Physically Based Dimensionless Features for Pluvial Flood Mapping With Machine Learning

Rapid delineation of flash flood extents is critical to mobilize emergency resources and to manage evacuations, thereby saving lives and property. Machine learning (ML) provides a promising solution for this rapid delineation, offering a computationally efficient alternative to high-resolution 2D flood models. However, even when trained on diverse geographic regions, ML models typically require retraining to perform well in new locations, and therefore often fail to generalize to never-before-seen conditions. To improve ML generalization, we apply Buckingham $\mathrm{\Pi }$ theorem to derive dimensionless terms across multiple spatial scales. These multiscale $\mathrm{\Pi }$ terms represent ratios of the relevant physical quantities governing the flooding process. Since the scaling laws of these dimensionless $\mathrm{\Pi }$ terms encode process similarity across physical scales, these $\mathrm{\Pi }$ terms enhance ML transferability to unseen locations. This is demonstrated by incorporating them as features in a logistic regression model for delineating flood extents. The features were calculated at different scales by varying accumulation thresholds for stream delineation. The ML flood maps, with an average AUC of 0.89, compared well with the results of 2D hydraulic models that are the basis of the Federal Emergency Management Agency flood hazard maps. The dimensionless $\mathrm{\Pi }$ features outperformed dimensional features, with some of the largest gains in the AUC (of 20%) occurring when the model was trained in one region and tested in another. Dimensionless and multi-scale $\mathrm{\Pi }$ 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.