  We apply a mean-field model of interactions between migrating barchan dunes,
the CAFE model, which includes spontaneous 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 in the north circumpolar region of Mars, three swarms in Morocco, and
one in Mauritania, each containing more than 1000 bedforms. When the sizes of
bedforms are rescaled by the mean size in each zone two attractor states
appear, with the Tarfaya zones all displaying a common distribution and the
Martian and Mauritanian zones sharing a different distribution. Comparison of
these attractor states with the outputs of the CAFE model reveals that the
Tarfaya-type distribution results from a preference for aggregation and
fragmentation interactions whereas the Mars-Mauritania distribution is more
likely a result of exchange-dominated interactions. We observe that there
appears to be a greater number of collisions happening in Tarfaya than in the
other areas which is consistent with a greater rate of
aggregation-fragmentation processes as suggested by our model. Our comparison
with the CAFE model also predicts a universal rule for the outputs of the
different types of interactions with exchange interactions favouring the
production of two dunes roughly equal in size. Fragmentation interactions often
result in three bedforms with volumes approximately in the ratio 1:1:2.
Finally, we find that spontaneous calving of dunes does not play an important
role in shaping the size distributions in barchan swarms.
