Bridging the gap between GLUE and formal statistical approaches: Approximate Bayesian computation

Hydrology and Earth System Sciences

Volumn 17, Issue 12, 2013, Pages 4831-4850

  Sadegh, M ^a   Vrugt, J A ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE BAYESIAN; DISCHARGE OBSERVATIONS; GENERALIZED LIKELIHOOD UNCERTAINTY ESTIMATION; LIKELIHOOD FUNCTIONS; MARKOV CHAIN MONTE CARLO SIMULATION; PREDICTIVE DISTRIBUTIONS; PREDICTIVE UNCERTAINTY; RESIDUAL DISTRIBUTION;

BAYESIAN NETWORKS; GLUES; GLUING;

POPULATION STATISTICS;

BAYESIAN ANALYSIS; CALIBRATION; DISCHARGE; HYDROLOGICAL REGIME; MARKOV CHAIN; MONTE CARLO ANALYSIS; PARAMETERIZATION; STATISTICAL ANALYSIS; UNCERTAINTY ANALYSIS;

UNITED STATES;

EID: 84890094491     PISSN: 10275606     EISSN: 16077938     Source Type: Journal    
DOI: 10.5194/hess-17-4831-2013     Document Type: Article

References (129)

1. Ajami, N. K., Duan, Q., and Sorooshian, S.: An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction, Water Resour. Res., 43, W01403, doi:10.1029/2005WR004745, 2007. (Pubitemid 46364281)
2. Aronica, G., Bates, P. D., and Horritt, M. S.: Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE, Hydrol. Proccess., 16, 2001-2016, 2002. (Pubitemid 34817324)
3. Barnes, C., Filippi, S., Stumpf, M. P. H., and Thorne, T.: Considerate approaches to achieving sufficiency for ABC model selection, available at: http://arxiv.org/pdf/1106.6281v2.pdf (last access: 1 December 2013), 2011.
4. Bates, B. C. and Campbell, E. P.: A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling,Water Resour. Res., 37, 937-947, 2001. (Pubitemid 32516048)
5. Beaumont, M. A., Zhang, W., and Balding, D. J.: Approximate Bayesian computation in population genetics, Genetics, 162, 2025-2035, 2002. (Pubitemid 36114682)
6. Beven, K. J. and Binley, A. M.: The future of distributed models: Model calibration and uncertainty prediction, Hydrol. Process., 6, 279-298, 1992.
7. Beven, K. J.: Prophecy, reality and uncertainty in distributed hydrological modeling, Adv. Water Resour., 16, 41-51, 1993.
8. Beven, K. and Freer, J.: Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, 11-29, 2001. (Pubitemid 32664993)
9. Beven, K. and Young, P.: Comment on "Bayesian recursive parameter estimation for hydrologic models" by M. Thiemann, M. Trosset, H. Gupta, and S. Sorooshian, Water Resour. Res., 39, 1116, doi:10.1029/2001WR001183, 2003.
10. Beven, K.: A manifesto for the equifinality thesis, J. Hydrol., 320, 18-36, 2006.
11. Beven, K., Smith, P. J., and Freer, J. E.: So why would a modeller choose to be incoherent?, J. Hydrol., 354, 15-32, 2008.
12. Beven, K.: Comment on "Equifinality of formal.(DREAM) and informal.( GLUE) Bayesian approaches in hydrologic modeling?" by Vrugt, J. A, ter Braak, C. J. F., Gupta, H. V., and Robinson, B. A., Stoch. Environ. Res. Risk As., 23, 1059-1060, doi:10.1007/s00477-008-0283-x, 2009.
13. Beven, K., Smith, P. J., and Wood, A.: On the colour and spin of epistemic error (and what we might do about it), Hydrol. Earth Syst. Sci., 15, 3123-3133, doi:10.5194/hess-15-3123-2011, 2011.
14. Bikowski, J., Huisman, J. A., Vrugt, J. A., Vereeken, H., and van der Kruk, J.: Inversion and sensitivity analysis of ground penetrating radar data with waveguide dispersion using deterministic and Markov chain Monte Carlo methods, Near Surf. Geophys., Special issue "Physics-based integrated characterization", 10, 641-652, doi:10.3997/1873-0604.2012041, 2012.
