Method to Estimate Optimal Parameters

Living reference work entry


Model, data, and parameter estimation are three fundamental elements in hydrologic process modeling and forecasting. Recent progresses in hydrologic modeling have been made toward more efficient and effective estimation of model parameters. In this chapter, classical and recently developed parameter optimization methods and their applications in hydrological model calibration are reviewed. Those methods include gradient-based optimization methods, direct search methods, and recently developed stochastic global optimization methods. A recently developed surrogate model approach, with the purpose to reduce computational burden of model which runs through replacing the hydrologic process model with a cheaper-to-run surrogate model, is also discussed. Extending from a single objective function parameter optimization, multiobjective optimization methods and their core concept in deriving trade-offs are also summarized. Examples are provided to demonstrate the strengths and limitations of optimization algorithms summarized in this chapter.


Optimization Hydrologic Model Evolutionary Algorithm Automatic Parameter Estimation Surrogate Model 


  1. K. Abbaspour, R. Schulin, M.T. Van Genuchten, Estimating unsaturated soil hydraulic parameters using ant colony optimization. Adv. Water Resour. 24(8), 827–841 (2001)CrossRefGoogle Scholar
  2. M.A. Abido, Optimal design of power-system stabilizers using particle swarm optimization. IEEE Trans. Energy Convers. 17(3), 406–413 (2002)CrossRefGoogle Scholar
  3. A. Afshar, F. Massoumi, A. Afshar, M.A. Mariño, State of the art review of ant colony optimization applications in water resource management. Water Resour. Manag. 29(11), 3891–3904 (2015)CrossRefGoogle Scholar
  4. I. Alaya, C. Solnon, K. Ghedira, Ant Colony Optimization for Multi-objective Optimization Problems (Citeseer, Patras, 2007), pp. 450–457.
  5. D. Angus, C. Woodward, Multiple objective ant colony optimisation. Swarm Intell. 3(1), 69–85 (2009)CrossRefGoogle Scholar
  6. R. Arsenault, A. Poulin, P. Côté, F. Brissette, Comparison of stochastic optimization algorithms in hydrological model calibration. J. Hydrol. Eng. 19(7), 1374–1384 (2013)CrossRefGoogle Scholar
  7. R. Arsenault, A. Poulin, P. Côté, F. Brissette, Comparison of stochastic optimization algorithms in hydrological model calibration. J. Hydrol. Eng. 19(7), 1374–1384 (2014)CrossRefGoogle Scholar
  8. M. Asadzadeh, B.A. Tolson, D.H. Burn, A new selection metric for multiobjective hydrologic model calibration. Water Resour. Res. 50(9), 7082–7099 (2014)CrossRefGoogle Scholar
  9. V. Babovic, M. Keijzer, Rainfall runoff modelling based on genetic programming. Hydrol. Res. 33(5), 331–346 (2002)CrossRefGoogle Scholar
  10. C. Balascio, D. Palmeri, H. Gao, Use of a genetic algorithm and multi-objective programming for calibration of a hydrologic model. Trans. ASAE 41(3), 615 (1998)CrossRefGoogle Scholar
  11. S. Bandyopadhyay, S. Saha, U. Maulik, K. Deb, A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans. Evol. Comput. 12(3), 269–283 (2008)CrossRefGoogle Scholar
  12. A. Bárdossy, T. Das, Influence of rainfall observation network on model calibration and application. Hydrol. Earth Syst. Sci. Discuss. 3(6), 3691–3726 (2006)CrossRefGoogle Scholar
  13. B. Bates, Calibration of the SFB model using a simulated annealing approach. Water Down Under 94: Surface Hydrology and Water Resources Papers; Preprints of Papers, 1 (1994)Google Scholar
  14. K. Behzadian, Z. Kapelan, D. Savic, A. Ardeshir, Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks. Environ. Model. Softw. 24(4), 530–541 (2009)CrossRefGoogle Scholar
