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Introduction

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Chaos in Hydrology

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Abstract

In simple terms, hydrology is the study of the waters of the Earth, including their occurrence, distribution, and movement. The constant circulation of water and its change in physical state is called the hydrologic cycle. The study of water started at least a few thousands years ago, but the modern scientific approach to the hydrologic cycle started in the seventeenth century. Since then, hydrology has witnessed a tremendous growth, especially over the last century, with significant advances in computational power and hydrologic data measurements. This chapter presents a general and introductory account of hydrology. First, the concept of the hydrologic cycle is described. Next, a brief history of the scientific development of hydrology is presented. Then, the concept of hydrologic system is explained, followed by a description of the hydrologic system model and model classification. Finally, the role of hydrologic data and time series modeling as well as the physical basis of time series modeling are highlighted.

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References

  • Abbott MB, Refsgaard JC (ed) (1996) Distributed hydrological modelling. Kluwer Academic Publishers, Dordrecht, The Netherlands

    Google Scholar 

  • Abrahart RJ, See LM, Dawson CW, Shamseldin AY, Wilby RL (2010) Nearly two decades of neural network hydrologic modeling. In: Sivakumar B, Berndtsson R (eds) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore, pp 267–346

    Chapter  Google Scholar 

  • Adams FD (1938) The birth and development of the geological sciences. Williams and Wilkins, Baltimore, MD

    Google Scholar 

  • Amorocho J (1967) The nonlinear prediction problems in the study of the runoff cycle. Water Resour Res 3(3):861–880

    Article  Google Scholar 

  • Amorocho J, Brandstetter A (1971) Determination of nonlinear functional response functions in rainfall-runoff processes. Water Resour Res 7(5):1087–1101

    Article  Google Scholar 

  • ASCE Task Committee (2000a) Artificial neural networks in hydrology. I: Preliminary concepts.ASCE. J Hydrol Eng 5(2):115–123

    Article  Google Scholar 

  • ASCE Task Committee (2000b) Artificial neural networks in hydrology. II: Hydrologic applications. ASCE. J Hydrol Eng 5(2):124–137

    Article  Google Scholar 

  • Babovic V (1996) Emergence, evolution, intelligence; hydroinformatics. Balkema Publishers, Rotterdam

    Google Scholar 

  • Bardossy A, Duckstein L (1995) Fuzzy rule-based modeling with applications to geophysical, biological and engineering systems. CRC Press, Boca Raton, FL, USA, p 256

    Google Scholar 

  • Beardmore N (1851) Manual of hydrology. Waterlow & Sons, London

    Google Scholar 

  • Beven KJ (1993) Prophecy, reality and uncertainty in distributed modeling. Adv Water Resour 16:41–51

    Article  Google Scholar 

  • Beven KJ (1997) Distributed hydrological modelling: applications of the TOPMODEL concept. John Wiley, Chichester, UK

    Google Scholar 

  • Beven KJ (2001) Rainfall-runoff modelling: the primer. Wiley, Chichester, UK

    Google Scholar 

  • Beven KJ (2002) Uncertainty and the detection of structural change in models of environmental systems. In: Beck MB (ed) Environmental foresight and models: a manifesto. Elsevier, The Netherlands, pp 227–250

    Chapter  Google Scholar 

  • Beven KJ (2006) On undermining the science? Hydrol Process 20:3141–3146

    Article  Google Scholar 

  • Biswas AK (1970) History of hydrology. North-Holland Publishing, Amsterdam

    Google Scholar 

  • Box GEP, Jenkins G (1970) Time series analysis, forecasting and control. Holden-Day, San Francisco

    Google Scholar 

  • Brutsaert W, Mawdsley JA (1976) The applicability of planetary boundary layer theory to calculate regional evapotranspiration. Water Resour Res 12:852–858

    Article  Google Scholar 

  • Chahine MT (1992) The hydrological cycle and its influence on climate. Nature 359:373–380

