Rapid delineation of flash flood extents is critical to mobilize emergency resources and to manage evacuations, thereby saving lives and property. Machine learning (ML) approaches enable rapid flood delineation with reduced computational demand compared to conventional high-resolution, 2D flood models. However, existing ML approaches are limited by a lack of generalization to never-before-seen conditions. Here, we propose a framework to improve ML model generalization based on dimensionless, multi-scale features that capture the similarity of the flooding process across regions. The dimensionless features are constrained with the Buckingham $\Pi$ theorem and used with a logistic regression model for a probabilistic determination of flood risk. The features were calculated at different scales by varying accumulation thresholds for stream delineation. The modeled flood maps compared well with the results of 2D hydraulic models that are the basis of the Federal Emergency Management Agency (FEMA) flood hazard maps. Dimensionless features outperformed dimensional features, with some of the largest gains (in the AUC) occurring when the model was trained in one region and tested in another. Dimensionless and multi-scale features in ML flood modeling have the potential to improve generalization, enabling mapping in unmapped areas and across a broader spectrum of landscapes, climates, and events.

翻译：快速划定山洪淹没范围对于调动应急资源和实施疏散管理至关重要，这有助于挽救生命和财产。与传统的二维高分辨率洪水模型相比，机器学习方法能以更低的计算需求实现快速洪水范围划定。然而，现有机器学习方法因缺乏对未见条件的泛化能力而受到限制。本文提出一个基于无量纲多尺度特征的框架，以提升机器学习模型的泛化能力，这些特征能够捕捉不同区域洪水过程的相似性。无量纲特征通过白金汉π定理进行约束，并与逻辑回归模型结合使用，以实现洪水风险的概率性判定。通过改变用于河道划定的汇流阈值，在不同尺度上计算了这些特征。建模所得的洪水淹没图与作为联邦应急管理局洪水灾害图基础的二维水力学模型结果吻合良好。无量纲特征的表现优于有量纲特征，其中部分最显著的性能提升（以AUC衡量）出现在模型在一个区域训练而在另一区域测试时。在机器学习洪水建模中采用无量纲和多尺度特征有望增强模型的泛化能力，从而实现在未测绘区域的制图，并适用于更广泛的地貌、气候和事件类型。