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

Abstract

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 hf 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 (EnKF) 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; hf data are more informative in a density-dependent than in a density-independent setting. The sole use of Sa information does not yield satisfactory updates of hf for the covariance localization scheme of the standard EnKF, while the sole use of hf 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 EnKF can significantly alleviate this issue.