The essence of kinematic models is as follows: properties of the topographic substrate (soil ground or rocks), its response to forcing, and the forces are not considered; i.e., we do not introduce dynamic equations of motion. Instead, a dependence of the rate of slope surface subsidence on the slope morphology (its height, inclination, profile, and horizontal curvature) is specified. This can be
... [Show full abstract] supplemented by the effect of external factors unrelated to the slope processes. Kinematic models provide insight into the development mechanism of a configuration specified for a certain time moment at a certain dependence of the slope subsidence rate on the form of the slope at the given initial and boundary conditions and under the influence of external factors (for example, tectonic motions). Such an approach is justified by the fact that the laws of substrate deformation needed for composing dynamic equations are poorly known. Therefore, we usually have to specify them with a high degree of uncertainty. At the same time, kinematic models allow us to obtain easily various and clear patterns of slope evolution at different scenarios of the denudation rate. Some of the simplest cases are described in [1‐4] and many other publications. In this work, we suggest a model of the development of a series of piedmonts (piedmont steps) appearing as a result of sequential impulses of tectonic uplifts. For simplicity, we shall limit ourselves to the two-dimensional case and consider a slope the morphology of which does not change along its horizontal extension. We shall consider that the velocity of the slope displacement at each point depends on its morphological characteristics: inclination and profile curvature at each given point, as well as on external factors, such as tectonic motions or accumulation and erosion of material. The influence of the absolute height can appear only on megaslopes, when the difference in climatic conditions is manifested in the course of weathering of rocks. However, here we shall not consider this aspect. Let us consider these factors separately. If z ( x , t ) is the height of the slope ( x is the coordinate axis directed across the slope and t is time), the rate of slope surface subsidence is . The inclination angle of the slope is