Moving graphs: Predicting barchan dune migration rates from their shapes

In this study, geometric perspectives on sand dune formation and motion are summarized, introduced, and combined to predict time-averaged velocities (migration rates) of barchan dunes directly from their shapes. First, it is proposed that smaller sediment accumulations outpace larger ones due to differences in surface-to-volume ratio. This ratio is defined by a bedform’s wavelength and its wind-facing gradient, implying that relatively fast-moving, flat sediment volumes will be preferentially moved away to reveal slower-moving, tilted morphologies like ripple and dune-covered surfaces. Second, a power balance between wind shear and dune motion is used to show that dunes with a higher sediment flux tend to be steeper. As the size and steepness of dunes can be measured from satellite images, the aforementioned relationships can be combined to predict a barchan dune’s speed directly from its geometry. The prediction is tested against satellite image time-series from nine active dunefields worldwide and is thereby shown to be universally accurate, making it the first successful prediction of its kind: R² = 0.92, P = 2.0e-122, n = 250. In addition to understanding dune migration rates, this study also provides insights into the horned barchan and mirrored parabolic dune shapes, as well as the relationship between sediment flux and wind shear, supporting the splash-dominated model of particle entrainment.