Multi-zone small slope approximation on dune surface scattering

In this paper, a barchan surface is chosen as a geometrical model which has a enough high dune and could be divided into five zones where each facet has nearly similar normal vector. Then each zone has a average local normal vector which is different from others. The local incident wave vector and the local scattered wave vector of each zone are obtained by the local normal vector. The conventional small slope approximation could be applied in the local coordinate of each zone. Finally, the local scattered wave vectors of each zone are synthesized in the global coordinate. So we called the method "Multi-zone Small Slope Approximation". The results show that the cross-polarization could be obtained in the global incident plane and the reciprocity is proved by both similar cross-polarizations.