A physically informed domain-independent data-driven inundation forecast model

Inundation maps with spatial and temporal distribution of the water depths are essential for protecting the population in case of pluvial flood events. Creating these maps in operational forecasting is currently not possible with traditional physically-based numerical models, as these are too slow for real-time predictions. Data-driven models are able to produce predictions in real-time, however, due to their domain-specific training, they are only applicable to the respective study site. Therefore, in this study, we propose a physically informed data-driven forecast system to overcome this limitation and provide spatial and temporal forecasts of water depth inundations in unknown areas. Our data-driven model is developed based on data from the catchment of Baiersdorf in Germany. It follows a Convolutional Neural Network (CNN) based on an image-to-image translation process and is trained on various flood-influencing factors, which represent catchment characteristics. We proposed a specific spatiotemporal prediction framework that: (1) enables temporal time-stepping of 10 min, higher than physically based hydraulic models with seconds, (2) data-driven domain-independent forecasts, tested on 23 unknown areas by a cross-validation, and (3) eliminates the need for downsampling for larger catchments (typical of data-driven forecast systems). Further, we integrate a 2-dimensional continuity equation together with a kinematic wave formulation for estimating the velocity in the loss function to enforce physically informed forecasts. Results on unknown areas produce Critical Success Index (CSI) values of about 74 % and mean Root Mean Squared Error (RMSE) values of 0.045 m. Our physically informed loss function was able to outperform a classical data-driven loss function and improved the RMSE by about 25 %.