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Black-Box Hydrological Models

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Handbook of Hydrometeorological Ensemble Forecasting

Abstract

This chapter discusses different types of black-box hydrological models that are based on input-output relationships rather than physical principles. They include antecedent precipitation index (API) models, regression models, time series models, artificial neural network (ANN) models, fuzzy logic models, and frequency analysis models. The purpose of this chapter is neither to provide a complete discussion of the theory of hydrological systems nor to offer a complete coverage of the studies published in the literature. Rather, the chapter is focused on presenting general theories and methods of different types of black-box models, basic model forms, and related applications in hydrology and water resources engineering.

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References

  • A.J. Abebe, D.P. Solomatine, R.G.W. Venneker, Application of adaptive fuzzy rule-based models for reconstruction of missing precipitation events. Hydrol. Sci. J. 45(3), 425–436 (2000)

    Article  Google Scholar 

  • R.J. Abrahart, L. See, Comparing neural network and autoregressive moving average techniques for the provision of continuous river flow forecasts in two contrasting catchments. Hydrol. Process. 14, 2157–2172 (2000)

    Article  Google Scholar 

  • H.Z. Abyaneh, Evaluation of multivariate linear regression and artificial neural networks in prediction of water quality parameters. J. Environ. Health Sci. Eng. 12, 40 (2014.) http://www.ijehse.com/content/12/1/40

  • J. Adamowski, H.F. Chan, S.O. Prasher, B. Ozga-Zielinski, A. Sliusarieva, Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Water Resour. Res. 48(1) (2012). https://doi.org/10.1029/2010WR009945

  • A. Afshar, M.A. Mariño, M. Ebtehaj, J. Moosavi, Rule-based fuzzy system for assessing groundwater vulnerability. J. Environ. Eng. 133(5), 532–540 (2007)

    Article  Google Scholar 

  • S. Ahmad, S.P. Simonovic, An artificial neural network model for generating hydrograph from hydro-meteorological parameters. J. Hydrol. 315, 236–251 (2005)

    Article  Google Scholar 

  • S. Ahmad, I.H. Khan, B.P. Parida, Performance of stochastic approaches for forecasting river water quality. Water Res. 35(18), 4261–4266 (2001)

    Article  Google Scholar 

  • S. Ali, N.C. Ghosh, R. Singh, Rainfall-runoff simulation using a normalized antecedent precipitation index. Hydrol. Sci. J. 55(2), 266–274 (2010)

    Article  Google Scholar 

  • M. Alp, H.K. Cigizoglu, Suspended sediment load simulation by two artificial neural network methods using hydrometeorological data. Environ. Model Softw. 22, 2–13 (2007)

    Article  Google Scholar 

  • A. Aziz, R. Abd, K.F.V. Wong, A neural-network approach to the determination of aquifer parameters. Ground Water 30(2), 164–166 (1992)

    Article  Google Scholar 

  • K. Aziz, A. Rahman, G. Fang, S. Shrestha, Application of artificial neural networks in regional flood frequency analysis: a case study for Australia. Stoch. Env. Res. Risk A. 28(3), 541–554 (2014)

    Article  Google Scholar 

  • R.T. Bailite, Predictions from ARMAX models. J. Econ. 12, 365–374 (1980)

    Article  Google Scholar 

  • A. Bárdossy, M. Disse, Fuzzy rule-based models for infiltration. Water Resour. Res. 29(2), 373–382 (1993)

    Article  Google Scholar 

  • A. Bárdossy, A. Bronstert, B. Merz, 1-, 2- and 3-dimensional modeling of water movement in the unsaturated soil matrix using a fuzzy approach. Adv. Water Resour. 18(4), 237–251 (1995)

    Article  Google Scholar 

  • J.J. Beauchamp, Comparison of regression and time-series methods for synthesizing missing streamflow records. Water Resour. Bull. 25, 961–975 (1989)

    Article  Google Scholar 

  • M.A. Benson, Factors influencing the occurrence of floods in a humid region of diverse terrain. U.S. Geol. Surv., Water-Supply Pap., 1580-B, 64 pp. (1962)

    Google Scholar 

  • R.B. Billings, D.E. Agthe, State-space versus multiple regression for forecasting urban water demand. J. Water Resour. Plann. Manag. 124(2), 113 (1998)

    Article  Google Scholar 

  • T. Bollerslev, Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31(3), 307–327 (1986)

