Physics-guided deep learning for radar rainfall nowcasting in flash-flood early warning: Lead-time skill and an illustrative utility proxy

Urban flash floods can be triggered by highly localised convective storms, for which 10–60 minutes of additional warning can materially affect emergency response. We study short-lead radar rainfall nowcasting over Amsterdam using 5 min KNMI radar composites (Oct 2024–Jan 2025). We construct 12 × 12 input–output sequences (60 min → 60 min) on a 200 × 200 pixel tile and compare a standard data-driven U–Net with a physics-guided variant that uses the same architecture but is trained with an additional physics-inspired regulariser. Specifically, we augment the baseline objective with a masked smoothness (TV-like) penalty on spatial gradients of predicted rain-rate fields in linear units, applied only over rainy pixels to encourage spatial coherence and reduce isolated artefacts. Models are trained in log(1 + R ) and evaluated in physical units (mm/h) on a held-out test set. On the test set, the physics-guided model improves continuous accuracy and threshold-based event detection relative to the baseline U–Net, and it also outperforms an Eulerian persistence benchmark. At τ = 0.1 mm h −1 it reduces the false-alarm ratio and increases the critical success index (CSI) while maintaining high recall; at the flood-relevant threshold τ = 1 mm h −1 it increases CSI and recall while reducing false alarms. Lead-time curves over 5–60 minutes show consistent gains, with the largest improvements at intermediate horizons (approximately 25–40 minutes) where baseline skill degrades most rapidly. Overall, the results indicate that a lightweight physics-inspired smoothness regulariser can improve the coherence and flood-threshold skill of radar rainfall nowcasts at actionable lead times without increasing inference-time cost. Code is available at https://github.com/katsiaryna-bahamazava/flash-flood-nowcasting .