Bathymetry Estimation in Complex River Morphology using UAV-based Remote Sensing and Physics-Informed Neural Networks Incorporating Secondary Flow Effects

Non-contact river monitoring is essential for understanding hydraulic phenomena and providing real-time disaster mitigation information during large-scale floods. Our previous research (Yorozuya et al., 2026) developed a method to inversely estimate riverbed elevation by integrating UAV-derived surface velocity (via PIV) and water surface geometry (via LiDAR) into a Physics-Informed Neural Networks (PINNs) framework using automatic differentiation of the governing equations. However, that approach relied on a uniform velocity correction factor across the entire reach, which led to significant underestimations of water depth in complex flow fields, such as those near spur dikes.

In this study, we propose an enhanced estimation algorithm that incorporates secondary flow effects into the momentum equations to improve bathymetric accuracy. Following the methodology of Iwasaki et al. (2013), we identify regions where surface velocity vectors exhibit curvature and account for the resultant increase in flow resistance. This approach aims to correctly identify water depth even in regions where surface velocities are low but hydraulic complexity is high.

Field experiments were conducted in a reach of the Kurobe River (bed slope ≈1/100, 20m wide by 50m long), characterized by a spur dike in the center of the domain. High-resolution water surface geometry and velocity fields were captured using a UAV-mounted LiDAR (DJI Zenmuse L2) and a photogrammetric camera (P1). These data were integrated into the PINNs loss functions, which were defined based on the continuity equation, the shallow water equations, and the conservation of discharge across cross-sections.

The results demonstrated a marked improvement in estimation reliability, particularly in the separation zones downstream of the spur dike. Without secondary flow considerations, the model estimated near-zero water depth in large wake vortices due to the low surface velocities. By incorporating secondary flow effects, the model correctly evaluated the increased apparent roughness due to flow curvature, yielding deeper and more accurate bathymetry consistent with ground-truth data obtained by boat-mounted ADCP. This study highlights the potential of using only UAV-based remote sensing to achieve high-precision bathymetric inversion in morphologically complex river environments.

Iwasaki, T., Shimizu, Y., and Kimura, I. (2013). An influence of modeling of secondary flows to simulation of free bars in rivers. Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering), Vol. 69, No. 3, 147–163.

Yorozuya et al. (2016) Seeing the unseen, RiverFlow2026 (Under review)