    Article  Google Scholar 

  • Chow VT (ed) (1964) Handbook of applied hydrology. McGraw-Hill, New York

    Google Scholar 

  • Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw-Hill, Singapore

    Google Scholar 

  • Chui CK (1992) An introduction to wavelets. Academic Press, Boston

    Google Scholar 

  • Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Dalton J (1802) Experimental essays on the constitution of mixed gases; on the force of steam or vapor from waters and other liquids, both in a Torricellian vacuum and in air; on evaporation; and on the expansion of gases by heat. Mem Proc Manch Lit Phil Soc 5:535–602

    Google Scholar 

  • Darcy H (1856) Les fontaines publiques de la ville de Dijon. V. Dalmont, Paris

    Google Scholar 

  • Dawdy DR (1969) Considerations involved in evaluating mathematical modeling of urban hydrologic systems. U. S. Geological Survey Water Supply Paper 1591-D, U. S. Department of Interior, Washington, D. C., D1-D18

    Google Scholar 

  • Dawdy DR (2007) Prediction versus understanding (The 2007 Ven Te Chow Lecture). ASCE J Hydrol Eng 12:1–3

    Article  Google Scholar 

  • Dawdy DR, Kalinin GP (1969) Mathematical modeling in hydrology. International Association of Scientific Hydrology Report, Mid-Decade Conference of the International Hydrological Decade, held in August in Surány, Hungary

    Google Scholar 

  • DeCoursey DG (1971) The stochastic approach to watershed modeling. Nordic Hydrol 11:186–216

    Google Scholar 

  • Dibike YB, Velickov S, Solomatine DP, Abbott M (2001) Model induction with support vector machines: introduction and applications. ASCE J Comput Civil Eng 15(2):208–216

    Article  Google Scholar 

  • Dooge JCI (1959) A general theory of the unit hydrograph. J Geophys Res 64(2):241–256

    Article  Google Scholar 

  • Dooge JCI (1965) Analysis of linear systems by means of Laguerre functions. Soc Indust Appl Math (SIAM) J Cont 2(3):396–408

    Google Scholar 

  • Dooge JCI (1967a) The hydrologic cycle as a closed system. Int Assoc Sci Hydrol Bull 13(1):58–68

    Article  Google Scholar 

  • Dooge JCI (1967b) A new approach to nonlinear problems in surface water hydrology: hydrologic systems with uniform nonlinearity. Int Assoc Sci Hydrol Publ 76:409–413

    Google Scholar 

  • Dooge JCI (1977) Problems and methods of rainfall-runoff modeling. In: Ciriani TA, Maione U, Wallis JR (eds) Mathematical models for surface water hydrology. John Wiley, New York, pp 71–108

    Google Scholar 

  • Driscoll FG (ed) (1986) Groundwater and wells. Johnson Division, St. Paul, Minnesota

    Google Scholar 

  • Duan Q, Gupta HV, Sorooshian S, Rousseau AN, Turcotte R (2003) Calibration of watershed models. Water Science and Application Series. American Geophysical Union, Washington vol 6, pp 1–346

    Google Scholar 

  • Eagleson PS, Brutsaert WH, Colbeck SC, Cummins KW, Dozier J, Dunne T, Edmond JM, Gupta VK, Jacoby JC, Manabe S, Nicholson SE, Nielsen DR, Rodríguez-Iturbe I, Rubin J, Sposito G, Swank WT, Zipser EJ, Burges S (1991) Opportunities in the hydrologic sciences. National Academy Press, Washington, DC, p 348

    Google Scholar 

  • Fiering MB (1967) Streamflow synthesis. Harvard University Press, Cambridge, Massachusetts

    Book  Google Scholar 

  • Foufoula-Georgiou E, Kumar P (eds) (1994) Wavelets in geophysics. Academic Press, San Diego, California, p 373

    Google Scholar 

  • Freeze RA (1971) Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin. Water Resour Res 7(2):347–366

    Article  Google Scholar 

  • Freeze RA, Cherry JA (1979) Groundwater. Prentice-Hall, Englewood Cliffs, New Jersey

