Intermediately complex models for the hydrological interactions in the atmosphere-vegetation-soil system

This paper investigates the hydrological interactions in the atmosphere-evegetation-soil system by using the bucket model and several new simplified intermediately complex models. The results of mathematical analysis and numerical simulations show that these models, despite their simplicity, can very clearly reveal the essential features of the rather complex hydrological system of atmosphere-ecosystem-soil. For given atmospheric variables, these models clearly demonstrate multiple timescales, the "red shift" of response spectra, multi-equilibria and limit cycles, bifurcation, abrupt change, self-organization, recovery, "desertification", and chaos. Most of these agree with observations. Especially, the weakening of "shading effect"of living canopy and the wilted biomass might be a major mechanism leading to the desertification in a relatively short period due to overgrazing, and the desertification in a relatively long period or in climate of change might be due to both Charney's mechanism and the shading effect. These Ideas could be validated with further numerical simulations. In the paper, some methods for improving the estimation of timescales in the soil water evolution responding to the forcing are also proposed.