Uncertainty, sensitivity and geostatistical studies of flow and contaminant transport in heterogeneous unsaturated zone (2020)

"The objectives of this study are: (1) to develop a methodology of estimating probability density functions (PDFs) of unsaturated hydraulic parameters when field samples are sparse, (2) to evaluate the predictive uncertainties in flow and contaminant transport due to parameter uncertainties in the layer- and local-scale heterogeneities of hydraulic parameters in unsaturated zone (UZ), (3) to investigate the contributions of the parameter uncertainties to the flow and transport uncertainties, and (4) to estimate the spatial correlation structures of hydraulic parameters by incorporating prior information and site measurements. At layer scale, the uncertainty assessment of flow and contaminant transport in UZ entails PDFs of the hydraulic parameters. A non-conventional maximum likelihood (ML) approach is used in this study to estimate the PDFs of water retention parameters (e.g., van Genuchten α and n ) for situations common in field scale applications where core samples are sparse and prior PDFs of the parameters are unknown. This study also investigates the effects of the uncertainties in the water retention parameters on the predictive uncertainties in flow and transport in UZ. By comparing the predictive uncertainties with and without incorporating the random water retention parameters, it is found that the random water retention parameters have limited effects on the mean predictions of the state variables including percolation flux, normalized cumulative mass arrival, and contaminant travel time. However, incorporating the uncertainties in the water retention parameters significantly increases the magnitude and spatial extent of predictive uncertainties of the state variables. The layer-scale uncertainty is specific to hydrogeologic layers, while the local-scale heterogeneity refers to the spatial variation of hydraulic properties within a layer. The local-scale heterogeneity is important in predicting flow path, velocity, and travel time of contaminants, but it is often neglected in modeling practices. This study incorporates the local-scale heterogeneity and examines its relative effects to the layer-scale uncertainty on flow and transport uncertainties in UZ. Results illustrate that local-scale heterogeneity significantly increases predictive uncertainties in the percolation fluxes and contaminant plumes, whereas the mean predictions are only slightly affected by the local-scale heterogeneity. Layer-scale uncertainty is more important than local-scale heterogeneity for simulating overall contaminant travel time, suggesting that it would be more cost-effective to reduce the layer-scale parameter uncertainty in order to reduce predictive uncertainty in contaminant transport. The sensitivity analysis is an important tool to direct the future field characterizations to reduce the predictive uncertainties in unsaturated flow and transport modeling. This study presents an integrated approach to evaluate the contributions of the uncertainties in input parameters to the predictive uncertainties in unsaturated flow and contaminant transport with and without the consideration of parameter correlations. This study also investigates the effects of parameter correlations on the sensitivity of flow and transport. When the input parameters are independent, the parameter uncertainty in permeability has the largest contributions to the uncertainties in percolation flux and mass arrival of the reactive contaminants. The sorption coefficient of the reactive contaminant becomes the dominant parameter in contributing to the uncertainty in overall contaminant transport at late stage. When the input parameters are correlated, the uncertainties in van Genuchten n and porosity have more contributions to the percolation flux and tracer transport uncertainties due to their correlations with the van Genuchten α and permeability, respectively. The rankings of parameter importance also change if the parameter correlations are taken into account, indicating that the significant effects of parameter correlations on the sensitivity of flow and contaminant transport in UZ. Improving the heterogeneity characterizations of hydraulic parameters is critical to reduce the predictive uncertainties in flow and contaminant transport. This study presents a coupled method of Bayesian updating and the adjoint state maximum likelihood cross validation (ASMLCV) to estimate the spatial correlation structures of hydraulic parameters with the incorporation of prior information and site measurements. The prior distribution is updated to yield the posterior distribution by the likelihood function estimated from the on-site measurements and ASMLCV. The mean of posterior probability distribution for spatial correlation scales can then be used for subsequent heterogeneous field generations by kriging. The good agreement between measured and kriged hydraulic data indicates that the coupled approach may improve the estimation of spatial correlation structure with sparse measurements and known prior information in the heterogeneous UZ."