  15. E.G. Bekele, J.W. Nicklow, Multi-objective automatic calibration of SWAT using NSGA-II. J. Hydrol. 341(3), 165–176 (2007)CrossRefGoogle Scholar
  16. R.W. Blanning, Construction and implementation of metamodels. Simulation 24(6), 177–184 (1975)CrossRefGoogle Scholar
  17. G. Bowden, G. Dandy, H. Maier, Ant colony optimisation of a general regression neural network for forecasting water quality, in Hydroinformatics 2002: Proceedings of the FIFTH INTERNATIONAL Conference on Hydroinformatics, ed. by R.A. Falconer et al., Cardiff (IWA Publishing, 2002), pp. 692–698Google Scholar
  18. L.E. Brazil, Multilevel Calibration Strategy for Complex Hydrologic Simulation Models (Colorado State University, Fort Collins, 1988)Google Scholar
  19. L. Breiman, Random forests. Mach. Learn. 45(1), 5–32 (2001). Scholar
  20. L. Breiman, J.H. Friedman, R.A. Olshen, C.J. Stone, Classification and Regression Trees (Wadsworth, Belmone, 1984)Google Scholar
  21. R.J.C. Burnash, The NWS river forecast system: Catchment modeling, in Computer Models of Watershed Hydrology, ed. by V.P. Singh (Water Resources Publications, Highlands Ranch, 1995), pp. 311–366Google Scholar
  22. V. Černý, Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. J. Optim. Theory Appl. 45(1), 41–51 (1985)CrossRefGoogle Scholar
  23. K. Chau, A split-step particle swarm optimization algorithm in river stage forecasting. J. Hydrol. 346(3), 131–135 (2007)CrossRefGoogle Scholar
  24. K. Chau, Application of a particle swarm optimization algorithm to hydrological problems, in Water Resources Research Progress, (Nova Science Publishers, New York, 2008), pp. 3–12Google Scholar
  25. C.-T. Cheng, M.-Y. Zhao, K. Chau, X.-Y. Wu, Using genetic algorithm and TOPSIS for Xinanjiang model calibration with a single procedure. J. Hydrol. 316(1), 129–140 (2006)CrossRefGoogle Scholar
  26. C.L. Chiu, J. Huang, Nonlinear time varying model of rainfall-runoff relation. Water Resour. Res. 6(5), 1277–1286 (1970)CrossRefGoogle Scholar
  27. W. Chu, X. Gao, S. Sorooshian, Improving the shuffled complex evolution scheme for optimization of complex nonlinear hydrological systems: Application to the calibration of the Sacramento soil-moisture accounting model. Water Resour. Res. 46(9), W09530 (2010)CrossRefGoogle Scholar
  28. W. Chu, X. Gao, S. Sorooshian, A new evolutionary search strategy for global optimization of high-dimensional problems. Inf. Sci. 181(22), 4909–4927 (2011)CrossRefGoogle Scholar
  29. W. Chu, T. Yang, X. Gao, Comment on “High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing” by Eric Laloy and Jasper A. Vrugt. Water Resour. Res. 50(3), 2775–2780 (2014)CrossRefGoogle Scholar
  30. C.C. Coello, M.S. Lechuga, MOPSO: A Proposal for Multiple Objective Particle Swarm Optimization (IEEE, Honolulu, 2002), pp. 1051–1056Google Scholar
  31. C.A.C. Coello, G.T. Pulido, M.S. Lechuga, Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)CrossRefGoogle Scholar
  32. P. Czyzżak, A. Jaszkiewicz, Pareto simulated annealing – A metaheuristic technique for multiple-objective combinatorial optimization. J. Multi-Criteria Decis. Anal. 7(1), 34–47 (1998)CrossRefGoogle Scholar
  33. K. Deb, Multi-objective Optimization Using Evolutionary Algorithms (Wiley, Chichester, 2001)Google Scholar
  34. K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II (Springer, Berlin, 2000), pp. 849–858Google Scholar
  35. K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  36. J.-L. Deneubourg, J.M. Pasteels, J.-C. Verhaeghe, Probabilistic behaviour in ants: A strategy of errors? J. Theor. Biol. 105(2), 259–271 (1983)CrossRefGoogle Scholar
  37. J.-L. Deneubourg, S. Aron, S. Goss, J.M. Pasteels, The self-organizing exploratory pattern of the argentine ant. J. Insect Behav. 3(2), 159–168 (1990)CrossRefGoogle Scholar
