Covariance-Informed Ensemble Score Filtering: Embedding Localized Covariance Geometry into Score-Based Transport
Abstract
Background-error covariance models are central to atmospheric data assimilation because they spread partial observational information across space, variables, and dynamically coupled scales. Ensemble and variational methods exploit this covariance geometry efficiently, but their standard analysis formulations are largely built around Gaussian or locally quadratic approximations. Score-based ensemble filtering provides a framework for nonlinear distributional transport, but existing Ensemble Score Filter (EnSF) formulations lack an intrinsic covariance-mediated pathway for propagating likelihood information from observed to unobserved state components. We introduce a covariance-informed ensemble score filter (CI-EnSF) that embeds localized forecast-error covariance geometry directly into the forward diffusion and reverse transport. The proposed forward diffusion is covariance-shaped in standardized state space and becomes isotropic under the corresponding control-variable transformation. This covariance structure continuously propagates observational information from observed to unobserved state components throughout the reverse transport analysis trajectory. Experiments with Lorenz-96 and surface quasi-geostrophic (SQG) dynamics show a clear regime dependence. For linear observations, a well-tuned LETKF is more accurate, while CI-EnSF maintains stable cycling and effective covariance-mediated information propagation. Under strongly nonlinear observations and under climatological initialization, CI-EnSF achieves lower analysis error and greater cycling robustness than Gaussian ensemble benchmarks such as the LETKF, with improvements extending across spatial scales in the nonlinear SQG experiment. These results suggest that the principal benefit of CI-EnSF arises from combining nonlinear distributional transport with the mature covariance geometry used in conventional data assimilation.
Related
- A tool for new Hybrid models: a swift algorithm to calculate the left inverse of a square root of a horizontally localized climatological ensemble covariance matrix
- Empirically informed AHP-FR modeling for multi-hazard susceptibility mapping in a mountainous transport corridors
- Ground roll suppression based on the synchrosqueezed wavelet transform and local adaptive subtraction filtering
- UAV close-range photogrammetry combined with adaptive octree-based point cloud filtering for rock joint extraction of open-pit mine slopes
- Modified Corn Straw Hydrogel Adsorbent Fabricated via Embedding for Removing Cu2+ and Pb2+ from Wastewater
BibTeX
@misc{liang2026covarianceinformed,
title = {{Covariance-Informed Ensemble Score Filtering: Embedding Localized Covariance Geometry into Score-Based Transport}},
author = {Siming Liang and Peter Jan van Leeuwen and Hristo G. Chipilski and Zezhong Zhang and Feng Bao and Guannan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32148},
eprint = {2610.32148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32148},
}
RIS
TY - UNPB
TI - Covariance-Informed Ensemble Score Filtering: Embedding Localized Covariance Geometry into Score-Based Transport
AU - Siming Liang
AU - Peter Jan van Leeuwen
AU - Hristo G. Chipilski
AU - Zezhong Zhang
AU - Feng Bao
AU - Guannan Zhang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32148
UR - https://arxiv.org/abs/2610.32148
AB - Background-error covariance models are central to atmospheric data assimilation because they spread partial observational information across space, variables, and dynamically coupled scales. Ensemble and variational methods exploit this covariance geometry efficiently, but their standard analysis formulations are largely built around Gaussian or locally quadratic approximations. Score-based ensemble filtering provides a framework for nonlinear distributional transport, but existing Ensemble Score Filter (EnSF) formulations lack an intrinsic covariance-mediated pathway for propagating likelihood information from observed to unobserved state components. We introduce a covariance-informed ensemble score filter (CI-EnSF) that embeds localized forecast-error covariance geometry directly into the forward diffusion and reverse transport. The proposed forward diffusion is covariance-shaped in standardized state space and becomes isotropic under the corresponding control-variable transformation. This covariance structure continuously propagates observational information from observed to unobserved state components throughout the reverse transport analysis trajectory. Experiments with Lorenz-96 and surface quasi-geostrophic (SQG) dynamics show a clear regime dependence. For linear observations, a well-tuned LETKF is more accurate, while CI-EnSF maintains stable cycling and effective covariance-mediated information propagation. Under strongly nonlinear observations and under climatological initialization, CI-EnSF achieves lower analysis error and greater cycling robustness than Gaussian ensemble benchmarks such as the LETKF, with improvements extending across spatial scales in the nonlinear SQG experiment. These results suggest that the principal benefit of CI-EnSF arises from combining nonlinear distributional transport with the mature covariance geometry used in conventional data assimilation.
ER -