Abstract
Advances in computational power, scientific concepts, and data measurements have led to the development of numerous nonlinear methods to study complex systems normally encountered in various scientific fields. These nonlinear methods often have very different conceptual bases and levels of sophistication and have been found suitable for studying many different types of systems and associated problems. Their relevance to hydrologic systems and ability to model and predict the salient characteristics of hydrologic systems have led to their extensive applications in hydrology over the past three decades or so. This chapter presents an overview of some of the very popular nonlinear methods that have found widespread applications in hydrology. The methods include: nonlinear stochastic methods, data-based mechanistic models, artificial neural networks, support vector machines, wavelets, evolutionary computing, fuzzy logic, entropy-based techniques, and chaos theory. For each method, the presentation includes a description of the conceptual basis and examples of applications in hydrology.
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References
Abarbanel HDI, Lall U (1996) Nonlinear dynamics of the Great Salt Lake: system identification and prediction. Climate Dyn 12:287–297
Abebe AJ, Solomatine DP, Venneker RGW (2000) Application of adaptive fuzzy rule-based models for reconstruction of missing precipitation events. Hydrol Sci J 45(3):425–436
Abrahart RJ, White SM (2001) Modelling sediment transfer in Malawi: comparing backpropagation neural network solutions against a multiple linear regression benchmark using small data sets. Phys Chem Earth Part B: Hydrol Oceans Atmos 26(1):19–24
Abrahart RJ, See LM, Kneale PE (1999) Using pruning algorithms and genetic algorithms to optimise network architectures and forecasting inputs in a neural network rainfall-runoff model. J Hydroinfor 1(2):103–114
Abrahart RJ, Kneale PE, See LM (eds) (2004) Neural networks for hydrological modelling. A.A. Balkema Publishers, Rotterdam, The Netherlands
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
Abrahart RJ, Mount NJ, Shamseldin AY (2012a) Neuroemulation: definition and key benefits for water resources research. Hydrol Sci J 57:407–423
Abrahart RJ, Anctil F, Coulibaly P, Dawson CW, Mount NJ, See LM, Shamseldin AY, Solomatine DP, Toth E, Wilby RL (2012b) Two decades of anarchy? Emerging themes and outstanding challenges for neural network river forecasting. Prog Phys Geogr 36(4):480–513
Adamkowski (2008) River flow forecasting using wavelet and cross-wavelet transform models. Hydrol Process 22(25):4877–4891
Adamowski J, Sun K (2010) Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semi-arid watersheds. J Hydrol 390:85–91
Aksoy H, Akar T, Unal NE (2004) Wavelet analysis for modeling suspended sediment discharge. Nord Hydrol 35(2):165–174
Alvisi S, Franchini M (2011) Fuzzy neural networks for water level and discharge forecasting with uncertainty. Environ Modell Softw 26:523–537
Alvisi S, Mascellani G, Franchini M, Bárdossy A (2006) Water level forecasting through fuzzy logic and artificial neural network approaches. Hydrol Earth Syst Sci 10:1–17
Aly AH, Peralta RC (1999) Optimal design of aquifer cleanup systems under uncertainty using a neural network and a genetic algorithm. Water Resour Res 35(8):2523–2532
Amorocho J (1967) The nonlinear prediction problems in the study of the runoff cycle. Water Resour Res 3(3):861–880
Amorocho J (1973) Nonlinear hydrologic analysis. Adv Hydrosci 9:203–251
Amorocho J, Brandstetter A (1971) Determination of nonlinear functional response functions in rainfall-runoff processes. Water Resour Res 7(5):1087–1101
Amorocho J, Espildora B (1973) Entropy in the assessment of uncertainty in hydrologic systems and models. Water Resour Res 9(6):1511–1522
Anandhi A, Srinivas VV, Nanjundiah RS, Nagesh Kumar D (2008) Downscaling precipitation to river basin in India for IPCC SRES scenarios using support vector machine. Int J Climatol 28(3):401–420
Aral MM, Guan J, Maslia ML (2001) Identification of contaminant source location and release history in aquifers. J Hydraul Eng ASCE 6(3):225–234
ASCE Task Committee (2000a) Artificial neural networks in hydrology. I: preliminary concepts. J Hydrol Engg. 5(2):115–123
ASCE Task Committee (2000b) Artificial neural networks in hydrology. II: hydrologic applications. J Hydrol Engg. 5(2):124–137
Asefa T, Kemblowski MW, Urroz G, McKee M, Khalil A (2004) Support vectors-based groundwater head observation networks design. Water Resour Res 40:W11509. doi:10.1029/2004WR003304
Asefa T, Kemblowski M, Lall U, Urroz G (2005) Support vector machines for nonlinear state space reconstruction: application to the Great Salt Lake time series. Water Resour Res 41:W12422. doi:10.1029/2004WR003785
Aytek A, Kişi Ö (2007) A genetic programming approach to suspended sediment modelling. J Hydrol 351(3–4):288–298
Babovic V (1996) Emergence evolution intelligence Hydroinformatics—a study of distributed and decentralised computing using intelligent agents. A. A. Balkema Publishers, Rotterdam, Holland
Babovic V (2000) Data mining and knowledge discovery in sediment transport. Comp Aid Civil Infrastr Engg 15(5):383–389
Babovic V, Rao R (2010) Evolutionary computing in hydrology. In: Sivakumar B, Berndtsson R (eds) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore, pp 347–369
Balascio CC, Palmeri DJ, Gao H (1998) Use of a genetic algorithm and multi-objective programming for calibration of a hydrologic model. Trans ASAE 44(3):615–619
Bárdossy A, Disse M (1993) Fuzzy rule-based models for infiltration. Water Resour Res 29(2):373–382
Bárdossy A, Duckstein L (1995) Fuzzy rule-based modeling in geophysical, economic, biological and engineering systems. CRS Press, Boca Raton, FL
Bárdossy A, Samaniego L (2002) Fuzzy rule-based classification of remotely sensed imagery. IEEE Trans on Geosci Rem Sens 40:362–374
Bárdossy A, Duckstein L, Bogardi I (1995) Fuzzy rule-based classification of atmospheric circulation patterns. Int J Climatol 5:1087–1097
Bárdossy A, Mascellani G, Franchini M (2006) Fuzzy unit hydrograph. Water Resour Res 42:W02401. doi:10.1029/2004WR003751
