Transport capacity and saturation mechanism in a real-space cellular automaton dune model

In a real-space cellular automaton dune model, individual physical processes such as erosion, deposition and transport are implemented by nearest neighbor interactions and a time-dependent stochastic process. Hence, the transport capacity, the saturation mechanism and the characteristic wavelength for the formation of dunes are emergent properties that can only be determined a posteriori from the output of the numerical simulations. Here we propose a simplified version of the model to establish asymptotic relations between the microscopic erosion-deposition-transport rate parameters and the characteristic length and time scales of the flux saturation mechanism. In particular, we show that, in the cellular automaton, the saturation length is a mean transport distance controlled by the deposition of mobile sedimentary cells. Then, we discuss how these results can be used to determine the sediment flux within dune fields and the rate parameters of a new class of discrete models that concentrate on the effect of heterogeneities in grain-size on dune morphodynamics.