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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