Method for Assessing Impacts of Parameter Uncertainty in Sediment Transport Modeling Applications Morgan D. Ruark 1 ; Jeffrey D. Niemann, M.ASCE 2 ; Blair P. Greimann, M.ASCE 3 ; and Mazdak Arabi, M.ASCE 4 Abstract: The predictions from a numerical sediment transport model inevitably include uncertainty because of assumptions in the model’ s mathematical structure, the values of parameters, and various other sources. In this paper, the writers aim to develop a method that quantifies the degree to which parameter values are constrained by calibration data and the impacts of the remaining parameter uncertainty on model forecasts. The method uses a new multiobjective version of generalized likelihood uncertainty estimation. The likelihoods of parameter values are assessed using a function that weights different output variables on the basis of their first-order global sensitivities, which are obtained from the Fourier amplitude sensitivity test. The method is applied to Sedimentation and River Hydraulics—One Dimension (SRH-1D) models of two flume experiments: an erosional case and a depositional case. Overall, the results suggest that the sensitivities of the model outputs to the parameters can be rather different for erosional and depositional cases and that the outputs in the depositional case can be sensitive to more parameters. The results also suggest that the form of the likelihood function can have a significant impact on the assessment of parameter uncertainty and its implications for the uncertainty of model forecasts. DOI: 10.1061/(ASCE)HY.1943-7900.0000343. © 2011 American Society of Civil Engineers. CE Database subject headings: Sensitivity analysis; Uncertainty principles; Sediment transport; Calibration; Parameters. Author keywords: Sensitivity analysis; Uncertainty principles; Sediment transport; Calibration; Parameters. Introduction The use of numerical sediment transport models has dramatically expanded over the past three decades. One-dimensional sediment transport models in particular are widely used to determine pos- sible impacts of watershed changes, evaluate water supply manage- ment, and predict impacts of proposed water resource systems on endangered species. Predictions from sediment transport models always entail uncertainty. Sources of uncertainty include: (1) sim- plifications in the model’ s representation of physical processes, (2) unknown initial and/or boundary conditions, (3) errors in the observations that are used to calibrate the model parameters, (4) errors in the values of model parameters, and (5) errors in model forcing (Clyde and George 2004; Gourley and Vieux 2006; Refsgaard et al. 2006; Murray 2007). For one-dimensional sedi- ment transport models, this uncertainty can encompass orders of magnitude in the computed sediment load and the amount of material eroded or deposited at critical locations (Simons et al. 2000; Davies et al. 2002; Eidsvik 2004). Past research has focused on uncertainty arising from sediment transport models or formulas (Davies et al. 2002; Pinto et al. 2006) and the active erosional proc- esses (Daebel and Gujer 2005; Harmel and King 2005; Jepsen 2006; Ziegler 2006) as well as methods to manage uncertainty (Osidele et al. 2003). Less attention has been paid to uncertainty throughout the entire parameter space, or global uncertainty (Chang et al. 1993), and the implications of parameter uncertainty. Models are typically calibrated by adjusting the parameters so that the model outputs reproduce a set of available observations. The per- formance of the model for the calibration period is usually reported, but little consideration is given to the extent to which the calibration data have constrained the values of the parameters and the behavior of the model for the forecast scenario. Bayesian methods offer a formal way to assess impacts of parameter uncertainty (or other uncertainties) on model predictions (Clyde and George 2004; Kuczera et al. 2006). Bayesian methods require the modeler to specify a prior joint probability distribu- tion for the uncertain parameters. The prior joint distribution is then combined with observations of model outputs from the calibration period to generate a posterior joint distribution for the parameters (Beven 2000). The updating of the joint distribution is done on the basis of a formal assessment of the likelihood of a set of parameter values given the observed model outputs (Clyde and George 2004). The posterior distribution of the parameter values is then used in the model for the forecast scenario to determine the implied distribu- tion of model outputs. The key advantage of Bayesian methods is that they utilize well-defined theoretical foundations, including a formal likelihood function for updating the joint probability distri- bution (Clyde and George 2004; Kuczera et al. 2006). Key limita- tions of Bayesian methods are that they can require inversion of large matrices, which can be a computational burden, and they often employ a variety of simplifying statistical assumptions in- cluding normality, independence, and homoscedasticity (Stedinger et al. 2008) that are often violated in sediment transport modeling applications. For example, heteroscedasticity is well documented for discharge hydrographs (Sorooshian and Dracup 1980) and is 1 Water Resources Engineer, CH2M Hill, 2020 SW 4th Ave., 3rd Floor, Portland, OR 97201-4958. 2 Associate Professor, Dept. of Civil and Environmental Engineering, Colorado State Univ., Campus Delivery 1372, Fort Collins, CO 80523- 1372 (corresponding author). E-mail: jniemann@engr.colostate.edu 3 Hydraulic Engineer, Sediment and River Hydraulics Group, Bureau of Reclamation, Denver Federal Center, Bldg. 67, Denver, CO 80225. 4 Assistant Professor, Dept. of Civil and Environmental Engineering, Colorado State Univ., Campus Delivery 1372, Fort Collins, CO 80523- 1372. Note. This manuscript was submitted on September 3, 2009; approved on October 14, 2010; published online on January 13, 2011. Discussion period open until November 1, 2011; separate discussions must be sub- mitted for individual papers. This paper is part of the Journal of Hydraulic Engineering, Vol. 137, No. 6, June 1, 2011. ©ASCE, ISSN 0733-9429/ 2011/6-623–636/$25.00. JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JUNE 2011 / 623 Downloaded 16 Jun 2011 to 129.82.229.120. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org