Bayazit M, Önöz B, Aksoy H (2001) Nonparametric streamflow simulation by wavelet or Fourier analysis. Hydrol Sci 46(4):623–634
Beaumont C (1979) Stochastic models in hydrology. Prog Phys Geogr 3:363–391
Berndtsson R, Jinno K, Kawamura A, Olsson J, Xu S (1994) Dynamical systems theory applied to long-term temperature and precipitation time series. Trends Hydrol 1:291–297
Beven KJ, Leedal DT, Smith PJ, Young PC (2012) Identification and representation of state dependent non-linearities in flood forecasting using the DBM methodology. In: Wang L, Garnier H (eds) System identification, environmetric modelling and control. Springer, Berlin, pp 341–366
Bidwell VJ (1971) Regression analysis of nonlinear catchment systems. Water Resour Res 7:1118–1126
Bogardi I, Bárdossy A, Duckstein L, Pongracz R (2003) Fuzzy logic in hydrology and water resources. Fuzzy logic in geology. Elsevier Science, Amsterdam, pp 153–190
Bras RL, Rodriguez-Iturbe I (1985) Random functions and hydrology. Addison-Wesley, Reading, Massachusetts
Bray M, Han D (2004) Identification of support vector machines for runoff modelling. J Hydroinf 6(4):265–280
Burn DH, Yulianti JS (2001) Waste-load allocation using genetic algorithms. J Wat Resour Plan Manage ASCE 127(2):121–129
Cao S, Knight DW (1997) Entropy-based approach of threshold alluvial channels. J Hydraul Res 35(4):505–524
Caughey TK (1971) Nonlinear theory of random vibrations. Advances in Applied Mechanics, vol 11. Academic Press, New York
Cayar M, Kavvas ML (2009) Ensemble average and ensemble variance behavior of unsteady, one-dimensional groundwater flow in unconfined, heterogeneous aquifers: an exact second-order model. Stoch Environ Res Risk Assess 23:947–956
Chang F-J, Chen L (1998) Real-coded genetic algorithm for rule-based flood control reservoir management. Wat Resour Manage 12:185–198
Chang F-J, Lai J-S, Kao L-S (2003) Optimisation of operation rule curves and flushing schedule in a reservoir. Hydrol Process 17:1623–1640
Chang L-C, Chang F-J, Tsai Y-H (2005) Fuzzy exemplar-based inference system for flood forecasting. Water Resour Res 41:W02005. doi:10.1029/2004W003037
Chang F-J, Chang L-C, Wang Y-S (2007) Enforced self-organizing map neural networks for river flood forecasting. Hydrol Process 21:741–749
Chang L-C, Chang F-J, Wang Y-P (2009) Autoconfiguring radial basis function networks for chaotic time series and flood forecasting. Hydrol Process 23:2450–2459
Chappell NA, Tych W, Chotai A, Bidin K, Sinun W, Thang HC (2006) BARUMODEL: combined data based mechanistic models of runoff response in a managed rainforest catchment. Forest Ecol Manage 224:58–80
Chen HS, Chang N-B (1998) Water pollution control in the river basin by fuzzy genetic algorithm-based multiobjective programming modeling. Wat Sci Tech 37(8):55–63
Chen J, Adams BJ (2006) Integration of artificial neural networks with conceptual models in rainfall-runoff modeling. J Hydrol 318(1–4):232–249
Chen L (2003) Real coded genetic algorithm optimization of long term reservoir operation. J Ame Water Resour Assoc 39(5):1157–1165
Chen ST, Yu PS, Tang YH (2010) Statistical downscaling of daily precipitation using support vector machines and multivariate analysis. J Hydrol 47(5):721–738
Cheng CT, Ou CP, Chau KW (2002) Combining a fuzzy optimal model with a genetic algorithm to solve multi-objective rainfall-runoff model calibration. J Hydrol 268:72–86
Choy KY, Chan CW (2003) Modelling of river discharges and rainfall using radial basis function networks based on support vector regression. Int J Syst Sci 34(14–15):763–773
Chidthong Y, Tanaka H, Supharatid S (2009) Developing a hybrid multi-model for peak flood forecasting. Hydrol Process 23:1725–1738
Chiu CL (1987) Entropy and probability concepts in hydraulics. J Hydraul Eng 113(5):583–600
Chiu CL (1991) Application of entropy concept in open channel flow study. J Hydraul Eng 117(5):615–628
Chui CK (1992) An introduction to wavelets. Academic Press, Boston
Cieniawski SE, Eheart JW, Ranjithan S (1995) Using genetic algorithms to solve a multiobjective groundwater monitoring problem. Water Resour Res 31(2):399–409
Cigizoglu H (2005) Application of generalized regression neural networks to intermittent flow forecasting and estimation. J Hydrol Eng 10(4):336–341
Cortes C, Vapnik V (1995) Support-vector machines. Mach Learn 20:273–297
Coulibaly P, Burn DH (2006) Wavelet analysis of variability in annual Canadian streamflows. Water Resour Res 40(3):W03105. doi:10.1029/2003WR002667
Coulibaly P, Anctil F, Aravena R, Bobée B (2001) Artificial neural network modeling of water table depth fluctuation. Water Resour Res 37(4):885–896
Coulibaly P, Dibike YB, Anctil F (2005) Downscaling precipitation and temperature with temporal neural networks. J Hydrometeor 6(4):483–496
Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, 204 pp
Çimen M (2008) Estimation of daily suspended sediments using support vector machines. Hydrol Sci J 53(3):656–666
Dandy GC, Simpson AR, Murphy LJ (1996) An improved genetic algorithm for pipe network optimisation. Water Resour Res 32(2):449–458
Darwin C (1859) On the origin of species by means of natural selection, or the preservation of favoured races in the struggle for life. John Murray, London
Daubechies I (1988) Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math XLI:901–996
Daubechies I (1990) The wavelet transform, time-frequency localization and signal analysis. IEEE Trans Inform Theory 36(5):961–1005
Daubechies I (1992) Ten lectures on Wavelets. CSBM-NSF Series Appli Math, SIAM Publications, 357 pp
Dawson CW, Wilby RL (2001) Hydrological modelling using artificial neural networks. Prog Phys Geog 25(1):80–108
Dawson CW, Abrahart RJ, Shamseldin AY, Wilby RL (2006) Flood estimation at ungauged sites using artificial neural networks. J Hydrol 319(1–4):391–409
de Araujo JC (2007) Entropy-based equation to assess hillslope sediment production. Earth Surf Process Landf 32:2005–2018
Dhanya CT, Nagesh Kumar D (2010) Nonlinear ensemble prediction of chaotic daily rainfall. Adv Water Resour 33:327–347
Dhanya CT, Nagesh Kumar D (2011) Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs. J Hydrol 403:292–306
Dibike YB, Velickov S, Slomatine D, Abbott MB (2001) Model induction with support vector machines: introduction and applications. J Comp Civil Eng 15(3):208–216
