Evaluation of linear and nonlinear sediment transport equations using hillslope morphology

Although some simple erosive processes like soil creep or tillage redistribution may be satisfactorily described by linear diffusive equations, the complexity of erosion phenomena requires the use of more complete nonlinear equations. Roering et al. [Roering, J.J., Kichner, J.W., Dietrich, W.E., 1999. Evidence for nonlinear, diffusive transport on hillslopes and implications for landscape morphology. Water Resour. Res., 35 853-870.] have proposed a single test, based on the relationship between the curvature and gradient of a hillslope, rather then using a linear diffusion equation. Nevertheless this test, based on steady state conditions, is not complete as it is shown in this work with a counter-example. The hillslope profile used by Roering et al. [Roering, J.J., Kichner, J.W., Dietrich, W.E., 1999. Evidence for nonlinear, diffusive transport on hillslopes and implications for landscape morphology. Water Resour. Res., 35 853-870.], (Fig. 2) can be generated either by a linear diffusion equation under transient conditions or a nonlinear diffusion equation under steady state conditions. Additional information on the soil profile changes would give a more complete interpretation of the hillslope evolution.