4.7 Article

A Kalman filter powered by H2-matrices for quasi-continuous data assimilation problems

Journal

WATER RESOURCES RESEARCH
Volume 50, Issue 5, Pages 3734-3749

Publisher

AMER GEOPHYSICAL UNION
DOI: 10.1002/2013WR014607

Keywords

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Funding

  1. US Department of Energy, National Energy Technology Laboratory (DOE, NETL) [DE-FE0009260]
  2. National Science Foundation -Division of Mathematical Sciences [1228275]
  3. The Global Climate and Energy Project (GCEP) at Stanford
  4. Direct For Mathematical & Physical Scien
  5. Division Of Mathematical Sciences [1228275] Funding Source: National Science Foundation

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Continuously tracking the movement of a fluid or a plume in the subsurface is a challenge that is often encountered in applications, such as tracking a plume of injected CO2 or of a hazardous substance. Advances in monitoring techniques have made it possible to collect measurements at a high frequency while the plume moves, which has the potential advantage of providing continuous high-resolution images of fluid flow with the aid of data processing. However, the applicability of this approach is limited by the high computational cost associated with having to analyze large data sets within the time constraints imposed by real-time monitoring. Existing data assimilation methods have computational requirements that increase superlinearly with the size of the unknowns m. In this paper, we present the HiKF, a new Kalman filter (KF) variant powered by the hierarchical matrix approach that dramatically reduces the computational and storage cost of the standard KF from O(m(2)) to O(m), while producing practically the same results. The version of HiKF that is presented here takes advantage of the so-called random walk dynamical model, which is tailored to a class of data assimilation problems in which measurements are collected quasi-continuously. The proposed method has been applied to a realistic CO2 injection model and compared with the ensemble Kalman filter (EnKF). Numerical results show that HiKF can provide estimates that are more accurate than EnKF and also demonstrate the usefulness of modeling the system dynamics as a random walk in this context.

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