15. Brazier R. E, Beven, K. J., Anthony, S. G., and Rowan, J. S.: Implications of model uncertainty for the mapping of hillslope-scale soil erosion predictions, Earth Surf. Process. Landf., 26, 1333-1352, 2001. (Pubitemid 33071799)
16. Bulygina, N. and Gupta, H.: Correcting the mathematical structure of a hydrological model via Bayesian data assimilation, Water Resour. Res., 47, W05514, doi:10.1029/2010WR009614, 2011.
17. Burnash, R. J., Ferral, R. L., and McGuire, R. A.: A Generalized Streamflow Simulation System: Conceptual Modeling for Digital Computers, US Department of Commerce National Weather Service and State of California Department of Water Resources, 1973.
18. Butts, M. B., Payne, J. T., Kristensen, M., and Madsen, H.: An evaluation of the impact of model structure on hydrological modeling uncertainty for streamflow simulation, J. Hydrol., 298, 242-266, 2004. (Pubitemid 39098776)
19. Christensen, S.: A synthetic groundwater modeling study of the accuracy of GLUE uncertainty intervals, Nord. Hydrol., 35, 45-59, 2004. (Pubitemid 38135755)
20. Chu, W., Gao, X., and Sorooshian, S.: 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, W09530, doi:10.1029/2010WR009224, 2010.
21. Clark, M. P. and Slater, A. G.: Probabilistic quantitative precipitation estimation in complex terrain, J. Hydrometeorol., 7, 3-22, 2006.
22. Clark, M. P., Slater, A. G., Rupp, D. E., Woods, R. A., Vrugt, J. A., Gupta, H. V., Wagener, T., and Hay, L. E.: Framework for Understanding Structural Errors(FUSE): A modular framework to diagnose differences between hydrological models, Water Resour. Res., 44, W00B02, doi:10.1029/2007WR006735, 2008.
23. DeChant, C. M. and Moradkhani, H.: Examining the effectiveness and robustness of sequential data assimilation methods for quantification of uncertainty in hydrologic forecasting, Water Resour. Res., 48, W04518, doi:10.1029/2011WR011011, 2012.
24. Del Moral, P., Doucet, A., and Jasra, A.: An adaptive sequential Monte Carlo method for approximate Bayesian computation, Technical Report, Imperial College London, 2008.
25. Dette, H., Munk, A., and Wagner, T.: Estimating the variance in nonparametric regression-What is a reasonable choice?, J. Royal Stat. Soc. Ser. B, Part 4, 60, 751-764, 1998. (Pubitemid 128656810)
26. Diggle, P. J. and Gratton, R. J.: Monte Carlo methods of inference for implicit statistical models, J. Royal Stat. Soc. Ser. B, 46, 193-227, 1984.
27. Duan, Q., Gupta, V. K., and Sorooshian, S.: Effective and efficient global optimization for conceptual rainfall-runoff models, Water Resour. Res., 28, 1015-1031, 1992.
28. Fenicia, F., Savenije, H. H. G., Matgen, P., and Pfister, L.: A comparison of alternative multiobjective calibration strategies for hydrological modeling, Water Resour. Res., 43, W03434, doi:10.1029/2006WR005098, 2007. (Pubitemid 46682804)
29. Feyen, L, Beven, K. J., De Smedt, F., and Freer, J. E.: Stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology: conditioning on head observations, Water Resour. Res., 37, 625-638, 2001. (Pubitemid 32526062)
30. Franks, S. W., Beven, K. J., Quinn, P. F., and Wright, I. R.: On the sensitivity of soil-vegetation-atmosphere transfer(SVAT) schemes: equifinality and the problem of robust calibration, Agr. Forest Meteorol., 86, 63-75, 1997. (Pubitemid 27291592)
31. Freer, J., Beven, K., and Ambroise, B.: Bayesian estimation of uncertainty in runoff prediction and the value of data: An application of the GLUE approach, Water Resour. Res., 32, 2161-2173, 1996.
32. Georgakakos, K. P., Seo, D. J., Gupta, H., Schaake, J., and Butts, M. B.: Towards the characterization of streamflow simulation uncertainty through multimodel ensembles, J. Hydrol., 298, 222-241, 2004. (Pubitemid 39098775)
33. Grelaud, A., Robert, C., Marin, J., Rodolphe, F., and Taly, J.: ABC likelihood-free methods for model choice in Gibbs random fields, Bayesian Analysis, 4, 317-336, 2009.
