Pi theorem formulation of flood mapping

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.