  38. K. Doerner, W.J. Gutjahr, R.F. Hartl, C. Strauss, C. Stummer, Pareto ant colony optimization: A metaheuristic approach to multiobjective portfolio selection. Ann. Oper. Res. 131(1–4), 79–99 (2004)CrossRefGoogle Scholar
  39. M. Dorigo, Optimization, learning and natural algorithms. Ph.D. Thesis, Politecnico di Milano (in Italian) 1992Google Scholar
  40. M. Dorigo, C. Blum, Ant colony optimization theory: A survey. Theor. Comput. Sci. 344(2), 243–278 (2005)CrossRefGoogle Scholar
  41. M. Dorigo, T. Stützle, Ant Colony Optimization: Overview and Recent Advances. Techreport, IRIDIA, Universite Libre de Bruxelles (2009)Google Scholar
  42. M. Dorigo, V. Maniezzo, A. Colorni, Ant system: Optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B Cybern. 26(1), 29–41 (1996)CrossRefGoogle Scholar
  43. M. Dorigo, M. Birattari, T. Stutzle, Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006)CrossRefGoogle Scholar
  44. Q. Duan, S. Sorooshian, H.V. Gupta, Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour. Res. 28, 1015 (1992)CrossRefGoogle Scholar
  45. Q. Duan, S. Sorooshian, V.K. Gupta, Optimal use of the SCE-UA global optimization method for calibrating watershed models. J. Hydrol. 158, 265 (1994)CrossRefGoogle Scholar
  46. Q. Duan, J. Schaake, V. Andreassian, S. Franks, G. Goteti, H.V. Gupta, Y.M. Gusev, F. Habets, A. Hall, L. Hay, T. Hogue, M. Huang, G. Leavesley, X. Liang, O.N. Nasonova, J. Noilhan, L. Oudin, S. Sorooshian, T. Wagener, E.F. Wood, Model parameter estimation experiment (MOPEX): An overview of science strategy and major results from the second and third workshops. J. Hydrol. 320(1–2), 3–17 (2006)CrossRefGoogle Scholar
  47. R.C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in Micro Machine and Human Science, 1995, MHS ’95. Proceedings of the Sixth International Symposium on, Nagoya, 4–6 October 1995 (IEEE, New York, 1995), pp. 39–43.
  48. R. Eglese, Simulated annealing: A tool for operational research. Eur. J. Oper. Res. 46(3), 271–281 (1990)CrossRefGoogle Scholar
  49. C. Fen, C. Chan, H. Cheng, Assessing a response surface-based optimization approach for soil vapor extraction system design. J. Water Resour. Plann. Manag. 135(3), 198–207 (2009)CrossRefGoogle Scholar
  50. F. Francés, J.I. Vélez, J.J. Vélez, Split-parameter structure for the automatic calibration of distributed hydrological models. J. Hydrol. 332(1), 226–240 (2007)CrossRefGoogle Scholar
  51. M. Franchini, Use of a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models. Hydrol. Sci. J. 41(1), 21–39 (1996)CrossRefGoogle Scholar
  52. M. Franchini, G. Galeati, Comparing several genetic algorithm schemes for the calibration of conceptual rainfall-runoff models. Hydrol. Sci. J. 42(3), 357–379 (1997)CrossRefGoogle Scholar
  53. J. Friedman, Multivariate adaptive regression splines. Ann. Stat. 19(1), 1–67 (1991)CrossRefGoogle Scholar
  54. T.Y. Gan, G.F. Biftu, Automatic calibration of conceptual rainfall-runoff models: Optimization algorithms, catchment conditions, and model structure. Water Resour. Res. 32(12), 3513–3524 (1996)CrossRefGoogle Scholar
  55. Y. Gan, Q. Duan, W. Gong, C. Tong, Y. Sun, W. Chu, A. Ye, C. Miao, Z. Di, A comprehensive evaluation of various sensitivity analysis methods: A case study with a hydrological model. Environ. Model. Softw. 51, 269–285 (2014)CrossRefGoogle Scholar
  56. Y. Gao, H. Guan, Z. Qi, Y. Hou, L. Liu, A multi-objective ant colony system algorithm for virtual machine placement in cloud computing. J. Comput. Syst. Sci. 79(8), 1230–1242 (2013)CrossRefGoogle Scholar
  57. M.K. Gill, Y.H. Kaheil, A. Khalil, M. McKee, L. Bastidas, Multiobjective particle swarm optimization for parameter estimation in hydrology. Water Resour. Res. 42(7), 417–431 (2006).