34. Gupta, V. K. and Sorooshian, S.: Uniqueness and observability of conceptual rainfall-runoff model parameters: the percolation process examined, Water Resour. Res., 19, 269-276, 1983.
35. Gupta, V. K. and Sorooshian, S.: The relationship between data and the precision of parameter estimates of hydrological models, J. Hydrol., 81, 57-77, 1985.
36. Gupta, H. V., Sorooshian, S., and Yapo, P. O.: Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information,Water Resour. Res., 34, 751-763, 1998. (Pubitemid 28159454)
37. Gupta, H., Thiemann, M., Trosset, M., and Sorooshian, S.: Reply to comment by K. Beven and P. Young on "Bayesian recursive parameter estimation for hydrologic models", Water Resour. Res., 39, 1117, doi:10.1029/2002WR001405, 2003.
38. Hall, P., Kay, J.W., and Titterington, D. M.: Asymptotically optimal difference-based estimation of variance in nonparametric regression, Biometrika, 77, 521-528, 1990.
39. Haario, H., Saksman, E., and Tamminen, J.: Adaptive proposal distribution for random walk Metropolis algorithm, Comput. Stat., 14, 375-395, 1999.
40. Haario, H., Saksman, E., and Tamminen, J.: An adaptive Metropolis algorithm, Bernoulli, 7, 223-242, 2001. (Pubitemid 33793059)
41. Hankin, B. G., Hardy, R., Kettle, H., and Beven, K. J.: Using CFD in a GLUE framework to model the flow and dispersion characteristics of a natural fluvial dead zone, Earth Surf. Process. Landf., 26, 667-687, 2001. (Pubitemid 32541293)
42. Hansson, K. and Lundin, C.: Equifinality and sensitivity in freezing and thawing simulations of laboratory and in situ data, Cold Reg. Sci. Technol., 44, 20-37, 2006. (Pubitemid 43115543)
43. Huard, D. and Mailhot, A.: A Bayesian perspective on input uncertainty in model calibration: Application to hydrological model "abc", Water Resour. Res., 42, W07416, doi:10.1029/2005WR004661, 2006. (Pubitemid 44300483)
44. Ibbitt, R. P.: Effects of random data errors on the parameter values for a conceptual model, Water Resour. Res., 8, 70-78, 1972.
45. Ibbitt, R. P. and O'Donnell, T.: Designing conceptual catchment models for automatic fitting methods, Mathematical Models in Hydrology Symposium, IAHS-AISH, Publication No. 2, 461-475, 1974.
46. Jacquin, A. P., and Shamseldin, A. Y.: Development of a possibilistic method for the evaluation of predictive uncertainty in rainfall-runoff modeling, Water Resour. Res., 43, W04425. doi:10.1029/2006WR005072, 2007. (Pubitemid 46799531)
47. Jensen, J. B.: Parameter and Uncertainty Estimation in Groundwater Modelling, PhD thesis, Department of Civil Engineering, Aalborg University, Series Paper No. 23, 2003.
48. Jimenez, R., Verde, L., Peiris, H., and Kosowsky, A.: Fast cosmological parameter estimation from microwave background temperature and polarization power spectra, Phys. Rev., D70, 023005, doi:10.1103/PhysRevD.70.023005, 2004. (Pubitemid 44947211)
49. Johnston, P. R. and Pilgrim, D.: Parameter optimization for watershed models, Water Resour. Res., 12, 477-486, 1976.
50. Joyce, P. and Marjoram, P.: Approximately suficient statistics and Bayesian computation, Stat. Appl. Genet. Molec. Biol., 7, 1544-6115, doi:10.2202/1544-6115.1389, 2008.
51. Kaipio, J. P., Seppänen, A., Somersalo, E., and Haario, H.: Posterior covariance related optimal current patterns in electrical impedance tomography, Inverse Problems, 20, 919-936, 2004.
52. Kavetski, D., Kuczera, G., and Franks, S. W.: Semi-distributed hydrological modeling: A "saturation path" perspective on TOPMODEL and VIC, Water Resour. Res., 39, 1246 doi:10.1029/2003WR002122, 2003.
53. Kavetski, D., Kuczera, G., and Franks, S.W.: Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory,Water Resour. Res., 42, W03407, doi:10.1029/2005WR004368, 2006a.
