An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction

[1] The conventional treatment of uncertainty in rainfall-runoff modeling primarily attributes uncertainty in the input-output representation of the model to uncertainty in the model parameters without explicitly addressing the input, output, and model structural uncertainties. This paper presents a new framework, the Integrated Bayesian Uncertainty Estimator (IBUNE), to account for the major uncertainties of hydrologic rainfall-runoff predictions explicitly. IBUNE distinguishes between the various sources of uncertainty including parameter, input, and model structural uncertainty. An input error model in the form of a Gaussian multiplier has been introduced within IBUNE. These multipliers are assumed to be drawn from an identical distribution with an unknown mean and variance which were estimated along with other hydrological model parameters by a Monte Carlo Markov Chain (MCMC) scheme. IBUNE also includes the Bayesian model averaging (BMA) scheme which is employed to further improve the prediction skill and address model structural uncertainty using multiple model outputs. A series of case studies using three rainfall-runoff models to predict the streamflow in the Leaf River basin, Mississippi, are used to examine the necessity and usefulness of this technique. The results suggest that ignoring either input forcings error or model structural uncertainty will lead to unrealistic model simulations and incorrect uncertainty bounds.

[1]  S. Sorooshian,et al.  Stochastic parameter estimation procedures for hydrologie rainfall‐runoff models: Correlated and heteroscedastic error cases , 1980 .

[2]  Brendan A. Wintle,et al.  The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models , 2003 .

[3]  C. Diks,et al.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation , 2005 .

[4]  G. Evensen.  Using the Extended Kalman Filter with a Multilayer Quasi-Geostrophic Ocean Model , 1992 .

[5]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[6]  Robert J. Abrahart,et al.  Multi-model data fusion for river flow forecasting: an evaluation of six alternative methods based on two contrasting catchments , 2002 .

[7]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[8]  D. Madigan,et al.  Bayesian Model Averaging for Linear Regression Models , 1997 .

[9]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[10]  M. B. Beck,et al.  Water quality modeling: A review of the analysis of uncertainty , 1987 .

[11]  A. Brath,et al.  A stochastic approach for assessing the uncertainty of rainfall‐runoff simulations , 2004 .

[12]  Peter K. Kitanidis,et al.  Adaptive filtering through detection of isolated transient errors in rainfall‐runoff models , 1980 .

[13]  S. Sorooshian,et al.  Multimodel Combination Techniques for Analysis of Hydrological Simulations: Application to Distributed Model Intercomparison Project Results , 2006 .

[14]  E. George,et al.  Journal of the American Statistical Association is currently published by American Statistical Association. , 2007 .

[15]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[16]  S. Richardson,et al.  Variable selection and Bayesian model averaging in case‐control studies , 2001, Statistics in medicine.

[17]  Larry Brazil,et al.  Multilevel calibration strategy for complex hydrologic simulation models , 1988 .

[18]  A. Shamseldin,et al.  Methods for combining the outputs of different rainfall–runoff models , 1997 .

[19]  A. P. Dawid,et al.  Bayesian Model Averaging and Model Search Strategies , 2007 .

[20]  Peter K. Kitanidis,et al.  Real‐time forecasting with a conceptual hydrologic model: 1. Analysis of uncertainty , 1980 .

[21]  Michael Ghil,et al.  Advanced data assimilation in strongly nonlinear dynamical systems , 1994 .

[22]  Adrian E. Raftery,et al.  MODEL SELECTION AND ACCOUNTING FOR MODEL UNCERTAINTY IN LINEAR REGRESSION MODELS , 2007 .

[23]  Keith Beven,et al.  The future of distributed models: model calibration and uncertainty prediction. , 1992 .

[24]  Aaron M. Ellison,et al.  Bayesian inference in ecology , 2004 .

[25]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[26]  Kuolin Hsu,et al.  Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter , 2005 .

[27]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[28]  Dong-Jun Seo,et al.  Towards the characterization of streamflow simulation uncertainty through multimodel ensembles , 2004 .

[29]  M. Trosset,et al.  Bayesian recursive parameter estimation for hydrologic models , 2001 .

[30]  Soroosh Sorooshian,et al.  Multi-objective global optimization for hydrologic models , 1998 .

[31]  Soroosh Sorooshian,et al.  A framework for development and application of hydrological models , 2001, Hydrology and Earth System Sciences.

[32]  A. Raftery,et al.  Using Bayesian Model Averaging to Calibrate Forecast Ensembles , 2005 .

[33]  A. Raftery,et al.  Discussion: Performance of Bayesian Model Averaging , 2003 .

[34]  George Kuczera,et al.  Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm , 1998 .

[35]  S. Sorooshian,et al.  A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters , 2002 .

[36]  K. Mitchell,et al.  Simple water balance model for estimating runoff at different spatial and temporal scales , 1996 .

[37]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[38]  Adrian E. Raftery,et al.  Bayesian model averaging: development of an improved multi-class, gene selection and classification tool for microarray data , 2005, Bioinform..

[39]  S. P. Neuman,et al.  Maximum likelihood Bayesian averaging of uncertain model predictions , 2003 .

[40]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[41]  M. Steel,et al.  Benchmark Priors for Bayesian Model Averaging , 2001 .

[42]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information , 1998 .

[43]  Soroosh Sorooshian,et al.  Multi-Model Combination Techniques for Hydrological Forecasting: Application to Distributed Model Intercomparison Project Results , 2005 .