Sustainable soil and water resources: modelling soil erosion and its impact on the environment

With the projected increase in world population to 9 billion by 2050, along with per capita income growth, the demand for land and water resources is going to increase significantly. Conversion of land to intensive agriculture has led to dramatic decreases in plant, animal and insect biodiversity, with approximately 40% of the world’s land surface now covered by croplands and pastures. Intensive agricultural practices cause erosion and lead to transport of soil particles and associated sorbed chemical (fertilizers, pesticides and herbicides) contaminants, which are responsible for significant degradation in the quality of both surface and subsurface water bodies. Soil erosion is an outcome of complex interactions between precipitation, physical transport, topography and conservation management strategies; and there have been many physically based mathematical models developed over the past 20 years that attempt to make predictions of erosion rates as a function of these interactions. These have been applied across scales corresponding to the laboratory, plot, hillslope and watershed with varying degrees of success. Two particular characteristic features of erosion data from both the laboratory and field scale that almost all these models have yet to reproduce reliably are hysteresis in the water discharge versus sediment discharge relationship, and the size distributions of transported sediment. We show that the model of Hairsine and Rose is able to produce the known common types of hysteresis curves, these being clockwise, counter-clockwise, figure 8 (both flow orientations), and that these forms are in keeping with measured data in the literature. Numerical simulations demonstrate that such curves are a consequence of (i) the soil’s sediment size distribution and (ii) the existence and evolution of a deposited layer of non-cohesive sediment on top of original un-eroded cohesive soil. It is shown that the initial state of this layer prior to a rainfall event plays a significant role in determining which type of hysteresis loop evolves. An application to published experimental data for flow-driven erosion down a rill is then considered. Excellent agreement between measured and suspended sediment concentrations was found throughout the hysteretic cycle.