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Versatile Uses of the Entropy Concept in Water Resources

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Entropy and Energy Dissipation in Water Resources

Part of the book series: Water Science and Technology Library ((WSTL,volume 9))

Abstract

The concept of entropy, which originated in classical thermodynamics, has found versatile uses in hydrology and water resources. The investigations in one group of applications basically rely on the concept of “thermodynamic entropy”, where problems associated with river morphology and river hydraulics are handled by a rather non-probabilistic approach. The second group of studies use the concept of “informational entropy” within a probabilistic context to define uncertainties in hydrologic variables, hydrologic systems and their models, and parameters of probability distribution functions. Although it has a very short history in hydrology and water resources, informational entropy has found a wider range of applications in this field, as compared to the thermodynamic entropy. The presented paper discusses the versatile uses of informational entropy in water resources, summarizing the progress obtained so far in developing the concept into a widely accepted technique. Besides the already covered areas of application, new fields where entropy can be used effectively are proposed to cover basically problems in environmental engineering. In view of current research results, the merits and limitations using entropy in water resources engineering problems are discussed, followed by the conclusion that there is a definite need for further investigations so that entropy becomes a principal technique in hydrology and water resources.

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References

  • Alpaslan, N., 1983, Mathematical Simulation Model of Completely Mixed Activated Sludge Processes. Izmir, Dokuz Eylul University, Faculty of Engineering and Architecture, Institute of Science and Technology, Ph.D. Thesis no. 7, (in Turkish).

    Google Scholar 

  • Alpaslan, N., 1984, Modeling and Mathematical Simulation of Completely Mixed Activated Sludge Processes. Izmir, Environment ′84 Proceedings of V. Turkish-German Environmental Engineering Symposium, Izmir, Dokuz Eylul University, Faculty of Engineering and Architecture, Environmental Engineering Department and Institut fur Siedlungswasserbau, Wassergute und Abfallwirtschaft der Universitaet Stuttgart.

    Google Scholar 

  • Amorocho, J. and B. Espildora, 1973, Entropy in the Assessment of Uncertainty of Hydrologic Systems and Models. Water Resources Research, 9 (6), pp. 1551–1522.

    Article  Google Scholar 

  • Arora, K. and V.P. Singh, 1986, An Evaluation of Seven Methods for Estimating Parameters of the EVI Distribution. Paper presented at the Int. Symp. on Flood Frequency and Risk Analysis, Louisiana State University, Baton Rouge, LA, USA.

    Google Scholar 

  • Baran, T. and N.B. Harmancioglu, 1990, Assessment of Mathematical Models with Exponential Functions Describing Karstic Spring Discharges. UKAM, IAHS & IAH, International Symposium and Field Seminar on Hydrogeologic Processes in Karst Terraines, Session X on Modeling, Antalya, Turkey, (October, 1990), 15p. + figures.

    Google Scholar 

  • Caselton, W.F. and T. Husain, 1980, Hydrologic Networks: Information Transmission, J. Water Resources Planning and Management Division, ASCE, 106, WR2, (July, 1980 ), 503–529.

    Google Scholar 

  • Cetiner, A., 1988, Hydrologic Information Transfer in River Basins Fed by Karstic Spring Effluents (in Turkish). Izmir, Dokuz Eylul University, Institute of Technological Sciences, Civil Engineering Department, M.Sc. Thesis in Hydrology and Hydraulic Structures, no. 21 (dir: N. Harmancioglu).

    Google Scholar 

  • Chapman, T.G., 1986, Entropy As a Measure of Hydrologic Data Uncertainty. Journal of Hydrology, no. 85, pp. 111–126.

    Article  Google Scholar 

  • Davy, B.W. and T.R.H. Davies, 1979, Entropy Concepts in Fluvial Geomorphology: A Reevaluation. Water Resources Research, no. 15 (1), pp. 103–106.