    Google Scholar 

  • Furey PR, Gupta VK (2005) Effects of excess-rainfall on the temporal variability of observed peak discharge power laws. Adv Water Resour 28:1240–1253

    Article  Google Scholar 

  • Furey PR, Gupta VK (2007) Diagnosing peak-discharge power laws observed in rainfall–runoff events in Goodwin Creek experimental watershed. Adv Water Resour 30:2387–2399

    Article  Google Scholar 

  • Gelhar LW (1993) Stochastic subsurface hydrology. Prentice-Hall, Englewood Cliffs, New Jersey

    Google Scholar 

  • Govindaraju RS (ed) (2002) Stochastic methods in subsurface contaminant hydrology. ASCE, New York

    Google Scholar 

  • Govindaraju RS, Rao AR (2000) Artificial neural networks in hydrology. Kluwer Acadmic Publishers, Amsterdam

    Book  Google Scholar 

  • Gumbel EJ (1941) The return period of flood flows. Ann Math Stat 12(2):163–190

    Article  Google Scholar 

  • Gupta VK (2004) Emergence of statistical scaling in floods on channel networks from complex runoff dynamics. Chaos Soliton Fract 19:357–365

    Article  Google Scholar 

  • Gupta VK, Waymire E (1998) Spatial variability and scale invariance in hydrologic regionalization. In: Sposito G (ed) Scale dependence and scale invariance in hydrology. Cambridge University Press, Cambridge, pp 88–135

    Chapter  Google Scholar 

  • Gupta VK, Rodríguez-Iturbe I, Wood EF (eds) (1986) Scale problems in hydrology: runoff generation and basin response. Reidel Publishing Company, FD, p 244

    Google Scholar 

  • Gupta VK, Castro SL, Over TM (1996) On scaling exponents of spatial peak flows from rainfall and river network geometry. J Hydrol 187:81–104

    Article  Google Scholar 

  • Gupta VK, Troutman BM, Dawdy DR (2007) Towards a nonlinear geophysical theory of floods in river networks: an overview of 20 years of progress. In: Tsonis AA, Elsner JB (eds) Twenty years of nonlinear dynamics in geosciences. Springer Verlag

    Google Scholar 

  • Haan CT (1994) Statistical methods in hydrology. Iowa University Press, Iowa

    Google Scholar 

  • Harley BM (1967) Linear routing in uniform flow channels. M. Eng. Sc. Thesis, National University of Ireland, University College, Cork, Ireland

    Google Scholar 

  • Haykin S (1999) Neural networks: a comprehensive foundation. Prentice Hall International Inc, New Jersey

    Google Scholar 

  • Hele-Shaw HS (1898) The flow of water. Nature 58:34–36

    Article  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI

    Google Scholar 

  • Horden RH (1998) The hydrologic cycle. In: Herschy RW, Fairbridge RW (eds) Encyclopedia of hydrology and water resources. Kluwer Academic Publishers, Dordrecht, The Netherlands, pp 400–404

    Google Scholar 

  • Horton RE (1933) The role of infiltration in the hydrologic cycle. Trans Am Geophys Union 14:446–460

    Article  Google Scholar 

  • Horton RE (1945) Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology. Bull Geol Soc Am 56:275–370

    Article  Google Scholar 

  • Hsu KL, Gupta HV, Gao X, Sorooshian S, Imam B (2002) Self-organizing linear output map (SOLO): an artificial neural network suitable for hydrologic modeling and analysis. Water Resour Res 38(12). doi:10.1029/2001WR000795

  • Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Am Soc Civ Eng 116:770–799

    Google Scholar 

  • Hydrologic Engineering Center (1995) HEC-HMS: Hydrologic modeling system user’s manual. U. S, Army Corps of Engineers, Davis, CA

    Google Scholar 

  • Hydrologic Engineering Cener (1998) HEC-RAS: river analysis system user’s manual. U.S. Army Corps of Engineers, Davis, CA