54. Kavetski, D., Kuczera, G., and Franks, S. W.: Bayesian analysis of input uncertainty in hydrological modeling: 2. Application, Water Resour. Res., 42, W03408, doi:10.1029/2005WR004376, 2006b.
55. Kavetski, D., Kuczera, G., and Franks, S.W.: Calibration of conceptual hydrological models revisited: 1. Overcoming numerical artifacts, J. Hydrol., 320., 173-186, doi:10.1016/j.jhydrol.2005.07.012, 2006c.
56. Kavetski, D. and Clark, M. P.: Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction, Water Resour. Res., 46, W10511, doi:10.1029/2009WR008896, 2010.
57. Khu, S. T. and Madsen, H.: Multiobjective calibration with Pareto preference ordering: An application to rainfallrunoff model calibration, Water Resour. Res., 41, W03004, doi:10.1029/2004WR003041, 2005. (Pubitemid 40589246)
58. Kuczera, G.: On the relationship between the reliability of parameter estimates and hydrologic time series used in calibration, Water Resour. Res., 18, 146-154, 1982.
59. Kuczera, G.: Improved parameter inference in catchment models, 1. Evaluating parameter uncertainty,Water Resour. Res., 19, 1151-1162, doi:10.1029/WR019i005p01151, 1983a.
60. Kuczera, G.: Improved parameter inference in catchment models: 2. Combining different kinds of hydrologic data and testing their compatibility, Water Resour. Res., 19, 1163-1172, 1983b.
61. Kuczera, G. and Parent, E.: Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm, J. Hydrol., 211, 69-85, 1998. (Pubitemid 29014557)
62. Kuczera, G., Kavetski, D., Franks, S., and Thyer, M.: Towards a Bayesian total error analysis of conceptual rainfall-runoff models: Characterizing model error using storm-dependent parameters, J. Hydrol., 331, 161-177, doi:10.1016/j.jhydrol.2006.05.010, 2006. (Pubitemid 44646456)
63. Kuczera, G., Kavetski, D., Renard, B., and Thyer, M.: A limitedmemory acceleration strategy for MCMC sampling in hierarchical Bayesian calibration of hydrological models, Water Resour. Res., 46, W07602, doi:10.1029/2009WR008985, 2010.
64. Laloy, E. and Vrugt, J. A.: High-dimensional posterior exploration of hydrologic models using multiple-try DREAM(ZS) and high-performance computing, Water Resour. Res., 48, W01526, doi:10.1029/2011WR010608, 2012.
65. Lamb, R., Beven, K., and Myrabø, S.: Use of spatially distributed water table observations to constrain uncertainty in a rainfallrunoff model, Adv. Water Resour., 22, 305-317, 1998. (Pubitemid 29145481)
66. Mantovan, P. and Todini, E.: Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology, J. Hydrol., 330, 368-381, doi:10.1016/j.jhydrol.2006.04.046, 2006. (Pubitemid 44528546)
67. Marjoram, P., Molitor, J., Plagnol, V., and Tavaré, S.: Markov chain Monte Carlo without likelihoods, Proc. Natl. Acad. Sci. USA, 100, 15324-15328, 2003. (Pubitemid 38020988)
68. Marshall, L. A., Sharma, A., and Nott, D. J.: Towards dynamic catchment modelling: A Bayesian hierarchical mixtures of experts framework, Hydrol. Process., 21, 847-861, 2007. (Pubitemid 46510578)
69. Mazi, K., Koussis, A. D., Restrepo, P. J., and Koutsoyiannis, D.: A groundwater-based, objective-heuristic parameter optimization method for a precipitation-runoff model and its application to a semi-arid basin, J. Hydrol., 290, 243-258, 2004. (Pubitemid 38448806)
70. McMichael, C. E., Hope, A. S., and Loaiciga, H. A.: Distributed hydrological modeling in California semi-arid shrublands: MIKE SHE model calibration and uncertainty estimation, J. Hydrol., 317, 307-324, 2006. (Pubitemid 41774119)
71. Mertens, J., Madsen, H., Feyen, L., Jacques, D., and Feyen, J.: Including prior information in the estimation of effective soil parameters in unsaturated zone modelling, J. Hydrol., 294, 251-269, 2004. (Pubitemid 38791098)
72. Montanari, A. and Brath, A.: A stocastic approach for assessing the uncertainty of rainfall-runoff simulations, Water Resour. Res., 40, W01106, doi:10.1029/2003WR002540, 2004.
