A Novel Physically-Based Interpolation Method for Bathymetic Data

Resumen

Accurate Digital Terrain Models (DTMs) are essential for reliable two- and three-dimensional hydrodynamic and sediment transport modeling in rivers. These DTMs are typically derived from survey data, but full coverage of the modeling domain is rarely achieved. As a result, interpolation—or even extrapolation—of bathymetric data becomes necessary. Common interpolation methods, such as Inverse Distance Weighting (IDW) or Triangular Irregular Networks (TIN), are often used but can introduce unphysical artifacts that compromise model accuracy. Moreover, these methods do not support extrapolation in a systematic or physically meaningful way. This paper presents a novel physically-based interpolation technique for bathymetric data. The method involves solving the Shallow Water Equations (SWE) to obtain a tentative flow field, which is then used as input for a custom partial differential equation (PDE) solver implemented in OpenFOAM to propagate the surveyed bathymetric data. The process is applied iteratively: the flow field is updated using the latest bathymetry, and the bathymetry is updated using the new solution from the solver. Although computationally intensive, this approach produces artifact-free DTMs with minimal user intervention, making it particularly well-suited for river modeling applications.