Ensemble smoother assimilation of hydraulic head and return flow data to estimate hydraulic conductivity distribution

Numerical groundwater models, frequently used to enhance understanding of the hydrologic and chemical processes in local or regional aquifers, are often hindered by an incomplete representation of the parameters which characterize these processes. In this study, we present the use of a data assimilation algorithm that incorporates all past model results and data measurements, an ensemble smoother (ES) to provide enhanced estimates of aquifer hydraulic conductivity (K) through assimilation of hydraulic head (H) and groundwater return flow volume (RFV) measurements into groundwater model simulation results. On the basis of the Kalman filter methodology, residuals between forecasted model results and measurements, together with covariances between model results at measurement locations and nonmeasurement locations, are used to correct model results. Parameter estimation is achieved by incorporating model parameters into the algorithm, thus allowing the correlation between H, RFV, and K to correct the K fields. The applicability of the ES is demonstrated using a synthetic two-dimensional transient groundwater modeling simulation. Sensitivity analyses are carried out to show the performance of the ES in regard to measurement error, number of measurements, number of assimilation times, correlation length of the K fields, and the number of stream gage locations. Results show that the departure of the K fields from a reference K field is greatly reduced through data assimilation and demonstrate that the ES scheme is a promising alternative to other inverse modeling techniques because of low computational burden and the ability to run the algorithm entirely independent of the groundwater model simulation.