Entropy-based Model for Gully Erosion - A combination of probabilistic and deterministic components

Gullies are a major threat to ecosystems, potentially leading to land degradation, groundwater depletion, crop loss, debris flow, and desertification. Gullies are also characterized by having a fast development and turning into primary sediment sources. Despite their impact, we have but scarce understanding of how gully erosion evolves and how to model it. In this paper, we propose a new gully erosion model that is based on the classical premise of net shear stress, i.e., hydraulic shear stress minus critical (resistant) shear stress, to calculate detachment rates. In order to calculate hydraulic shear stress, we developed a new equation derived from the principle of minimum cross-entropy; it was validated with laboratory measures from the literature with a Nash-Sutcliffe Efficiency of 0.95. Soil samples were analysed in the laboratory to assess critical shear stress and other soil properties. The novel gully erosion model was implemented in three gully impacted locations with catchment areas ranging from 10^-2 to 10⁺¹ ha. To assess channel geometry and eroded volumes, we used Unmanned Aerial Vehicle and Structure-from-Motion technique. The model successfully estimated long-term erosion rates, its efficiency was 0.77, and it is recommended for catchments up to 8 ha. Therefore, the new model provides planners and stakeholders with a tool to assess gully erosion, sediment yield and geometry in most areas.