Articles | Volume 11, issue 2
Hydrol. Earth Syst. Sci., 11, 1047–1063, 2007

Special issue: Thresholds and pattern dynamics: a new paradigm for predicting...

Hydrol. Earth Syst. Sci., 11, 1047–1063, 2007

  02 Apr 2007

02 Apr 2007

Rainfall threshold for hillslope outflow: an emergent property of flow pathway connectivity

P. Lehmann1,2,*, C. Hinz2, G. McGrath2, H. J. Tromp-van Meerveld3,4, and J. J. McDonnell5,** P. Lehmann et al.
  • 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.