  Barchan dunes emerge as a collective phenomena involving the generation of
thousands of them in so called barchan dune fields. By measuring the size and
position of dunes in Moroccan barchan dune fields, we find that these dunes
tend to distribute uniformly in space and follow an unique size distribution
function. We introduce an analyticalmean-field approach to show that this
empirical size distribution emerges from the interplay of dune collisions and
sand flux balance, the two simplest mechanisms for size selection. The
analytical model also predicts a scaling relation between the fundamental
macroscopic properties characterizing a dune field, namely the inter-dune
spacing and the first and second moments of the dune size distribution.
