Dynamic and static models of gully erosion

The main causes of gully formation are anthropogenic factors: the clearing of native forests, tilling of fallow lands and associated change of the hydrological conditions in the rainfall–runoff system. Gully channels formation is very rapid during the period of gully initiation, when morphological characteristics of a gully (length, depth, width, area, and volume) are far from stable. This period is relatively short, about 5% of a gullyʹs lifetime. For the most part of a gullyʹs lifetime, its size is near stable, maximum value. These two stages of gully development led to two types of gully erosion models: (1) dynamic models to predict rapid changes of gully morphology at the first period of gully development; (2) static models to calculate final morphometric parameters of stable gullies. The dynamic gully model is based on the solution of the equations of mass conservation and gully bed deformation. The model of straight slope stability was used for prediction of gully side walls inclination. The static gully model is based on the assumption of final morphological equilibrium of a gully; when averaged for several years, elevations and width of gully bottom do not change. This stability is associated with a negligible rate both of erosion and sedimentation at the gully bottom. It means that flow velocity is less than the threshold value for erosion initiation, but is more than the critical velocity of wash load sedimentation. The dynamic and static gully models were verified on the data on gullies morphology and dynamics from Yamal peninsula (Russia) and New South Wales (Australia).