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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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).
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.
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.
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.
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.
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.
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).
Chapman, T.G., 1986, Entropy As a Measure of Hydrologic Data Uncertainty. Journal of Hydrology, no. 85, pp. 111–126.
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.
Fisher, R.A., 1966, Design of Experiments. Edinburgh, Oliver and Boyd Ltd., 8th ed., 248p.
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.
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.
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.
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.
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.
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.
Harmancioglu, N.B. and V. Yevjevich, 1987. Transfer of Hydrologic Information Among River Points. Journal of Hydrology, n. 91, pp. 103–118
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.
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.
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.
Husain, T., 1989, Hydrologic Uncertainty Measure and Network Design. Water Resources Bulletin, v. 25, no. 3, pp. 527–534.
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.
Jaynes, E.T., 1957a, Information Theory and Statistical Mechanics I. Phys.Rev., no. 106, pp. 620–630.
Jaynes, E.T., 1957b, Information Theory and Statistical Mechanics II. Phys.Rev., no. 108, pp. 171–190.
Jaynes, E.T., 1961, Probability Theory in Science and Engineering. McGraw-Hill, New York.
Jaynes, E.T., 1982, On the Rationale of Entropy Methods. Proc. IEEE, no. 70 (19), pp. 939–959.
Jaynes, E.T., 1983, Papers on Probability, Statistics and Statistical Physics (ed. by R.D. Rosenkrantz). Dordrecht, D. Reidel, vol. 158.
Jowitt, P.W. 1979, The Extreme Value Type-1 Distribution and the Principle of Maximum Entropy. Journal of Hydrology, no. 42, pp. 23–38.
Khinchin, A.I., 1957, Mathematical Foundations of Information Theory. Dover Publ., New York, 120 p.
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.
Leopold, L.B. and W.B. Langbein, 1962, The Concept of Entropy in Landscape Evaluation. USGS Prof. Paper 500-A, pp. A1 - A20.
Linfoot, E.H., 1957, An Information Measure of Correlation. Information and Control, no. 1, pp. 85–89.
Padmanabhan, G. and A.R. Rao, 1988, Maximum Entropy Spectral Analysis of Hydrologic Data. Water Resources Research, no. 24 (9), pp. 1519–1534.
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.
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.
Scheidegger, A.E., 1967, A Thermodynamic Analogy for Meander Systems. Water Resources Research, no. 3 (4), pp. 1041–1046.
Shannon, C.E., 1948a, A Mathematical Theory of Communications, I and II. Bell System Tech. Journal, no. 27, pp. 379–423.
Shannon, C.E., 1948b, A Mathematical Theory of Communication, III and IV. Bell System Tech. Journal, no. 27, pp. 623–656.
Shannon, C.E. and W. Weaver, 1949, The Mathematical Theory of Communication. The University of Illinois Press, Urbana, Illinois.
Sharp, W.E., 1970, Stream Orders As a Measure of Sample Source Uncertainty. Water Resources Research, no. 6 (3), pp. 919–926.
Singh, V.P., 1987, On Application of the Weibull Distribution in Hydrology. Water Resources Management, no. 1, pp. 33–43.
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.
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.
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.
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.
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.
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.
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.
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.
Sonuga, J.O., 1972, Principle of Maximum Entropy in Hydrological Frequency Analysis. Journal of Hydrology, no. 17, pp. 177–191.
Sonuga, J.O., 1976, Entropy Principle Applied to Rainfall-Runoff Process. Journal of Hydrology, no. 30, pp. 81–94.
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.
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.
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).
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.
Yang, G.T., 1971, Potential Energy and Stream Morphology. Water Resources Research, no. 7 (2), pp. 311–322.
Yevjevich, V., 1987, Stochastic Models in Hydrology. Stochastic Hydrology and Hydraulics, no. 1 (1987), pp. 17–36.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-94-011-2430-0_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5072-2
Online ISBN: 978-94-011-2430-0
eBook Packages: Springer Book Archive