  58. D.E. Golberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addion Wesley, Estados Unidos, 1989), p. 102Google Scholar
  59. W. Gong, Q. Duan, An adaptive surrogate modeling-based sampling strategy for parameter optimization and distribution estimation (ASMO-PODE). Environ. Model Softw. 95, 61–75 (2017)CrossRefGoogle Scholar
  60. W. Gong, Q. Duan, J. Li, C. Wang, Z. Di, A. Ye, C. Miao, Y. Dai, Multiobjective adaptive surrogate modeling-based optimization for parameter estimation of large, complex geophysical models. Water Resour. Res. 52(3), 1984–2008 (2016)CrossRefGoogle Scholar
  61. V. Granville, M. Krivánek, J.-P. Rasson, Simulated annealing: A proof of convergence. IEEE Trans. Pattern Anal. Mach. Intell. 16(6), 652–656 (1994)CrossRefGoogle Scholar
  62. H.V. Gupta, S. Sorooshian, P.O. Yapo, Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information. Water Resour. Res. 34(4), 751–763 (1998)CrossRefGoogle Scholar
  63. H.V. Gupta, S. Sorooshian, T.S. Hogue, D.P. Boyle, Advances in automatic calibration of watershed models, in Calibration of Watershed Models, (American Geophysical Union, Washington, DC, 2003), pp. 9–28CrossRefGoogle Scholar
  64. W.K. Hastings, Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970)CrossRefGoogle Scholar
  65. M.I. Hejazi, X. Cai, D.K. Borah, Calibrating a watershed simulation model involving human interference: An application of multi-objective genetic algorithms. J. Hydroinf. 10(1), 97–111 (2008)CrossRefGoogle Scholar
  66. J.H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence (University of Michigan Press, Ann Arbor, 1975)Google Scholar
  67. R. Jin, W. Chen, T.W. Simpson, Comparative studies of metamodelling techniques under multiple modeling criteria. Struct. Multidisc. Optim. 23, 1–13 (2001)CrossRefGoogle Scholar
  68. D. Jones, A taxonomy of global optimization methods based on response surfaces. J. Glob. Optim. 21, 345–383 (2001)CrossRefGoogle Scholar
  69. D. Jones, M. Schonlau, W. Welch, Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13(4), 455–492 (1998)CrossRefGoogle Scholar
  70. B. Kamali, S.J. Mousavi, K.C. Abbaspour, Automatic calibration of HEC-HMS using single-objective and multi-objective PSO algorithms. Hydrol. Process. 27(26), 4028–4042 (2013)CrossRefGoogle Scholar
  71. J. Kennedy, Encyclopedia of Machine Learning (Springer, Berlin, 2011), pp. 760–766Google Scholar
  72. J. Kennedy, J.F. Kennedy, R.C. Eberhart, Y. Shi, Swarm Intelligence (Morgan Kaufmann, San Francisco, 2001)Google Scholar
  73. B. Khakbaz, B. Imam, K. Hsu, S. Sorooshian, From lumped to distributed via semi-distributed: Calibration strategies for semi-distributed hydrologic models. J. Hydrol. 418, 61–77 (2012)CrossRefGoogle Scholar
  74. S. Kirkpatrick, Optimization by simulated annealing: Quantitative studies. J. Stat. Phys. 34(5–6), 975–986 (1984)CrossRefGoogle Scholar
  75. P.K. Kitanidis, R.L. Bras, Real-time forecasting with a conceptual hydrologic model: 2. Applications and results. Water Resour. Res. 16(6), 1034–1044 (1980)CrossRefGoogle Scholar
  76. J. Kollat, P. Reed, T. Wagener, When are multiobjective calibration trade-offs in hydrologic models meaningful? Water Resour. Res. 48(3), 520–539 (2012).
