| In hydrogeological studies, a distinction is made between the inverse problem, whereby aquifer parameters are estimated via measurements of system response, and the forward problem, in which the parameters are used as input to models that predict flow and transport. Hydrogeological modeling must often rely on limited data due to budgetary constraints, making inversion difficult and prediction highly uncertain. This study examines some new approaches to the effective use of sparse data in hydrogeological problems.; The inverse problem is approached by using concentration data collected on a plane of multilevel sampling ports orthogonal to the mean flow direction, avoiding the need for widespread, three-dimensional measurements. The concentrations are transformed into indicator variables, whose expected value and covariance structure in the orthogonal plane are used to infer the log conductivity variance and geometric mean, vertical and horizontal correlation lengths, and local dispersivity values. The effects of control plane size and location, ambient groundwater concentrations, and measurement error on the inference process are investigated, and the method is illustrated using data from the Cape Cod tracer test site.; In solving the forward problem, there is an inherent uncertainty in predictions because the exact spatial distribution of parameter values in the flow field is unknown. The problem is often approached in a Monte Carlo fashion. Using field data in a local sense, conditioning, limits the possible flow field realizations to those that honor the measurement values at their locations. Because the variability between realizations is reduced, so is the uncertainty in transport predictions. However, generating conditional realizations is computationally burdensome, and many conditional studies have been restricted to two dimensional flow. Herein, an efficient three-dimensional groundwater flow model that incorporates field measurements is developed. Velocity field realizations are generated directly, eliminating the computationally demanding need to solve the flow equation. The model is used to examine the effects that local conditioning has in reducing the uncertainty of the flow field and transport predictions. |