    Article  Google Scholar 

  • J. Bougadis, K. Adamowski, R. Diduch, Short-term municipal water demand forecasting. Hydrol. Process. 19, 137–148 (2005). https://doi.org/10.1002/hyp.5763

    Article  Google Scholar 

  • G.E.P. Box, G.M. Jenkins, Time Series Analysis: Forecasting and Control (Holden-Day, San Francisco, 1976)

    Google Scholar 

  • F.J. Chang, H.F. Hu, Y.C. Chen, Counterpropagation fuzzy–neural network for streamflow reconstruction. Hydrol. Process. 15(2), 219–232 (2001)

    Article  Google Scholar 

  • S.P. Charles, M.A. Bari, A. Kitsios, B.C. Bates, Effect of GCM bias on downscaled precipitation and runoff projections for the Serpentine catchment, western Australia. Int. J. Climatol. 27, 1673–1690 (2007)

    Article  Google Scholar 

  • V.T. Chow, Handbook of Applied Hydrology (McGraw-Hill, New York, 1964)

    Google Scholar 

  • V.T. Chow, D.R. Maidment, L.W. Mays, Applied Hydrology (McGraw-Hill, New York, 1988)

    Google Scholar 

  • T.A. Clair, J.M. Ehrman, Using neural networks to assess the influence of changing seasonal climates in modifying discharge, dissolved organic carbon, and nitrogen export in eastern Canadian rivers. Water Resour. Res. 34(3), 447–455 (1998)

    Article  Google Scholar 

  • M. Cobaner, Evapotranspiration estimation by two different neuro-fuzzy inference systems. J. Hydrol. 398, 292–302 (2011)

    Article  Google Scholar 

  • P. Coulibaly, N.D. Evora, Comparison of neural network methods for infilling missing daily weather records. J. Hydrol. 341, 27–41 (2007)

    Article  Google Scholar 

  • I. Daliakopoulos, P. Coulibaly, I. Tsanis, Ground water level forecasting using artificial neural networks. J. Hydrol. 309(1-4), 229–240 (2005)

    Article  Google Scholar 

  • T. Dalrymple, Flood frequency methods. U.S. Geol. Surv. Water Supply Pap., 1543-A, 11–51 (1960)

    Google Scholar 

  • C.W. Dawson, R.J. Abrahart, Evaluation of two different methods for the antecedent precipitation index in neural network river stage forecasting. Geophys. Res. Abstr. 07522, 9 (2007)

    Google Scholar 

  • C. Dou, W. Woldt, I. Bogardi, M. Dahab, Steady State Groundwater Flow Simulation With Imprecise Parameters. Water Resour. Res. 31(11), 2709–2719 (1995)

    Article  Google Scholar 

  • C. Dou, W. Woldt, I. Bogardi, Fuzzy rule-based approach to describe solute transport in the unsaturated zone. J. Hydrol. 220(1), 74–85 (1999)

    Article  Google Scholar 

  • G. Dumedah, P. Coulibaly, Evaluation of statistical methods for infilling missing values in high-resolution soil moisture data. J. Hydrol. 400(1-2), 95–102 (2011)

    Article  Google Scholar 

  • S.R. Durrans, S. Tomic, Comparison of parametric tail estimators for low-flow frequency analysis. J. Am. Water Resour. Assoc. 37(5), 1203–1214 (2001)

    Article  Google Scholar 

  • J.K. Eischeid, P.A. Pasteris, H.F. Diaz, M.S. Plantico, N.J. Lott, Creating a serially complete, national daily time series of temperature and precipitation for the Western United States. J. Appl. Meteorol. 39, 1580–1591 (2000)

    Article  Google Scholar 

  • S. El Aldouni, T. Ouarda, X. Zhang, R. Roy, B. Bobee, Generalized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resour. Res. 43, 1–13 (2007)

    Google Scholar 

  • A.K. Eldaw, J.D. Salas, L.A. Garcia, Long-range forecasting of the Nile River flows using climatic forcing. J. Appl. Meteorol. 42(7), 890–904 (2003)

    Article  Google Scholar 

  • R.F. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of United Kindom inflation. Econometrica 50(4), 987–1007 (1982)

    Article  Google Scholar 

  • M.A. Fedora, R.L. Beschta, Storm runoff simulation using an antecedent precipitation index (API) model. J. Hydrol. 112, 121–133 (1989)

