A Nonlinear Model for Topsoil Erosion Caused by Heavy Rain

Abstract

In this paper, a nonlinear mathematical model is proposed and analysed to study the effect of heavy rain on the topsoil erosion and crop-yield. It is shown that as the velocity of rain water along the soil surface increases, the fertile topsoil depth decreases and this depth may be very small if soil is exposed continuously to the stresses generated by heavy rain. A model to conserve the fertile topsoil is also proposed. By analyzing the conservation model it is shown that the economy would follow a sustainable path if suitable efforts are adopted in time.