Skip to main content
SpringerLink
Log in

Entropy in environmental and water resources

  • Reference work entry
Encyclopedia of Hydrology and Lakes

Part of the book series: Encyclopedia of Earth Science ((EESS))

Introduction

The term entropy as a scientific concept was initially used in thermodynamics as early as the 1850s by Clasius. Later in 1877, Boltzmann provided a probabilistic interpretation of the concept within the context of statistical mechanics. The explicit relationship between entropy and probability was developed in the early 1900s by Planck. Finally, Shannon (1948a, b) used the concept to present an economical description of the properties of long sequences of symbols, and applied the results to a number of basic problems in coding theory and data transmission. With his remarkable contributions, Shannon developed the basis of modern information theory. Later, Jaynes (1957a, b) re-evaluated the method of maximum entropy and applied it to a variety of problems involving the determination of unknown parameters from incomplete data (Papoulis, 1991).

Since the pioneering work of Shannon (1948a, b), much attention has been focused on the use of entropy and energy dissipation rate...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 629.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  • Aczel, J. and Daroczy, Z., 1975. On Measures of Information and Their Characterization. Academic Press, New York.

    Google Scholar 

  • Alpaslan, N., 1994. Assessment of treatment plant efficiencies by the entropy principle. Time Series Analysis in Hydrology and Environmental Engineering, Proceedings of the International Conference on Stochastic and Statistical Methods in Hydrology and Environmental Engineering (eds K.W. Hipel, A.I. McLeod, U.S. Panu and V.P. Singh), Kluwer Academic Publishers, Dordrecht Water Science and Technology Library, Vol. 10/3, pp. 177–190.

    Google Scholar 

  • Alpaslan, N., Harmancioglu, N.B. and V.P. Singh, 1992. The role of the entropy concept in design and evaluation of water quality monitoring networks, Entropy and Energy Dissipation in Water Resources in (eds V.P. Singh and M. Fiorentino), Dordecht, Kluwer Academic Publishers, Water Science and Technology Library, pp. 261–282.

    Google Scholar 

  • Amorocho, J. and Espildora, B., 1973. Entropy in the assessment of uncertainty of hydrologic systems and models. Water Resources Research, 9(6), 1551–1522.

    Google Scholar 

  • Arora, K. and Singh, V.P., 1987a. On statistical intercomparison of EVI estimators by Monte Carlo simulation. Advances in Water Resources, 10(2), 87–107.

    Google Scholar 

  • Arora, K. and Singh, V.P., 1987b. An Evaluation of Seven Methods for Estimating Parameters of the EVI Distribution, in Hydrologic Frequency Modeling (ed. V.P. Singh), D. Reidel, Boston, pp. 383–394.

    Google Scholar 

  • Arora, K. and Singh, V.P., 1989. A comparative evaluation of the estimates of log-Pearson type (LP) 3 distribution. Journal of Hydrology, 105, 19–37.

    Google Scholar 

  • Baran, T. and Harmancioglu, N.B., 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 Terrains, Session X on Modeling, Antalya, Turkey, October 1990, 15pp. + figures.

    Google Scholar 

  • Barbe, D.E., Cruise, J.F. and Singh, V.P., 1991. Solution of the three-constraint entropy-based velocity distribution. Journal of Hydraulic Engineering, ASCE, 117(10), 1389–1396.

    Google Scholar 

  • Barbe, D.E., Cruise, J.F. and Singh, V.P., 1994. Derivation of a Distribution for the Piezometric Head in Groundwater Flow Using Entropy in Stochastic and Statistical Methods in Hydrology, Vol. 2, (ed. K.W. Hipel), Kluwer Academic Publishers, Dordrecht, pp. 151–161.

    Google Scholar 

  • Behara, M. and Chawla, J.S., 1974. Generalized gamma-entropy. Selecta, Statistica Canadiana, 2, 15–38.

    Google Scholar 

  • Boltzmann, L., 1872. Weitere Studien uber das Warmegleichgewich unter Gasmolekulen. K. Acad. Wiss. (Wein) Sitzb., II Abt., 66, 275.

    Google Scholar 

  • Burg, J.P., 1975. Maximum Spectral Analysis. PhD Dissertation, Stanford University, Palo Alto, California.