    Google Scholar 

  • IPCC (2014) Climate change 2014—impacts, adaptation and vulnerability. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Field CB, Barros VR, Dokken DJ, Mach KJ, Mastrandrea MD, Bilir TE, Chatterjee M, Ebi KL, Estrada YO, Genova RC, Girma B, Kissel ES, Levy AN, MacCracken S, Mastrandrea PR, White LL (eds.)], Cambridge University Press, Cambridge

    Google Scholar 

  • Jacoby SLS (1966) A mathematical model for nonlinear hydrologic systems. J Geophys Res 71(20):4811–4824

    Article  Google Scholar 

  • Jain A, Sudheer KP, Srinivasulu S (2004) Identification of physical processes inherent in artificial neural network rainfall runoff models. Hydrol Process 18(3):571–581

    Article  Google Scholar 

  • Kalma JD, Sivapalan M (1996) Scale issues in hydrological modeling. Wiley, London

    Google Scholar 

  • Kantz H, Schreiber T (2004) Nonlinear time series analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Kirchner JW (2006) Getting the right answers for the right reasons: linking measurements, analyses, and models to advance the science of hydrology. Water Resour Res 42:W03S04. doi:10.1029/2005WR004362

  • KlemeÅ¡ V (1978) Physically based stochastic hydrologic analysis. Adv Hydrosci 11:285–352

    Article  Google Scholar 

  • KlemeÅ¡ V (1982) Empirical and causal models in hydrology. Scientific basis of water-resources management. National Academic Press, Washington, DC, pp 95–104

    Google Scholar 

  • KlemeÅ¡ V (1986) Dilettantism in hydrology: Transition or destiny? Water Resour Res 22(9):177S–188S

    Article  Google Scholar 

  • Konikow LF, Bredehoeft JD (1992) Ground-water models cannot be validated. Adv Water Resour 15:75–83

    Article  Google Scholar 

  • Koza JR (1992) Genetic programing: on the programming of computers by natural selection. MIT Press, Cambridge, MA

    Google Scholar 

  • Kuichling E (1889) The relation between the rainfall and the discharge of sewers in populous districts. Trans Am Soc Civ Eng 20:1–56

    Google Scholar 

  • Labat D (2005) Recent advances in wavelet analyses: Part 1. A review of concepts. J Hydrol 314:275–288

    Google Scholar 

  • Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141

    Article  Google Scholar 

  • MacNeill IB, Umphrey GJ (1987) Stochastic hydrology. Kluwer Academic Publishers, Boston

    Google Scholar 

  • Maidment DR (ed) (1993) Handbook of hydrology. McGraw-Hill, New York

    Google Scholar 

  • Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636–638

    Article  Google Scholar 

  • Mandelbrot BB (1975) On the geometry of homogeneous turbulence, with stress on the fractal dimension of the isosurfaces of scalars. J Fluid Mech 72:401–416

    Article  Google Scholar 

  • Mandelbrot BB (1977) Fractals: form, chance and dimension. W. H, Freeman and Co, New York

    Google Scholar 

  • Mandelbrot BB (1983) The fractal geometry of nature. Freeman, New York

    Google Scholar 

  • Mandelbrot BB, Wallis JR (1968) Noah, Joseph and operational hydrology. Water Resour Res 4(5):909–918

    Article  Google Scholar 

  • Mandelbrot BB, Wallis JR (1969) Some long run properties of geophysical records. Water Resour Res 5(2):321–340

    Article  Google Scholar 

  • Manning R (1891) On the flow of water in open channels and pipes. Trans Inst Civ Eng Ireland 20:161–207

    Google Scholar 

  • McDonnell JJ, Woods RA (2004) On the need for catchment classification. J Hydrol 299:2–3

    Article  Google Scholar 

  • Menabde M, Sivapalan M (2001) Linking space-time variability of river runoff and rainfall fields: a dynamic approach. Adv Wat Resour 24:1001–1014