    Article  Google Scholar 

  • R.I.C.C. Francis, J.A. Renwick, A regression-based assessment of the predictability of New Zealand climate anomalies. Theor. Appl. Climatol. 60, 21–36 (1998)

    Article  Google Scholar 

  • M. Friedman, A. Kandel, Introduction to Pattern Recognition: Statistical, Structural, Neural, and Fuzzy Logic Approaches, Series in Machine Perception Artificial Intelligence, vol 32 (World Scientific, Singapore, 1999)

    Google Scholar 

  • W.E. Fuller, Flood flows. Trans. ASCE 77(1293), 564–617 (1914)

    Google Scholar 

  • D. Gautam, K. Holz, Rainfall-runoff modelling using adaptive neuro-fuzzy systems. J. Hydroinf. 3, 3–10 (2001)

    Article  Google Scholar 

  • T. Glade, M.J. Crozier, P. Smith, Applying probability determination to refine landslide-triggering rainfall thresholds using an empirical (Antecedent Daily Rainfall Model). Pure Appl. Geophys. 157(6/8), 1059–1079 (2000)

    Article  Google Scholar 

  • C.T. Haan, Statistical Methods in Hydrology, 2nd edn. (Iowa State University Press, Ames, 2002.) 496 pp

    Google Scholar 

  • M. Hallack-Alegria, D.W. Watkins, Annual and warm season drought intensity-duration-frequency analysis for Sonora, Mexico. J. Clim. 20(9), 1897–1909 (2007)

    Article  Google Scholar 

  • S. Haykin, Neural Networks (MacMillan, London, 1994)

    Google Scholar 

  • Z. He, X. Wen, H. Liu, J. Du, A comparative study of artificial neural network, adaptive neuro fuzzy inference system and support vector machine for forecasting river flow in the semiarid mountain region. J. Hydrol. 509, 379–386 (2014)

    Article  Google Scholar 

  • R.J. Heggen, Normalized antecedent precipitation index. J. Hydrol. Eng. ASCE 6(5), 377–381 (2001)

    Article  Google Scholar 

  • B.C. Hewitson, R.G. Crane, Climate downscaling: techniques and application. Clim. Res. 7, 85–95 (1996)

    Article  Google Scholar 

  • J.D. Hewlett, A.R. Hibbert, Factors affecting the response of small watersheds to precipitation in humid regions, in Forest Hydrology, ed. by W. E. Sopper, H. W. Lull, (Pergamon Press, Oxford, 1967), pp. 275–290.

    Google Scholar 

  • Y.S. Hong, M.R. Rosen, R.R. Reeves, Dynamic fuzzy modeling of storm water infiltration in urban fractured aquifers. J. Hydrol. Eng. 7(5), 380–391 (2002)

    Article  Google Scholar 

  • Y. Hong, R.F. Adler, F. Hossain, S. Curtis, G.J. Huffman, A first approach to global runoff simulation using satellite rainfall estimation. Water Resour. Res. 43, W08502 (2007). https://doi.org/10.1029/2006WR005739

    Article  Google Scholar 

  • J.R.M. Hosking, J.R. Wallis, Regional frequency analysis: an approach based on L-moments (Cambridge University Press, Cambridge, 1997)

    Book  Google Scholar 

  • J.R.M. Hosking, J.R. Wallis, E.F. Wood, An appraisal of the regional flood frequency procedure in the UK Flood Studies Report. Hydrol. Sci. J. 30, 85–109 (1985)

    Article  Google Scholar 

  • J.R.M. Hosking, J.R. Wallis, Some statistics useful in regional frequency analysis: Water Resource Research, 29(2), 271–281 (1993)

    Article  Google Scholar 

  • J.F.T. Houston, Groundwater system simulation by time series techniques. Ground Water 21, 301–310 (1983)

    Article  Google Scholar 

  • K.-L. Hsu, H.V. Gupta, S. Sorooshian, Artificial neural network modeling of the rainfall-runoff process. Water Resour. Res. 31, 2517–2530 (1995)

    Article  Google Scholar 

  • K.L. Hsu, X. Gao, S. Sorooshian, H.V. Gupta, Precipitation estimation from remotely sensed information using artificial neural networks. J. Appl. Meteorol. 36(9), 1176–1190 (1997)

    Article  Google Scholar 

  • Y. Huang, X. Chen, et al., A fuzzy-based simulation method for modelling hydrological processes under uncertainty. Hydrol. Process. 24(25), 3718–3732 (2010)

