Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models

Bernardo, 1994 Beven, 1992, Future of distributed models: model calibration and uncertainty prediction, Hydrological Processes, 6, 279, 10.1002/hyp.3360060305 Beven, 2001, Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, Journal of Hydrology, 249, 11, 10.1016/S0022-1694(01)00421-8 Beven, 2006, A manifesto for the equifinality thesis, Journal of Hydrology, 320, 18, 10.1016/j.jhydrol.2005.07.007 Beven, 2007, Comment on “Hydrological forecasting uncertainty assessment: incoherence of the GLUE methodology” by Pietro Mantovan and Ezio Todini, Journal of Hydrology, 338, 315, 10.1016/j.jhydrol.2007.02.023 Beven, 2008, So just why would a modeller choose to be incoherent?, Journal of Hydrology, 354, 15, 10.1016/j.jhydrol.2008.02.007 Blasone, 2008, Uncertainty assessment of integrated distributed hydrological models using GLUE with Markov chain Monte Carlo sampling, Journal of Hydrology, 353, 18, 10.1016/j.jhydrol.2007.12.026 Blasone, 2008, Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling, Advances in Water Resources, 31, 630, 10.1016/j.advwatres.2007.12.003 Carlos, 1980, Efficient tests for normality, homoscedasticity and serial independence of regression residuals, Economics Letters, 6, 255, 10.1016/0165-1765(80)90024-5 Chib, 1995, Understanding the Metropolis-Hastings algorithm, American Statistician, 49, 327, 10.2307/2684568 Engeland, 2002, Bayesian estimation of parameters in a regional hydrological model, Hydrology and Earth System Sciences, 6, 883, 10.5194/hess-6-883-2002 Engeland, 2010, Evaluation of statistical models for forecast errors from the HBV model, Journal of Hydrology, 384, 142, 10.1016/j.jhydrol.2010.01.018 Engeland, 2005, Assessing uncertainties in a conceptual water balance model using Bayesian methodology, Hydrological Sciences Journal, 50, 45, 10.1623/hysj.50.1.45.56334 Freer, 1996, Bayesian estimation of uncertainty in runoff prediction and the value of data: an application of the GLUE approach, Water Resources Research, 32, 2161, 10.1029/95WR03723 Gelman, 1992, Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457, 10.1214/ss/1177011136 Gong, 2009, Large-scale runoff routing with an aggregated network-response function, Journal of Hydrology, 368, 237, 10.1016/j.jhydrol.2009.02.007 Gupta, 2003, Reply to comment by K. Beven and P. Young on “Bayesian recursive parameter estimation for hydrologic models”, Water Resources Research, 39, 1117, 10.1029/2002WR001405 Jin, 2010, Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model, Journal of Hydrology, 383, 147, 10.1016/j.jhydrol.2009.12.028 Krzysztofowicz, 1997, Transformation and normalization of variates with specified distributions, Journal of Hydrology, 197, 286, 10.1016/S0022-1694(96)03276-3 Krzysztofowicz, 1999, Bayesian theory of probabilistic forecasting via deterministic hydrologic model, Water Resources Research, 35, 9, 10.1029/1999WR900099 Krzysztofowicz, 2000, Hydrologic uncertainty processor for probabilistic river stage forecasting, Water Resources Research, 36, 11, 10.1029/2000WR900108 Kuczera, 1998, Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm, Journal of Hydrology, 211, 69, 10.1016/S0022-1694(98)00198-X Li, L., Xia, J., Xu, C.-Y., Chu, J., Wang, R., 2009. Analyse the sources of equifinality in hydrological model using GLUE methodology. In: Hydroinformatics in Hydrology, Hydrogeology and Water Resources, Proceedings of Symposium JS.4 at the Joint IAHS & IAH Convention, Hyderabad, India, September 2009. IAHS Publ. no. 331, pp. 130–138. Liu, 2005, Flood forecasting using a fully distributed model: application of the TOPKAPI model to the Upper Xixian Catchment, Hydrology and Earth System Sciences, 9, 347, 10.5194/hess-9-347-2005 Mantovan, 2006, Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology, Journal of Hydrology, 330, 368, 10.1016/j.jhydrol.2006.04.046 Maranzano, 2004, Identification