  77. V. Kulandaiswamy, C. Subramanian, A nonlinear approach to runoff studies, in Proceedings of the International Hydrology Symposium, vol. 1, (Colorado State University, Fort Collins, 1967), pp. 72–79Google Scholar
  78. D.N. Kumar, M.J. Reddy, Ant colony optimization for multi-purpose reservoir operation. Water Resour. Manag. 20(6), 879–898 (2006)CrossRefGoogle Scholar
  79. C. Kuok, C.P. Chan, Particle swarm optimization for calibrating and optimizing Xinanjiang model parameters. Int. J. Adv. Sci. Appl. 3, 115 (2012)Google Scholar
  80. F. Kursawe, Parallel Problem Solving from Nature: 1st Workshop, PPSN I Dortmund, FRG, October 1–3, 1990 Proceedings, ed. by H.-P. Schwefel, R. Männer (Springer Berlin Heidelberg, Berlin, 1991), pp. 193–197Google Scholar
  81. G.-F. Lin, C.-M. Wang, A nonlinear rainfall–runoff model embedded with an automated calibration method – Part 2: The automated calibration method. J. Hydrol. 341(3–4), 196–206 (2007)CrossRefGoogle Scholar
  82. S.Y. Liong, T.R. Gautam, S.T. Khu, V. Babovic, M. Keijzer, N. Muttil, Genetic programming: a new paradigm in rainfall runoff modeling. J. Am. Water Resour. Assoc. 38(3), 705–718 (2002)CrossRefGoogle Scholar
  83. X. Liu, T. Yang, K. Hsu, C. Liu, S. Sorooshian, Evaluating the streamflow simulation capability of PERSIANN-CDR daily rainfall products in two river basins on the Tibetan plateau. Hydrol. Earth Syst. Sci. 21(1), 169 (2017)CrossRefGoogle Scholar
  84. H. Lü, T. Hou, R. Horton, Y. Zhu, X. Chen, Y. Jia, W. Wang, X. Fu, The streamflow estimation using the Xinanjiang rainfall runoff model and dual state-parameter estimation method. J. Hydrol. 480, 102–114 (2013)CrossRefGoogle Scholar
  85. R. Ludwig, I. May, R. Turcotte, L. Vescovi, M. Braun, J.-F. Cyr, L.-G. Fortin, D. Chaumont, S. Biner, I. Chartier, The role of hydrological model complexity and uncertainty in climate change impact assessment. Adv. Geosci. 21, 63–71 (2009)CrossRefGoogle Scholar
  86. S. Madadgar, A. Afshar, An improved continuous ant algorithm for optimization of water resources problems. Water Resour. Manag. 23(10), 2119–2139 (2009)CrossRefGoogle Scholar
  87. H. Madsen, Automatic calibration of a conceptual rainfall–runoff model using multiple objectives. J. Hydrol. 235(3), 276–288 (2000)CrossRefGoogle Scholar
  88. H. Madsen, Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives. Adv. Water Resour. 26(2), 205–216 (2003)CrossRefGoogle Scholar
  89. H. Madsen, G. Wilson, H.C. Ammentorp, Comparison of different automated strategies for calibration of rainfall-runoff models. J. Hydrol. 261(1), 48–59 (2002)CrossRefGoogle Scholar
  90. H.R. Maier, A.R. Simpson, A.C. Zecchin, W.K. Foong, K.Y. Phang, H.Y. Seah, C.L. Tan, Ant colony optimization for design of water distribution systems. J. Water Resour. Plan. Manag. 129(3), 200–209 (2003)CrossRefGoogle Scholar
  91. H.R. Maier, Z. Kapelan, J. Kasprzyk, J. Kollat, L.S. Matott, M. Cunha, G.C. Dandy, M.S. Gibbs, E. Keedwell, A. Marchi, Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions. Environ. Model Softw. 62, 271–299 (2014)CrossRefGoogle Scholar
  92. R. Moussa, N. Chahinian, Comparison of different multi-objective calibration criteria using a conceptual rainfall-runoff model of flood events. Hydrol. Earth Syst. Sci. 13(4), 519–535 (2009)CrossRefGoogle Scholar
  93. J.A. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)CrossRefGoogle Scholar
  94. V. Nourani, S. Talatahari, P. Monadjemi, S. Shahradfar, Application of ant colony optimization to optimal design of open channels. J. Hydraul. Res. 47(5), 656–665 (2009)CrossRefGoogle Scholar
  95. A. O’Hagan, Bayesian analysis of computer code outputs: a tutorial. Reliab. Eng. Syst. Saf. 91(10–11), 1290–1300 (2006)CrossRefGoogle Scholar
  96. R.E. Olarte, N. Obregon, Comparison between a simple GA and an ant system for the calibraton of a rainfall-runoff model, in 6th International Conference on Hydroinformatics (in 2 volumes, with CD-ROM) (World Scientific Publishing Company, Singapore, 2004), pp. 842–849, ISBN 981-238-787-0CrossRefGoogle Scholar
  97. A. Ostfeld, Ant colony optimization for water resources systems analysis–Review and challenges, in Ant Colony Optimization Methods and Applications (Technion Israel Institute of Technology, Israel, 2011), p. 147CrossRefGoogle Scholar
  98. M.A. Panduro, C.A. Brizuela, L.I. Balderas, D.A. Acosta, A comparison of genetic algorithms, particle swarm optimization and the differential evolution method for the design of scannable circular antenna arrays. Prog, Electromagn. Res. B 13, 171–186 (2009)CrossRefGoogle Scholar
  99. D. Pilgrim, Travel times and nonlinearity of flood runoff from tracer measurements on a small watershed. Water Resour. Res. 12(3), 487–496 (1976)CrossRefGoogle Scholar
  100. J. Pintér, Continuous global optimization software: A brief review. Optima 52(1–8), 270 (1996)Google Scholar
  101. N.V. Queipo, R.T. Haftka, W. Shyy, T. Goel, R. Vaidyanathan, P. Kevin Tucker, Surrogate-based analysis and optimization. Prog. Aerosp. Sci. 41(1), 1–28 (2005)CrossRefGoogle Scholar
  102. C. Rasmussen, C. Williams, Gaussian Processes for Machine Learning (MIT Press, Cambridge, MA, 2006)Google Scholar
  103. S. Razavi, B.A. Tolson, D.H. Burn, Review of surrogate modeling in water resources. Water Resour. Res. 48(7), 401–433 (2012).