    Article  Google Scholar 

  • Menabde M, Veitzer S, Gupta VK, Sivapalan M (2001) Tests of peak flow scaling in simulated self-similar river networks. Adv Wat Resour 24:991–999

    Article  Google Scholar 

  • Metcalf and Eddy, Inc., University of Florida, and Water Resources Engineers, Inc., (1971) Storm water management model, vol. 1. Final Report, 11024DOC07/71 (NTIS PB-203289), U.S. EPA, Washington, DC

    Google Scholar 

  • Miller WA, Woolhiser DA (1975) Choice of models. In: Yevjevich VM (ed) Unsteady flow in open channels. Water Resources Publications, Littleton, Colorado

    Google Scholar 

  • Minshall NE (1960) Predicting storm runoff on small experimental watersheds. J Hydraul Div Am Soc Eng 86(HYB):17–38

    Google Scholar 

  • Morel-Seytoux HJ (1978) Derivation of equations for variable rainfall infiltration. Water Resour Res 14(4):561–568

    Article  Google Scholar 

  • Morrison JE, Smith JA (2001) Scaling properties of flood peaks. Extremes 4(1):5–22

    Article  Google Scholar 

  • Moss ME, Bryson MC (1974) Autocorrelation structure of monthly streamflows. Water Resour Res 10(4):737–744

    Article  Google Scholar 

  • Nace RL (1974) General evolution of the concept of the hydrological cycle. Three centuries of scientific hydrology. UNESCO-World Meteorological Organization-International Association of Hydrological Sciences, Paris, pp 40–48

    Google Scholar 

  • Nash JE (1958) Determining runoff from rainfall. Proc Instit Civil Eng Ireland 10:163–184

    Google Scholar 

  • Neitsch SL, Arnold JG, Kiniry JR, Williams JR (2005) Soil and water assessment tool theoretical documentation, Version 2005. USDA.ARS Grassland, Soil and Water Research Laboratory, Temple, TX

    Google Scholar 

  • O’Connor KM (1976) A discrete linear cascade model for hydrology. J Hydrol 29:203–242

    Article  Google Scholar 

  • O’Donnell T (1960) Instantaneous unit hydrograph derivation by harmonic analysis. Int Assoc Sci Hydrol Publ 51:546–557

    Google Scholar 

  • O’Meara WA (1968) Linear routing of lateral inflow in uniform open channels. M. E. Sc. Thesis, The National University of Ireland, University College, Cork, Ireland

    Google Scholar 

  • Ogden FL, Dawdy DR (2003) Peak discharge scaling in a small hortonian watershed. J Hydrol Eng 8(2):64–73

    Article  Google Scholar 

  • Parlange MB, Katul GG, Cuenca RH, Kavvas ML, Nielsen DR, Mata M (1992) Physical basis for a time series model of soil water content. Water Resour Res 28(9):2437–2446

    Article  Google Scholar 

  • Pegram GGS (1977) Physical justification of continuous streamflow model. In: Morel-Seytoux HJ, Salas JD, Sanders TG, Smith RE (eds) Modeling hydrologic processes. Proceedings of Fort Collins III international hydrol Symposium, pp 270–280

    Google Scholar 

  • Quimpo R (1971) Structural relation between parametric and stochastic hydrology models. In: Mathematical models in hydrology, Warsaw Symposium (IAHS Publication 100) 1:151–157

    Google Scholar 

  • Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics A 1:318–333

    Google Scholar 

  • Rodriguez-Iturbe I, Rinaldo A (1997) Fractal river basins: chance and self-organization. Cambridge University Press, Cambridge

    Google Scholar 

  • Rodriguez-Iturbe I, De Power FB, Sharifi MB, Georgakakos KP (1989) Chaos in rainfall. Water Resour Res 25(7):1667–1675

    Article  Google Scholar 

  • Salas JD, Smith RA (1981) Physical basis of stochastic models of annual flows. Water Resour Res 17(2):428–430

