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Adaptive multi-fidelity probabilistic collocation-based Kalman filter for subsurface flow data assimilation: numerical modeling and real-world experiment

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Abstract

The ensemble Kalman filter (EnKF) has received substantial attention in hydrologic data assimilation due to its ease of implementation. In EnKF, a large enough ensemble size is often required to ensure accuracy, which may result in considerable computational overhead, especially for large-scale problems. Motivated by recent developments in multi-fidelity simulation, we develop a novel data assimilation method that provides an alternative to EnKF, namely adaptive multi-fidelity probabilistic collocation-based Kalman filter (AMF-PCKF). The appealing feature is to approximate the system response with polynomial chaos expansion (PCE) using the adaptive multi-fidelity probabilistic collocation method, which improves the computational efficiency without sacrificing accuracy. This constitutes the forecast step of AMF-PCKF, while the analysis step is established by sequentially updating the PCE coefficients. As demonstrated by a synthetic numerical case of heat transport in unsaturated flow and a real-world two-phase flow experiment, AMF-PCKF can provide more accurate estimations than EnKF under the same amount of computation, even when the number of unknown parameters is as high as 100.

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Acknowledgements

This work is supported by the National Key Research and Development Program of China (Grant 2018YFC1800303) and the National Natural Science Foundation of China (Grants 41771254 and 41807007). Data and computer codes used are available from the repository of Mendeley Data. The link is as follows: https://data.mendeley.com/datasets/3pv8yvp236/draft?a=4439fe6f-3efc-4305-afa6-93098b67a4bd.

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Authors and Affiliations

  1. Key Laboratory of Soil Environment and Pollution Remediation, Institute of Soil Science, Chinese Academy of Sciences, Nanjing, 210008, China

    Jun Man

  2. College of Environmental and Resource Sciences, Zhejiang Provincial Key Laboratory of Agricultural Resources and Environment, Zhejiang University, Hangzhou, 310058, China

    Jun Man, Qiang Zheng & Lingzao Zeng

  3. Department of Environmental Sciences, University of California, Riverside, Riverside, CA, 92521, USA

    Laosheng Wu

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  1. Jun Man
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  2. Qiang Zheng
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  3. Laosheng Wu
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  4. Lingzao Zeng
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Correspondence to Lingzao Zeng.

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Man, J., Zheng, Q., Wu, L. et al. Adaptive multi-fidelity probabilistic collocation-based Kalman filter for subsurface flow data assimilation: numerical modeling and real-world experiment. Stoch Environ Res Risk Assess 34, 1135–1146 (2020). https://doi.org/10.1007/s00477-020-01815-y

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