Data assimilation in groundwater modelling: ensemble Kalman filter versus ensemble smoothers

Abstract

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.

Identification of contaminant source and hydraulic conductivity field based on an ILUES-SOM surrogate model

“…van Leeuwen and Evensen (van Leeuwen and Evensen 1996) proposed a variant of EnKF: ensemble smoother (ES). It has been shown that ES can obtain similar results to EnKF but with a much lower computational cost (Li et al 2018)， and widely used in hydrogeology and reservoir research (Bailey and Baù 2010;Bailey et al 2012;Lima et al 2020). But when the system is highly nonlinear, iterative application of ES (IES) are needed (Chen and Oliver 2012).…”

Effects of Auto‐Adaptive Localization on a Model Calibration Using Ensemble Methods

“…Ensemble methods like IES have been referred to as “derivative free” methods (Kovachki and Stuart 2019) for data assimilation because they rely on an approximate gradient between parameters and observations generated using Monte Carlo, whereas traditional approaches require a minimum of one forward model run for every perturbed parameter as well as one run for the base parameter set to construct the Jacobian sensitivity matrix used to determine a parameter upgrade; IES uses empirical correlations from a Monte‐Carlo style ensemble to build an approximate Jacobian matrix (Li et al 2018; Yu et al 2020). Large efficiencies can be realized because filling this approximated Jacobian matrix is based on the number of user specified realizations rather than the number of parameters (Chen and Oliver 2013; White 2018).…”

Accelerating Groundwater Data Assimilation With a Gradient‐Free Active Subspace Method

“…Due to their Monte Carlo nature, ensemble‐based methods are easy to implement and are becoming increasingly popular in subsurface data assimilation (Emerick & Reynolds, 2013; L. Li et al., 2018; Panzeri et al., 2013; Skjervheim & Evensen, 2011). To guarantee performance, a relatively large ensemble size is usually required.…”