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This paper presents a new formulation of consensus filters for parabolic PDEs. Using modal decompositions, the information a given distributed filter transmits to and receives from the remaining networked filters depends on the modal information needed. If a given distributed filter can completely reconstruct a specific mode or modes of the PDE, then it does not need any information from any of the networked filters. Similarly, if a distributed filter cannot adequately reconstruct a given mode, then it receives information from the filter that can completely reconstruct that specific mode. This then presents a connectivity which is based on the information needed. This consensus protocol which is dictated by the information a filter does not have but needs, is essentially a projection of information needed onto the unobservable space. This is demonstrated for a diffusion PDE in 1D and subsequently its abstraction is formulated for Riesz-spectral systems. Numerical studies demonstrate the proposed modal consensus filters.
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Diffusion‐Based Smoothers for Spatial Filtering of Gridded Geophysical Data
Abstract We describe a new way to apply a spatial filter to gridded data from models or observations, focusing on low‐pass filters. The new method is analogous to smoothing via diffusion, and its implementation requires only a discrete Laplacian operator appropriate to the data. The new method can approximate arbitrary filter shapes, including Gaussian filters, and can be extended to spatially varying and anisotropic filters. The new diffusion‐based smoother's properties are illustrated with examples from ocean model data and ocean observational products. An open‐source Python package implementing this algorithm, called gcm‐filters, is currently under development.
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- PAR ID:
- 10449820
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Advances in Modeling Earth Systems
- Volume:
- 13
- Issue:
- 9
- ISSN:
- 1942-2466
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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