  104. P.M. Reed, D. Hadka, J.D. Herman, J.R. Kasprzyk, J.B. Kollat, Evolutionary multiobjective optimization in water resources: The past, present, and future. Adv. Water Resour. 51, 438–456 (2013)CrossRefGoogle Scholar
  105. R.G. Regis, C.A. Shoemaker, A stochastic radial basis function method for the global optimization of expensive functions. INFORMS J. Comput. 19, 497–509 (2007)CrossRefGoogle Scholar
  106. D.A. Savic, G.A. Walters, J.W. Davidson, A genetic programming approach to rainfall-runoff modelling. Water Resour. Manag. 13(3), 219–231 (1999)CrossRefGoogle Scholar
  107. P. Serafini, Multiple Criteria Decision Making (Springer, Berlin, 1994), pp. 283–292CrossRefGoogle Scholar
  108. M. Shafii, F.D. Smedt, Multi-objective calibration of a distributed hydrological model (WetSpa) using a genetic algorithm. Hydrol. Earth Syst. Sci. 13(11), 2137–2149 (2009)CrossRefGoogle Scholar
  109. Y. Shi, Particle Swarm Optimization: Developments, Applications and Resources (IEEE, Seoul, 2001), pp. 81–86.
  110. A.R. Simpson, G.C. Dandy, L.J. Murphy, Genetic algorithms compared to other techniques for pipe optimization. J. Water Resour. Plan. Manag. 120(4), 423–443 (1994)CrossRefGoogle Scholar
  111. T.W. Simpson, J.D. Peplinski, P.N. Koch, J.K. Allen, Metamodels for computer-based engineering design: Survey and recommendations. Eng. Comput. 17, 129–150 (2001)CrossRefGoogle Scholar
  112. K.P. Singh, Nonlinear instantaneous unit hydrograph theory. J. Hydraul. Div. Am. Soc. Civ. Eng. 90, 313–347 (1964)Google Scholar
  113. V.P. Singh, Computer Models of Watershed Hydrology (Water Resources Publications, Englewood, 1995)Google Scholar
  114. B.E. Skahill, J. Doherty, Efficient accommodation of local minima in watershed model calibration. J. Hydrol. 329(1), 122–139 (2006)CrossRefGoogle Scholar
  115. E. Snelson, Flexible and efficient Gaussian process models for machine learning. Ph.D. thesis, Gatsby Computational Neuroscience Unit, University College London 2007Google Scholar
  116. A. Sóbester, S. Leary, A. Keane, On the design of optimization strategies based on global response surface approximation models. J. Glob. Optim. 33(1), 31–59 (2005)CrossRefGoogle Scholar
  117. K. Socha, M. Dorigo, Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185(3), 1155–1173 (2008)CrossRefGoogle Scholar
  118. S. Sorooshian, Surface water hydrology: On-line estimation. Rev. Geophys. 21(3), 706–721 (1983)CrossRefGoogle Scholar
  119. P. Srivastava, J. Hamlett, P. Robillard, R. Day, Watershed optimization of best management practices using AnnAGNPS and a genetic algorithm. Water Res. Res. 38(3), 3-1 (2002)CrossRefGoogle Scholar
  120. B. Suman, Study of simulated annealing based algorithms for multiobjective optimization of a constrained problem. Comput. Chem. Eng. 28(9), 1849–1871 (2004)CrossRefGoogle Scholar
  121. N.R. Sumner, P.M. Fleming, B.C. Bates, Calibration of a modified SFB model for twenty-five Australian catchments using simulated annealing. J. Hydrol. 197(1), 166–188 (1997)CrossRefGoogle Scholar
  122. Q. Sun, D. Kong, C. Miao, Q. Duan, T. Yang, A. Ye, Z. Di, W. Gong, Variations in global temperature and precipitation for the period of 1948 to 2010. Environ. Monit. Assess. 186(9), 5663–5679 (2014)CrossRefGoogle Scholar
  123. A. Suppapitnarm, K. Seffen, G. Parks, P. Clarkson, A simulated annealing algorithm for multiobjective optimization. Eng. Optim. 33(1), 59–85 (2000)CrossRefGoogle Scholar