Dodov B, Foufoula-Georgiou E (2005) Incorporating the spatio-temporal distribution of rainfall and basin geomorphology into nonlinear analysis of streamflow dynamics. Adv Water Resour 28(7):711–728
Dooge JCI (1967) A new approach to nonlinear problems in surface water hydrology: hydrologic systems with uniform nonlinearity. Int Assoc Sci HydrolPubl 76:409–413
Dubois D (1980) Fuzzy sets and systems, theory and applications. Academic Press, New York
Elshorbagy A, Simonovic SP, Panu US (2002) Estimation of missing streamflow data using principles of chaos theory. JHydrol 255:123–133
Erickson M, Mayer A, Horn J (2002) Multi-objective optimal design of groundwater remediation systems: application of the niched Pareto genetic algorithm (NPGA). Adv Water Resour 25(1):51–65
Farge M (1992) Wavelet transforms and their applications to turbulence. Annu Rev Fluid Mech 24:395–457
Farmer DJ, Sidorowich JJ (1987) Predicting chaotic time series. Phys Rev Lett 59:845–848
Fausett L (1994) Fundamentals of neural networks. Prentice Hall, Englewood, NJ
Faybishenko B (2002) Chaotic dynamics in flow through unsaturatedfractured media. Adv Water Resour 25(7):793–816
Fernando DAK, Shamseldin AY (2009) Investigation of internal functioning of the radial-basis-function neural network river flow forecasting models. ASCE J Hydrol Eng 14:286–292
Fiorentino M, Claps P, Singh VP (1993) An entropy-based morphological analysis of river-basin networks. Water Resour Res 29(4):1215–1224
Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. John Wiley, New York
Fontane DG, Gates TK, Moncada E (1997) Planning reservoir operations with imprecise objectives. J Water Resour Plann Manage 123(3):154–162
Foufoula-Georgiou E, Kumar P (eds) (1995) Wavelets in Geophysics. Academic Press, New York
Franchini M (1996) Using a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models. Hydrol Sci J 41(1):21–40
French MN, Krajewski WF, Cuykendall RR (1992) Rainfall forecasting in space and time using a neural network. J Hydrol 137(1–4):1–31
Gan TY, Gobena AK, Wang Q (2007) Precipitation of southwestern Canada: Wavelet, scaling, multifractal analysis, and teleconnection to climate anomalies. J Geophys Res 112(D10110). doi:10.1029/2006JD007157
Gaucherel C (2002) Use of wavelet transform for temporal characterisation of remote watersheds. J Hydrol 269(3–4):101–121
Gaume E, Gosset R (2003) Over-parameterisation, a major obstacle to the use of artificial neural networks in hydrology? Hydrol Earth Syst Sci 7(5):693–706
Goldberg DE (1989) Genetic algorithms in search, optimisation, and machine learning. Addison-Wesley, Reading
Govindaraju RS (2002) Stochastic methods in subsurface contaminant hydrology. American Society of Civil Engineers, New York
Govindaraju RS, Rao AR (eds) (2000) Artificial neural networks in hydrology. Kluwer Academic Publishers, Dordrecht, The Netherlands
Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9:189–208
Gupta I, Gupta A, Khanna P (1999) Genetic algorithm for optimisation of water distribution systems. Environ Modell Softw 14:437–446
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
Hamel L (2009) Knowledge discovery with support vector machines. Wiley-Interscience, USA 246 pp
Harmancioglu NB, Singh VP, Alpaslan N (1992) Versatile uses of the entropy concept in water resources. In: Singh VP, Fiorentino M (eds) Entropy and energy dissipation in water resources. Kluwer, Dordrecht, Netherlands, pp 91–118
Harms AA, Campbell TH (1967) An extension to the Thomas-Fiering model for the sequential generation of streamflow. Water Resour Res 3(3):653–661
Haykin S (1994) Neural networks: a comprehensive foundation. MacMillan, New York, USA
Hecht-Nielsen R (1990) Neurocomputing. Addison-Wesley, Reading, Massachusetts, USA
Heil CE, Walnut DF (1989) Continuous and discrete wavelet transforms. SIAM Review 31(4):628–666
Hense A (1987) On the possible existence of a strange attractor for the southern oscillation. Beitr Phys Atmos 60(1):34–47
Hill J, Hossain F, Sivakumar B (2008) Is correlation dimension a reliable proxy for the number of dominant influencing variables for modeling risk of arsenic contamination in groundwater? Stoch Environ Res Risk Assess 22(1):47–55
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI
Hong Y-S, Bhamidimarri R (2003) Evolutionary self-organising modelling of a municipal wastewater treatment plant. Wat Res 37:1199–1212
Hossain F, Sivakumar B (2006) Spatial pattern of arsenic contaminationin shallow wells of Bangladesh: regional geology and nonlinear dynamics. Stoch Environ Res Risk Assess 20(1–2):66–76
Hsu K-L, Gupta HV, Sorooshian S (1995) Artificial neural network modeling of the rainfall-runoff process. Water Resour Res 31(10):2517–2530
Hsu K-L, 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):W01302. doi:10.1029/2001WR000795
Hundecha Y, Bárdossy A, Theisen HW (2001) Development of a fuzzy logic-based rainfall-runoff model. Hydrol Sci J 46(3):363–376
Jacoby SLS (1966) A mathematical model for nonlinear hydrologic systems. J Geophys Res 71(20):4811–4824
Jain A, Srinivasulu S (2004) Development of effective and efficient rainfall-runoff models using integration of deterministic, real-coded genetic algorithms and artificial neural network techniques. Water Resour Res 40:W04302
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
Jawerth B, Sweldens W (1994) An overview of wavelet based multiresolution analyses. SIAM review 36(3):377–412
Jayawardena AW, Fernando DAK (1998) Use of radial basis function type artificial neural networks for runoff simulation. Comput-Aided Civ Infrastruct Engng 13:91–99
Jayawardena AW, Lai F (1994) Analysis and prediction of chaos in rainfall and stream flow time series. J Hydrol 153:23–52
Jaynes ET (1957a) Information theory and statistical mechanics, I. Phys Rev 106:620–630
Jaynes ET (1957b) Information theory and statistical mechanics, II. Phys Rev 108:171–190
Jaynes ET (1979) Concentration of distributions at entropy maxima. Paper presented at the 19th NBER-NSF Seminar on Bayesian Statistics, Montreal, October 1979. In: Jaynes ET, Papers on Probability, Statistics, and Statistical Physics, edited by Rosenkratz RD, Reidel Publishing Company, Boston, 1983, pp 315–336
