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Numerical experiments show that variations of an order of magnitude in transmissivity or hydraulic conductivity can cause significant dispersion even when relatively small values of dispersivity are assumed. Such variations should be represented in a deterministic model of solute transport in order to describe the flow field adequately and to realistically simulate dispersion. In an example of a field application to an alluvial aquifer, a satisfactory match to observed field data was obtained using a small (0.01 m) value of longitudinal dispersivity and a grid spacing fine enough to show field‐scale alluvial heterogeneities. When large (~30 m) values of longitudinal dispersivity were used, computed solute concentrations were about half of observed values in parts of the aquifer. Modeling efforts with grid spacings two to six times wider than alluvial channels in the aquifer produced ground‐water flow and solute‐transport simulations which did not adequately match field data.

Groundwater modelling calls for an effective and robust data integrating method to fill the gap between the model and observation 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, a groundwater model is updated sequentially with measured data such as hydraulic head and concentration. As an alternative to the EnKF, the ensemble smoother (ES) has been proposed for updating groundwater models using all the data together, with much less computational cost. To further improve the performance of the ES, an iterative ES has been proposed for continuously updating the model 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 modelling. Hydraulic head data modelled on the basis of the reference conductivity field are used to inversely estimate conductivities at unsampled locations. Results are evaluated in terms of the characterization of conductivity and groundwater flow predictions. It is concluded that (a) the iterative ES works better than the standard ES because of its continuous updating and (b) the iterative ES could achieve results comparable with those of the EnKF, with less computational cost. These findings show that the iterative ES should be paid much more attention for data assimilation in groundwater modelling.

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