  124. Y. Tang, P. Reed, T. Wagener, How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration? Hydrol. Earth Syst. Sci. Discuss. 2(6), 2465–2520 (2005)CrossRefGoogle Scholar
  125. M. Thyer, G. Kuczera, B.C. Bates, Probabilistic optimization for conceptual rainfall-runoff models: A comparison of the shuffled complex evolution and simulated annealing algorithms. Water Resour. Res. 35(3), 767–773 (1999)CrossRefGoogle Scholar
  126. J.A. Vrugt, H.V. Gupta, W. Bouten, S. Sorooshian, A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resour. Res. 39(8), 1201–1213 (2003a).
  127. J.A. Vrugt, H.V. Gupta, L.A. Bastidas, W. Bouten, S. Sorooshian, Effective and efficient algorithm for multiobjective optimization of hydrologic models. Water Resour. Res. 39(8), 1214–1233 (2003b).
  128. Q. Wang, The genetic algorithm and its application to calibrating conceptual rainfall-runoff models. Water Resour. Res. 27(9), 2467–2471 (1991)CrossRefGoogle Scholar
  129. Q. Wang, Using genetic algorithms to optimise model parameters. Environ. Model Softw. 12(1), 27–34 (1997)CrossRefGoogle Scholar
  130. H. Wang, W. Guo, ACO Optimizing Neural Network for Macroscopic Water Distribution System Modeling (IEEE, Kuala Lumpur, 2010), pp. 367–370.
  131. Y.C. Wang, P.S. Yu, T.C. Yang, Comparison of genetic algorithms and shuffled complex evolution approach for calibrating distributed rainfall–runoff model. Hydrol. Process. 24(8), 1015–1026 (2010)CrossRefGoogle Scholar
  132. C. Wang, Q.Y. Duan, W. Gong, A.Z. Ye, Z.H. Di, C.Y. Miao, An evaluation of adaptive surrogate modeling based optimization with two benchmark problems. Environ. Model. Softw. 60, 167–179 (2014)CrossRefGoogle Scholar
  133. P.A. Whigham, P.F. Crapper, Time series modelling using genetic programming: An application to rainfall-runoff models. Adv. Genet. Program 3, 89–104 (1999)Google Scholar
  134. D.H. Wolpert, W.G. Macready, No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)CrossRefGoogle Scholar
  135. C.F.J. Wu, M. Hamada, Experiments: Planning, Analysis, and Optimization, 2nd edn. (Wiley, New York, 2009)Google Scholar
  136. S.-J. Wu, H.-C. Lien, C.-H. Chang, Calibration of a conceptual rainfall–runoff model using a genetic algorithm integrated with runoff estimation sensitivity to parameters. J. Hydroinf. 14(2), 497–511 (2012)CrossRefGoogle Scholar
  137. J. Yang, P. Reichert, K.C. Abbaspour, J. Xia, H. Yang, Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China. J. Hydrol. 358(1–2), 1–23 (2008)CrossRefGoogle Scholar
  138. T. Yang, X. Gao, S.L. Sellars, S. Sorooshian, Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville–Thermalito complex. Environ. Model Softw. 69, 262–279 (2015)CrossRefGoogle Scholar
  139. T. Yang, X. Gao, S. Sorooshian, X. Li, Simulating California reservoir operation using the classification and regression-tree algorithm combined with a shuffled cross-validation scheme. Water Resour. Res. 52(3), 1626–1651 (2016)CrossRefGoogle Scholar
  140. T. Yang, A.A. Asanjan, M. Faridzad, N. Hayatbini, X. Gao, S. Sorooshian, An enhanced artificial neural network with a shuffled complex evolutionary global optimization with principal component analysis. Inf. Sci. 418, 302–316 (2017a)CrossRefGoogle Scholar