Jothiprakash V, Garg V (2009) Reservoir sedimentation estimation using artificial neural network. J Hydrol Eng 14(9):1035–1040
Jowitt PW (1991) A maximum entropy view of probability-distributed catchment models. Hydrol Sci J 36(2):123–134
Kang S, Lin H (2007) Wavelet analysis of hydrological and water quality signals in an agricultural watershed. J Hydrol 338:1–14
Kapur JN (1989) Maximum entropy models in science and engineering. Wiley, New Delhi, India
Karamouz M, Ahmadi A, Moridi A (2009) Probabilistic reservoir operation using Bayesian stochastic model and support vector machine. Adv Water Resour 32(11):1588–1600
Karpouzos DK, Delay F, Katsifarakis KL, de Marsily G (2001) A multipopulation genetic algorithm to solve the inverse problem in hydrogeology. Water Resour Res 37(9):2291–2302
Kavvas ML (2003) Nonlinear hydrologic processes: conservation equations for determining their means and probability distributions. ASCE J Hydrol Eng 8(2):44–53
Kavvas ML, Delleur JW (1981) A stochastic cluster model of daily rainfall sequences. Water Resour Res 17(4):1151–1160
Khalil M, Panu US, Lennox WC (2001) Groups and neural networks based streamflow data infilling procedures. J Hydrol 241(3–4):153–176
Khan MS, Coulibaly P (2006) Application of support vector machine in lake water level prediction. J Hydrol Eng 11(3):199–205
Kim TW, Valdés JB (2003) A nonlinear model for drought forecasting based on conjunction of wavelet transforms and neural networks. J Hydrol Engg 8:319–328
Kişi Ö (2006) Generalized regression neural networks for evapotranspiration modeling. Hydrol Sci J 51(6):1092–1105
Kişi Ö (2007) Evapotranspiration modelling from climatic data using a neural computing technique. Hydrol Process 21(14):1925–1934
Kişi Ö, Çimen M (2009) Evapotranspiration modelling using support vector machines. Hydrol Sci J 54(5):918–928
Kişi Ö, Çimen M (2011) A wavelet-support vector machine conjunction model for monthly streamflow forecasting. J Hydrol 399:132–140
Kişi Ö, Karahan ME, Şen Z (2006) River suspended sediment modeling using a fuzzy logic approach. Hydrol Process 20:4351–4362
Klein LR, Preston RS (1969) Stochastic nonlinear models. Econometrica 37(1):95–106
Klemeš V (1978) Physically based stochastic hydrologic analysis. Adv Hydrosci 11:285–352
Klir GJ, St Clair UH, Yuan B (1997) Fuzzy set theory foundations and applications. Prentice Hall, New Jersey, 245 pp
Kolmogorov AN (1956) Aysmptotic characteristics of some completely bounded metric spaces. Dokl Akad Nauk SSSR 108:585–589
Kolmogorov AN (1958) New metric invariant of transitive dynamical systems and endomorphisms of Lebesgue spaces. Dokl Akad Nauk SSSR 119(N5):861–864
Kosko B (1993) Fuzzy thinking: the new science of fuzzy logic. Hyperion, NY
Koutsoyiannis D (1992) A nonlinear disaggregation method with a reduced parameter set for simulation of hydrologic series. Water Resour Res 28(12):3175–3191
Koutsoyiannis D (2005a) Uncertainty, entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling. Hydrol Sci J 50(3):381–404
Koutsoyiannis D (2005b) Uncertainty, entropy, scaling and hydrological stochastics. 2. Time dependence of hydrological processes and time scaling. Hydrol Sci J 50(3):405–426
Koutsoyiannis D (2006) On the quest for chaotic attractors in hydrological processes. Hydrol Sci J 51(6):1065–1091
Koutsoyiannis D (2007) Discussion of “Generalized regression neural networks for evapotranspiration modelling” by O. Kişi. Hydrol Sci J 52(4):832–835
Koutsoyiannis D, Xanthopoulos T (1990) A dynamic model for short-scale rainfall disaggregation. Hydrol Sci J 35(3):303–322
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge, MA
Krasovskaia I (1997) Entropy-based grouping of river flow regimes. J Hydrol 202:173–191
Krasovskaia I, Gottschalk L (1992) Stability of river flow regimes. Nord Hydrol 23:137–154
Krstanovic PF, Singh VP (1991a) A univariate model for longterm streamflow forecasting: I. Development. Stochastic Hydrol Hydraul 5:173–188
Krstanovic PF, Singh VP (1991b) A univariate model for longterm streamflow forecasting: II. Application. Stochastic Hydrol Hydraul 5:189–205
Krstanovic PF, Singh VP (1993a) A real-time flood forecasting model based on maximum entropy spectral analysis: I. Development. Water Resour Manage 7:109–129
Krstanovic PF, Singh VP (1993b) A real-time flood forecasting model based on maximum entropy spectral analysis: II. Application. Water Resour Manage 7:131–151
Kumar P (1996) Role of coherent structure in the stochastic dynamic variability of precipitation. J Geophys Res 101(26):393–404
Kumar P, Foufoula-Georgiou E (1993) A multicomponent decomposition of spatial rainfall fields. Segregation of large and small scale features using wavelet transform. Water Resour Res 29(8):2515–2532
Kumar P, Foufoula-Georgiou E (1997) Wavelet analysis for geophysical applications. Rev Geophys 35(4):385–412
Kyoung MS, Kim HS, Sivakumar B, Singh VP, Ahn KS (2011) Dynamic characteristics of monthly rainfall in the Korean peninsula under climate change. Stoch Environ Res Risk Assess 25(4):613–625
Labat D (2005) Recent advances in wavelet analyses: Part 1. A review of concepts. J Hydrol 314:275–288
Labat D (2008) Wavelet analysis of annual discharge records of the world’s largest rivers. Adv Water Resour 31:109–117
Labat D (2010a) Wavelet analysis in hydrology. In: Sivakumar B, Berndtsson R (eds) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore, pp 371–410
Labat D (2010b) Cross wavelet analyses of annual continental freshwater discharge and selected climate indices. J Hydrol 385:269–278
Labat D, Ababou R, Mangin A (2000) Rainfall-runoff relations for karstic springs - Part II: Continuous wavelet and discrete orthogonal multiresolution analyses. J Hydrol 238:149–178
Labat D, Ronchail J, Guyot J-L (2005) Recent advances in wavelet analyses: Part 2—Amazon, Parana, Orinoco and Congo discharges time scale variability. J Hydrol 314:289–311
Lall U (1995) Recent advances in nonparametric function estimation: hydraulic applications. U.S. National Report for International Union of Geodesy and Geophysics 1991–1994. Rev Geophys 33:1092–1102
Lall U, Sharma A (1996) A nearest neighbor bootstrap for resampling hydrologic time series. Water Resour Res 32(3):679–693
