Uncertainty Analysis of Stochastic Solute Transport in a Heterogeneous Aquifer

Abstract

The uncertainty of predicting stochastic solute transport in an aquifer with heterogeneous hydraulic conductivity was quantified. Two sources of uncertainty were considered in the analysis including uncertainty that stems from inability to exactly predict the hydraulic conductivity at unmeasured locations and uncertainty that results from imperfect knowledge of the parameters in stochastic model. Hydraulic conductivity field was simulated using a random space function model while considering the nugget effect. The posterior distribution of parameters in the model was then obtained using Bayesian inference method of Markov Chain Monte Carlo (MCMC) Metropolis-Hastings (MH) algorithm. Inferred optimal parameter set was lastly used to generate conditional hydraulic conductivity fields to simulate solute transport in groundwater. As an illustrative example, a hypothetical steady two-dimensional flow in a heterogeneous aquifer was adopted. Results showed that the uncertainty of predicting solute transport in groundwater decreased when more conditional data were included, which was attributed to the fact that the optimal parameter value approached its hypothetical value in the posterior parameter distributions under the scenario of using more conditional data. Another important finding was that the degree of uncertainty for predictive variance is much higher in the area of higher solute concentration while the uncertainty for predictive absolute error shows no obvious trend when determining the distribution of solute concentration. We concluded that a balance may exist between global and local uncertainty for predictive absolute error. At last, the relative importance of parameter uncertainty to uncertainty of predictive solute transport was revealed. The variance and nugget ranked the top two important factors, followed by the expected value and the integral scale of the spatial stochastic process.