    Article  Google Scholar 

  • Fisher, R.A., 1966, Design of Experiments. Edinburgh, Oliver and Boyd Ltd., 8th ed., 248p.

    Google Scholar 

  • Harmancioglu, N., 1980, Measuring the Information Content of Hydrological Processes by the Entropy Concept (in Turkish). Ph.D. Thesis in Hydrology and Hydraulic Structures, no. 4, Ege University, Faculty of Engineering, 164 p.

    Google Scholar 

  • Harmancioglu, N., 1981, Measuring the Information Content of Hydrological Processes by the Entropy Concept. Centennial of Ataturk’s Birth, Journal of the Civil Eng. Faculty of Ege Univ., pp. 13–38.

    Google Scholar 

  • Harmancioglu, N., 1984, Entropy Concept as Used in Determination of Optimum Sampling Intervals. Proceedings of Hydrosoft ′84, International Conference on Hydraulic Engineering Software, Portoroz, Yugoslavia, pp.6–99 and 6–110.

    Google Scholar 

  • Harmancioglu, N.B. and V. Yevjevich, 1985, Transfer of Hydrologic Information Along Rivers Partially Fed by Karstified Limestones. Proc. of Int. Symp. on Karst Water Resources, Ankara, IAHS Publ. 161, pp.131.-161.

    Google Scholar 

  • Harmancioglu, N.B. and V. Yevjevich, 1986, Transfer of Information Among Water Quality Variables of the Potomac River, Phase III: Transferable and Transferred Information. Report to D.C. Water Resources Research Center of the University of the District of Columbia, Washington, D.C., June 1986, 81 p.

    Google Scholar 

  • Harmancioglu, N. and T. Baran, 1989, Effects of Recharge Systems on Hydrologic Information Transfer Along Rivers. IAHS, Proc. of the Third Scientific Assembly-New Directions for Surface Water Modeling, IAHS Publ. 181, pp. 223–233.

    Google Scholar 

  • Harmancioglu, N.B. and V. Yevjevich, 1987. Transfer of Hydrologic Information Among River Points. Journal of Hydrology, n. 91, pp. 103–118

    Article  Google Scholar 

  • Harmancioglu, N. and N. Alpaslan, 1991, Water Quality Monitoring Network Design: A problem of Multi-Objective Decision Making. Paper submitted to AWRA, Water Resources Bulletin to be published in August 1991.

    Google Scholar 

  • Harmancioglu, N.B., Yevjevich, V. and J.T.B. Obeysekera, 1986, Measures of Information Transfer Between Variables. Proc. of Fourth Int. Hydrol. Symp. on Multivariate Analysis of Hydrologic Processes, (ed.:H.W.Shen et al.), pp.481–499.

    Google Scholar 

  • Harmancioglu, N., A. Ozer, N. Alpaslan, 1987, Evaluation of Water Quality data (in Turkish). Ankara, Chamber of Civil Engineers of Turkey, IX. Technical Congress Proceedings, November 16–20, 1987, vol. 11, pp. 113–129.

    Google Scholar 

  • Husain, T., 1989, Hydrologic Uncertainty Measure and Network Design. Water Resources Bulletin, v. 25, no. 3, pp. 527–534.

    Article  Google Scholar 

  • Jain, D. and V.P. Singh, 1987, Estimating Parameters of EVI Distribution of Flood Frequency Analysis. Water Resources Bulletin, v. 23, no. 1, pp. 59–71.

    Article  Google Scholar 

  • Jaynes, E.T., 1957a, Information Theory and Statistical Mechanics I. Phys.Rev., no. 106, pp. 620–630.

    Article  Google Scholar 

  • Jaynes, E.T., 1957b, Information Theory and Statistical Mechanics II. Phys.Rev., no. 108, pp. 171–190.

    Article  Google Scholar 

  • Jaynes, E.T., 1961, Probability Theory in Science and Engineering. McGraw-Hill, New York.

