Mathematical model for evaluation of the effect of soil erosion on soil productivity

Abstract

AbstractThis paper is concerned with the development of a stochastic model for evaluating the long‐term effect of soil erosion on soil productivity. Due to random variations in annual crop yield, the effect of erosion on crop production is not easily detectable in the short run, but becomes gradually evident over a sufficiently long time period. Under these circumstances, it seems that an experimental approach to this problem may be very difficult. The long period of time over which such an experiment has to be conducted may result in prohibitively high costs. In addition, it also means that eventual resolution of this problem must be postponed until a distant future time. The stochastic model formulated here provides us with a useful tool to assess the trend in quantitative changes in crop production due to erosion and to project future crop losses. The model is a discrete parameter stochastic process. Its derivation is based on a single assumption that the annual loss rates form a sequence of independent random variables {Zi}1∞ (in this paper, we consider only two particular cases: (a) {Zi}1∞ is a sequence of constants; (b) {Zi}1∞ is a sequence of independent identically distributed random variables). For these particular cases, we obtained its marginal n‐dimensional distribution function and correlation function. One of the principal model features is its simple structure and remarkable lack of restrictive and unrealistic assumptions.