References

HESS

Hydrology and Earth System Sciences

HESS

Hydrol. Earth Syst. Sci.

1607-7938

Copernicus Publications

Göttingen, Germany

10.5194/hess-11-1047-2007

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

Lehmann

¹ ² ⁶ Hinz

² McGrath

² Tromp-van Meerveld

H. J.

³ ⁴ McDonnell

J. J.

⁵ ⁷

Institute of Terrestrial Ecology, Swiss Federal Institute of Technology, ETH Zurich, Switzerland

School of Earth and Geographical Sciences, The University of Western Australia, Crawley, Australia

Simon Fraser University, Department of Geography, Burnaby BC, Canada

School of Architecture, Civil and Environmental Engineering, EPFL Lausanne, Switzerland

Water 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

02 04 2007

11 2 1047 1063

2007

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Generic License. To view a copy of this licence, visit https://creativecommons.org/licenses/by-nc-sa/2.5/

This article is available from https://hess.copernicus.org/articles/11/1047/2007/hess-11-1047-2007.html

The full text article is available as a PDF file from https://hess.copernicus.org/articles/11/1047/2007/hess-11-1047-2007.pdf

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. <br><br> 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.

References 1

Berkowitz, B. and Ewing, R. P.: Percolation theory and network modeling – applications in soil physics, Surveys in Geophysics, 19, 23–72, 1998.

Berkowitz, B. and Balberg, I.: Percolation theory and its application to groundwater hydrology, Water Resources Research, 29(4), 775–794, 1993.

Bonell, M.: Selected challenges in outflow generation research in forests from the hillslope to headwater drainage basin scale, Journal of the American Water Resources Association, 34(4), 765–785, 1998.

Broadbent, S. R. and Hammersley, J. M.: Percolation Processes I. Crystals and Mazes, Proceedings of the Cambridge Philosophical Society, 53(3), 629–641, 1957.

Burns, D. A., Hooper, R. P., McDonnell, J. J., Freer, J. E., Kendall, C., and Beven, K.: Base cation concentrations in subsurface flow from a forested hillslope: The role of flushing frequency, Water Resources Research, 34, 3535–3544, 1998.

Essam, J. W.: Percolation theory, Reports on Progress in Physics, 43, 833–912, 1980.

Freer, J., McDonnell, J. J., Beven, K. J., Brammer, D., Burns, D., Hooper, R. P., and Kendall, C.: Topographic controls on subsurface storm flow at the hillslope scale for two hydrologically distinct small catchments, Hydrological Processes, 11, 1347–1352, 1997.

Freer, J., McDonnell, J. J., Beven, K. J., Peters, N. E., Burns, D. A., Hopper, R. P., Aulenbach, B., and Kendall, C.: The role of bedrock topography on subsurface storm flow, Water Resources Research, 38(12), 1269, https://doi.org/10.1029/2001WR000872, 2002.

Holden, J.: Hydrological connectivity of soil pipes determined by ground-penetrating radar tracer detection, Earth Surface Processes and Landforms, 29, 437–442, 2004.

Hunt, A. G.: Percolation theory for flow and transport in porous media, Lecture Notes in Physics, 674, Springer, Berlin, 2005.

Kirkby, M. J.: Hillslope runoff process and models, J. Hydrol., 100, 315–339, 1988.

McDonnell, J. J.: Where does water go when it rains? Moving beyond the variable source area concept of rainfall-outflow response, Hydrological Processes, 17(2) 1869–1875, 2003.

Mosley, M. P.: Streamflow generation in a forested watershed, Water Resour. Res., 15, 795–806, 1979.

Sahimi, M.: Applications of Percolation Theory, Taylor and Francis, London, 1994.

Scherrer, S. and Naef, F.: Decision scheme to indicate dominant hydrological flow processes on temperate grassland, Hydrological Processes, 17(2), 391–401, 2003.

Sidle, R. C., Tsuoyama, Y., Noguchi, S., Hosoda, I., Fujieda, M., and Shimizu, T.: Introduction to seasonal hydrologic response at various spatial scales in a small forested catchment, Hitachi Ohta, Japan, J. Hydrol., 168, 227–250, 1995.

Sidle, R. C., Noguchi, S., Tsuboyama, Y., and Laursen, K.: A conceptual model of preferential flow systems in forested hillslopes: evidence of self organization, Hydrological Processes, 15, 1675–1692, 2001.

Spence, C. and Woo, M.-K.: Hydrology of subarctic Canadian shield: soil-filled valleys, J. Hydrol., 279, 151–156, 2003.

Stauffer, D. and Aharony, A.: Introduction to Percolation Theory, 2nd edition, Taylor and Francis, London (second printing), 1994.

Tani, M.: Outflow generation processes estimated from hydrological observations on a steep forested hillslope with a thin soil layer, J. Hydrol., 200, 84–109, 1997.

Tromp-van Meerveld, H. J. and McDonnell, J. J.: Threshold relations in subsurface stormflow 1. A 147 storm analysis of the Panola hillslope, Water Resources Research, 42, W02410, https://doi.org/10.1029/2004WR003778, 2006a.

Tromp-van Meerveld, H. J. and McDonnell, J. J.: Threshold relations in subsurface stormflow 2. The fill and spill hypothesis, Water Resources Research, 42, W02411, https://doi.org/10.1029/2004WR003800, 2006b.

Tromp-van Meerveld, H. J. and McDonnell, J. J.: On the interrelations between topography, soil depth, soil moisture, transpiration rates and species distribution at the hillslope scale, Advances in Water Resources, 29, 293–310, 2006c.

Tromp-van Meerveld, H. J., Peters, N. E., and McDonnell, J. J.: Effect of bedrock permeability on subsurface stormflow and the water balance of a trenched hillslope at the Panola Mountain Research Watershed, Georgia, USA, Hydrol. Processes, 21, 750–769, 2007.

Uchida, T., Kosugi, K., and Mizuyama, T.: Outflow characteristics of pipeflow on rainfall-outflow phenomena in mountainous watershed, J. Hydrol., 222, 18–36, 1999.

Uchida, T., Tromp-van Meerveld, I., and McDonnell, J.: The role of lateral pipe flow in hillslope outflow response: an intercomparison of non-linear hillslope response, J. Hydrol., 311, 117–133, 2005.

Weiler, M., McDonnell, J., Tromp-van Meerveld, I., and Uchida, T.: Subsurface stormflow, Encyclopedia of Hydrological Sciences, Wiley and Sons, 2005.

Weiler, M., Uchida, T., and McDonnell, J.: Connectivity due to preferential flow controls water flow and solute transport at the hillslope scale, Proceedings of MODSIM 2003, Townsville, Australia, 2003.

Western, A. W., Blöschl, G., and Grayson, R. B.: Towards capturing hydrologically significant connectivity in spatial patterns, Water Resources Research, 37(1), 83–97, 2001.

Whipkey, R. Z.: Subsurface stormflow from forested slopes, Bulletin of the International Association of Scientific Hydrology, 10, 74–85, 1965.