Lambrakis N, Andreou AS, Polydoropoulos P, Georgopoulos E, Bountis T (2000) Nonlinear analysis and forecasting of a brackish karstic spring. Water Resour Res 36(4):875–884
Lamorski K, Pachepsky Y, Slawihski C, Walczak RT (2008) Using support vector machines to develop pedotransfer functions for water retention of soils in Poland. Soil Sci Soc Am J 72(5):1243–1247
Lane SN (2007) Assessment of rainfall–runoff models based upon wavelet analysis. Hydrol Process 21:586–607
Lau KM, Weng HY (1995) Climate signal detection using wavelet transform: how to make a time series sing. Bull Am Meteorol Soc 76:2391–2402
Lees MJ (2000) Data-based mechanistic modelling and forecasting of hydrological systems. J Hydroinform 2:15–34
Leopold LB, Langbein WB (1962) The concept of entropy in landscape evolution. Geol Surv Prof Pap 500-A, USGS, U.S. Department of the Interior, Washington, DC, 1–55
Lin G-F, Chen G-R, Wu M-C, Chou Y-C (2009a) Effective forecasting of hourly typhoon rainfall using support vector machines. Water Resour Res 45:W08440. doi:10.1029/2009WR007911
Lin G-F, Chen G-R, Huang P-Y, Chou Y-C (2009b) Support vector machine-based models for hourly reservoir inflow forecasting during typhoon-warning periods. J Hydrol 372(1–4):17–29
Lin G-F, Lin H-Y, Wu M-C (2013) Development of support-vector machine-based model for daily pan evaporation estimation. Hydrol Process 27:3115–3127
Liong SY, Sivapragasam C (2002) Flood stage forecasting with support vector machines. J Am Water Res Assoc 38(1):173–186
Liong SY, Gautam TR, Khu ST, Babovic V, Muttil N (2002) Genetic programming: A new paradigm in rainfall-runoff modelling. J Am Water Resour Assoc 38(3):705–718
Liu Q, Islam S, Rodriguez-Iturbe I, Le Y (1998) Phase-space analysis of daily streamflow: characterization and prediction. Adv Water Resour 21:463–475
Lohani AK, Goel NK, Bhatia KKS (2007) Deriving stage-discharge-sediment concentration relationships using fuzzy logic. Hydrol Sci J 52(4):793–807
Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141
Mahabir C, Hicks FE, Robinson Fayek A (2003) Application of fuzzy logic to forecast seasonal runoff. Hydrol Process 17(18):3749–3762
Maier HR, Dandy GC (1996) The use of artificial neural networks for the prediction of water quality parameters. Water Resour Res 32(4):1013–1022
Maier HR, Dandy GC (2000) Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environ Model Softw 15(1):101–123
Maity R, Bhagwat PP, Bhatnagar A (2010) Potential of support vector regression for prediction of monthly streamflow using endogenous property. Hydrol Process 24:917–923
Makkeasorn A, Chang N-B, Beaman M, Wyatt C, Slater C (2006) Soil moisture estimation in a semiarid watershed using RADARSAT-1 satellite imagery and genetic programming. Water Resour Res 42(W09401), doi:10.1029/2005WR004033
Mallat S (1989) A theory for multiresolution signal decomposition: The wavelet representation. IEEE Tran Pattern Anal Mach Intel 11(7):674–693
Mamdani EH, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Man-Machine Studies 7(1):1–13
Manzoni S, Porporato A, D’Odorico P, Laio F, Rodriguez-Iturbe I (2004) Soil nutrient cycles as a nonlinear dynamical system. Nonlinear Processes Geophys 11:589–598
Maruan D, Kurths J (2004) Cross wavelet analysis: significance testing and pitfalls. Nonlinear Process Geophys 11:505–514
McIntyre N, Young PC, Orellana B, Marshall M, Reynolds B, Wheater H (2011) Identification of nonlinearity in rainfall-flow response using data-based mechanistic modeling. Water Resour Res 47:W03515. doi:10.1029/2010WR009851
McKinney DC, Lin MD (1994) Genetic algorithm solution of groundwater management models. Water Resour Res 30(6):1897–1906
Minns AW, Hall MJ (1996) Artificial neural networks as rainfall-runoff models. Hydrol Sci J 41(3):399–417
Minshall NE (1960) Predicting storm runoff on small experimental watersheds. J Hydraul Div Am Soc Eng. 86(HYB):17–38
Montesinos P, Garcia-Guzman A, Ayuso JL (1999) Water distribution network optimisation using a modified genetic algorithm. Water Resour Res 35(11):3467–3473
Moradkhani H, Hsu K-L, Gupta HV, Sorooshian S (2004) Improved streamflow forecasting using self-organizing radial basis fucntion artificial neural networks. J Hydrol 295:246–262
Mujumdar PP, Sasikumar K (1999) A fuzzy risk approach for seasonal water quality management in a river system. Water Resour Res 38(1):1–9
Mulligan AE, Brown LC (1998) Genetic algorithms for calibrating water quality models. J Environ Eng ASCE 124(3):202–211
Nayak PC, Sudheer KP, Rangan DM, Ramasastri KS (2004) A neuro-fuzzy computing technique for modeling hydrological time series. J Hydrol 291:52–66
Niu J (2010) A comprehensive analysis of terrestrial hydrological processes over the Pearl River basin in South China. Ph.D. thesis, 202 pp, University of Hong Kong, Hong Kong
Niu J (2012) Precipitation in the Pearl River basin, South China: scaling, regional patterns, and influence of large-scale climate anomalies. Stoch Environ Res Risk Assess 27(5):1253–1268
Niu J, Sivakumar (2013) Scale-dependent synthetic streamflow generation using a continuous wavelet transform. J Hydrol 496:71–78
Ochieng G, Otieno F (2009) Data-based mechanistic modelling of stochastic rainfall-flow processes by state dependent parameter estimation. Environ Modell Softw 24:279–284
Oliveira R, Loucks DP (1997) Operating rules for multi-reservoir systems. Water Resour Res 33(4):839–852
Ozaki T (1980) Nonlinear time series models for nonlinear random vibrations. J Appl Probab 17:84–93
Özelkan EC, Duckstein L (2001) Fuzzy conceptual rainfall-runoff models. J Hydrol 253:41–68
Özelkan EC, Ni F, Duckstein L (1996) Relationship between monthly atmospheric circulation patterns and precipitation: fuzzy logic and regression approaches. Water Resour Res 32:2097–2103
Pal NR, Pal SK (1991) Entropy: a new definition and its applications. IEEE Trans Syst Man Cyber 21(5):1260–1270
Parasuraman K, Elshorbagy A, Carey S (2007) Modeling the dynamics of evapotranspiration process using genetic programming. Hydrol Sci J 52(3):563–578
Pázman A (2010) Nonlinear statistical models. Springer, Mathematics and its applications series 259 pp
Pesti G, Shrestha BP, Duckstein L, Bogardi I (1996) A fuzzy rule-based approach to drought assessment. Water Resour Res 32:1741–1747
