  We propose a dynamical model for the erosive growth of a channel in a
granular medium driven by subsurface water flow. The model is inferred from
experimental data acquired with a laser-aided imaging technique. The evolution
equation for transverse sections of a channel has the form of a non-locally
driven Burgers equation. With fixed coefficients this equation admits an
asymptotic similarity solution. Ratios of the granular transport coefficients
can therefore be extracted from the shape of channels that have evolved in
steady driving conditions.
