Modeling the morphology of gully cross sections in the Yuanmou Dry-hot Valley

Characterizing gully cross sections (GCs) is essential for calculating the volume and erosion rate of the gully. However, little research has focused on modeling the morphology of GCs. This study investigated 456 GCs with a laser distance meter located at the mouth, middle, and head of 152 gullies in the Yuanmou Dry-hot Valley of China; mapped them with AutoCAD software; fitted them with 2nd-6th degree polynomial functions, and discussed the correlation between the coefficients and the morphology of GCs. The results showed that: (1) using a 2nd-degree polynomial function (y=ax(2)+bx+c) to describe the morphology of GCs produced a better result than other polynomial functions; (2) the coefficient a of 2nd-degree polynomial function was correlated with depth (r=-0.226, p<0.01), gradient (r=0.545, p<0.01), and activities; and (3) the symmetry axis (-b/2a) of 2nd-degree polynomial function increased with gully change from left-deflection to right-skewed, and the absolute value showed the asymmetrical degree (r=0.216, p<0.01). This study will not only help to understand the morphology and evolution of gullies, but will also provide a scientific basis for prevention of gully erosion.