Pongracz R, Bogardi I, Duckstein L (1999) Application of fuzzy rule-based modeling technique to regional drought. J Hydrol 224:100–114
Porporato A, Ridolfi R (1997) Nonlinear analysis of river flow time sequences. Water Resour Res 33(6):1353–1367
Priestley MB (1988) Non-linear and non-stationary time series analysis. Academic Press, London
Puente CE, Obregon N (1996) A deterministic geometric representation of temporal rainfall. Results for a storm in Boston. Water Resour Res 32(9):2825–2839
Rao SG, Rao RA (1984) Nonlinear stochastic model of rainfall runoff process. Water Resour Res 20(2):297–309
Ratto N, Young PC, Romanowicz R, Pappenberger F, Saltelli A, Pagano A (2007) Uncertainty, sensitivity analysis and the role of data based mechanistic modelling in hydrology. Hydrol Earth Syst Sci 11:1249–1266
Rauch W, Harremoes P (1999) Genetic algorithms in real time control applied to minimise transient pollution from urban wastewater systems. Water Res 33(5):1265–1277
Regonda S, Sivakumar B, Jain A (2004) Temporal scaling in river flow: can it be chaotic? Hydrol Sci J 49(3):373–385
Rényi A (1961) On measures of entropy and information. Proc 4th Berkeley Symposium on Math Stat Prob, vol 1. Berkeley, CA, pp 547–561
Ritzel BJ, Wayland Eheart J, Ranjithan S (1994) Using genetic algorithms to solve a multiple objective groundwater pollution containment problem. Water Resour Res 30(5):1589–1603
Rodriguez-Iturbe I, De Power FB, Sharifi MB, Georgakakos KP (1989) Chaos in rainfall. Water Resour Res 25(7):1667–1675
Rodriguez-Iturbe I, Entekhabi D, Bras RL (1991) Nonlinear dynamics of soil moisture at climate scales, 1. Stochastic analysis. Water Resour Res 27(8):1899–1906
Romanowicz RJ, Young PC, Beven KJ (2006) Data assimilation and adaptive forecasting of water levels in the River Severn catchment. Water Resour Res 42(W06407). doi:10.1029/2005WR005373
Romanowicz RJ, Young PC, Beven KJ, Pappenberger F (2008) A data based mechanistic approach to nonlinear flood routing and adaptive flood level forecasting. Adv Water Resour 31:1048–1056
Roques S, Meyer Y (eds) (1993) Progress in wavelet analysis and applications. Edit Frontières, 785 pp
Rosenthal H, Binia J (1988) On the epsilon entropy of mixed random variables. IEEE Trans Inf Theory 34(5):1110–1114
Ross JT (1995) Fuzzy logic with engineering applications. McGraw-Hill, NY, 593 pp
Saco P, Kumar P (2000) Coherent modes in multiscale variability of streamflow over the United States. Water Resour Res 36(4):1049–1067
Salas JD, Smith RA (1981) Physical basis of stochastic models of annual flows. Water Resour Res 17(2):428–430
Salas JD, Delleur JW, Yevjevich V, Lane WL (1995) Applied modeling of hydrologic time series. Water Resources Publications, Littleton, Colorado
Salas JD, Kim HS, Eykholt R, Burlando P, Green TR (2005) Aggregation and sampling in deterministic chaos: implications for chaos identification in hydrological processes. Nonlinear Processes Geophys 12:557–567
Samsudin R, Saad P, Shabri A (2011) River flow time series using least squares support vector machines. Hydrol Earth Syst Sci 15:1835–1852
Savic DA, Khu ST (2005) Evolutionary computing in hydrological sciences. In: Anderson MG (ed) Encyclopedia of hydrological sciences. John Wiley & Sons Ltd, London, pp 2–18
Savic DA, Walters GA, Davidson GW (1999) A genetic programming approach to rainfall-runoff modeling. Water Resour Manage 13:219–231
Schaefli B, Maraun D, Holschneider M (2007) What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology. Adv Water Resour 30:2511–2525
Schertzer D, Tchiguirinskaia I, Lovejoy S, Hubert P, Bendjoudi H (2002) Which chaos in the rainfall-runoff process? A discussion on ‘Evidence of chaos in the rainfall-runoff process’ by Sivakumar et al. Hydrol Sci J 47(1):139–147
Schwefel HP (1981) Numerical optimisation of computer models. John Wiley, Chichester
Seber GAF, Wild CJ (2003) Nonlinear regression. Wiley-Interscience, New Jersey
See LM, Openshaw S (2000a) A hybrid multi-model approach to river level forecasting. Hydrol Sci J 45(4):523–536
See L, Openshaw S (2000b) Applying soft computing approaches to river level forecasting. Hydrol Sci J 44(5):763–779
Serrano SE (1995) Analytical solutions of the nonlinear groundwater flow equation in unconfined aquifers and the effect of heterogeneity. Water Resour Res 31(11):2733–2742
Shamseldin AY (1997) Application of a neural network technique to rainfall-runoff modelling. J Hydrol 199(3–4):272–294
Shannon CE (1948) The mathematical theory of communications, I and II. Bell Syst Tech J 27:379–423
Sharifi MB, Georgakakos KP, Rodriguez-Iturbe I (1990) Evidence of deterministic chaos in the pulse of storm rainfall. J Atmos Sci 47:888–893
Simonovic SP (2009) Managing water resources: methods and tools for a systems approach. UNESCO, Paris
Singh VP (1979) A uniformly nonlinear hydrologic cascade model. Irrigation Power 36(3):301–317
Singh VP (1988) Hydrologic systems: rainfall-runoff modelling, vol 1. Prentice Hall, Englewood Cliffs, NJ
Singh VP (1997) The use of entropy in hydrology and water resources. Hydrol Process 11:587–626
Singh VP (1998) Entropy-based parameter estimation in hydrology. Kluwer, Boston 365 pp
Singh VP (2010a) Entropy theory for derivation of infiltration equations. Water Resour Res 46:W03527
Singh VP (2010b) Entropy theory for movement of moisture in soils. Water Resour Res 46:W03516
Singh VP (2010c) Tsallis entropy theory for derivation of infiltration equations. Trans ASABE 53(2):447–463
Singh VP (2011) Hydrologic synthesis using entropy theory: review. J Hydrol Eng 16(5):421–433
Singh VP (2013) Entropy theory and its application in environmental and water engineering. Wiley, Oxford, UK
Singh VP, Fiorentino M (1992) A historical perspective of entropy applications in water resources. In: Singh VP, Fiorentino M (eds) Entropy and energy dissipation in water resources. Kluwer, Dordrecht, Netherlands, pp 21–61
Singh VP, Guo H (1995a) Parameter estimation for 2-parameter Pareto distribution by POME. Water Resour Manage 9:81–93
Singh VP, Guo H (1995b) Parameter estimation for 3-parameter generalized Pareto distribution by the principle of maximum entropy (POME). Hydrol Sci J 40(2):165–181
Singh VP, Zhang L (2008a) At-a-station hydraulic geometry: I. Theoretical development. Hydrol Process 22:189–215
