Toward a Reliable Prediction of Streamflow Uncertainty: Characterizing and Optimization of Uncertainty Using MCMC Bayesian Framework

Streamflow quantification in the southeastern (SE) landscape is subject to a range of uncertainties due to spatially heterogeneous and complex nature of the coastal plain hydrological system. This paper aims to address the question of how the parameter and total uncertainty quantifications in the Soil & Water Assessment Tool (SWAT) model can effectively influence on streamflow prediction in the Waccamaw River watershed, a low-gradient forested wetland dominated coastal plain landscape, in North and South Carolina. In this study a Markov Chain Monte Carlo (MCMC) Differential Evolution Adaptive Metropolis (DREAM) algorithm for Bayesian inference implemented to SWAT in R to capture the uncertainty propagation of daily streamflow dynamics during calibration period (2003-2005). The marginal posterior distributions of eighteen important streamflow parameters values are well identified by DREAM within their prior ranges. In this study a Gelman Rubin diagnostic of <1.2 was achieved for all parameters after about 40000 iterations, indicating that DREAM algorithm well sampled the posteriors. A parallelized MCMC algorithm demonstrated appropriate likelihood function and reduced the error in the hydrological quantity. Further the degree to which all uncertainties are accounted for is quantified and bracketed 72% and 70% of daily measured flow by the 95% prediction uncertainty (95PPU) in the upstream and downstream outlets respectively. The results also indicated that low flow value has high impact on the parametric uncertainty while the variation of uncertainty propagation narrows in the case of high flow events. The posterior distributions of output further indicated that flow parameters in the upstream and downstream portions have non-unique posterior distributions and the corresponding model processes appear to be sensitive to a nonlinear function of the shallow soil properties and river hydraulic characteristics. In particular, DREAM algorithm showed flexibility for parallel implementation on distributed watershed model; efficiently estimates the posterior probability density function and can be therefore practice as a basic approach for a data assimilation framework under hydrological dynamics.