Technical Papers
Aug 20, 2014

Sediment Graphs Based on Entropy Theory

Publication: Journal of Hydrologic Engineering
Volume 20, Issue 6

Abstract

Using the entropy theory, this paper derives an instantaneous unit sediment graph (IUSG or USG) to determine sediment discharge and the relation between sediment yield and runoff volume. The derivation of IUSG requires an expression of the effective sediment erosion intensity whose relation with rainfall is revisited. The entropy theory provides an efficient way to estimate the parameters involved in the derivations. Sediment discharge is also computed using the instantaneous unit hydrograph (IUH), which can also be derived using the entropy theory. This method works as well as the IUSG method, especially when the peak sediment discharge and peak runoff occur at the same time. The entropy theory yields the probability distribution of sediment yield and of sediment discharge, which can then be used to estimate uncertainty in sediment yield prediction.

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References

Chen, V. J., and Kuo, C. Y. (1986). “A study of synthetic sediment graphs for ungagged watersheds.” J. Hydrol., 84(1–2), 35–54.
Chiu, C. L. (1987). “Entropy and probability concepts in hydraulics.” J. Hydraul. Eng., 583–600.
Chiu, C. L., Jin, W., and Chen, Y. C. (2000). “Mathematical models of distribution of sediment concentration.” J. Hydraul. Eng., 16–23.
Choo, T. H. (2000). “An efficient method of the suspended sediment-discharge measurement using entropy concept.” Water Eng. Res., 1(2), 95–105.
Cui, H., and Singh, V. P. (2014). “Suspended sediment concentration in open channels using tsallis entropy.” J. Hydrol. Eng., 966–977.
De Araujo, J. C. (2007). “Entropy-based equation to assess hillslope sediment production.” Earth Surf. Processes Landforms, 32(13), 2005–2018.
Figueiredo, E. E., and Bathurst, J. C. (2007). “Runoff and sediment yield predictions in a semiarid region of Brazil using SHETRAN.” IAHS Decade on: Prediction in Ungaged Basins, D. Schertzer, P. Hubert, S. Koide, and K. Takeuchi, International Association of Hydrological Sciences, Wallingford, U.K., 258–266.
Foster, G. R., and Lane, L. J. (1983). “Erosion by concentrated flow in farm fields.” Proc., D.B. Simons Symp. on Erosion and Sedimentation, Colorado State Univ., Fort Collins, CO, 9.56–9.82.
Hairsine, P. B., and Rose, C. W. (1992). “Modeling water erosion due to overland flow using physical principles. 1: Sheet flow.” Water Resour. Res., 28(1), 237–243.
Jaynes, E. T. (1957a). “Information theory and statistical mechanics. I.” Phys. Rev., 106(4), 620–630.
Jaynes, E. T. (1957b). “Information theory and statistical mechanics. II.” Phys. Rev., 108(2), 171–190.
Jaynes, E. T. (1982). “On the rationale of maximum entropy methods.” Proc. IEEE, 70(9), 939–952.
Jin, D., Chen, H., and Guo, Q. (1999). “A preliminary experimental study on non-linear relationship between sediment yield and drainage network development.” Int. J. Sediment Res., 14(2), 9–18.
Kirkby, M. J., et al. (2002). “MEDRUSH-a basin scale physically based model for forecasting runoff and sediment yield.” Chapter 16, N: Mediterranean desertification: A mosaic of processes and responses, N. S. Geeson, C. J. Brandt, and J. B. Thornes, eds., Wiley, Chichester, U.K., 203–207.
Lane, L. J., and Nearing, M. A., eds. (1989). “Water erosion prediction project: Hillslope profile model documentation.” NSERL Rep., USDA-ARS, West Lafayette, IN.
Lienhard, J. H. (1964). “A statistical mechanical prediction of the dimensionless unit hydrograph.” J. Geophys. Res., 69(24), 5231–5238.
Morgan, R. P. C., et al. (1998). “The European soil erosion model (EUROEM). A Process based approach for predicting soil loss from fields and small catchments.” Earth Surf. Processes Landforms, 23(6), 527–544.
Nearing, M. A., Nichols, M. H., Stone, J. J., Renard, K. G., and Simanton, J. R. (2007). “Sediment yields from unit-source semiarid watersheds at Walnut Gulch.” Water Resour. Res., 43(6), W06426.
Nunes, J. P., de Lima, J. L. M. P., Singh, V. P., de Lima, M. I. P., and Vieira, G. N. (2006). “Numerical modeling of surface runoff and erosion due to moving storms at the drainage basin scale.” J. Hydrol., 330(3–4), 709–720.
Renard, K. G., Foster, G. R., Weesies, G. A., McCool, D. K., and Yoder, D. S. (1993). “Predicting soil erosion by water-A guide to conservation planning with the revised universal soil loss equation (RUSLE).” Agricultural Research Service, USDA, Washington, DC.
Rendon-Herrero, O. (1974). “Estimation of washload produced by certain small watersheds.” J. Hydraul. Div., 109(HY7), 835–848.