Singh VP, Zhang L (2008b) At-a-station hydraulic geometry: II. Calibration and testing. Hydrol Process 22:216–228
Singh VP, Yang CT, Deng ZQ (2003a) Downstream hydraulic geometry relations: 1. Theoretical development. Water Resour Res 39(12):1–15
Singh VP, Yang CT, Deng ZQ (2003b) Downstream hydraulic geometry relations: 2. Calibration and testing. Water Resour Res 39(12):1–10
Sivakumar B (2000) Chaos theory in hydrology: important issues and interpretations. J Hydrol 227(1–4):1–20
Sivakumar B (2002) A phase-space reconstruction approach to prediction of suspended sediment concentration in rivers. J Hydrol 258:149–162
Sivakumar B (2004a) Chaos theory in geophysics: past, present and future. Chaos Soliton Fract 19(2):441–462
Sivakumar B (2004b) Dominant processes concept in hydrology: moving forward. Hydrol Process 18(12):2349–2353
Sivakumar B (2005a) Correlation dimension estimation of hydrologic series and data size requirement: myth and reality. Hydrol Sci J 50(4):591–604
Sivakumar B (2005b) Hydrologic modeling and forecasting: role of thresholds. Environ Model Softw 20(5):515–519
Sivakumar B (2008a) Dominant processes concept, model simplification and classification framework in catchment hydrology. Stoch Env Res Risk Assess 22(6):737–748
Sivakumar B (2008b) The more things change, the more they stay the same: the state of hydrologic modeling. Hydrol Process 22:4333–4337
Sivakumar B (2009) Nonlinear dynamics and chaos in hydrologic systems:latest developments and a look forward. Stoch Environ Res Risk Assess 23:1027–1036
Sivakumar B, Berndtsson R (2010a) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore
Sivakumar B, Berndtsson R (2010b) Nonlinear dynamics and chaos in hydrology. In: Sivakumar B, Berndtsson R (eds) Advances in data-based approaches for hydrologic modeling and forecasting. World Scientific Publishing Company, Singapore, pp 411–461
Sivakumar B, Jayawardena AW (2002) An investigation of the presence of low-dimensional chaotic behavior in the sediment transport phenomenon. Hydrol Sci J 47(3):405–416
Sivakumar B, Singh VP (2012) Hydrologic system complexity and nonlinear dynamic concepts for a catchment classification framework. Hydrol Earth Syst Sci 16:4119–4131
Sivakumar B, Phoon KK, Liong SY, Liaw CY (1999) A systematic approach to noise reduction in chaotic hydrological time series. J Hydrol 219(3–4):103–135
Sivakumar B, Berndttson R, Olsson J, Jinno K (2001a) Evidence of chaos in the rainfall-runoff process. Hydrol Sci J 46(1):131–145
Sivakumar B, Sorooshian S, Gupta HV, Gao X (2001b) A chaotic approach to rainfall disaggregation. Water Resour Res 37(1):61–72
Sivakumar B, Berndtsson R, Olsson J, Jinno K (2002a) Reply to ‘which chaos in the rainfall-runoff process?’ by Schertzer et al. Hydrol Sci J 47(1):149–158
Sivakumar B, Jayawardena AW, Fernando TMGH (2002b) River flow forecasting: Use of phase-space reconstruction and artificial neural networks approaches. J Hydrol 265(1–4):225–245
Sivakumar B, Persson M, Berndtsson R, Uvo CB (2002c) Is correlation dimension a reliable indicator of low-dimensional chaos in short hydrological time series? Water Resour Res 38(2). doi:10.1029/2001WR000333
Sivakumar B, Harter T, Zhang H (2005) Solute transport in a heterogeneous aquifer: a search for nonlinear deterministic dynamics. Nonlinear Processes Geophys 12:211–218
Sivakumar B, Jayawardena AW, Li WK (2007) Hydrologic complexity and classification: a simple data reconstruction approach. Hydrol Process 21(20):2713–2728
Sivaprakasam C, Muttil N (2005) Discharge rating curve extension: a new approach. Water Resour Manage 19(5):505–520
Smith LC, Turcotte D, Isacks BL (1998) Stream flow characterization and feature detection using a discrete wavelet transform. Hydrol Process 12:233–249
Sonuga JO (1972) Principle of maximum entropy in hydrologic frequency analysis. J Hydrol 17(3):177–219
Sonuga JO (1976) Entropy principle applied to the rainfall-runoff process. J Hydrol 30:81–94
Srikanthan R, McMahon TA (1983) Stochastic simulation of daily rainfall for Australian stations. Trans ASAE:754–766
Steinwart I, Christmann A (2008) Support vector machines. Springer, Germany, 602 pp
Sudheer KP, Jain A (2004) Explaining the internal behaviour of artificial neural network river flow models. Hydrol Process 18(4):833–844
Sujono J, Shikasho S, Hiramatsu K (2004) A comparison of techniques for hydrograph recession analysis. Hydrol Process 18:403–413
Şen Z (2009) Fuzzy logic and hydrologic modeling. CRC Press, Boca Raton, FL
Şen Z, Oztopal A (2001) Genetic algorithms for the classification and prediction of precipitation occurrence. Hydrol Sci J 46(2):255–267
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cyber 15(1):116–132
Tayfur G, Moramarco T (2008) Predicting hourly-based flow discharge hydrographs from level data using genetic algorithms. J Hydrol 352(1–2):77–93
Tayfur G, Ozdemir S, Singh VP (2003) Fuzzy logic algorithm for runoff-induced sediment transport from bare soil surfaces. Adv Water Resour 26:1249–1256
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
Tong H (1983) Threshold models in non-linear time series analysis. Springer-Verlag
Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79(1):62–78
Tripathi S, Srinivas VV, Nanjundian RS (2006) Downscaling of precipitation for climate change scenarios: a support vector machine approach. J Hydrol 330(3–4):621–640
Tsallis C (1988) Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52(1–2):479–487
Tsukamoto Y (1979) An approach to fuzzy reasoning method. In: Gupta MM, Ragade RK, Yager RR (eds) Advances in fuzzy set theory and application. North-Holland, Amsterdam, pp 137–149
Tuma NB, Hannan MT (1984) Social dynamics: models and methods. Academic Press, Orlando, FL, p 602
Vairavamoorthy K, Ali M (2000) Optimal design of water distribution systems using genetic algorithms. Comp Aided Civil Infrastructure Eng 15:374–382
Valencia DR, Schaake JL (1973) Disaggregation processes in stochastic hydrology. Water Resour Res 9(3):211–219
Vapnik V (1998) The nature of statistical learning theory. Springer Verlag, New York, USA
Vasques JA, Maier HR, Lence BJ, Tolson BA, Foschi RO (2000) Achieving water quality system reliability using genetic algorithms. J Environ Eng ASCE 126(10):954–962
