in a multivariate statistical learning algorithm based on decision trees (random forest). The highest predictive power was reached when the peak 30 min rainfall intensity was added to the ID variables, while no improvement was achieved by considering antecedent rainfall for debris-flow predictions in Illgraben. Although the increase in predictive performance with the random forest model over the classical ID threshold was small, such a framework could be valuable for future studies if more predictors are available from measured or modelled data.

中文翻译：

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基于高寒流域降雨的泥石流预测评价方法

泥石流的预测是相关的，因为这种类型的自然灾害会对人类和基础设施构成威胁。泥石流（和滑坡）预警系统通常依赖于降雨强度-持续时间 (ID) 阈值。存在多种竞争方法来确定此类 ID 阈值，但尚未在多个尺度上进行客观和彻底的比较，并且在其制定中经常缺少验证和不确定性评估。因此，更新、解释、概括和比较降雨阈值具有挑战性。使用瑞士高山集水区 (Illgraben) 17 年的降雨和 67 次泥石流记录，我们确定了 ID 阈值和相关不确定性作为记录持续时间的函数。此外，我们比较了两种基于线性回归和/或真实技能统计最大化的降雨定义方法。这些方法与众所周知的频率论方法之间的主要区别在于，还考虑了非触发降雨事件来获得 ID 阈值参数。根据所应用的方法，ID 阈值参数及其不确定性显着不同。我们发现 25 个泥石流足以将 ID 阈值参数的不确定性限制为±30% 用于我们的研究站点。我们进一步证明了如果使用具有区域降雨产品的区域滑坡数据集而不是具有局部降雨测量的局部滑坡数据集，这两种方法的预测性能会发生变化。因此，一个重要的发现是确定 ID 阈值的理想方法取决于可用的滑坡和降雨数据集。此外，对于本地数据集，我们测试了在基于决策树（随机森林）的多元统计学习算法中，是否可以通过考虑其他降雨特性（例如前期降雨、最大强度）来提高 ID 阈值性能。当峰值 30 分钟降雨强度添加到 ID 变量时，达到最高预测能力，而在 Illgraben 的泥石流预测中考虑前期降雨并没有取得任何改善。尽管随机森林模型对经典 ID 阈值的预测性能提高很小，但如果从测量或建模数据中可以获得更多预测因子，则这样的框架对于未来的研究可能很有价值。