Investigating the Effect of Hydraulic Data and Heterogeneity on Stochastic Inversion of a Physically Based Groundwater Model

Abstract:

This research explores the interactions between data quantity, data quality and heterogeneity resolution on stochastic inversion of a physically based model. To further investigate aquifer heterogeneity, simulations are used to examine the impact of geostatistical models on inversion quality, as well as the spatial sensitivity to heterogeneity using local and global methods. The model domain is a two-dimensional steady-state confined aquifer with lateral flows through two hydrofacies with alternating patterns.

To examine general effects, the control variable method was adopted to reveal the impact of three factors on estimated hydraulic conductivity (K) and hydraulic head boundary conditions (BCs): (1) data availability, (2) data error, and (3) characterization of heterogeneity. Results show that fewer data increase model sensitivity to measurement error and heterogeneity. Extremely large data errors can cause severe model deterioration, regardless of sufficient data availability or high resolution representation of heterogeneity. Smaller data errors can alleviate the bias caused by the limited observations. For heterogeneity resolution, once general patterns of geological structures are captured, its influence is minimal compared to the other factors.

Next, two geostatistical models (spherical and exponential variograms), were used to explore the representation of heterogeneity under the same nugget effects. The results show that stochastic inversion based on the exponential variogram improves both the precision and accuracy of the inverse model, as compared to the spherical variogram. This difference is particularly important for determining accurate BCs through stochastic inversion.

Last, sensitivity analysis was conducted to further investigate the effect of varying the K of each hydrofacies on model inversion. Results from the partial local method show that the inversion is more sensitive to perturbations of K in regions with high heterogeneity. Using the variance-based global sensitivity method reveals that errors in sampling hydraulic head and fluxes at hydrofacies interfaces plays a prominent role in model accuracy.