    Article  Google Scholar 

  • Y. Hundecha, A. Bardossy, H.W. Werner, Development of a fuzzy logic-based rainfall-runoff model. Hydrol. Sci. J. 46(3), 363–376 (2001)

    Article  Google Scholar 

  • A.P. Jacquin, A.Y. Shamseldin, Development of rainfall-runoff models using Takagi–Sugeno fuzzy inference systems. J. Hydrol. 329, 154–173 (2006)

    Article  Google Scholar 

  • S.K. Jain, A. Das, D.K. Srivastava, Application of ANN for Reservoir Inflow Prediction and Operation. J. Water Resour. Plan. Man. ASCE, 125(5), 263–271 (1999)

    Article  Google Scholar 

  • J.S.R. Jang, C.T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing (Prentice-Hall, Englewood Cliffs, NJ, 1997)

    Google Scholar 

  • B. Janos, D. Lucien, H.R. Omar, Practical generation of synthetic rainfall event time series in a semi-arid climatic zone. J. Hydrol. 103, 357–373 (1988)

    Article  Google Scholar 

  • C. Jorge, Forecasting water consumption in Spain using univariate time series models. Proc IEEE Span. Comput. Intell. Soc. 2007, 415–423 (2007)

    Google Scholar 

  • M. Karamouz, S. Sara Nazif, M. Falahi, Hydrology and Hydroclimatology: Principles and Applications (CRC Press, Boca Raton, 2012)

    Book  Google Scholar 

  • N.K. Kasabov, Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering (MIT Press, Cambridge, MA, 1996)

    Google Scholar 

  • M.N. Khaliq, T.B.M.J. Ouarda, J.-C. Ondo, P. Gachon, B. Bobée, Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: A review. J. Hydrol. 329, 534–552 (2006)

    Article  Google Scholar 

  • Ö. KiÅŸi, Streamflow forecasting using different artificial neural network algorithms. J. Hydrol. Eng. 12(5), 532–539 (2007)

    Article  Google Scholar 

  • G. Kite, Use of time series analyses to detect climatic change. J. Hydrol. 111, 259–279 (1989)

    Article  Google Scholar 

  • T.R. Kjeldsen, J.C. Smithers, R.E. Schulze, Flood frequency analysis at ungauged sites in the KwaZulu-Natal Province, South Africa. Water SA 27(3), 315–324 (2001)

    Article  Google Scholar 

  • G.J. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications (Prentice Hall, Upper Saddle River, 1995)

    Google Scholar 

  • M. A. Kohler, R. K. Linsley, Predicting the Runoff from Storm Rainfall, U.S. Weather Bureau Research Paper No. 34 (1951)

    Google Scholar 

  • R. Kruse, J.E. Gebhardt, F. Klowon, Foundations of Fuzzy Systems (Wiley, New York, 1994)

    Google Scholar 

  • M. Kumar, N. Raghuwanshi, R. Singh, W. Wallender, W. Pruitt, Estimating evapotranspiration using artificial neural network. J. Irrig. Drain. Eng. 128(4), 224–233 (2002)

    Article  Google Scholar 

  • R. Kumar, C. Chatterjee, S. Kumar, A.K. Lohani, R.D. Singh, Development of regional flood frequency relationships using L-moments for Middle Ganga Plains Subzone 1(f) of India. Water Resour. Manag. 17(4), 243–257 (2003)

    Article  Google Scholar 

  • G. Lachtermacher, J.D. Fuller, Backpropagation in hydrological time series forecasting, in Stochastic and Statistical Methods in Hydrology and Environmental Engineering, (Springer, Cham, 1994), pp. 229–242

    Chapter  Google Scholar 

  • X. Lana, A. Burgueno, Daily dry-wet behavior in Catalonia (NE Spain) from the viewpoint of the first and second order Markov chains. Int. J. Clim. 18, 793–815 (1998)

    Article  Google Scholar 

  • X. Lana, M.D. Martínez, A. Burgueño, C. Serra, Return period maps of dry spells for Catalonia (northeastern Spain) based on the Weibull. Hydrol. Sci. J. 53, 48–64 (2008)

    Article  Google Scholar 

  • S.A. Lawal, W.E. Watt, Non-zero lower limit in low flow frequency analysis? Water Resour. Bull. 32(6), 1159–1166 (1996)

    Article  Google Scholar 

  • M. Leclerc, T.B.M.J. Ouarda, Non-stationary regional flood frequency analysis at ungauged sites. J. Hydrol. 343, 254–264 (2007)

