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Data Assimilation in Density‐Dependent Subsurface Flows via Localized Iterative Ensemble Kalman Filter
Author(s) -
Xia ChuanAn,
Hu Bill X.,
Tong Juxiu,
Guadagnini Alberto
Publication year - 2018
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2017wr022369
Subject(s) - data assimilation , ensemble kalman filter , covariance , kalman filter , extended kalman filter , mathematics , covariance intersection , computer science , mathematical optimization , algorithm , statistics , meteorology , physics
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 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 (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; 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 EnKF, 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 EnKF can significantly alleviate this issue.