Low-rank Kalman filtering for efficient state estimation of subsurface advective contaminant transport models
KAUST DepartmentEarth Science and Engineering Program
Applied Mathematics and Computational Science Program
Physical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Earth Sciences and Engineering Program
Earth Fluid Modeling and Prediction Group
Computational Transport Phenomena Lab
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AbstractAccurate knowledge of the movement of contaminants in porous media is essential to track their trajectory and later extract them from the aquifer. A two-dimensional flow model is implemented and then applied on a linear contaminant transport model in the same porous medium. Because of different sources of uncertainties, this coupled model might not be able to accurately track the contaminant state. Incorporating observations through the process of data assimilation can guide the model toward the true trajectory of the system. The Kalman filter (KF), or its nonlinear invariants, can be used to tackle this problem. To overcome the prohibitive computational cost of the KF, the singular evolutive Kalman filter (SEKF) and the singular fixed Kalman filter (SFKF) are used, which are variants of the KF operating with low-rank covariance matrices. Experimental results suggest that under perfect and imperfect model setups, the low-rank filters can provide estimates as accurate as the full KF but at much lower computational effort. Low-rank filters are demonstrated to significantly reduce the computational effort of the KF to almost 3%. © 2012 American Society of Civil Engineers.
SponsorsThis publication utilized work supported in part by funds from the KAUST GCR Collaborative Fellow program.
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Reply to "comment on 'Ensemble Kalman filter with the unscented transform'"Luo, Xiaodong; Moroz, Irene M.; Hoteit, Ibrahim (Elsevier BV, 2010-09)This is a reply to the comment of Dr. Sakov on the work "Ensemble Kalman filter with the unscented transform" of Luo and Moroz (2009) . © 2010 Elsevier B.V. All rights reserved.
Ensemble Kalman filtering with residual nudgingLuo, X.; Hoteit, Ibrahim (Co-Action Publishing, 2012-10-03)Covariance inflation and localisation are two important techniques that are used to improve the performance of the ensemble Kalman filter (EnKF) by (in effect) adjusting the sample covariances of the estimates in the state space. In this work, an additional auxiliary technique, called residual nudging, is proposed to monitor and, if necessary, adjust the residual norms of state estimates in the observation space. In an EnKF with residual nudging, if the residual norm of an analysis is larger than a pre-specified value, then the analysis is replaced by a new one whose residual norm is no larger than a pre-specified value. Otherwise, the analysis is considered as a reasonable estimate and no change is made. A rule for choosing the pre-specified value is suggested. Based on this rule, the corresponding new state estimates are explicitly derived in case of linear observations. Numerical experiments in the 40-dimensional Lorenz 96 model show that introducing residual nudging to an EnKF may improve its accuracy and/or enhance its stability against filter divergence, especially in the small ensemble scenario.
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