    Article  Google Scholar 

  • Y.H. Lim, D.L. Voeller, Regional flood estimations in Red River using L-moment-based index-flood and Bulletin 17B Procedures. J. Hydrol. Eng. 14(9), 1002–1016 (2009)

    Article  Google Scholar 

  • S. Liu, L. Leslie, M. Speer, R. Bunker, Predicting forest fire danger using improved model derived soil-moisture and antecedent precipitation. International Congress on Modelling and Simulation, Townsville, Australia, July 14–17, 2003

    Google Scholar 

  • Y.L. Loukas, Adaptive Neuro-Fuzzy Inference System, An Instant and Architecture-Free Predictor for Improved QSAR Studies. J. Med. Chem. 44(17), 2772–2783 (2001)

    Article  Google Scholar 

  • T. Ma, C. Li, Z. Lu, B. Wang, An effective antecedent precipitation model derived from the power-law relationship between landslide occurrence and rainfall level. Geomorphology 216, 187–192 (2014)

    Article  Google Scholar 

  • D. Machiwal, M.K. Jha, Time series analysis of hydrologic data for water resources planning and management: A review. J. Hydrol. Hydromech. 54(3), 237–257 (2006)

    Google Scholar 

  • A. Makarau, M.R. Jury, Predictability of Zimbabwe summer rainfall. Int. J. Climatol. 17, 1421–1432 (1997)

    Article  Google Scholar 

  • J.M. Mejia, J. Rousselle, Disaggregation Models in hydrology revisited. Water Resour. Res. 12, 185–186 (1976). https://doi.org/10.1029/WR012i002p00185

    Article  Google Scholar 

  • A.K. Mishra, V.R. Desai, Drought forecasting using stochastic models. Stoch. Environ. Res. Risk Assess. 19, 326–339 (2005)

    Article  Google Scholar 

  • A. Moatmari, M. Longoni, R. Rosso, A seasonal long memory stochastic model for the simulation of daily rived flows. Phys. Chem. Earth (B) 24(4), 319–324 (1999)

    Article  Google Scholar 

  • S. Mohan, N. Arumugam, Forecasting weekly reference crop evapotranspiration series. Hydrol. Sci. J. 40(6), 689–720 (1995)

    Article  Google Scholar 

  • T.J. Mulvaney, On the use of self-registering rain and flood gauges. Trans. Inst. Civ. Eng. Ireland 4(2), 1–8 (1850)

    Google Scholar 

  • R.J. Nathan, T.A. McMahon, Practical Aspects of Low-Flow Frequency Analysis. Water Resour. Res. 26(9), 2135–2141 (1990)

    Google Scholar 

  • D.W. Newton, J.C. Herrin, Assessment of commonly used methods of estimating flood frequency. Transportation Research Record, Series 896, Washington, DC, pp. 10–30 (1982)

    Google Scholar 

  • T. Ouarda, S. El-Aldouni, Bayesian nonstationarity frequency analysis of hydrological variables. J. Amer. Water Resour. Assoc. 47, 496–505 (2011)

    Article  Google Scholar 

  • T. Öztekin, Wakeby distribution for representing annual extreme and partial duration rainfall series. Meteorol. Appl. 14, 381–387 (2007)

    Article  Google Scholar 

  • G.R. Pandey, V.T.V. Nguyen, A comparative study of regression based methods in regional flood frequency analysis. J. Hydrol. 225, 92–101 (1999)

    Article  Google Scholar 

  • K. Pearson, On the generalized probable error in multiple normal correlation. Biometrika 6, 59–68 (1908)

    Article  Google Scholar 

  • P. Pekarova, J. Pekar, Long-term discharge prediction for the Turnu Severin station (the Danube) using a linear autoregressive model. Hydrol. Process. 20, 1217–1228 (2006)

    Article  Google Scholar 

  • G. Pesti, B.P. Shrestha, L. Duckstein, I. Bogárdi, A fuzzy rule-based approach to drought assessment. Water Resour. Res. 32(6), 1741–1747 (1996)

    Article  Google Scholar 

  • A. Piegat, Fuzzy Modeling and Control. Studies in Fuzziness and Soft Computing (Book 69) (Springer, Berlin, 2001)

    Google Scholar 

  • D. H. Pilgrim (ed.), Australian Rainfall and Runoff: A Guide to Flood Estimation, Volumes I and II (Institution of Engineers Australia, Canberra, 1998)