    Article  Google Scholar 

  • Salas JD, Delleur JW, Yevjevich V, Lane WL (1995) Applied modeling of hydrologic time series. Water Resources Publications, Littleton, Colorado

    Google Scholar 

  • See LM, Jain A, Dawson CW, Abrahart RJ (2008) Visualisation of hidden neuron behaviour in a neural network rainfall-runoff model. In: Abrahart RJ, See LM, Solomatine DP (eds) Practical hydroinformatics: computational intelligence and technological developments in water applications. Springer-Verlag, Berlin, Germany, pp 87–99

    Chapter  Google Scholar 

  • Selvalingam S (1977) ARMA and linear tank models. In: Morel-Seytoux HJ, Salas JD, Sanders TG, Smith RE (eds) Modeling hydrologic processes. Proceedings of Fort Collins III international hydrol symposium, pp 297–313

    Google Scholar 

  • Singh VP (1988) Hydrologic systems: vol 1. Rainfall-runoff modeling, Prentice Hall, New Jersey

    Google Scholar 

  • Singh VP (1995) Computer models of watershed hydrology. Water Resources Publications, Highlands Ranch CO

    Google Scholar 

  • Singh VP (1997) The use of entropy in hydrology and water resources. Hydrol Process 11:587–626

    Article  Google Scholar 

  • Singh VP (1998) Entropy-based parameter estimation in hydrology. Kluwer Academic, Dordrecht, The Netherlands

    Book  Google Scholar 

  • Singh VP (2013) Entropy theory and its application in environmental and water engineering. John Wiley and Sons, Oxford, UK

    Book  Google Scholar 

  • Sivakumar B (2000) Chaos theory in hydrology: important issues and interpretations. J Hydrol 227(1–4):1–20

    Article  Google Scholar 

  • Sivakumar B (2003) Forecasting monthly streamflow dynamics in the western United States: a nonlinear dynamical approach. Environ Model Softw 18(8–9):721–728

    Article  Google Scholar 

  • Sivakumar B (2004a) Chaos theory in geophysics: past, present and future. Chaos Soliton Fract 19(2):441–462

    Article  Google Scholar 

  • Sivakumar B (2004b) Dominant processes concept in hydrology: moving forward. Hydrol Process 18(12):2349–2353

    Article  Google Scholar 

  • Sivakumar B (2005) Hydrologic modeling and forecasting: role ofthresholds. Environ Model Softw 20(5):515–519

    Article  Google Scholar 

  • Sivakumar B (2008a) Dominant processes concept, model simplification and classification framework in catchment hydrology. Stoch Env Res Risk Assess 22:737–748

    Article  Google Scholar 

  • Sivakumar B (2008b) Undermining the science or undermining Nature? Hydrol Process 22(6):893–897

    Article  Google Scholar 

  • Sivakumar B (2008c) The more things change, the more they stay the same: the state of hydrologic modeling. Hydrol Process 22:4333–4337

    Article  Google Scholar 

  • Sivakumar B (2009) Nonlinear dynamics and chaos in hydrologic systems:latest developments and a look forward. Stoch Environ Res Risk Assess 23:1027–1036

    Article  Google Scholar 

  • Sivakumar B, Berndtsson R (2010) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore

    Book  Google Scholar 

  • Sivakumar B, Singh VP (2012) Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework. Hydrol Earth Syst Sci 16:4119–4131

    Article  Google Scholar 

  • Sivakumar B, Sorooshian S, Gupta HV, Gao X (2001) A chaotic approach to rainfall disaggregation. Water Resour Res 37(1):61–72

    Article  Google Scholar 

  • Sivapalan M, Takeuchi K, Franks SW, Gupta VK, Karambiri H, Lakshmi V, Liang X, McDonnell JJ, Mendiondo EM, O’Connell PE, Oki T, Pomeroy JW, Schertzer D, Uhlenbrook S, Zehe E (2003) IAHS decade on predictions in ungauged basins (PUB), 2003–2012: shaping an exciting future for the hydrological sciences. Hydrol Sci J 48(6):857–880

