Abstract. 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. Unfortunately, no standardized procedures exist for the determination of such ID thresholds, 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 length. Furthermore, we compared two methods for rainfall definition which consider both triggering and non-triggering events, 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 here 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 was used instead of a local one, with important implications for ID-threshold determination. Furthermore, 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 30-min maximum accumulated rainfall 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 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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高山流域的泥石流预测降雨阈值的局限性

摘要。泥石流的预测是相关的，因为这种自然灾害可能对人类和基础设施构成威胁。泥石流（和滑坡）预警系统通常依赖降雨强度持续时间（ID）阈值。不幸的是，目前尚无用于确定此类ID阈值的标准化程序，并且在其制定中常常缺少验证和不确定性评估。结果，更新，解释，概括和比较降雨阈值是具有挑战性的。使用瑞士高山流域（艾尔格拉本）的17年降雨记录和67条泥石流，我们确定了ID阈值和相关的不确定性，作为记录长度的函数。此外，我们比较了两种同时定义触发事件和非触发事件的降雨定义方法，基于线性回归和/或True Skill Statistic最大化。这些方法与众所周知的频频方法之间的主要区别在于，此处还考虑了非触发降雨事件以获取ID阈值参数。根据所采用的方法，ID阈值参数及其不确定性差异很大。我们发现，对于我们的研究站点，有25条泥石流足以将ID阈值参数的不确定性限制为±30％。如果使用区域滑坡数据集而不是本地滑坡数据集，我们进一步证明了这两种方法在预测性能方面的变化，这对确定ID阈值具有重要意义。此外，我们测试了ID阈值性能是否可以通过考虑其他降雨特性（例如先前的降雨，最大强度）在基于决策树（随机森林）的多元统计学习算法中。当将最大30分钟的最大累积降雨量添加到ID变量中时，达到了最高的预测能力，而在Illgraben的泥石流预测中考虑前期降雨并没有改善。尽管随机森林模型的预测性能增加很小，但是如果可以从测量或建模数据中获得更多预测变量，则这种框架对于将来的研究可能是有价值的。