    Google Scholar 

  • A.S. Polebitski, R.N. Palmer, Seasonal residential water demand forecasting for census tracts. J. Water Resour. Plan. Manag. 136(1), 27–36 (2009)

    Article  Google Scholar 

  • R. Pongracz, J. Bartholy, I. Bogardi, Fuzzy rule-based prediction of monthly precipitation. Phys. Chem. Earth BHydrol. Oceans Atmos. 26(9), 663–667 (2001)

    Article  Google Scholar 

  • M.P. Rajurkar, U.C. Kothyari, U.C. Chaube, Modeling of the daily rainfall-runoff relationship with artificial neural network. J. Hydrol. 285, 96–113 (2004)

    Article  Google Scholar 

  • H. Raman, V. Chandramouli, Deriving a general operating policy for reservoirs using neural networks. J. Water Resour. Plan. Manag. 122(5), 342–347 (1996)

    Article  Google Scholar 

  • H. Raman, N. Sunilkumar, Multi-variate modeling of water resources time series using artificial neural networks. Hydrol. Sci. J. 40, 145–163 (1995)

    Article  Google Scholar 

  • B. Renard, M. Lang, P. Bois, Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: case study with peak-over-threshold data. Stoch. Env. Res. Risk Asess. 21, 97–112 (2006)

    Article  Google Scholar 

  • H.C. Riggs, Streamflow characteristics: Developments in water science 22 (Elsevier, Amsterdam, 1985)

    Google Scholar 

  • L.L. Rogers, F.U. Dowla, Optimization of groundwater remediation using artificial neural networks with parallel solute transport modeling. Water Resour. Res. 30(2), 457–481 (1994)

    Article  Google Scholar 

  • S.O. Russell, P.F. Campbell, Reservoir operating rules with fuzzy programming. J. Water Resour. Plann. Manag. 122(3), 165–170 (1996)

    Article  Google Scholar 

  • B. Saf, Regional flood frequency analysis using L-moments for the west Mediterranean region of Turkey. Water Resour. Manag. 23(3), 531–551 (2009)

    Article  Google Scholar 

  • J.D. Salas, Analysis and modeling of hydrologic time series, Chapter 19, in Handbook of Hydrology, ed. by D. R. Maidement (McGraw-Hill, New York, 1993)

    Google Scholar 

  • J.D. Salas, J.W. Deulleur, V. Yevjevich, W.L. Lane, Applied Modeling of Hydrologic Time Series (Water Resources Publications, Littleton, 1980)

    Google Scholar 

  • A. Sankarasubramanian, U. Lall, Flood quantiles in a changing climate: seasonal forecasts and causal relations. Water Resour. Res. 39, 4.1–4.12 (2003)

    Article  Google Scholar 

  • K.E. Saxton, A.M. ASCE, A.T. Lenz, F. ASCE, Antecedent retention indexes predict soil moisture. J. Hydraul. Div. ASCE 93(HY4, Proc. Paper 5351), 223–241 (1967)

    Google Scholar 

  • K. Schulz, B. Huwe, Water flow modeling in the unsaturatedzone with imprecise parameters using a fuzzy approach. J. Hydrol. 201, 211–229, (1997). https://doi.org/10.1016/S0022-1694(97)00038-3.

    Article  Google Scholar 

  • L. See, S. Openshaw, Applying soft computing approaches to river level forecasting. Hydrol. Sci. J. 44(5), 763–778 (1999)

    Article  Google Scholar 

  • A.Y. Shamseldin, Application of a neural network technique to rainfall-runoff modeling. J. Hydrol. 199, 272–294 (1997)

    Article  Google Scholar 

  • V.N. Sharda, S.O. Prasher, R.M. Patel, P.R. Ojasvi & Chandra Prakash. Performance of Multivariate Adaptive Regression Splines (MARS) in predicting runoff in mid-Himalayan micro-watersheds with limited data / Performances de régressions par splines multiples et adaptives (MARS) pour la prévision d’écoulement au sein de micro-bassins versants Himalayens d’altitudes intermédiaires avec peu de données. Hydrol. Sci. J. 53(6), 1165–1175 (2008). https://doi.org/10.1623/hysj.53.6.1165

    Article  Google Scholar 

  • Q.X. Shao, H. Wong, M. Li, W.C. Ip, Streamflow forecasting using functional-coefficient time series model with periodic variation. J. Hydrol. 368, 88–95 (2009)

