Rainfall threshold for hillslope outflow: an emergent property of flow pathway connectivity
1Institute of Terrestrial Ecology, Swiss Federal Institute of Technology, ETH Zurich, Switzerland
2School of Earth and Geographical Sciences, The University of Western Australia, Crawley, Australia
3Simon Fraser University, Department of Geography, Burnaby BC, Canada
4School of Architecture, Civil and Environmental Engineering, EPFL Lausanne, Switzerland
5Water Resources Section, Delft University of Technology, Delft, The Netherlands
*now at: Laboratory of Soil and Environmental Physics, EPF Lausanne, Switzerland
**on leave from: Dept. of Forest Engineering, Oregon State University, Corvallis, USA
Abstract. Nonlinear relations between rain input and hillslope outflow are common observations in hillslope hydrology field studies. In this paper we use percolation theory to model the threshold relationship between rainfall amount and outflow and show that this nonlinear relationship may arise from simple linear processes at the smaller scale. When the rainfall amount exceeds a threshold value, the underlying elements become connected and water flows out of the base of the hillslope. The percolation approach shows how random variations in storage capacity and connectivity at the small spatial scale cause a threshold relationship between rainstorm amount and hillslope outflow.
As a test case, we applied percolation theory to the well characterized experimental hillslope at the Panola Mountain Research Watershed. Analysing the measured rainstorm events and the subsurface stormflow with percolation theory, we could determine the effect of bedrock permeability, spatial distribution of soil properties and initial water content within the hillslope. The measured variation in the relationship between rainstorm amount and subsurface flow could be reproduced by modelling the initial moisture deficit, the loss of free water to the bedrock, the limited size of the system and the connectivity that is a function of bedrock topography and existence of macropores. The values of the model parameters were in agreement with measured values of soil depth distribution and water saturation.
Lehmann, P., Hinz, C., McGrath, G., Tromp-van Meerveld, H. J., and McDonnell, J. J.: Rainfall threshold for hillslope outflow: an emergent property of flow pathway connectivity, Hydrol. Earth Syst. Sci., 11, 1047-1063, doi:10.5194/hess-11-1047-2007, 2007.