Ensemble Kalman Filter versus Ensemble Smoother for Data Assimilation in Groundwater Modeling

Groundwater modeling calls for an effective and robust integrating method to fill the gap between the model and data. The Ensemble Kalman Filter (EnKF), a real-time data assimilation method, has been increasingly applied in multiple disciplines such as petroleum engineering and hydrogeology. In this approach, the groundwater models are sequentially updated using measured data such as hydraulic head and concentration data. As an alternative to the EnKF, the Ensemble Smoother (ES) was proposed with updating models using all the data together, and therefore needs a much less computational cost. To further improve the performance of the ES, an iterative ES was proposed for continuously updating the models by assimilating measurements together. In this work, we compare the performance of the EnKF, the ES and the iterative ES using a synthetic example in groundwater modeling. The hydraulic head data modeled on the basis of the reference conductivity field are utilized to inversely estimate conductivities at un-sampled locations. Results are evaluated in terms of the characterization of conductivity and groundwater flow and solute transport predictions. It is concluded that: (1) the iterative ES could achieve a comparable result with the EnKF, but needs a less computational cost; (2) the iterative ES has the better performance than the ES through continuously updating. These findings suggest that the iterative ES should be paid much more attention for data assimilation in groundwater modeling.