    Google Scholar 

  • Caselton, W.F. and Husain, T., 1980. Hydrologic networks: information transmission, Journal of Water Resources Planning and Management Division, ASCE, 106(WR2), 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.

    Google Scholar 

  • Chapman, T.G., 1986. Entropy as a measure of hydrologic data uncertainty. Journal of Hydrology, 85, 111–126.

    Google Scholar 

  • Chiu, C.L., 1988. Entropy and 2D-velocity distribution in open channels. Journal of Hydraulic Engineering, ASCE, 114(7), 738–756.

    Google Scholar 

  • Chiu, C.L., 1989. Velocity distribution in open channel flow. Journal of Hydraulic Engineering, ASCE, 115(5), 576–594.

    Google Scholar 

  • Christensen, R.A., 1981. An exploratory application of entropy minimax to weather prediction: estimating the likelihood of multiyear droughts in California, in Entropy Minimax Sourcebook, Vol. IV: Applications (ed. R.A. Christensen), Entropy Limited, Lincoln, Massachusetts, pp. 495–544.

    Google Scholar 

  • Davy, B.W. and Davies, T.R.H., 1979. Entropy concepts in fluvial geomorphology: a reevaluation. Water Resources Research, 15(1), 103–106.

    Google Scholar 

  • Eilbert, R.F. and Christensen, R.A., 1983. Performance of the entropy hydrological forecasts for California water years 1948–1977. Journal of Climate and Applied Meteorology, 22, 1654–1657.

    Google Scholar 

  • Fisher, R.A., 1966. Design of Experiments, 8th edn, Oliver and Boyd, Edinburgh, 248 pp.

    Google Scholar 

  • Fiorentino, M., Claps, P. and Singh, V.P., 1993. An entropy-based morphological analysis of river basin networks. Water Resources Research, 29(4), 1215–1224.

    Google Scholar 

  • Fiorentino, M., Singh, V.P. and Arora, K., 1987a. On the two-component extreme-value distribution and its point and regional estimators, in Regional Flood Frequency Analysis (ed. V.P. Singh), D. Reidel Publishing Co., Boston, pp. 252–272.

    Google Scholar 

  • Fiorentino, M., Arora, K. and Singh, V.P., 1987b. The two-component extreme-value distribution for food frequency analysis: another look and derivation of a new estimation method. Stochastic Hydrology and Hydraulics, 1, 199–208.

    Google Scholar 

  • Goulter, I. and Kusmulyono, A., 1993. Entropy theory to identify water quality violators in environmental management, in Geo-Water and Engineering Aspects (eds R. Chowdhury and M. Sivakumar), A.A. Balkema, Rotterdam, pp. 149–154.

    Google Scholar 

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

    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 Engineering Faculty of Ege University, 13–38.

    Google Scholar 

  • Harmancioglu, N., 1984. Entropy concept as used in determination of optimum sampling intervals, in Proceedings of Hydrosoft '84, International Conference on Hydraulic Engineering Software, Portoroz, Yugoslavia, pp. 96–102.

    Google Scholar 

  • Harmancioglu, N., 1994a. Assessment of information and uncertainty related to floods, in Coping with Floods (eds G. Rossi, N.B. Harmancioglu and V. Yevjevich), Kluwer Academic Publishers, NATO-ASI Series, Series E, Vol. 257, pp. 171–184.

    Google Scholar 

  • Harmancioglu, N., 1994b. An entropy-based approach to station discontinuance, in Time Series Analysis in Hydrology and Environmental Engineering, Proceedings of the International Conference on Stochastic and Statistical Methods in Hydrology and Environmental Engineering (eds K.W. Hipel, A.I. McLeod, U.S. Panu and V.P. Singh), Kluwer Academic Publishers, Water Science and Technology Library, Vol. 10/3, pp. 163–176.

    Google Scholar 

  • Harmancioglu, N.B. and Alpaslan, N., 1992. Water quality monitoring network design: a problem of multi-objective decision making, AWRA, Water Resources Bulletin, Special Issue on Multiple-Objective Decision Making in Water Resources, 28, pp. 1–14.