    Article  Google Scholar 

  • Snyder WM (1955) Hydrograph analysis by the method of least squares. J Hyd Div, Proc Ame Soc Civ Eng 81(793), 25 pp

    Google Scholar 

  • Snyder WM (1971) The parametric approach to watershed modeling. Nordic Hydrol 11:167–185

    Google Scholar 

  • Snyder WM, Stall JB (1965) Men, models, methods, and machines in hydrologic analysis. J Hyd Div, Proc Ame Soc Civ Eng 91(HY2):85–99

    Google Scholar 

  • Sorooshian S, Gupta VK (1983) Automatic calibration of conceptual rainfall-runoff models: the question of parameter observability and uniqueness. Water Resour Res 19(1):251–259

    Article  Google Scholar 

  • Sudheer KP, Jain A (2004) Explaining the internal behavior of artificial neural network river flow models. Hydrol Process 18(4):833–844

    Article  Google Scholar 

  • Thomas HA, Fiering MB (1962) Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation. In: Mass A et al (eds) Design of water resource systems. Harvard University Press, Cambridge, Massachusetts, pp 459–493

    Google Scholar 

  • Tsonis AA (1992) Chaos: from theory to applications. Plenum Press, New York

    Book  Google Scholar 

  • UNESCO (1974) Contributions to the development of the concept of the hydrological cycle. Sc. 74/Conf.804/Col. 1, Paris

    Google Scholar 

  • Veitzer SA, Gupta VK (2001) Statistical self-similarity of width function maxima with implications to floods. Adv Wat Resour 24:955–965

    Article  Google Scholar 

  • Vapnik V (1995) The nature of statistical learning theory. Springer-Verlag, Germany

    Book  Google Scholar 

  • Vogel RM (1999) Stochastic and deterministic world views. J Water Resour Plan Manage 125(6):311–313

    Article  Google Scholar 

  • Woolhiser DA (1971) Deterministic approach to watershed modeling. Nordic Hydrol 11:146–166

    Google Scholar 

  • Woolhiser DA (1973) Hydrologic and watershed modeling: state of the art. Trans Ame Soc Agr Eng 16(3):553–559

    Article  Google Scholar 

  • Woolhiser DA (1975) The watershed approach to understanding our environment. J Environ Qual 4(1):17–21

    Article  Google Scholar 

  • Yevjevich VM (1963) Fluctuations of wet and dry years. Part 1. Research data assembly and mathematical models. Hydrology Paper 1, Colorado State University, Fort Collins, Colorado, pp 1–55

    Google Scholar 

  • Yevjevich VM (1968) Misconceptions in hydrology and their consequences. Water Resour Res 4(2):225–232

    Article  Google Scholar 

  • Yevjevich VM (1972) Stochastic processes in hydrology. Water Resour Publ, Fort Collins, Colorado

    Google Scholar 

  • Young PC (1984) Recursive estimation and time-series analysis. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Young PC, Beven KJ (1994) Database mechanistic modeling and rainfall-flow non-linearity. Environmetrics 5(3):335–363

    Article  Google Scholar 

  • Young PC, Ratto M (2009) A unified approach to environmental systems modeling. Stoch Environ Res Risk Assess 23:1037–1057

    Article  Google Scholar 

  • Young PC, Parkinson SD, Lees M (1996) Simplicity out of complexity in environmental systems: Occam’s Razor revisited. J Appl Stat 23:165–210

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inform. Control 8(3):338–353

    Article  Google Scholar 

  • Zadeh LA, Klir GJ, Yuan B (1996) Fuzzy sets, fuzzy logic and fuzzy systems. World Scientific Publishers, Singapore

    Book  Google Scholar 

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, Australia

    Bellie Sivakumar

  2. Department of Land, Air and Water Resources, University of California, Davis, CA, USA

    Bellie Sivakumar

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Sivakumar, B. (2017). Introduction. In: Chaos in Hydrology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2552-4_1

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