Dependence of Uncertainty in Parameter Estimation in Non-stationary Heterogeneous Aquifers on the Number and Spatial Distribution of Observation Wells

Even with the many recent advances made in the use of inverse modeling techniques for parameter estimation, in practice, model calibration, to a large extent still relies on trial and error methods. These methods use available data from observation wells that are limited in number and are not necessarily optimally located. These limitations introduce uncertainty to estimated parameters, thus introducing errors to predications that are made using the calibrated model. To reduce calibration uncertainty, modelers in addition to "hard data" based on standard aquifer tests and drawdown observations, rely on localized "soft data" that are less quantitative. To develop an improved understanding of how additional data on drawdown observations and soft data on other geologic features reduce the parameter estimation uncertainty, a set of experiments was conducted in a three-dimensional synthetic aquifer. This three-dimensional test aquifer with dimensions 208 (L) x 117 (W) x 57 cm (H) was constructed using five well-characterized sands in a laboratory test tank. The aquifer consists of two regions. The first, a stationary spatially correlated random field has a log-normally distributed hydraulic conductivity with a mean lnK = 4.02 (K in m/day) and variance of ?2lnK = 1.2. A structured heterogeneity was introduced by embedding into the stationary field a second region with a lens-like layer of find sand, resulting in the composite aquifer heterogeneity to be non-stationary. The boundary heads in the aquifer was controlled with two end reservoirs. Three pumping wells with different screen depths were placed in the aquifer. The pressure distribution within the aquifer was measured at 92 monitoring locations using an automated pressure measuring system. A number of experimental simulations were conducted to generate a data set on the aquifer response to various pumping excitations. The forward modeling code MODFLOW-2000 and the inverse modeling code UCODE were used in data analysis. The data set and the modeling tools were used to conduct number of investigations on parameter estimation uncertainty with the goal of developing a model calibration protocol that uses both hard and soft data. This paper presents the results of a study that investigates the relationship between parameter uncertainties and the number and spatial distribution of the observation points. The preliminary results suggest that the parameter accuracy is not only related to the number of observations, but also to the spatial distribution of the observation points in the three dimensional space. This suggests a well-designed observation well network improves the calibration accuracy of model and hence reducing the prediction errors.