    Google Scholar 

  • Harmancioglu, N. and Baran, T., 1989. Effects of recharge systems on hydrologic information transfer along rivers. IAHS, Proceedings of the Third Scientific Assembly–New Directions for Surface Water Modeling, IAHS Publ. 181, pp. 223–233.

    Google Scholar 

  • Harmancioglu, N.B. and Singh, V.P., 1991. An information-based approach to monitoring and evaluation of water quality data, in Advances in Water Resources Technology (ed. G. Tsakiris). Proc. of the European Conference ECOWARM, A.A. Balkema, Rotterdam pp. 377–386.

    Google Scholar 

  • Harmancioglu, N.B. and Yevjevich, V., 1985. Transfer of hydrologic information along rivers partially fed by karstified limestones, in Proceedings of International Symposium on Karst Water Resources, Ankara, IAHS Publ. 161, pp. 161–171.

    Google Scholar 

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

    Google Scholar 

  • Harmancioglu, N.B. and Yevjevich, V., 1987. Transfer of hydrologic information among river points. Journal of Hydrology, 91, 103–118.

    Google Scholar 

  • Harmancioglu, N.B., Yevjevich, V. and Obeysekera, J.T.B., 1986. Measures of information transfer between variables. Proceedings of Fourth International Hydrological Symposium on Multivariate Analysis of Hydrologic Processes, (eds H.W. Shen et al.), pp. 481–499.

    Google Scholar 

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

    Google Scholar 

  • Harmancioglu, N.B., Singh, V.P. and Alpaslan, N., 1992a. Versatile uses of the entropy concept in water resources, in Entropy and Energy Dissipation in Water Resources (eds V.P. Singh and M. Fiorentino), Kluwer Academic Publishers, Dordrecht, Water Science and Technology Library, pp. 91–117.

    Google Scholar 

  • Harmancioglu, N.B., Alpaslan, N. and Singh, V.P., 1992b. Application of the entropy concept in design of water quality monitoring networks, in Entropy and Energy Dissipation in Water Resources, (eds V.P. Singh and M. Fiorentino), Kluwer Academic Publishers, Dordrecht, Water Science and Technology Library, pp. 261–283.

    Google Scholar 

  • Harmancioglu, N.B., Singh, V.P. and Alpaslan, N., 1992c. Design of water quality monitoring networks, in Geomechanics and Water Engineering in Environmental Management, (ed. R.N. Chowdhury), A.A. Balkema, Rotterdam, Ch. 8, pp. 267–296.

    Google Scholar 

  • Harmancioglu, N.B., Alpaslan, N. and Singh, V.P., 1994. Assessment of the entropy principle as applied to water quality monitoring network design, in Time Series Analysis in Hydrology and Environmental Engineering, Proceedings of the International Conference on Stochastic and Statistical Methods in Hydrology and Environmental Engineering (eds K.W. Hipel, A.I. McLeod, U.S. Panu and V.P. Singh), Kluwer Academic Publishers, Water Science and Technology Library, Vol. 10/3, pp. 135–148.

    Google Scholar 

  • Havrada, J.H. and Charvat, F., 1967. Quantification methods of classificatory processes: concept of structural entropy. Kybernatica, 3, 30–35.

    Google Scholar 

  • Husain, T., 1989. Hydrologic uncertainty measure and network design. Water Resources Bulletin, 25(3), 527–534.

    Google Scholar 

  • Jain, D. and Singh, V.P., 1986. Estimating parameters of EVI distribution of flood frequency Analysis. Water Resources Bulletin, 23(1), 59–71.

    Google Scholar 

  • Jaynes, F.T., 1957a. Information theory and statistical mechanics I. Phys. Rev., 106, 620–630.

    Google Scholar 

  • Jaynes, E.T., 1957b. Information theory and statistical mechanics II. Phys. Rev., 108, 171–190.

    Google Scholar 

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

    Google Scholar 

  • Jaynes, E.T., 1979. Concentration of distributions at entropy maxima. in E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics (ed. R.D. Rosenkratz), D. Reidel, Boston, pp. 315–335.

    Google Scholar 

  • Jaynes, E.T., 1982. On the rationale of entropy methods. Proceedings of IEEE, 70(19), 939–959.

