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A Runoff Simulation Model Based on Hillslope Topography

  • Mike Kirkby
Part of the Water Science and Technology Library book series (WSTL, volume 6)

Abstract

The detailed model presented is a development of an exponential store model (TOPMODEL) previously described (Beven and Kirkby, 1979). The continuity equation for saturated sub-surface flow is expressed in terms of unit runoff which emphasizes the relatively low spatial variation in rates. For this reason kinematic wave solutions have not been used to solve the partial differential equation. A single unsaturated and a saturated store are considered at each point down the hillslope length, the former delaying infiltration and the latter providing downslope sub-surface flow and establishing saturated contributing areas.

The total sub-surface flow at saturation, slope gradient and hillslope plan form are used to generate flow differences down the length of the hillslope profile. Simulations show the generation of saturated overland flow at downslope sites where flow converges, superimposed on a hydrograph which is largely controlled by the convex (in profile) divide area. This suggests that for most natural slopes, the runoff delivered to channel banks may be estimated efficiently from two separate linked component models. The first forecasts spatially uniform flow at rates determined by topography and soils in the hilltop divide areas. This model is able to forecast the changing saturated area on which the second component model forecasts the saturated overland flow. This or another appropriate hillslope flow model may be combined with a flow routing algorithm for the channel network to give catchment hydrological response. In simple cases of spatially constant network routing velocity, the resulting combined model is identical to the Geomorphological Unit Hydrograph of Rodríguez-Iturbe, providing an explicit physical meaning for his theoretical unit response functions as the hillslope base unit hydrograph.

Keywords

Overland Flow Unit Hydrograph Saturated Deficit Slow Peak Slope Base 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Beven, K.J., 1979. On the Generalized Kinematic Routing Method, Water Resources Research, 15: pp. 1238–1242.CrossRefGoogle Scholar
  2. Beven, K.J., 1983. Introducing Spatial Variability Into TOPMODEL: Theory and Preliminary Results, Report to Department of Environmental Sciences, University of Virginia, 35 pp.Google Scholar
  3. Beven, K.J. and Kirkby, M.J., 1979. A Physically Based Variable Contributing Area Model of Basin Hydrology, Hydrological Sciences Bulletin, 24: pp. 43–69.CrossRefGoogle Scholar
  4. Beven, K.J., Kirkby, M.J., Schofield, N. and Tagg, A.F., 1984. Testing a Physically-based Flood Forecasting Model (TOPMODEL) for Three U.K. Catchments, J. Hydrology, 69: pp. 119–143.CrossRefGoogle Scholar
  5. Beven, K. J., and Wood, E.F., 1983. Catchment Geomorphology and the Dynamics of Runoff Contributing Areas, J. Hydrology, 65: pp. 139–158.CrossRefGoogle Scholar
  6. Carson, M.A., and Kirkby, M.J., 1972. Hillslope Form and Process, Cambridge University Press, 475 pp.Google Scholar
  7. Green, W.H., and Ampt, G.A., 1911. Studies on Soil Physics. 1. The Flow of Air and Water Through Soils, J. Agric. Soils, 4: pp. 1–24.Google Scholar
  8. Gupta, V.K., Waymire, E., and Rodriguéz-Iturbe, I. 1986. On Scale, Gravity and Network Structure in Basin Runoff, (this issue). D. Reidel Publishing Company.Google Scholar
  9. Kirkby, M.J., 1976. Tests of the Random Network Model, and Its Application to Basin Hydrology, Earth Surface Processes, 1: pp. 197–212.CrossRefGoogle Scholar
  10. Kirkby, M.J., 1980. The Stream Head as a Significant Geomorphic Threshold, in Thresholds in Geomorphology, edited by D.R. Coates; and J.D. Vitek, George Allen & Unwin, 498 pp., Chapter 4, pp. 53–73.Google Scholar
  11. Rodriguéz-Iturbe, I., and Valdés, J.B., 1979. The Geomorphologic Structure of Hydrologic Response, Water Resources Research, 15: pp. 1490–1420.Google Scholar
  12. Smith, T.R., and Bretherton, F.P., 1972. Stability and the Conservation of Mass in Drainage Basin Evolution, Water Resources Research, 8: pp. 1506–1524.CrossRefGoogle Scholar
  13. Surkan, A.J., 1969. Synthetic Hydrographs: Effects of Network Geometry, Water Resources Research, 5: pp. 112–128.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Mike Kirkby

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