    Article  Google Scholar 

  • J. Shiri, A.H. Nazemi, A.A. Sadraddini, G. Landeras, O. Kisi, A.F. Fard, P. Marti, Global cross-station assessment of neuro-fuzzy models for estimating daily reference evapotranspiration. J. Hydrol. 480, 46–57 (2013)

    Article  Google Scholar 

  • J. Shiri, P. Marti, A.H. Nazemi, A.A. Sadraddini, O. Kisi, Local vs. external training of neuro-fuzzy and neural networks models for estimating reference evapotranspiration assessed through k-fold testing. Hydrol. Res. 46(1), 72–88 (2014). https://doi.org/10.2166/nh.2013.112

    Article  Google Scholar 

  • C. Shu, D.H. Burn, Homogeneous pooling group delineation for flood frequency analysis using a fuzzy expert system with genetic enhancement. J. Hydrol. 291(1-2), 132–149 (2004)

    Article  Google Scholar 

  • K. Schulz, B. Huwe, Water flow modeling in the unsaturatedzone with imprecise parameters using a fuzzy approach. J. Hydrol. 201, 211–229 (1997). https://doi.org/10.1016/S0022-1694(97)00038-3

    Article  Google Scholar 

  • W.T. Sittner, C.E. Schauss, J.C. Monro, Continuous hydrograph synthesis with an API type hydrological model. Water Resour. Res. 5(5), 1007–1022 (1969)

    Article  Google Scholar 

  • J.R. Stedinger, R.M. Vogel, E. Foufoula-Georgiou, Frequency analysis of extreme events, Chapter 18, in Handbook of Applied Hydrology, ed. by D. R. Maidment (McGraw-Hill, New York, 1993), pp. 1–66

    Google Scholar 

  • W.G. Strupczewski, V.P. Singh, H.T. Mitosek, Non-stationary approach to at-site flood frequency modelling, III. Flood analysis of Polish rivers. J. Hydrol. 248, 152–167 (2001)

    Article  Google Scholar 

  • M. Sugeno, G.T. Kang, Structure identification of fuzzy model. Fuzzy Sets Syst. 28, 15–33 (1988)

    Article  Google Scholar 

  • T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC-15(1), 116–132 (1985)

    Article  Google Scholar 

  • D.M. Thomas, M.A. Benson, Generalization of streamflow characteristics from drainage-basin characteristics, US Geological Survey, Water Supply Paper, 1975 (1970)

    Google Scholar 

  • United States Water Resources Council, Guidelines for determining flood flow frequency Bull. 17B, U.S. Water Resour. Counc. Hydrol. Comm., Washington, DC (1982)

    Google Scholar 

  • R.D. Valencia, J.C. Schaake, Disaggregation processes in stochastic hydrology. Water Resour. Res. 9, 580–585 (1973). https://doi.org/10.1029/WR009i003p00580

    Article  Google Scholar 

  • F.C. Van Geer, A.F. Zuur, An extension of Box-Jenkins transfer/noise models for spatial interpolation of groundwater head series. J. Hydrol. 192, 65−80 (1997)

    Google Scholar 

  • W. Viessman Jr., G.L. Lewis, Introduction to Hydrology, 4th edn. (Harper Collins, New York, 1996)

    Google Scholar 

  • R.M. Vogel, C.N. Kroll, Generalized low-flow frequency relationships for ungaged sites in Massachusetts. Water Resour. Bull. 26(2), 241–253 (1990)

    Article  Google Scholar 

  • R.M. Vogel, I. Wilson, Probability distribution of annual maximum, mean, and minimum streamflows in the United States. ASCE J. Hydrol. Eng. 1(2), 69–76 (1996)

    Article  Google Scholar 

  • R.M. Vogel, W.O. Thomas Jr., T.A. McMahon, Flood-flow frequency model selection in Southwestern United States. J. Water Resour. Plann. Manag. 119(3), 353–366 (1993)

    Article  Google Scholar 

  • L.X. Wang, A Course in Fuzzy Systems and Control (Prentice-Hall, Englewood Cliffs, 1997)

    Google Scholar 

  • W.D. Weeks, W.C. Boughton, Tests of ARMA model forms for rainfall-runoff modeling. J. Hydrol. 91, 29–47 (1987)