    Google Scholar 

  • Jaynes, E.T., 1983. Papers on Probability, Statistics and Statistical Physics (ed. R.D. Rosenkrantz), D. Reidel, Dordrecht, Studies in Epistemology, Logic, Methodology and Philosophy of Science, Vol. 158.

    Google Scholar 

  • Jowitt, P.W., 1979. The extreme value type-1 distribution and the principle of maximum entropy. Journal of Hydrology, 42, 23–38.

    Google Scholar 

  • Kapoor, V., 1990. Spatial uniformity of power and the altitudinal geometry of river networks. Water Resources Research, 26(10), 2303–2310.

    Google Scholar 

  • Kapur, J.N., 1967. Generalised entropies of order a and type b. Mathematics Seminar, 4, 79–94.

    Google Scholar 

  • Kapur, J.N., 1968. On information of order a and b. Proceedings of the Indian Academy of Science, 48A, 65–76.

    Google Scholar 

  • Kapur, J.N., 1986. Four families of measures of entropy. Indian Journal of Pure and Applied Mathematics, 17(4), 429–449.

    Google Scholar 

  • Kennedy, J.F., Richardson, P.D. and Sutera, S.P., 1964. Discussion of ‘Geometry of river channels’ by W.R. Langbein. Journal of the Hydraulics Division, Proceedings of ASCE, 90(HY6), 332–347.

    Google Scholar 

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

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1987. A multivariate stochastic flood analysis using entropy. in Hydrologic Frequency Modeling (ed. V.P. Singh), D. Reidel, Dordrecht, pp. 515–540.

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1988a. Application of Entropy Theory to Multivariate Hydrologic Analysis, Vol. 2. Technical Report WRR9, Water Resources Program, Dept. of Civil Engineering, Louisiana State University, Baton Rouge, LA, pp. 271–557.

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1988b. Application of Entropy Theory to Multivariate Hydrologic Analysis, Vol. 1, Technical Report WRR9, Water Resources Program, Dept. of Civil Engineering, Louisiana State University, Baton Rouge, LA pp. 1–271.

    Google Scholar 

  • Krstanovic, P.F. and Sing, V.P., 1991a. A univariate model for long-term streamflow forecasting: 1. Development. Stochastic Hydrology and Hydraulics, 5, 173–188.

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1991b. A univariate model for long-term streamflow forecasting: 1. Application. Stochastic Hydrology and Hydraulics, 5, 189–205.

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1993a. Evaluation of rainfall networks using entropy: I. Theoretical development. Water Resources Management, 6, 279–293.

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1993b. Evaluation of rainfall networks using entropy: II. Application. Water Resources Management, 6, 295–314.

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1993c. A real-time flood forecasting model based on maximum entropy spectral analysis: 1. Development. Water Resources Management, 7(2), 109–130.

    Google Scholar 

  • Krstanovic, P.F. and Singh, V.P., 1993d. A real-time flood forecasting model based on maximum entropy spectral analysis: II. Application. Water Resources Management, 7(2), 131–152.

    Google Scholar 

  • Leopold, L.B. and Langbein, W.B., 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, 1, 85–89.

    Google Scholar 

  • Nordin, C.F., 1977. Discussion of ‘Applicability of Unit Stream Power Equation’ by C.T. Yang and J.B. Stall. Journal of the Hydraulics Division, Proceedings of ASCE, 103(HY2), 209–211.

    Google Scholar 

  • Padmanabhan, G. and Rao, A.R., 1988. Maximum entropy spectral analysis of hydrologic data. Water Resources Research, 24(9), 1519–1534.

    Google Scholar 

  • Panu, U.S. and Unny, T.E., 1979. Entropy concept in feature extraction and hydrologic time series analysis, in Proceedings Third International Hydrology Symposium, Colorado State University, Fort Collins, Colorado, pp. 100–115.

    Google Scholar 

  • Papoulis, A., 1991. Probability, Random Variables and Stochastic Processes. McGraw-Hill, New York. Ch. 15.

    Google Scholar 

  • Paulson, A.S. and Garrison, C.B., 1973. Entropy as a measure of the areal concentration of water oriented industry. Water Resources Research, 9(2), 263–269.

