Combining dual-continuum approach with diffusion wave model to include a preferential flow component in hillslope scale modeling of shallow subsurface runoff

In the absence of overland flow, shallow subsurface runoff is one of the most important mechanisms determining hydrological responses of headwater catchments to rainstorms. Subsurface runoff can be triggered by preferential flow of infiltrating water frequently occurring in heterogeneous and structured soils as a basically one-dimensional (1D) vertical process. Any attempt to include effects of preferential flow in hydrological hillslope studies is limited by the fact that the thickness of the permeable soil is mostly small compared to the length of the hillslope. The objective of this study is to describe preferential flow effects on hillslope-scale subsurface runoff by combining a 1D vertical dual-continuum approach with a 1D lateral flow equation. The 1D vertical flow of water in a variably saturated soil is described by a coupled set of Richards’ equations and the 1D saturated lateral flow of water on less permeable bedrock by the diffusion wave equation. The numerical solution of the combined model was used to study rainfall-runoff events on the Tomsovska hillslope by comparing simulated runoff with observed trench discharge data. The dual-continuum model generated the observed rapid runoff response, which served as an input for the lateral flow model. The diffusion wave model parameters (i.e., length of the contributing hillslope, effective porosity, and effective hydraulic conductivity) indicate that the hillslope length that contributed to subsurface drainage is relatively short (in the range of 25–50 m). Significant transformation of the 1D vertical inflow signal by lateral flow is expected for longer hillslopes, smaller effective conductivities, and larger effective porosities. The physically-based combined modeling approach allows for a consistent description of both preferential flow in a 1D vertical soil profile and lateral subsurface hillslope flow in the simplest way.