Data assimilation to retrieve unknown bathymetry in shallow water model

Floods are among the most destructive and costly natural disasters. While risk assessment and management have helped mitigate their impact in recent decades, climate change is expected to increase both their frequency and severity. This underscores the urgent need for predictive tools to better anticipate and prevent the adverse effects of flooding. Two-dimensional Shallow-Water (SW) hydraulic models offer a reliable solution for flood prediction, providing critical information such as floodplain extent, water levels and flow velocities. However, these models require boundary conditions (such as input flows), precise topography and bathymetry (i.e. riverbed geometry) as well as parameters to be calibrated (such as terrain roughness.  Unfortunately, such data are often sparse or entirely unavailable in many regions due to the high cost and logistical challenges of in situ measurements. In particular, if the topography can be obtained using LiDAR acquisition of Numerical Terrain Models, the bathymetry remains unaccessible because LiDAR signal does not pass through the water surface.

In this context, Data Assimilation (DA)—a method that optimally combines uncertain models with observations—becomes particularly valuable for estimating such missing data or parameters. Our study proposes an innovative approach to reconstruct riverbed geometry by assimilating flood extent information derived from satellite imagery, specifically Synthetic Aperture Radar (SAR) data, which can reliably detect floodwater extents.

To account for observational uncertainty, we generate a probabilistic flood map from SAR images, where each pixel’s value represents its probability of being water, based on observed backscatter. Using a tempered particle filter (TPF), we assimilate multiple SAR-derived probabilistic flood maps into an ensemble of hydraulic simulations (referred to as "particles"). These simulations share the same model architecture but incorporate randomly sampled riverbed geometries. 

To evaluate our methodology, we conducted a synthetic twin experiment based on a real-world case study of the River Severn near Tewkesbury, UK—a region prone to frequent flooding. We first perform a hydraulic simulation (the "control run") using a reference riverbed geometry and realistic boundary conditions. From this simulation, we generate several synthetic probabilistic flood maps, which were then assimilated into a second simulation to estimate the riverbed geometry using the TPF.

Our results demonstrate the effectiveness of this approach: the estimated riverbed geometry closely matches the reference. Additionally, contingency maps reveal strong agreement between the flood extents predicted by the control run and those obtained through the DA experiment.