73. Montanari, A.: Large sample behaviors of the generalized likelihood uncertainty estimation(GLUE) in assessing the uncertainty of rainfall-runoff simulations, Water Resour. Res., 41, W08406, doi:10.1029/2004WR003826, 2005. (Pubitemid 41393335)
74. Montanari A. and Grossi, G.: Estimating the uncertainty of hydrological forecasts: A statistical approach, Water Resour. Res., 44, W00B08, doi:10.1029/2008WR006897, 2008.
75. Moradkani, H., Hsu, K., Gupta, H., and Sorooshian, S.: Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter,Water Resour. Res., 41, W05012, doi:10.1029/2004WR003604, 2005a. (Pubitemid 40856462)
76. Moradkhani, H., Sorooshian, S., Gupta, H. V., and Houser, P. R.: Dual state-parameter estimation of hydrological models using ensemble Kalman filter, Adv. Water Resour., 28, 135-147, 2005b. (Pubitemid 40102390)
77. Muleta, M. K. and Nicklow, J.W.: Sensitivity and uncertainty analysis coupled with automatic calibration for a distributed watershed model, J. Hydrol., 306, 127-145, 2005. (Pubitemid 40678746)
78. Nash, J. E.: A unit hydrograph study with particular reference to British catchments, Proc.-Instit. Civil Eng., 17, 249-282, 1960.
79. Nash, J. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I-A discussion of principles, J. Hydrol., 10, 282-290, 1970.
80. Nissinen, A., Heikkinen, L. M., Kolehmainen, V., and Kaipio, J. P.: Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography, Measure. Sci. Technol., 20, 105504, doi:10.1088/0957-0233/20/10/105504, 2009.
81. Nott, D. J., Marshall, L., and Brown, J.: Generalized likelihood uncertainty estimation (GLUE) and approximate Bayesian computation: What's the connection?,Water Resour. Res., 48, W12602, doi:10.1029/2011WR011128, 2012.
82. Pauwels, V. R. N.: A multi-start weight-adaptive recursive parameter estimation method, Water Resour. Res., 44, W044156, doi:10.1029/2007WR005866, 2008. (Pubitemid 351748452)
83. Pritchard, J. K., Seielstad, M. T., Perez-Lezaun, A., and Feldman, M. T.: Population Growth of Human Y Chromosomes: A Study of Y Chromosome Microsatellites, Molecul. Biol. Evolut., 16, 1791-1798, 1999.
84. Ratmann, O., Andrieu, C.,Wiuf, C., and Richardson, S.: Model criticism based on likelihood-free inference, with an application to protein network evolution, Proc. Natl. Acad. Sci. USA, 106, 1-6, 2009.
85. Reichle, R. H.: Data assimilation methods in the earth sciences, Adv. Water Resour., 31, 1411-1418, 2008.
86. Reichert, P. and Mieleitner, J.: Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time-dependent parameters, Water Resour. Res., 45, W10402, doi:10.1029/2009WR007814, 2009.
87. Renard, B., Kavetski, D., Leblois, E., Thyer, M., Kuczera, G., and Franks, S.W.: Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation, Water Resour. Res., 47, W11516, doi:10.1029/2011WR010643, 2011.
88. Restrepo-Posada, J. P.: Automatic parameter estimation of a large conceptual rainfall-runoff model: a maximum likelihood approach, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, p. 330, 1982.
89. Rice, J.: Bandwidth choice for nonparametric kernel regression, Ann. Statist., 12, 1215-1230, 1984.
90. Rings, J., Vrugt, J. A., Schoups, G., Huisman, J. A., and Vereecken, H.: Bayesian model averaging using particle filtering and Gaussian mixture modeling: Theory, concepts, and simulation experiments, Water Resour. Res., 48, W05520, doi:10.1029/2011WR011607, 2012.
91. Romanowicz R. J., Beven, K. J., and Tawn, J.: Bayesian calibration of flood inundation models, edited by: Anderson, M. G. and Walling, D. E., Floodplain Processes, Wiley, Chichester, 333-360, 1996.
92. Sadegh, M. and Vrugt, J. A.: Approximate Bayesian computation using DREAM Markov chain Monte Carlo simulation,Water Resour. Res., in review, 2013.