Rendon-Herrero, O. (1978). “Unit sediment graph.” Water Resour. Res., 14(5), 889–901.
Rendon-Herrero, O., Singh, V. P., and Chen, V. J. (1980). “ER-ES watershed relationship.” Proc., Int. Symp. on Water Resources Systems, Vol. 1, Univ. of Roorkee, Roorkee, India, II-8-41-7.
Shannon, C. E. (1948). “A mathematical theory of communication.” Bell Syst. Tech. J., 27(3), 379–423.
Sharma, T. C., and Dickinson, W. T. (1979a). “Unit step and frequency response functions applied to the watershed fluvial system.” J. Hydrol., 40(3–4), 323–335.
Sharma, T. C., and Dickinson, W. T. (1979b). “Discrete dynamic model of watershed sediment yield.” J. Hydraul. Div., 105(HY5), 555–571.
Singh, V. P. (1983). “Analytical solutions of kinematic equations for erosion on a plane: 2. Rainfall of finite duration.” Adv. Water Resour., 6(2), 88–95.
Singh, V. P. (1989). Hydrologic systems: Watershed modeling, Prentice Hall, Englewood Cliffs, NJ.
Singh, V. P. (1998). Entropy-based parameter estimation in hydrology, Kluwer, Boston.
Singh, V. P. (2010a). “Entropy theory for derivation of infiltration equations.” Water Resour. Res., 46(3), W03527.
Singh, V. P. (2010b). “Tsallis entropy theory for derivation of infiltration equations.” Trans. ASABE, 3(2), 447–463.
Singh, V. P. (2010c). “Entropy theory for movement of moisture in soils.” Water Resour. Res., 46, W03516.
Singh, V. P. (2011). “An IUH equation based on entropy theory.” Trans. ASABE, 54(1), 1–10.
Singh, V. P., Baniukiewicz, A., and Chen, V. J. (1982). “An instantaneous unit sediment graph study for small upland watersheds.” Modeling components of hydrologic cycle, V. P. Singh, ed., Water Resources Publications, Littleton, CO, 539–554.
Singh, V. P., and Chen, V. J. (1982). “On the relation between sediment yield and runoff volume.” Modeling components of hydrologic cycle, V. P. Singh, ed., Water Resources Publications, Littleton, CO, 555–570.
Singh, V. P., and Krstanovic, P. F. (1987). “A stochastic model for sediment yield using the principle of maximum entropy.” Water Resour. Res., 23(5), 781–793.
Singh, V. P., and Regl, R. R. (1983). “Analytical solutions of kinematic equations for erosion on a plane: l. Rainfall of infinite duration.” Adv. Water Resour., 6(1), 2–10.
Smith, R. E., Goodrich, D. C., Woolhiser, D. A., and Unkrich, C. L. (1995). “KINEROS: A kinematic runoff and erosion model.” Chapter 20, Computer models of watershed hydrology, V. P. Singh, Water Resources Publications, Littleton, CO, 697–732.
Soil Conservation Society of America. (1977). “Soil erosion: Prediction and control.” Proc., National Conf. on Soil Erosion, Purdue Univ., West Lafayette, IN.
Srivastava, P. K., Rastogi, R. A., and Chauhan, H. S. (1984). “Prediction of storm sediment yield from a small watershed.” J. Agric. Eng., 21(1–2), 121–126.
Tyagi, J. V., Mishra, S. K., Singh, R., and Singh, V. P. (2008). “SCS-CN based time-distributed sediment yield model.” J. Hydrol., 352(3–4), 388–403.
Williams, J. R. (1975). “Sediment routing for agricultural watersheds.” Water Resour. Bull., 11(5), 965–974.
Williams, J. R. (1978). “Unit sediment graph.” Water Resour. Res., 14(5), 889–901.
Williams, J. R., and Berndt, H. D. (1977). “Sediment yield prediction based on watershed hydrology.” Trans. ASAE, 20(6), 1100–1104.
Wischmeier, W. H., and Smith, D. D. (1978). Predicting rainfall erosion losses—A guide to conservation planning, USDA, Washington, DC.

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Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 20Issue 6June 2015

History

Received: Mar 25, 2014
Accepted: Jul 17, 2014
Published online: Aug 20, 2014
Discussion open until: Jan 20, 2015
Published in print: Jun 1, 2015

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Authors

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Vijay P. Singh, F.ASCE
Distinguished Professor and Caroline & William N. Lehrer Distinguished Chair in Water Engineering, Dept. of Biological and Agricultural Engineering, Dept. of Civil and Environmental Engineering, Texas A & M Univ., College Station, TX 77843-2117.
Huijuan Cui [email protected]
Graduate Student, Water Management and Hydrologic Science Program, Texas A & M Univ., College Station, TX 77843-2117 (corresponding author). E-mail: [email protected]
Aaron Byrd
Research Hydraulic Engineer and Branch Chief, Hydrologic Systems Branch, Coastal and Hydraulics Laboratory, Engineer Research Development Center, U.S. Army Corps of Engineers, Vicksburg, MS 39181.

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