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Journal of Data Science


High-Dimensional Nonlinear Spatio-Temporal Filtering by Compressing Hierarchical Sparse Cholesky Factors
Volume 20, Issue 4 (2022): Special Issue: Large-Scale Spatial Data Science, pp. 461–474
Pub. online: 3 October 2022      Type: Statistical Data Science      Open accessOpen Access
Received
1 August 2022
Accepted
28 September 2022
Published
3 October 2022

Abstract

Spatio-temporal filtering is a common and challenging task in many environmental applications, where the evolution is often nonlinear and the dimension of the spatial state may be very high. We propose a scalable filtering approach based on a hierarchical sparse Cholesky representation of the filtering covariance matrix. At each time point, we compress the sparse Cholesky factor into a dense matrix with a small number of columns. After applying the evolution to each of these columns, we decompress to obtain a hierarchical sparse Cholesky factor of the forecast covariance, which can then be updated based on newly available data. We illustrate the Cholesky evolution via an equivalent representation in terms of spatial basis functions. We also demonstrate the advantage of our method in numerical comparisons, including using a high-dimensional and nonlinear Lorenz model.

Supplementary material

 Supplementary Material
R code to reproduce our results and figures is available at https://github.com/katzfuss-group/CHVfilter.

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Copyright
2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
basis functions data assimilation hierarchical Vecchia approximation Lorenz model unscented Kalman filter

Funding
MK was partially supported by National Science Foundation (NSF) Grants DMS–1654083 and DMS–1953005, and by the National Aeronautics and Space Administration (80NM0018F0527).

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