Path length and sediment transport estimation from DEMs of difference: a signal processing approach

The difficulties of measuring bedload transport in gravel-bed rivers have given rise to the morphological method wherein sediment transport can be inferred from changes in riverbed elevation and estimates of the distance traveled by sediment: its path length. Because current methods for estimating path length are time- and labor-intensive, we present a method to estimate a characteristic path length from repeat digital elevation models (DEMs of difference, i.e., DoDs). We propose an automated method to extract the spacing between erosional and depositional sites on the DoD by the application of variational mode decomposition (VMD), a signal processing method, to quantify the spacing as a proxy for path length. We developed this method using flume experiments where bed topography and sediment flux were measured and then applied it to published field data with physical path length measured from tracer measurements. Our sediment transport estimates were not significantly different than the measured sediment flux at lower discharges in the lab. However, we observed an underestimation of sediment flux at the higher discharges in the flume study. We interpret this as a limit of the method in confined settings, where sediment transport becomes decoupled from morphological changes. We also explore how the time between survey acquisitions, the morphological active width relative to the channel width, and DoD thresholding techniques affect the proposed method and the potential issues they pose for the morphological method in general.