Venugopal V, Foufoula-Georgiou E (1996) Energy decomposition of rainfall in the time-frequency-scale domain using wavelet packets. J Hydrol 187:3–27
Wang QJ (1991) The genetic algorithm and its application to calibrating conceptual rainfall-runoff models. Water Resour Res 27(9):2467–2471
Wang Q, Gan TY (1998) Biases of correlation dimension estimates of streamflow data in the Canadian prairies. Water Resour Res 34(9):2329–2339
Wardlaw R, Sharif M (1999) Evaluation of genetic algorithms for optimal reservoir system operation. J Wat Resour Plan Manage ASCE 125(1):25–33
Whigham PA, Rechnagel F (2001) Predicting chlorophyll-a in freshwater lakes by hybridising process-based models and genetic algorithms. Ecol Model 146:243–251
Wilby RL, Abrahart RJ, Dawson CW (2003) Detection of conceptual model rainfall-runoff processes inside an artificial neural network. Hydrol Sci J 48(2):163–181
Wilcox BP, Seyfried MS, Matison TM (1991) Searching for chaotic dynamics in snowmelt runoff. Water Resour Res 27(6):1005–1010
Wolf A, Swift JB, Swinney HL, Vastano A (1985) Determining Lyapunov exponents from a time series. Physica D 16:285–317
Wu CL, Chau KW, Li YS (2008) River stage prediction based on a distributed support vector regression. J Hydrol 358(1–2):96–111
Wu CL, Chau KW, Li YS (2009) Predicting monthly streamflow using data-driven models coupled with data-preprocessing techniques. Water Resour Res 45:W08432. doi:10.1029/2007WR006737
Xiong LH, Shamseldin AY, O’Connor KM (2001) A nonlinear combination of the forecasts of rainfall-runoff models by the first order Takagi-Sugeno fuzzy system. J Hydrol 245(1–4):196–217
Yang CT (1971) Potential energy and stream morphology. Water Resour Res 2(2):311–322
Yevjevich VM (1972) Stochastic processes in hydrology. Water Resources Publications, Fort Collins, Colorado
Young PC (1974) Recursive approaches to time-series analysis. Bull Inst Math Appl 10:209–224
Young (1992) Parellel processes in hydrology and water: a unified time series approach. J Inst Water Environ Manage 6:598–612
Young PC (1993) Time variable and state dependent modelling of nonstationary and nonlinear time series. In: Subba Rao T (ed) Developments in time series analysis, Chapman and Hall, London, pp 374–413
Young PC (1998) Data-based mechanistic modeling of environmental, ecological, economic and engineering systems. Environ Model Softw 13:105–122
Young PC (2001) Data-based mechanistic modelling and validation of rainfall-flow processes. In: Anderson MG, Bates PD (eds) Model validation: perspectives in hydrological science. Wiley, Chichester, pp 117–161
Young PC (2002) Advances in real-time flood forecasting. Philos Trans R Soc, Phys Eng Sci 360(9):1433–1450
Young PC (2003) Top-down and data-based mechanistic modelling of rainfall-flow dynamics at the catchment scale. Hydrol Process 17:2195–2217
Young PC (2006) The data-based mechanistic approach to the modelling, forecasting and control of environmental systems. Annu Rev Control 30:169–182
Young PC (2010a) Gauss, Kalman and advances in recursive parameter estimation. J Forecast 30:104–146
Young PC (2010b) Real-time updating in flood forecasting and warning. In: Pender GJ, Faulkner H (eds) Flood Risk Science and Management. Wiley-Blackwell, Oxford, UK, pp 163–195
Young PC (2011) Recursive estimation and time-series analysis: an introduction for the student and practitioner. Springer, Berlin
Young PC (2013) Hypothetico-inductive data-based mechanistic modeling of hydrological systems. Water Resour Res 49:915–935. doi:10.1992/wrcr.20068
Young PC, Beck MB (1974) The modelling and control of water quality in a river system. Automatica 10:455–468
Young PC, Beven KJ (1994) Data-based mechanistic modeling and rainfall-flow non-linearity. Environmetrics 5(3):335–363
Young PC, Garnier H (2006) Identification and estimation of continuous-time, data-based mechanistic models for environmental systems. Environ Model Softw 21:1055–1072
Young PC, Lees MJ (1993) The active mixing volume: a new concept in modelling environmental systems. In: Barnett V, Turkman K (eds) Statistics for the Environment. Wiley, Chichester, pp 3–43
Young PC, Parkinson S (2002) Simplicity out of complexity. In: Beck MB (ed) Environmental foresight and models: a manifesto. Elservier, Oxford, pp 251–294
Young PC, Ratto M (2009) A unified approach to environmental systems modeling. Stoch Environ Res Risk Assess 23:1037–1057
Young PC, Parkinson SD, Lees MJ (1996) Simplicity out of complexity: Occam’s razor revisited. J Appl Stat 23:165–210
Young PC, Chotai A, Beven KJ (2004) Data-based mechanistic modelling and the simplification of environmental systems. In: Wainwright J, Mullgan M (eds) Environmental modelling: finding simplicity in complexity. Wiley, Chichester, pp 371–388
Young PC, Castelletti A, Pianosi F (2007) The data-based mechanistic approach in hydrological modelling. In: Castelletti A, Sessa RS (eds) Topics on system analysis and integrated water resource management. Elsevier, Amsterdam, pp 27–48
Yu X, Liong SY (2007) Forecasting of hydrologic time series with ridge regression in feature space. J Hydrol 332(3–4):290–302
Yu XY, Liong SY, Babovic V (2004) EC-SVM approach for real-time hydrologic forecasting. J Hydroinf 6(3):209–233
Zadeh LA (1965) Fuzzy sets. Inform. Control 8:338–353
Zadeh LA (1968) Fuzzy algorithms. Inf. Control 12:94–102
Zadeh LA, Klir GJ, Yuan B (1996) Fuzzy sets, fuzzy logic and fuzzy systems. World Scientific Publishers, Singapore
Zhang X, Srinivasan R, Bosch D (2009) Calibration and uncertainty analysis of the SWAT model using genetic algorithms and Bayesian model averaging. J Hydrol 374(3–4):307–317
Zhou Y, Ma Z, Wang L (2002) Chaotic dynamics of the flood series in the Huaihe River Basin for the last 500 years. J Hydrol 258:100–110
Zou R, Lung W-S, Wu J (2007) An adaptive neural network embedded GA approach for inverse water quality modeling. Water Resour Res 43:W08427. doi:10.1029/2006WR005158
Zurek WH (1989) Algorithmic randomness and physical entropy. Phys Rev A 40(8):4731–4751
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Sivakumar, B. (2017). Modern Nonlinear Time Series Methods. In: Chaos in Hydrology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2552-4_4
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