Debris flow magnitudes: a global catalog

The episodic occurrence of debris flow events in response to stochastic precipitation and wildfire events makes hazard prediction challenging. Previous work has shown that frequency-magnitude distributions of non-fire-related debris flows follow a power law, but less is known about the distribution of post-fire debris flows. As a first step in parameterizing hazard models, we use frequency-magnitude distributions and cumulative distribution functions to compare volumes of post-fire debris flows to non-fire-related debris flows. Due to the large number of events required to parameterize frequency-magnitude distributions, and the relatively small number of post-fire event magnitudes recorded in the literature, we collected data on 73 recent post-fire events in the field. The resulting catalog of 988 debris flow events is presented as an appendix to this article. We found that the empirical cumulative distribution function of post-fire debris flow volumes is composed of smaller events than that of non-fire-related debris flows. In addition, the slope of the frequency-magnitude distribution of post-fire debris flows is steeper than that of non-fire-related debris flows, evidence that differences in the post-fire environment tend to produce a higher proportion of small events. We propose two possible explanations: 1) post-fire events occur on shorter return intervals than debris flows in similar basins that do not experience fire, causing their distribution to shift toward smaller events due to limitations in sediment supply, or 2) fire causes changes in resisting and driving forces on a package of sediment, such that a smaller perturbation of the system is required in order for a debris flow to occur, resulting in smaller event volumes.

泥石流（debris flow）事件随随机降水与野火事件间歇性暴发，这使得灾害预测工作极具挑战性。既往研究表明，非野火相关泥石流的频率-规模分布（frequency-magnitude distribution）服从幂律分布（power law），但目前学界对火后泥石流（post-fire debris flows）的分布特征仍缺乏充分认知。作为开展灾害模型参数化（parameterizing hazard models）的首要步骤，我们采用频率-规模分布与累积分布函数（cumulative distribution function），对比了火后泥石流与非野火相关泥石流的体积差异。由于构建频率-规模分布需要大量事件样本，而现有文献中记录的火后泥石流规模数据相对较少，我们通过野外调查收集了近期73起火后泥石流事件的相关数据。最终得到的包含988起泥石流事件的数据集目录，作为本文附录予以刊发。研究发现，火后泥石流体积的经验累积分布函数（empirical cumulative distribution function）所覆盖的事件规模，整体小于非野火相关泥石流的对应分布。此外，火后泥石流的频率-规模分布斜率较非野火相关泥石流更为陡峭，这表明火后环境的差异往往会催生更高比例的小型泥石流事件。我们提出两种可能的解释：其一，相较于未受野火影响的相似流域，火后泥石流的重现周期（return intervals）更短，受沉积物供给（sediment supply）限制，其分布整体向小型事件偏移；其二，野火会改变沉积物团块的抗阻力与驱动力（resisting and driving forces），使得泥石流触发所需的系统扰动（perturbation）阈值更低，进而导致事件体积偏小。