Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model

We apply a mean-field model of interactions between migrating barchan dunes, the CAFE model, which includes calving, aggregation, fragmentation, and mass-exchange, yielding a steady-state size distribution that can be resolved for different choices of interaction parameters. The CAFE model is applied to empirically measured distributions of dune sizes in two barchan swarms on Mars, three swarms in Morocco, and one in Mauritania, each containing ~1000 bedforms, comparing the observed size distributions to the steady-states of the CAFE model. We find that the distributions in the Martian swarm are very similar to the swarm measured in Mauritania, suggesting that the two very different planetary environments however share similar dune interaction dynamics. Optimisation of the model parameters of three specific configurations of the CAFE model shows that the fit of the theoretical steady-state is often superior to the typically assumed log-normal. In all cases, the optimised parameters indicate that mass-exchange is the most frequent type of interaction. Calving is found to occur rarely in most of the swarms, with a highest rate of only 9\% of events, showing that interactions between multiple dunes rather than spontaneous calving are the driver of barchan size distributions. Finally, the implementation of interaction parameters derived from 3D simulations of dune-pair collisions indicates that sand flux between dunes is more important in producing the size distributions of the Moroccan swarms than of those in Mauritania and on Mars.