Abstract
A simple model is developed to investigate the relative role of network geometry and hillslopes in basin response. The network geometry is quantified in a function, termed the width function, that reflects the distribution of runoff with flow distance from the outlet. The model consists of two components: the routing component of the initial distribution (width function) through the network by means of a simplified diffusion approximation; and the hillslope component. The latter is also considered in an idealized manner with the purpose of investigating the relative importance of both components. Various assumptions are tested through qualitative comparison of the model output with a recorded event.
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References
Clark, C.O., 1945. Storage and the Unit Hydrograph, Am. Soc. of Civ. Engrs. Trans., Vol. 110, pp. 1419–1446.
Dooge, J.C.I., 1959. A General Theory of the Unit Hydrograph, J. Geophys. Res., Vol. 64, No. 2, pp. 241–256.
Dooge, J.C.I., 1973. Linear Theory of Hydrologic Systems, Tech. Bul. 1468, U.S. Department of Agriculture, Washington, DC.
Duff, G.F.D., and D. Naylor, 1966. Differential Equations of Applied Mathematics, John Wiley, New York.
Dunne, T., 1983. Relation of Field Studies and Modeling in the Prediction of Storm Runoff, In: Scale Problems in Hydrology, (eds.) I. RodrÃguez-Iturbe and V.K. Gupta, J. Hydrol., Vol. 65.
Feller, W., 1971. An Introduction to Probability Theory and Its Applications, II, John Wiley, New York.
Gupta, V.K., and E.C. Waymire, 1983. On the Formulation of an Analytical Approach to Hydrologic Response and Similarity at the Basin Scale, J. Hydrol., Vol. 65, pp. 95–123.
Gupta, V.K., E. Waymire, and I. RodrÃguez-Iturbe, 1986. On Scales, Gravity and Network Structure in Basin Runoff, Chapter 8, in: Scale Problems in Hydrology (ed.) I. RodrÃguez-Iturbe, V.K. Gupta, E.F. Wood, Reidel Publishing.
Gupta, V.K., E. Waymire, and C.T. Wang, 1980. A Representation of an Instantaneous Unit Hydrograph from Geomorphology, Water Resources Research, Vol. 16, No. 5, pp. 855–862.
Horton, R.E., 1932. Drainage Basin Characteristics, EOS Trans., AGU, No. 13, pp. 350–361.
Horton, R.E., 1945. Erosional Development of Streams and Their Drainage Basins: Hydro-physical Approach to Quantitative Morphology, Bul. Geol. Soc. Amer., Vol. 56, pp. 275–370.
Kirkby, M.J., 1976. Tests of Random Network Model, and its Application to Basin Hydrology, Earth. Surf. Proc., Vol. 1, pp. 197–212.
Lighthill, M.J., and G.B. Whitham, 1955. On Kinematic Waves: I. Flood Movement in Long Rivers, Proc. Roy. Soc. A, Vol. 229, pp. 281–316.
Mesa, O., 1982. On an Analytical Approach for Coupling Hydrologic Response and Geomorphology, unpublished M.S. thesis, Department of Civil Engineering, University of Mississippi.
Mifflin, E.R., 1984. On the Role of Network Geometry in Basin Response, M.S. Thesis, University of Mississippi.
Rogers, W.R., 1972. New Concepts in Hydrograph Analysis, Water Resources Research, Vol. 8, No. 4, pp. 973–981.
RodrÃguez-Iturbe, I., and J.B. Valdés, 1979. The Geomorphic Structure of Hydrologic Response, Water Resources Research, Vol. 15, No. 6, pp. 1409–1420.
Ross, C.N., 1921. Calibration of Flood Discharge by the Use of a Time-contour Plan, Trans. Inst, of Engrs., Vol. II: 85, Australia.
Sherman, L.K., 1932. Streamflow from Rainfall from the Unit Hydrograph Method, Eng. News Record, Vol. 103, pp. 501–505.
Troutman, B.M., and M.R. Karlinger, 1984. On the Expected Width Function for Topographically Random Channel Networks, J. of Appl. Prob., Vol. 22, pp. 836–849.
Troutman, B.M., and M.R. Karlinger, 1985. Unit Hydrograph Approximations Assuming Linear Flow Through Topologically Random Channel Networks, Water Resources Research, Vol. 21, No. 5, pp. 743–754.
Troutman, B.M., and M.R. Karlinger, 1986. Averaging Properties of Channel Networks Using Methods in Stochastic Branching Theory, (this issue).
Zoch, R.T., 1934. On the Relation Between Rainfall and Streamflow, Monthly Weather Rev., Vol. 62, pp. 315–322.
Zoch, R.T., 1936. On the Relation Between Rainfall and Streamflow, Monthly Weather Rev., Vol. 64, pp. 105–121.
Zoch, R.T., 1937. On the Relation Between Rainfall and Streamflow, Monthly Weather Rev., Vol. 65, pp. 135–147.
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Mesa, O.J., Mifflin, E.R. (1986). On the Relative Role of Hillslope and Network Geometry in Hydrologic Response. In: Gupta, V.K., RodrÃguez-Iturbe, I., Wood, E.F. (eds) Scale Problems in Hydrology. Water Science and Technology Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4678-1_1
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DOI: https://doi.org/10.1007/978-94-009-4678-1_1
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