An integral-balance nonlinear model to simulate changes in soil moisture, groundwater and surface runoff dynamics at the hillslope scale

• Published in: Advances in water resources 2014-09, Vol.71, p.125-139
• Main Authors: Curtu, Rodica, Mantilla, Ricardo, Fonley, Morgan, Cunha, Luciana K., Small, Scott J., Jay, Laurent O., Krajewski, Witold F.
• Format: Article
• Language: English
• Subjects: Dynamical systems; Dynamics; Earth sciences; Earth, ocean, space; Exact sciences and technology; Hillslope model; Hydrogeology; Hydrology; Hydrology. Hydrogeology; Mathematical models; Nonlinear ODE system; Runoff; Scale (ratio); Shale Hills watershed; Soil (material); Soil moisture; Surface vs. subsurface interactions; Unsaturated
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2014.06.003

•We propose a nonlinear ODE model for changes in water storage at the hillslope scale.•The model is tested using data collected in the Shale Hills watershed.•It replicates observations of water storages in unsaturated and saturated layers.•It explains the observed double-peak hydrographs by infiltration excess runoff.•The simplified ODE system can reproduce data as close as a detailed PDE model. We present a system of ordinary differential equations (ODEs) capable of reproducing simultaneously the aggregated behavior of changes in water storage in the hillslope surface, the unsaturated and the saturated soil layers and the channel that drains the hillslope. The system of equations can be viewed as a two-state integral-balance model for soil moisture and groundwater dynamics. Development of the model was motivated by the need for landscape representation through hillslopes and channels organized following stream drainage network topology. Such a representation, with the basic discretization unit of a hillslope, allows ODEs-based simulation of the water transport in a basin. This, in turn, admits the use of highly efficient numerical solvers that enable space–time scaling studies. The goal of this paper is to investigate whether a nonlinear ODE system can effectively replicate observations of water storage in the unsaturated and saturated layers of the soil. Our first finding is that a previously proposed ODE hillslope model, based on readily available data, is capable of reproducing streamflow fluctuations but fails to reproduce the interactions between the surface and subsurface components at the hillslope scale. However, the more complex ODE model that we present in this paper achieves this goal. In our model, fluxes in the soil are described using a Taylor expansion of the underlying storage flux relationship. We tested the model using data collected in the Shale Hills watershed, a 7.9-ha forested site in central Pennsylvania, during an artificial drainage experiment in August 1974 where soil moisture in the unsaturated zone, groundwater dynamics and surface runoff were monitored. The ODE model can be used as an alternative to spatially explicit hillslope models, based on systems of partial differential equations, which require more computational power to resolve fluxes at the hillslope scale. Therefore, it is appropriate to be coupled to runoff routing models to investigate the effect of runoff and its uncertainty propagation across scales. However, thi