Low-rank Kalman filtering for efficient state estimation of subsurface advective contaminant transport models
KAUST DepartmentApplied Mathematics and Computational Science Program
Computational Transport Phenomena Lab
Earth Fluid Modeling and Prediction Group
Earth Science and Engineering Program
Environmental Science and Engineering Program
Physical Sciences and Engineering (PSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/562146
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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 (Physica D: Nonlinear Phenomena, Elsevier BV, 2010-09) [Article]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.
A Two-update Ensemble Kalman Filter for Land Hydrological Data Assimilation with an Uncertain ConstraintKhaki, M.; Ait-El-Fquih, Boujemaa; Hoteit, Ibrahim; Forootan, E.; Awange, J.; Kuhn, M. (Journal of Hydrology, Elsevier BV, 2017-10-25) [Article]Assimilating Gravity Recovery And Climate Experiment (GRACE) data into land hydrological models provides a valuable opportunity to improve the models’ forecasts and increases our knowledge of terrestrial water storages (TWS). The assimilation, however, may harm the consistency between hydrological water fluxes, namely precipitation, evaporation, discharge, and water storage changes. To address this issue, we propose a weak constrained ensemble Kalman filter (WCEnKF) that maintains estimated water budgets in balance with other water fluxes. Therefore, in this study, GRACE terrestrial water storages data are assimilated into the World-Wide Water Resources Assessment (W3RA) hydrological model over the Earth’s land areas covering 2002 – 2012. Multi-mission remotely sensed precipitation measurements from the Tropical Rainfall Measuring Mission (TRMM) and evaporation products from the Moderate Resolution Imaging Spectroradiometer (MODIS), as well as ground-based water discharge measurements are applied to close the water balance equation. The proposed WCEnKF contains two update steps; first, it incorporates observations from GRACE to improve model simulations of water storages, and second, uses the additional observations of precipitation, evaporation, and water discharge to establish the water budget closure. These steps are designed to account for error information associated with the included observation sets during the assimilation process. In order to evaluate the assimilation results, in addition to monitoring the water budget closure errors, in-situ groundwater measurements over the Mississippi River Basin in the US and the Murray-Darling Basin in Australia are used. Our results indicate approximately 24% improvement in the WCEnKF groundwater estimates over both basins compared to the use of (constraint-free) EnKF. WCEnKF also further reduces imbalance errors by approximately 82.53% (on average) and at the same time increases the correlations between the assimilation solutions and the water fluxes.
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