    Article  Google Scholar 

  • J.R. Westmacott, D.H. Burn, Climate change effects on the hydrologic regime within the Churchill-Nelson River Basin. J. Hydrol. 202(1-4), 263–279 (1997)

    Article  Google Scholar 

  • R.L. Wilby, L.E. Hay, G.H. Leavesley, A comparison of downscaled and raw GCM output: implications for climate change scenarios in the San Juan River basin, Colorado. J. Hydrol. 225, 67–91 (1999)

    Article  Google Scholar 

  • C.L. Wu, K.W. Chau, Rainfall–runoff modeling using artificial neural network coupled with singular spectrum analysis. J. Hydrol. 399, 394–409 (2011)

    Article  Google Scholar 

  • L. Xiong, A.Y. Shamseldin, K.M. O’Connor, A non-linear combination of the forecasts of rainfall-runoff models by the first-order Takagi–Sugeno fuzzy system. J. Hydrol. 245, 196–217 (2001)

    Article  Google Scholar 

  • L. Xiong, K.M. O’Connor, S. Guo, Comparison of three updating schemes using artificial neural network in flow forecasting. Hydrol. Earth. Sys. Sci. 8(2), 247–255 (2004)

    Article  Google Scholar 

  • A. Yasar, M. Bilgili, E. Simsek, Water demand forecasting based on stepwise multiple nonlinear regression analysis. Arab. J. Sci. Eng. 37(8), 2333–2341 (2012)

    Article  Google Scholar 

  • X.Y. Yu, S.Y. Liong, Forecasting of hydrologic time series with ridge regression in feature space. J. Hydrol. 332, 290–302 (2007)

    Article  Google Scholar 

  • P.S. Yu, T.C. Yang, Fuzzy multi-objective function for rainfall-runoff model calibration. J. Hydrol. 238, 1), 1–1),14 (2000)

    Article  Google Scholar 

  • S. Yue, C.Y. Wang, Possible regional probability distribution type of Canadian annual streamflow by L-moments. Water Resour. Manag. 18(5), 425–438 (2004)

    Article  Google Scholar 

  • M.A. Yurdusev, M. Firat, Adaptive neuro fuzzy inference system approach for municipal water consumption modeling, An application to Izmir, Turkey. J. Hydrol. 365(3-4), 225–234 (2009)

    Article  Google Scholar 

  • L.A. Zadeh, Fuzzy sets. Inf. Control. 8, 338–353 (1965)

    Article  Google Scholar 

  • C.M. Zealand, D.H. Burn, S.P. Simonovic, Short term streamflow forecasting using artificial neural networks. J. Hydrol. 214, 32–48 (1999)

    Article  Google Scholar 

  • H.J. Zimmermann, Fuzzy Set Theory and Its Applications, 4th edn. (Kluwer Academic Publishers, Boston, 2001)

    Book  Google Scholar 

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Acknowledgment

We are indebted to Yixing Yin, Yukun Hou, Qiang Zeng, and Xin-e Tao for their help in preparation of this chapter with proofreading and in supplying references, drawing figures, rewriting parts of the text, etc. We are also thankful to the two anonymous reviewers whose comments improved this chapter.

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Authors and Affiliations

  1. Department of Geosciences, University of Oslo, Oslo, Norway

    Chong-Yu Xu

  2. Department of Hydrology and Water Resources, Wuhan University, Wuhan, China

    Lihua Xiong

  3. Department of Biological and Agricultural Engineering and Zachry Department of Civil Engineering, Texas A and M University, College Station, TX, USA

    Vijay P. Singh

Authors
  1. Chong-Yu Xu
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  2. Lihua Xiong
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  3. Vijay P. Singh
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Correspondence to Vijay P. Singh .

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Editors and Affiliations

  1. Faculty of Geographical Science, Beijing Normal University, Beijing, China

    Qingyun Duan

  2. European Centre for Medium-Range Weather Forecasts, ECMWF, Reading, UK

    Florian Pappenberger

  3. National Center for Atmospheric Research, Boulder, CO, USA

    Andy Wood

  4. Department of Meteorology, Reading University, Reading, UK

    Hannah L. Cloke

  5. U.S. National Weather Service (retired), Annapolis, MD, USA

    John C. Schaake

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Xu, CY., Xiong, L., Singh, V.P. (2019). Black-Box Hydrological Models. In: Duan, Q., Pappenberger, F., Wood, A., Cloke, H., Schaake, J. (eds) Handbook of Hydrometeorological Ensemble Forecasting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39925-1_21

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