Time-varying System Identification of Bedform Dynamics Using Modal Decomposition

Abstract

Measuring sediment transport in riverbeds has long been a challenging research problem in geomorphology and river engineering. Traditional approaches rely on direct measurements using sediment samplers. Although such measurements are often considered ground truth, they are intrusive, labor-intensive, and prone to large variability. As an alternative, sediment flux can be inferred indirectly from the kinematics of migrating bedforms and temporal changes in bathymetry. While such approaches are helpful, bedform dynamics are nonlinear and multiscale, making it difficult to determine the contributions of different scales to the overall sediment flux. Fourier decomposition has been applied to examine bedform scaling, but it treats spatial and temporal variability separately. In this work, we introduce Dynamic Mode Decomposition (DMD) as a data-driven framework for analyzing riverbed evolution. By incorporating this representation into the Exner equation, we establish a link between modal dynamics and net sediment flux. This formulation provides a surrogate measure for scale-dependent sediment transport, enabling new insights into multiscale bedform-driven sediment flux in fluvial channels.