Assessment of the planimetric morphology of barchan dunes

•The curvature of Barchan parabolas were determined using mathematical modeling.•The relation between migration rates with morphological properties was determined.•The long term change of barchans shape was assessed.

Migration of sand dunes is accounted as one of the most important natural disasters in arid and desert regions. In this study, high resolution images are combined with field measurements in order to quantitatively study the migration and long term changes in the shape and morphology of barchans. The results indicated a power correlation between height and width of barchans (R2 ≈ 0.93). It also indicated that the outline of barchans can approximately be described by a parabola. Besides, the focal length, the curvatures (windward, leeward) and the brink parabola of the barchans were calculated; using differential geometry and mathematical modeling. Surprisingly, there was no significant difference between focal length and mean curvature of barchan parabola from 2001 to 2011 (p-value > 0.05). It seems the general shape of the studied barchans has not changed for long periods of time. The minimum and the maximum annual displacements of the barchans were 9 and 22 m, respectively, in the study area. It was also demonstrated that the best morphologic estimators for migration rate of dunes are in this order: width, mean curvature of windward parabola and height, focal length of windward parabola, and length.