A simple two‐parameter model for scaling hillslope surface runoff |
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| Authors: | Gary J Sheridan Philip J Noske Patrick NJ Lane Owen D Jones Christopher B Sherwin |
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| Institution: | 1. Department of Forest and Ecosystem Science, The University of Melbourne, Victoria, Australia;2. Cooperative Research Centre for Forestry, Sandy Bay, TAS, Australia;3. Department of Mathematics and Statistics, The University of Melbourne, Victoria, Australia |
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| Abstract: | The objective of this research was to develop and parameterise a physically justified yet low‐parameter model to quantify observed changes in surface runoff ratios with hillslope length. The approach starts with the assumption that a unit of rainfall‐excess runoff generated at a point is a fraction β of precipitation P (m) which travels some variable distance down a slope before reinfiltrating, depending on the local rainfall, climate, soils, etc. If this random distance travelled Y is represented by a distribution, then a survival function will describe the probability of this unit of runoff travelling further than some distance x (m). The total amount of per unit width runoff Q (m2) flowing across the lower boundary of a slope of length λ (m) may be considered the sum of all the proportions of the units of rainfall excess runoff integrated from the lower boundary x = 0 to the upper boundary x = λ of the slope. Using these assumptions we derive a model Q(λ) = βPμλ/(μ + λ), (μ > 0, 0 ≤ β ≤ 1, λ ≥ 0) that describes the change in surface runoff with slope length, where μ (m) is the mean of the random variable Y. Dividing both sides of this equation by Pλ yields a simple two‐parameter equation for the dimensionless hillslope runoff ratio Qh(λ) = βμ/(μ + λ). The model was parameterised with new rainfall and runoff data collected from three replicates of bounded 2 m wide plots of four different lengths (0.5, 1.0, 2.0 and 4.0 m) for 2 years from a forested SE Australian site, and with 32 slope length–runoff data sets from 12 other published studies undertaken between 1934 and 2010. Using the parameterised model resulted in a Nash and Sutcliffe statistic between observed and predicted runoff ratio (for all data sets combined) of 0.93, compared with –2.1 when the runoff ratio was fixed at the value measured from the shortest plot. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | scaling connectivity slope length overland flow infiltration excess |
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