Combining dual-continuum approach with diffusion wave model to include a preferential flow component in hillslope scale modeling of shallow subsurface runoff Jaromir Dusek a,⇑ , Tomas Vogel a , Michal Dohnal a , Horst H. Gerke b a Czech Technical University in Prague, Faculty of Civil Engineering, Prague, Czech Republic b Leibniz-Centre for Agricultural Landscape Research (ZALF), Institute of Soil Landscape Research, Müncheberg, Germany article info Article history: Received 12 August 2011 Received in revised form 6 March 2012 Accepted 16 May 2012 Available online 23 May 2012 Keywords: Shallow subsurface runoff Hillslope discharge Preferential flow Dual-permeability model Richards’ equation Boussinesq equation abstract 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 bed- rock 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 contrib- uting 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 transfor- mation 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. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Shallow subsurface runoff (also referred to as interflow, storm- flow or throughflow) is recognized as one of the most important mechanisms determining hydrological responses of headwater catchments to rainstorms. It usually develops as shallow saturated lateral flow at the sloping interface between a more permeable surface soil layer and the less permeable underlying soil or bedrock strata. Normally, this type of flow occurs only for a short period of time as an immediate response to an intense rainfall event. The on- set of shallow subsurface runoff is commonly accelerated by the presence of preferential pathways in a soil profile. Thus, preferen- tial flow is recognized as a significant factor in runoff formation at the hillslope scale [e.g., 1–3]. Transport processes at the hillslope scale are inherently of three-dimensional (3D) nature. Recently, a few applications of 3D modeling based on Richards’ equation for water flow and advec- tion-dispersion equation for solute transport were presented [4– 6]. Nevertheless, the water dynamics at the hillslope scale are more frequently described using two-dimensional (2D) models [e.g., 7– 9]. However, the 2D approaches are still difficult to apply for large spatial configurations (i.e., hundreds of meters long hillslopes) since computationally demanding numerical solution of the gov- erning equations is required. Therefore, subsurface water dynamics in a hillslope segment was proposed to be decoupled to one- dimensional vertical flow and one-dimensional (1D) lateral flow along the soil/bedrock interface [10–12]. Saturated subsurface flow can be, in principle, described by a one-dimensional diffusion wave (Boussinesq-type) equation. However, the approach of coupling the two one-dimensional models represents a substantial simplifi- cation of the reality such that it needs additional experimental evidence. The validity of such simplification for describing fast flow 0309-1708/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.advwatres.2012.05.006 ⇑ Corresponding author. Address: Department of Hydraulics and Hydrology, Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7, 166 29 Prague, Czech Republic. Tel.: +420 22435 4355; fax: +420 22435 4793. E-mail address: dusek@mat.fsv.cvut.cz (J. Dusek). Advances in Water Resources 44 (2012) 113–125 Contents lists available at SciVerse ScienceDirect Advances in Water Resources journal homepage: www.elsevier.com/locate/advwatres