Analysis of hysteretic behaviour of a hillslope-storage kinematic wave model for subsurface flow

The objective of this work is to analyse the storage-flux hysteretic behaviour of a simplified model for subsurface flow processes. The subsurface flow dynamics is analysed by means of a model based on the kinematic wave assumptions and by using a width weighting/depth averaging scheme which allows to map the three-dimensional soil mantle into a one-dimensional profile. Continuity and a kinematic form of Darcy's law lead to a hillslope-storage kinematic wave equation for subsurface flow, solvable with the method of characteristics. Adopting a second order polynomial function to describe the bedrock slope and an exponential function to describe the variation of the width of the hillslope with hillslope distance, we derive general solutions to the hillslope-storage kinematic wave equations, applicable to a wide range of hillslopes. These solutions provide a physical basis for deriving two geometric parameters α and ψ which define the hydrological similarity between hillslopes with respec...