Equation for high-rate gully erosion

An approach to gully erosion is presented in this paper. The approach is based on general equations derived from theoretical considerations. The equations apply to a situation of intense erosion rate, such as at peak discharge during the few critical rainstorms, able to generate or to widen gullies. ons linking gully widening to gully deepening are derived. They do not depend on the way in which concentrated flow aggressiveness is estimated. The equation expressing gully width/depth relationship was successfully compared with data from the literature. unoff aggressiveness was estimated through unit stream power and bottom flow shear stress, the width/discharge relationships found were similar to those expected on the basis of previous studies (e.g., Leopold and Maddock [U. S. Geol. Surv. Prof. Pap. 252 (1953) 57 pp.]) even if slope gradient explicitly appears in contrast with empirical evidence. Only threshold conditions for gullies indicate that flow shear stress (for laminar flow conditions) can explain the observed trends. This astonishing result most probably indicates that gully initiation needs more complex contexts to be explained than the one here used (based on a Montgomery and Dietrich [1994. Landscape dissection and drainage area–slope thresholds. In: M.J. Kirkby (ed.), Process Models and Theoretical Geomorphology. Wiley, 221–246] approach). ction of the proposed equations have been arranged into a research model and an example of the outcome has been given for two situations typical of cropland in southern Tuscany (Italy). The results indicate that the spatial distribution of soil characteristics and of land use influences significantly gully generation and evolution. This further confirms that gully morphological thresholds cannot be explained by simple approaches.