of likelihood and prior dependence structures for hydrologic uncertainty processor, Journal of Hydrology, 290, 1, 10.1016/j.jhydrol.2003.11.021 Montanari, 2005, Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall–runoff simulations, Water Resources Research, 41, W08406, 10.1029/2004WR003826 Montanari, 2004, A stochastic approach for assessing the uncertainty of rainfall–runoff simulations, Water Resources Research, 40, W01106, 10.1029/2003WR002540 Nash, 1970, River flow forecasting through conceptual models – Part 1-a. Discussion of principles, Journal of Hydrology, 10, 282, 10.1016/0022-1694(70)90255-6 Reggiani, 2008, A Bayesian approach to decision-making under uncertainty: an application to real-time forecasting in the river Rhine, Journal of Hydrology, 356, 56, 10.1016/j.jhydrol.2008.03.027 Stedinger, 2008, Appraisal of the generalized likelihood uncertainty estimation (GLUE) method, Water Resources Research, 44, W00B06, 10.1029/2008WR006822 Thiemann, 2001, Bayesian recursive parameter estimation for hydrologic models, Water Resources Research, 37, 10, 10.1029/2000WR900405 Todini, 2007, Hydrological catchment modelling: past, present and future, Hydrology and Earth System Sciences, 11, 468, 10.5194/hess-11-468-2007 Todini, 2008, A model conditional processor to assess predictive uncertainty in flood forecasting, International Journal of River Basin Management, 6, 123, 10.1080/15715124.2008.9635342 Van der Waerden, 1952, Order tests for the two-sample problem and their power, Indagationes Mathematicae, 14, 453, 10.1016/S1385-7258(52)50063-5 Van der Waerden, 1953, Order tests for the two-sample problem and their power 2, Indagationes Mathematicae, 15, 303, 10.1016/S1385-7258(53)50039-3 Van der Waerden, 1953, Order tests for the two-sample problem and their power 3, Indagationes Mathematicae, 15, 311, 10.1016/S1385-7258(53)50040-X Vogel, 2008 Vrugt, 2003, A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters, Water Resources Research, 39, 8, 10.1029/2002WR001642 Vrugt, 2009, Equifinality of formal (DREAM) and informal (GLUE) bayesian approaches in hydrologic modeling?, Stochastic Environmental Research and Risk Assessment, 23, 1011, 10.1007/s00477-008-0274-y Wang, G., 2005. Theory and Method of Distributed Time-Variant Gain Model. Institute of Geographic Sciences and Natural Resources Research, CAS. Beijing. Ph.D. (in Chinese). Wang, 2009, Quantification of effects of climate variations and human activities on runoff by a monthly water balance model: a case study of the Chaobai River basin in northern China, Water Resources Research, 45, W00A11, 10.1029/2007WR006768 Widen-Nilsson, 2009, Model performance and parameter behavior for varying time aggregations and evaluation criteria in the WASMOD-M global water balance model, Water Resources Research, 45, W05418, 10.1029/2007WR006695 Widen-Nilsson, 2007, Global water-balance modelling with WASMOD-M: Parameter estimation and regionalisation, Journal of Hydrology, 340, 105, 10.1016/j.jhydrol.2007.04.002 Xia, 1997, A non-linear perturbation model considering catchment wetness and its application in river flow forecasting, Journal of Hydrology, 200, 164, 10.1016/S0022-1694(97)00013-9 Xia, 2005, Development of distributed time-variant gain model for nonlinear hydrological systems, Science in China Series D: Earth Sciences, 48, 713, 10.1360/03yd0183 Xiong, 2008, An empirical method to improve the prediction limits of the GLUE methodology in rainfall–runoff modeling, Journal of Hydrology, 349, 115, 10.1016/j.jhydrol.2007.10.029 Xu, 2002, WASMOD – the water and snow balance modelling system, 555 Yang, 2008, Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China, Journal of Hydrology, 358, 1, 10.1016/j.jhydrol.2008.05.012 Yang, 2007, Hydrological modelling of the Chaohe Basin in China: statistical model formulation and Bayesian inference, Journal of Hydrology, 340, 167, 10.1016/j.jhydrol.2007.04.006