  141. T. Yang, A.A. Asanjan, E. Welles, X. Gao, S. Sorooshian, X. Liu, Developing reservoir monthly inflow forecasts using artificial intelligence and climate phenomenon information. Water Resour. Res. 53(4), 2786–2812 (2017b)CrossRefGoogle Scholar
  142. T. Yang, Y. Tao, J. Li, Q. Zhu, L. Su, X. He, X. Zhang, Multi-criterion model ensemble of CMIP5 surface air temperature over China. Theor. Appl. Climatol. 132(3), 1057–1072 (2017c). Scholar
  143. P.O. Yapo, H.V. Gupta, S. Sorooshian, Multi-objective global optimization for hydrologic models. J. Hydrol. 204(1), 83–97 (1998)CrossRefGoogle Scholar
  144. M. Zambrano-Bigiarini, R. Rojas, A model-independent particle swarm optimisation software for model calibration. Environ. Model Softw. 43, 5–25 (2013)CrossRefGoogle Scholar
  145. A.C. Zecchin, H.R. Maier, A.R. Simpson, A. Roberts, M.J. Berrisford, M. Leonard, Max-min ant system applied to water distribution system optimization. Proc. Int. Congr. Model. Simul. (MODSIM) 2, 795–800 (2003)Google Scholar
  146. A.C. Zecchin, A.R. Simpson, H.R. Maier, A. Marchi, J.B. Nixon, Improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem. Water Resour. Res. 48(9), 795–800 (2012)Google Scholar
  147. Y. Zhang, F.H.S. Chiew, Relative merits of different methods for runoff predictions in ungauged catchments. Water Res. Res. 45(7), 412–425 (2009).
  148. X. Zhang, R. Srinivasan, M. Van Liew, Approximating SWAT model using artificial neural network and support vector machine. J. Am. Water Resour. Assoc. 45(2), 460–474 (2009a)CrossRefGoogle Scholar
  149. X. Zhang, R. Srinivasan, D. Bosch, Calibration and uncertainty analysis of the SWAT model using genetic algorithms and Bayesian model averaging. J. Hydrol. 374(3), 307–317 (2009b)CrossRefGoogle Scholar
  150. X. Zhang, R. Srinivasan, K. Zhao, M.V. Liew, Evaluation of global optimization algorithms for parameter calibration of a computationally intensive hydrologic model. Hydrol. Process. 23(3), 430–441 (2009c)CrossRefGoogle Scholar
  151. X. Zhang, R. Srinivasan, M.V. Liew, On the use of multi-algorithm, genetically adaptive multi-objective method for multi-site calibration of the SWAT model. Hydrol. Process. 24(8), 955–969 (2010)CrossRefGoogle Scholar
  152. Q. Zhu, K.I. Hsu, Y.P. Xu, T. Yang, Evaluation of a new satellite-based precipitation data set for climate studies in the Xiang River basin, southern China. Int. J. Climatol. 37, 4561 (2017)CrossRefGoogle Scholar
  153. E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRefGoogle Scholar
  154. E. Zitzler, K. Deb, L. Thiele, Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput. 8(2), 173–195 (2000)CrossRefGoogle Scholar

Authors and Affiliations

  1. 1.University of CaliforniaIrvineUSA
  2. 2.Civil & Environmental Engineering, The Henry Samueli School of EngineeringUniversity of CaliforniaIrvineUSA
  3. 3.Faculty of Geographical ScienceBeijing Normal UniversityBeijingChina
  4. 4.South China Botanical GardenChinese Academy of SciencesRichlandUSA

Section editors and affiliations

  • Dmitri Kavetski
    • 1
  • Kuolin Hsu
    • 2
  • Yuqiong Liu
    • 3
  1. 1.School of Civil, Environmental and Mining Engineering, University of AdelaideAdelaideAustralia
  2. 2.Civil & Environmental Engineering, The Henry Samueli School of Engineering, University of CaliforniaIrvineUSA
  3. 3.NASA Goddard Space Flight CenterWashington D.C.USA

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