93. Salamon, P. and Feyen, L.: Assessing parameter, precipitation, and predictive uncertainty in a distibuted hydrological model using sequential data assimilatiom with the particle filter, J. Hydrol., 376, 428-442, 2009.
94. Schoups, G. and Vrugt, J. A.: A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic and non-Gaussian errors, Water Resour. Res., 46, W10531, doi:10.1029/ 2009WR008933, 2010a.
95. Schoups, G., Vrugt, J. A., Fenicia, F., and van de Giesen, N. C.: Corruption of accuracy and efficiency of Markov Chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models,Water Resour. Res., 46, W10530, doi:10.1029/2009WR008648, 2010b.
96. Seifert, B., Gasser, T., and Wolf, A.: Nonparametric estimation of residual variance revisited, Biometrika, 80, 373-383, 1993.
97. Seibert, J.: Multi-criteria calibration of a conceptual runoff model using a genetic algorithm, Hydrol. Earth Syst. Sci., 4, 215-224, doi:10.5194/hess-4-215-2000, 2000.
98. Sisson, S. A., Fan, Y., and Tanaka, M. M.: Sequential Monte Carlo without likelihoods, Proc. Natl. Acad. Sci. USA, 104, 1760-1765, 2007. (Pubitemid 46239852)
99. Slater, A. G. and Clark, M. P.: Snow data assimilation via an ensemble Kalman filter, J. Hydrometeorol., 7, 478-493, 2006. (Pubitemid 44070416)
100. Smith, P., Beven, K. J., and Tawn, J. A.: Detection of structural inadequacy in process-based hydrological models: a particle-filtering approach, Water Resour. Res., 44, W01410, doi:10.1029/2006WR005205, 2008. (Pubitemid 351304135)
101. Smith, T., Sharma, A., Marshall, L., Mehrotra, R., and Sisson, S.: Development of a formal likelihood function for improved Bayesian inference of ephemeral catchments, Water Resour. Res., 46, W12551, doi:10.1029/2010WR009514, 2010.
102. Solomatine, D. P. and Shrestha, D. L.: A novel method to estimate model uncertainty using machine learning techniques,Water Resour. Res., 45, W00B11, doi:10.1029/2008WR006839, 2009.
103. Sorooshian, S. and Dracup, J.A.: Stochastic parameter estimation procedures for hydrologic rainfall-runoff models: Correlated and heteroscedastic error cases, Water Resour. Res., 16, 430-442, 1980.
104. Sorooshian, S., Gupta, V. K., and Fulton, J. L.: Evaluation of maximum likelihood parameter estimation techniques for conceptual rainfall-runoff models: influence of calibration data variability and length on model credibility, Water Resour. Res., 19, 251-259, 1983a. (Pubitemid 14256109)
105. Sorooshian, S. and Gupta, V.K.: Automatic calibration of conceptual rainfall-runoff models: the question of parameter observability and uniqueness, Water Resour. Res., 19, 260-268, 1983b. (Pubitemid 14256110)
106. Stedinger, J. R., Vogel, R. M., Lee, S. U., and Batchelder, R.: Appraisal of Generalized Likelihood Uncertainty Estimation( GLUE) Methodology, Water Resour. Res., 44, WOOB06, doi:10.1029/2008WR006822, 2008.
107. Stenerud, V. R., Kippe, V., Lie, K., and Datta-Gupta, A.: Adaptive multiscale streamline simulation and inversion for highresolution geomodels, Soc. Petrol. Eng. J., 13, 99-111, 2008. (Pubitemid 351583171)
108. Tadesse, A. and Anagnostou, E.N.: A statistical approach to ground radar-rainfall estimation, J. Atmos. Ocean Technol., 22, 1055-1071, 2005.
109. Tolson, B. A. and Shoemaker, C. A.: Dynamically dimensioned search algorithm for computationally efficient watershed model calibration, Water Resour. Res., 43, W01413, doi:10.1029/2005WR004723, 2007. (Pubitemid 46364291)
110. Troutman, B. M.: Errors and parameter estimation in precipitationrunoff modeling: I. Theory, Water Resour. Res., 21, 1195-1213, 1985a. (Pubitemid 17269685)
111. Troutman, B. M.: Errors and parameter estimation in precipitationrunoff modeling: II. Case study,Water Res. Res., 21, 1214-1222, 1985b. (Pubitemid 17269686)
112. Turner, B.M, and van Zandt, T.: A tutorial on approximate Bayesian computation, J. Mathe. Psychol., 56, 69-85, 2012.
