Physically based model for gully simulation: application to the Brazilian semiarid region

Abstract

Abstract. Gullies lead to land degradation and desertification as well as increasing environmental and societal threats, especially in arid and semiarid regions. Despite this fact, there is a lack of related research initiatives. In an effort to better understand soil loss in these systems, we studied small permanent gullies, which are a recurrent problem in the Brazilian northeastern semiarid region. The increase in sediment connectivity and the reduction of soil moisture, among other deleterious consequences, endanger this desertification-prone region and reduce its capacity to support life and economic activities. Thus, we propose a model to simulate gully-erosion dynamics, which is derived from the existing physically based models of Foster and Lane (1983) and Sidorchuk (1999). The models were adapted so as to simulate long-term erosion. A threshold area shows the scale dependency of gully-erosion internal processes (bed scouring and wall erosion). To validate the model, we used three gullies that were over 6 decades old in an agricultural basin in the Brazilian state of Ceará. The geometry of the channels was assessed using an unmanned aerial vehicle and the structure from motion technique. Laboratory analyses were performed to obtain soil properties. Local and regional rainfall data were gauged to obtain sub-daily rainfall intensities. The threshold value (cross-section area of 2 m2) characterizes when erosion in the walls, due to loss of stability, becomes more significant than sediment detachment in the wet perimeter. The 30 min intensity can be used when no complete hydrographs from rainfall are available. Our model could satisfactorily simulate the gully-channel cross-section area growth over time, yielding a Nash–Sutcliffe efficiency of 0.85 and an R2 value of 0.94.