Abstract. Declines in soil saturated hydraulic conductivity (Ks) as a result of saline and sodic irrigation water are a major cause of soil degradation. While it is understood that the mechanisms that lead to degradation can cause irreversible changes in Ks, existing models do not account for hysteresis between the degradation and rehabilitation processes. We develop the first model for the effect of saline and sodic water on Ks that explicitly includes hysteresis. As such, the idea that a soil's history of degradation and rehabilitation determines its future Ks lies at the center of our model. By means of a weight function, the model accounts for soil specific differences, such as clay content. The weight function also determines the form of the hysteresis curves, which are not restricted to a single shape, as in some existing models for irreversible soil processes. The concept of the weight function is used to develop a reversibility index, which allows for the quantitative comparison of different soils and their susceptibility to irreversible degradation. We discuss the experimental setup required to find a soil's weight function and show how the weight function determines the degree to which Ks is reversible, for a given soil. We demonstrate the feasibility of this procedure by presenting novel experimental results showcasing the presence of hysteresis in soil Ks, and using these results to calculate a weight function. Past experiments and models on the decline of Ks due to salinity and sodicity focus on degradation alone, ignoring any characterization of the degree to which declines in Ks are reversible. Our model and experimental results emphasize the need to measure reversal curves, obtained from rehabilitation measurements following mild declines in Ks. The developed model has the potential to significantly improve our ability to assess the risk of soil degradation, by allowing for the consideration of how the accumulation of small degradation events can cause significant land degradation.
Characterization of the equality of Cauchy means to quasiarithmetic means