    Google Scholar 

  • Jaynes, E.T., 1982, On the Rationale of Entropy Methods. Proc. IEEE, no. 70 (19), pp. 939–959.

    Article  Google Scholar 

  • Jaynes, E.T., 1983, Papers on Probability, Statistics and Statistical Physics (ed. by R.D. Rosenkrantz). Dordrecht, D. Reidel, vol. 158.

    Google Scholar 

  • Jowitt, P.W. 1979, The Extreme Value Type-1 Distribution and the Principle of Maximum Entropy. Journal of Hydrology, no. 42, pp. 23–38.

    Article  Google Scholar 

  • Khinchin, A.I., 1957, Mathematical Foundations of Information Theory. Dover Publ., New York, 120 p.

    Google Scholar 

  • Krstanovic, P.F. and V.P. Singh, 1986, A Multivariate Stochastic Flood Analysis Using Entropy. Paper presented at the Int. Symp. on Flood Frequency and Risk Analysis, Louisiana State.

    Google Scholar 

  • Leopold, L.B. and W.B. Langbein, 1962, The Concept of Entropy in Landscape Evaluation. USGS Prof. Paper 500-A, pp. A1 - A20.

    Google Scholar 

  • Linfoot, E.H., 1957, An Information Measure of Correlation. Information and Control, no. 1, pp. 85–89.

    Article  Google Scholar 

  • Padmanabhan, G. and A.R. Rao, 1988, Maximum Entropy Spectral Analysis of Hydrologic Data. Water Resources Research, no. 24 (9), pp. 1519–1534.

    Article  Google Scholar 

  • Panu, U.S.and T.E. Unny, 1977, Entropy Concept in Feature Extraction and Hydrologic Time Series Analysis. Proc. Third Int. Hydrol. Symp., Colorado State Univ., Fort Collins, Colorado.

    Google Scholar 

  • Paulson, A.S. and C.B. Garrison, 1973, Entropy As a Measure of the Areal Concentration of Water Oriented Industry. Water Resources Research, no. 9 (2), pp. 263–269.

    Article  Google Scholar 

  • Scheidegger, A.E., 1967, A Thermodynamic Analogy for Meander Systems. Water Resources Research, no. 3 (4), pp. 1041–1046.

    Article  Google Scholar 

  • Shannon, C.E., 1948a, A Mathematical Theory of Communications, I and II. Bell System Tech. Journal, no. 27, pp. 379–423.

    Google Scholar 

  • Shannon, C.E., 1948b, A Mathematical Theory of Communication, III and IV. Bell System Tech. Journal, no. 27, pp. 623–656.

    Google Scholar 

  • Shannon, C.E. and W. Weaver, 1949, The Mathematical Theory of Communication. The University of Illinois Press, Urbana, Illinois.

    Google Scholar 

  • Sharp, W.E., 1970, Stream Orders As a Measure of Sample Source Uncertainty. Water Resources Research, no. 6 (3), pp. 919–926.

    Article  Google Scholar 

  • Singh, V.P., 1987, On Application of the Weibull Distribution in Hydrology. Water Resources Management, no. 1, pp. 33–43.

    Article  Google Scholar 

  • Singh, V.P. and D. Jain, 1985, Comparing Methods of Parameter Estimation for EVI Distribution for Flood Frequency Analysis. Paper presented at the V th World Congress on Water Resources, Brussels, Belgium.

    Google Scholar 

  • Singh, V.P. and K. Singh, 1985a, Derivation of the Gamma Distribution by Using the Principle of Maximum Entropy. Water Resources Bulletin, no. 21 (6), pp. 941–962.

    Article  Google Scholar 

  • Singh, V.P.and K. Singh, 1985b, Derivation of the Pearson Type (PT) III Distribution by Using the Principle of Maximum Entropy (POME). Journal of Hydrology, no. 80, pp. 197–214.