    Google Scholar 

  • Renyi, A., 1961. On measures of entropy and information in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, pp. 547–561.

    Google Scholar 

  • Scheidegger, A.E., 1964. Some implications of statistical mechanics in geomorphology. IAHS bulletin, 9(1), pp. 12–16.

    Google Scholar 

  • Scheidegger, A.E., 1967. A thermodynamic analogy for meander systems. Water Resources Research, 3(4), 1041–1046.

    Google Scholar 

  • Schilperoot, T., Groot, S., Wetering, B.G.M. and Dijkman, F., 1982. Optimization of the Sampling Frequency of Water Quality Monitoring Networks, Waterloopkundig Laboratium Delft, Hydraulics Lab, Delft, The Netherlands.

    Google Scholar 

  • Shannon, C.E., 1948a. A mathematical theory of communications, I and II. Bell System Tech. Journal, 27, 379–423.

    Google Scholar 

  • Shannon, C.E., 1948b. A mathematical theory of communication, III and IV. Bell System Tech. Journal, 27, 623–656.

    Google Scholar 

  • Shannon, C.E. and Weaver, W., 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, 6(3), 919–926.

    Google Scholar 

  • Singh, V.P., 1987. On application of the Weibull distribution in hydrology. Water Resources Management, 1, 33–43.

    Google Scholar 

  • Singh, V.P., 1992. Entropy-based probability distributions for modeling of environmental and biological systems, in Structuring Biological Systems (ed. S.S. Iyengar), CRC Press, Ch. 6., pp. 167–208.

    Google Scholar 

  • Singh, V.P. and Fiorentino, M., 1992. A historical perspective of entropy applications in water resources, in Entropy and Energy Dissipation in Water Resources, (eds V.P. Singh and M. Fiorentino), Kluwer Academic Publishers, Dordrecht, Water Science and Technology Library, pp. 21–61.

    Google Scholar 

  • Singh, V.P. and Jain, D., 1985. Comparing methods of parameter estimation for EVI distribution for flood frequency analysis, in Proceedings of the Vth World Congress on Water Resources, Brussels, Belgium, pp. 1119–1132.

    Google Scholar 

  • Singh, V.P. and Krstanovic, P.F., 1986. Space design of rainfall networks using entropy, in Proceedings of the International Conference on Water Resources Needs and Planning in Drought Prone Areas, Khartoum, Sudan, pp. 173–188.

    Google Scholar 

  • Singh, V.P. and Krstanovic, P.F., 1987. A stochastic model for sediment yield using the principle of maximum entropy. Water Resources Research, 23(5), 781–793.

    Google Scholar 

  • Singh, V.P. and Krstanovic, P.F., 1988. A stochastic model for water quality constituents, in Proceedings of the 6th APD-IAHR Congress, Kyoto, Japan.

    Google Scholar 

  • Singh, V.P. and Rajagopal, A.K., 1987. Some recent advances in the application of the principle of maximum entropy (POME) in hydrology, in Water for the Future (eds J.C. Rodda and N.C. Matalas), Proceedings of the Rome Symposium, April 1987, IAHS Publication No. 164, pp. 353–364.

    Google Scholar 

  • Singh, V.P. and Singh, K., 1985a. Derivation of the gamma distribution by using the principle of maximum entropy. Water Resources Bulletin, 21(6), 941–962.

    Google Scholar 

  • Singh, V.P. and Singh, K., 1985b. Derivation of the Pearson type (PT) III distribution by using the principle of maximum entropy (POME). Journal of Hydrology, 80, 197–214.

    Google Scholar 

  • Singh, V.P. and Singh, K., 1985c. Pearson type III distribution and the principle of maximum entropy, in Proceedings of the Vth World Congress on Water Resources, Brussels, Vol. 3, pp. 1133–1146.

    Google Scholar 

  • Singh, V.P. and Singh, K., 1987. Parameter estimation for TPLN distribution for flood frequency analysis. Water Resources Bulletin, 23(6), 1185–1191.

    Google Scholar 

  • Singh, V.P. and Singh, K., 1988. Parameter estimation for log-Pearson type III distribution by POME. Journal of Hydraulic Engineering, 114(3), 112–122.

