Data Assimilation in Density-Dependent Subsurface Flows via Localized Iterative Ensemble Kalman Filter

Parameter estimation in variable-density groundwater flow systems is confronted with challenges of strong nonlinearity and heavy computational burden. Relying on a variant of the Henry problem, we evaluate the performance of a domain localization scheme of the iterative ensemble Kalman filter in the framework of data assimilation settings for variable-density groundwater flows in a seawater intrusion scenario. The performance of the approach is compared against (a) the corresponding domain localization scheme of the ensemble Kalman filter in its standard formulation as well as (b) a covariance localization scheme of the latter. The equivalent freshwater head, $h_f$, and salinity, $S_a$, are set as the target state variables. The randomly heterogeneous field of equivalent freshwater hydraulic conductivity, $K_f$, is considered as the system parameter field. Density-independent and density-driven flow settings are considered to evaluate the assimilation results using various methods and data. When only $h_f$ data are assimilated, all tested approaches perform generally well and a localization scheme embedded in the iterative ensemble Kalman filter appears to consistently outperform the domain localized version of the standard ensemble Kalman filter in a density-driven scenario; Dirichlet boundary conditions tend to show a more pronounced negative effect on estimating $K_f$ for density-independent than for density-dependent flow conditions; $h_f$ data are more informative in a density-dependent than in a density-independent setting. The sole use of $S_a$ information does not yield satisfactory updates of $h_f$ for the covariance localization scheme of the standard ensemble Kalman filter while the sole use of $h_f$ does. The domain localization scheme leads to difficulties in the attainment of global filter convergence when only $S_a$ data are used. A covariance localization scheme associated with a standard ensemble Kalman filter can significantly alleviate this issue.