    Article  Google Scholar 

  • Singh, V.P.and K.Singh, 1987, Parameter Estimation for TPLN Distribution for Flood Frequency Analysis. Water Resources Bulletin, vol.23, no.6., pp. 1185–1191.

    Google Scholar 

  • Singh, V.P.and P.F.Krstanovic, 1987, A Stochastic Model for Sediment Yield Using the Principle of Maximum Entropy. Water Resources Research, vol. 23, no. 5, pp. 781–793.

    Article  Google Scholar 

  • Singh, V.P., K. Singh and A.K. Rajagopal, 1985, Application of the Principle of Maximum Entropy (POME) to Hydrologic Frequency Analysis. Completion Report 06, Louisiana Water Resources Research Institute, Louisiana State Univ., Baton Rouge, Louisiana.

    Google Scholar 

  • Singh, V.P., Rajagopal, A.K. and K.Singh, 1986, Derivation of Some Frequency Distributions Using the Principle of Maximum Entropy (POME). Advanced Water Resources, no. 9 (2), pp. 91–106.

    Article  Google Scholar 

  • Singh, V.P.and A.K. Rajagopal, 1987. Some Recent Advances in the Application of the Principle of Maximum Entropy (POME) in Hydrology. Water for the Future (ed. by J.C. Rodda and N.C. Matalas), Proceedings of the Rome Symposium, April 1987, IAHS Publications, 164, pp. 353–364.

    Google Scholar 

  • Sonuga, J.O., 1972, Principle of Maximum Entropy in Hydrological Frequency Analysis. Journal of Hydrology, no. 17, pp. 177–191.

    Article  Google Scholar 

  • Sonuga, J.O., 1976, Entropy Principle Applied to Rainfall-Runoff Process. Journal of Hydrology, no. 30, pp. 81–94.

    Article  Google Scholar 

  • Templeman, A.B., 1989, Entropy and Civil Engineering Optimization. NATO/ASI on Optimization and Decision Support Systems in Civil Engineering, Edinburgh, June 1989, 17 p.

    Google Scholar 

  • Uslu, O. and A. Tanriover, 1979, Measuring the Information Content of Hydrological Processes (in Turkish). Istanbul, Proceedings of the First National Congress on Hydrology, Nov. 1979, pp. 437–443.

    Google Scholar 

  • Uslu, O. and Alpaslan, N., 1983, Sensitivity Analyses in Mathematical Models of Activated Sludge. Environment′83, Proceedings of I I. National Environmental Engineering Symposium, Izmir, Dokuz Eylul University, Faculty of Engineering and Architecture, Environmental Engineering Department and Turkish National Committee on Water Pollution Research and Control, (in Turkish).

    Google Scholar 

  • Uslu, O. and Alpaslan, N., 1984, A Study for the Mathematical Representation of a Biological Wastewater Treatment Systems. Istanbul, International Symposium on Environmental Management for Developing Countries, Preprints, Envitek AS, 11 p.

    Google Scholar 

  • Yang, G.T., 1971, Potential Energy and Stream Morphology. Water Resources Research, no. 7 (2), pp. 311–322.

    Article  Google Scholar 

  • Yevjevich, V., 1987, Stochastic Models in Hydrology. Stochastic Hydrology and Hydraulics, no. 1 (1987), pp. 17–36.

    Article  Google Scholar 

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© 1992 Springer Science+Business Media Dordrecht

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Harmancioglu, N.B., Singh, V.P., Alpaslan, N. (1992). Versatile Uses of the Entropy Concept in Water Resources. In: Singh, V.P., Fiorentino, M. (eds) Entropy and Energy Dissipation in Water Resources. Water Science and Technology Library, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2430-0_4

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  • DOI: https://doi.org/10.1007/978-94-011-2430-0_4

  • Publisher Name: Springer, Dordrecht

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  • Online ISBN: 978-94-011-2430-0

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