Evaluation of Parameter and Model Uncertainty in Simple Applications of a 1D Sediment Transport Model

AbstractThis paper separately evaluates two methods from Bayesian Statistics to estimate parameter and model uncertainty in simulations from a one-dimensional (1D) sediment transport model. The first method, multivariate shuffled complex evolution metropolis-uncertainty analysis (MSU), is an algorithm that identifies the most likely parameter values and estimates parameter uncertainty for models with multiple outputs. The second method, Bayesian model averaging (BMA), determines a combined prediction based on three sediment transport equations that are calibrated with MSU and evaluates the uncertainty associated with the selection of the transport equation. These tools are applied to simulations of three flume experiments. For these cases, MSU does not converge substantially faster than a previously used and simpler parameter uncertainty method, but its ability to consider correlation between parameters improves its estimate of the uncertainty. Also, the BMA results suggest that a combination of transport...

[1]  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 .

[2]  Keith Beven,et al.  Multi-objective parameter conditioning of a three-source wheat canopy model , 2004 .

[3]  G. Parker.  Surface-based bedload transport relation for gravel rivers , 1990 .

[4]  P. Bates,et al.  Identifiability of distributed floodplain roughness values in flood extent estimation , 2005 .

[5]  S. P. Neuman,et al.  Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 3. Application to Synthetic and Field Data , 1986 .

[6]  Jefferson S. Wong,et al.  Sensitivity of a hydraulic model to channel erosion uncertainty during extreme flooding , 2014 .

[7]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[8]  Bayesian updating of parameters for a sediment entrainment model via Markov chain Monte Carlo. , 2009 .

[9]  J. C. Ramírez,et al.  Estimation of aquifer parameters under transient and steady-state conditions , 1984 .

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

[11]  Y. Lai,et al.  Two-Dimensional Total Sediment Load Model Equations , 2008 .

[12]  Donald B. Rubin,et al.  Max-imum Likelihood from Incomplete Data , 1972 .

[13]  P. Wilcock,et al.  Experiments on Downstream Fining of Gravel: I. Narrow-Channel Runs , 1997 .

[14]  Kuolin Hsu,et al.  Neural Error Regression Diagnosis (NERD): A Tool for Model Bias Identification and Prognostic Data Assimilation , 2006 .

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

[16]  E. D. Andrews,et al.  Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river , 2009 .

[17]  Thomas Meixner,et al.  A global and efficient multi-objective auto-calibration and uncertainty estimation method for water quality catchment models , 2007 .

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

[19]  G. Pender,et al.  Selective bedload transport during the degradation of a well sorted graded sediment bed , 2001 .

[20]  Alexandros Agapitos,et al.  Ensemble Bayesian Model Averaging in Genetic Programming , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[21]  Henrik Madsen,et al.  Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling , 2008 .

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

[23]  Lee H. MacDonald,et al.  Monitoring Guidelines to Evaluate Effects of Forestry Activities on Streams in the Pacific Northwest and Alaska , 1991 .

[24]  M. Arabi,et al.  Method for Assessing Impacts of Parameter Uncertainty in Sediment Transport Modeling Applications , 2011 .

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

[26]  B. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[27]  Martyn P. Clark,et al.  Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling , 2008 .

[28]  Ivan Gajev.  Sensitivity and Uncertainty Analysis of BWR Stability , 2010 .

[29]  R. Müller,et al.  Formulas for Bed-Load transport , 1948 .

[30]  G. Parker,et al.  Reanalysis and Correction of Bed-Load Relation of Meyer-Peter and Müller Using Their Own Database , 2006 .

[31]  Jasper A. Vrugt,et al.  High‐dimensional posterior exploration of hydrologic models using multiple‐try DREAM(ZS) and high‐performance computing , 2012 .

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

[33]  Lei Chen,et al.  Analysis of parameter uncertainty in hydrological and sediment modeling using GLUE method: a case study of SWAT model applied to Three Gorges Reservoir Region, China , 2011 .

[34]  P. Wilcock,et al.  Surface-based Transport Model for Mixed-Size Sediment , 2003 .

[35]  Yeou-Koung Tung,et al.  Sensitivity and uncertainty analysis of a sediment transport model: a global approach , 1993 .

[36]  Jasper A. Vrugt,et al.  Combining multiobjective optimization and Bayesian model averaging to calibrate forecast ensembles of soil hydraulic models , 2008 .

[37]  Heiko Apel,et al.  Flood risk analyses—how detailed do we need to be? , 2009 .

[38]  Geof H. Givens,et al.  Computational Statistics Ed. 2 , 2012 .

[39]  Keith Beven,et al.  Influence of uncertain boundary conditions and model structure on flood inundation predictions. , 2006 .