113. Vrugt, J. A., Bouten, W., Gupta, H. V., and Sorooshian, S.: Toward improved identifiability of hydrologic model parameters: The information content of experimental data, Water Resour. Res., 38, 1312, doi:10.1029/2001WR001118, 2002.
114. Vrugt, J. A., Diks, C. G. H., Bouten, W., Gupta, H. V., and Verstraten, J. M.: Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation, Water Resour. Res., 41, W01017, doi:10.1029/2004WR003059, 2005. (Pubitemid 40359297)
115. Vrugt, J. A. and Robinson, B. A.: Improved evolutionary optimization from genetically adaptive multimethod search, Proc. Natl. Acad. Sci. USA, 104, 708-711, 2007. (Pubitemid 46154674)
116. Vrugt, J. A. and Sadegh, M.: Toward diagnostic model calibration and evaluation: Approximate Bayesian Computation, Water Resour. Res., 49, 1-11, doi:10.1002/wrcr.20354, 2013.
117. Vrugt, J. A., ter Braak, C. J. F., Clark, M. P., Hyman, J. M., and Robinson, B. A.: Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation,Water Resour. Res., 44, W00B09, doi:10.1029/2007WR006720, 2008a.
118. Vrugt, J. A., ter Braak, C. J. F., Gupta, H. V., and Robinson, B. A.: Equifinality of formal (DREAM) and informal.(GLUE) Bayesian approaches in hydrologic modeling?, Stoch. Environ. Res. Risk Ass., 23, 1011-1026, 2008b.
119. Vrugt, J. A., ter Braak, C. J. F., Gupta, H. V., and Robinson, B. A.: Response to comment by Keith Beven on "Equifinality of formal.(DREAM) and informal.(GLUE) Bayesian approaches in hydrologic modeling?", Stoch. Environ. Res. Risk Ass., 23, 1011-1026., doi:10.1007/s00477-008-0284-9, 2008c.
120. Vrugt, J. A., ter Braak, C. J. F., Diks, C. G. H., Higdon, D., Robinson, B. A., and Hyman, J. M.: Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling, Int. J. Nonlinear Sci. Numer. Simul., 10, 273-290, 2009a.
121. Vrugt, J. A., Robinson, B. A., and Hyman, J. M.: Self-adaptive multimethod search for global optimization in real-parameter spaces, IEEE Trans. Evolut. Comput., 13, 243-259, 2009b.
122. Vrugt, J. A., ter Braak, C. J. F., Diks, C. G. H., and Schoups, G.: Advancing hydrologic data assimilation using particle Markov chain Monte Carlo simulation: theory, concepts and applications, Adv. Water Resour., Anniversary Issue-35 Years, 51, 457-478, doi:10.1016/j.advwatres.2012.04.002, 2013.
123. Wagener, T., McIntyre, N., Lees, M. J., Wheater, H. S., and Gupta, H.V.: Towards reduced uncertainty in conceptual rainfall-runoff modelling: Dynamic identifiability analysis, Hydrol. Process., 17, 455-476, 2003. (Pubitemid 36234589)
124. Wang, Q.: The genetic algorithm and its application for calibrating conceptual rainfall-runoff models,Water Resour. Res., 27, 2467-2471, 1991.
125. Wang, X., He, X., Williams, J. R., Izaurralde, R. C., and Atwood, J. D.: Sensitivity and uncertainty analyses of crop yields and soil organic carbon simulated with EPIC, Trans. Am. Soc. Agricultural Eng., 48, 1041-1054, 2005. (Pubitemid 41138590)
126. Yapo, P. O., Gupta, H. V., and Sorooshian, S.: Calibration of conceptual rainfall-runoff models: Sensitivity to calibration data, J. Hydrol., 181, 23-48, 1996.
127. Yapo, P. O., Gupta, H. V., and Sorooshian, S.: Multi-objective global optimization for hydrologic models, J. Hydrol., 204, 83-97, 1998.
128. Young, P. C.: Advances in real-time flood-forecasting forecasting, Philosophical Transactions Royal Society, Phys. Eng. Sci., 360, 1433-1450, 2002.
129. Young, P. C.: Hypothetico-inductive data-based mechanistic modeling of hydrological systems, Water Resour. Res., 49, 915-935, doi:10.1002/wrcr.20068, 2013.