Modeling 3D-changes in the terrain relief due to slope erosion

The authors propose an algorithm for predictive monitoring of 3D-changes in the terrain relief due to the processes of slope erosion. The algorithm is based on the phenomenological law, from which it follows that the intensity of soil losses at the slope is proportional in magnitude and inverse in the direction of the declivity height gradient vector. In conjunction with the differential equation of mass balance, a mathematical model of the terrain relief change is built. The model enables calculating it at an arbitrary time according to its shape at the initial moment based on the solution of a standard mathematic boundary task. Comparing the results of solving such a problem with the data of cartographic monitoring makes it possible to establish a relationship between the slope erosion coefficient and the type of soil, vegetation cover, and meteorological conditions under which the studied area is located, and then predict changes in the terrain relief in the future.