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.

Figures (7)

• Figure 2: Riverbed topography visualization. (a) Illustrates 2D topography at a specific time. (b) Spatial bed elevation profile along a selected transect (shown in red line in Figure 1(a)). (c) Spatio-temporal evolution of the riverbed topography. The figure also describes the dimensions of the data. (d) Temporal bed elevation profile along a selected point.
• Figure 3: Schematic showing how a two-dimensional bed elevation snapshot is stacked into a one-dimensional column vector for constructing the DMD data matrix.
• Figure 4: Semicircular distribution of DMD eigenspectra estimated from spatio-temporal bed elevation data. Due to symmetry, only the upper half of the unit circle is shown. The semicircle is partitioned into four regions based on period ranges. Here, $N$ denotes the number of eigenvalues within each region. Eigenvalues inside the unit semicircle are annotated with their individual periods, while those on the unit semicircle are color-coded according to period.
• Figure 5: Comparison of real river bed elevation and that of DMD reconstructed snapshot at a transect.
• Figure 6: (a) Comparison of the probability distribution function between the real river bed elevation and that of the DMD reconstructed. (b) Scatter plot correlation between the original riverbed elevation and that of the DMD reconstructed.