A hysteretic model for rainfall-runoff of a simplifed catchment

The soil can be modelled as a porous medium in which the three phases of matter coexist and produce the emergent phenomenon of hysteresis.

Rate-independent hysteresis is a nonlinear phenomenon where the output depends not only on the current input but also the previous history of inputs to the system. In multiphase porous media such as soils, the hysteresis is in the relationship between the soil-moisture content, and the capillary pressure.

In this work, we develop a simplified hysteretic rainfall-runoff model consisting of the following subsystems that capture much of the physics of flow through a slab of soil:

1) A slab of soil where rainfall enters and if enough water is present in the soil, it will subsequently drain into the groundwater reservoir. This part of the model is represent by ODE with a Preisach operator.

2) A runoff component: If the rainfall exceeds the maximum infiltration rate of the soil, the excess will become surface runoff. This part of the model is represented by a series of two hysteretic reservoirs instead of the two linear reservoirs in the literature.

3) A ground water storage and outflow subsystem component: this is also modelled by a hysteretic reservoir. Finally, the outputs from the groundwater output and the overland flow are combined to give the total runoff. We will examine this model and compare it with non-hysteretic case both qualitatively and quantitively.