    Google Scholar 

  • Singh, V.P., Cruise, J.F. and Ma, M., 1989. A Comparative Evaluation of the Estimators of the Two Distributions by Monte Carlo Simulation Method. Technical Report WRR13, Water Resources Program, Dept. of Civil Eng., Louisiana State University, Baton Rouge, LA, 126 pp.

    Google Scholar 

  • Singh, V.P., Cruise, J.F. and Ma, M., 1990a. A comparative evaluation of the estimators of the three parameter lognormal distribution by Monte Carlo simulation. Computational Statistics and Data Analysis, 10, 71–85.

    Google Scholar 

  • Singh, V.P., Cruise, J.F. and Ma, M., 1990b. A comparative evaluation of the estimators of the Weibull distribution by Monte Carlo simulation. Journal of Statistical Computation and Simulation, 36, 229–241.

    Google Scholar 

  • Sonuga, J.O., 1972. Principle of maximum entropy in hydrological frequency analysis. Journal of Hydrology, 17, 177–191.

    Google Scholar 

  • Sonuga, J.O., 1976. Entropy principle applied to rainfall-runoff process. Journal of Hydrology, 30, 81–94.

    Google Scholar 

  • Tai, S. and Goda, T., 1980. Water quality assessment using the theory of entropy, in (ed. M.J. Stiff) River Pollution Control, USA, Ellis Horwood, Ch. 21, pp. 319–330.

    Google Scholar 

  • Tai, S. and Goda, T., 1985. Entropy analysis of water and waste-water treatment processes, International Journal of Environmental Studies, 25, 13–21.

    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 

  • Theil, H., 1970. Economics and Information Theory. North Holland, Amsterdam.

    Google Scholar 

  • Tirsch, F.S. and Male, J.W., 1984. River basin water quality monitoring network design, in Options for Reaching Water Quality Goals, Proceedings of 20th Annual Conference of AWRA (ed. J.M. Schad), AWRA Publications, pp. 149–156.

    Google Scholar 

  • Tomlin, S.G., 1969. A kinetic theory of distribution and similar problems. Environment and Planning, 1, 221.

    Google Scholar 

  • Tomlin, S.G., 1970. Time-dependent traffic distribution. Transportation Research, 4(1).

    Google Scholar 

  • Topsoe, F., 1974. Informationstheorie. B.G. Teubner, Stuttgart, 88 pp.

    Google Scholar 

  • Uslu, O. and A. Tanriover, 1979. Measuring the information content of hydrological processes (in Turkish), in Proceedings of the First National Congress on Hydrology, Istanbul, Nov. 1979, pp. 437–443.

    Google Scholar 

  • Van den Boss, A., 1971. Alternative interpretation of maximum entropy spectral analysis. IEEE Transactions on Information Theory, IT-17, 493–494.

    Google Scholar 

  • Wilson, A.G., 1970. The use of the concept of entropy in system modelling. Operational Research Quarterly, 21(2), 247–265.

    Google Scholar 

  • Yang, G.T., 1971a. Potential energy and stream morphology. Water Resources Research, 7(2), 311–322.

    Google Scholar 

  • Yang, G.T., 1971b. On river meanders. Journal of Hydrology, 13, 231–253.

    Google Scholar 

  • Yang, G.T., 1972. Unit stream power and sediment transport. Journal of Hydraulics Division, Proceedings of ASCE, 98(HY10), 1805–1826.

    Google Scholar 

  • Yevjevich, V., 1987. Stochastic models in hydrology. Stochastic Hydrology and Hydraulics, 1, 17–36.

    Google Scholar 

Cross reference

Download references

Authors
  1. N. B. Harmancioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. P. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Kluwer Academic Publishers

About this entry

Cite this entry

Harmancioglu, N.B., Singh, V.P. (1998). Entropy in environmental and water resources . In: Encyclopedia of Hydrology and Lakes. Encyclopedia of Earth Science. Springer, Dordrecht . https://doi.org/10.1007/1-4020-4497-6_76

Download citation

  • DOI: https://doi.org/10.1007/1-4020-4497-6_76

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-412-74060-2

  • Online ISBN: 978-1-4020-4497-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation