the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Feb 2026
Investigating Information Transfer in CO2 Flux Inversions: An Analysis of Ensemble Kalman Filter Based on Monte Carlo Simulations
Abstract. Top-down atmospheric CO2 inversions are essential for estimating surface carbon fluxes, yet significant inter-system discrepancies highlight an incomplete understanding of how observational information is transferred to flux estimates. This study introduces a diagnostic strategy to explicitly investigate this information transfer, primarily in an Ensemble Kalman Filter (EnKF) system, with a comparative analysis of 4D-Var. Using Monte Carlo simulations, we analyze the spatial and temporal correlation patterns between CO2 concentrations and fluxes, which play a crucial role in the inversion process by tracing information flow via the influence matrix. Our results reveal that these correlation scales are dictated by the autocorrelation structures of the fluxes themselves. We identify a resonance-like effect wherein correlated fluxes amplify concentration-flux correlations, while uncorrelated fluxes suppress them. The absence of this suppression for prescribed fluxes (e.g., anthropogenic emissions) can cause systematic signal misattribution. We further demonstrate that 4D-Var relies also heavily on flux autocorrelations due to its cost function’s localized gradient. In both methods, the prior’s critical role is mediated through the transitivity of strong autocorrelations. This process-oriented perspective offers mechanistic insights for reconciling inversion results, optimizing observing networks, and strengthening carbon budget assessments.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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Supplement
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(13870 KB) - Metadata XML
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Supplement
(15407 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
- RC1: 'Comment on egusphere-2026-615', Anonymous Referee #1, 02 Mar 2026
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RC2: 'Comment on egusphere-2026-615', Anonymous Referee #2, 10 Mar 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-615/egusphere-2026-615-RC2-supplement.pdf
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AC1: 'Comment on egusphere-2026-615', Ying Li, 26 Apr 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-615/egusphere-2026-615-AC1-supplement.pdf
Peer review completion
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2026-615', Anonymous Referee #1, 02 Mar 2026
The study addresses a critical knowledge gap in top-down atmospheric inversions: the internal “information transfer” mechanism by which pointwise observations are translated into flux estimates. This paper introduces a paradigm shift in understanding atmospheric CO2 inversions by moving beyond the traditional view of the prior covariance matrix B as a static statistical assumption. While the community has long recognized that B is important, this study is the first to mechanistically dissect how B fundamentally governs the spatial resolution, detection sensitivity, and cross-contamination risks of the entire inversion system, using a perturbation-response strategy with high-resolution 500-member simulations in the Ensemble Kalman Filter (EnKF) framework. It explained how correlated and uncorrelated flux components, respectively, amplify or suppress observational influence. The paper is generally well structured and clearly written. I recommend publication after minor revisions addressing the points below.
1. The study relies on a 500-member ensemble to minimize noise in remote areas. Is 500 members the “convergence point” where spurious correlations become negligible for the 27km resolution used?
2. Table 1: In the “Perturbation variance” column, “40% of mean” is used. Ensure it is clear whether this refers to the standard deviation or the variance itself.
3. In Section 3.1.1 (Line 222), it is mentioned that negative correlations occasionally arise and may be attributed to “negative diffusivity”. Please discuss briefly the effects on the Kalman gain calculation.
4. It is suggested that following observation-based short correlation lengths (e.g., <100 km) is not recommended, for sparse observation networks. Please clarify if the “600 km” recommendation is specific to the East Asian domain or a general rule of thumb for any region with similar station density? Furthermore, some emphasis is needed to avoid interpreting this as an observationally derived or physically “true” correlation length.
5. The comparison between EnKF and 4D-Var in the discussion is entirely theoretical. Without running an actual 4D-Var experiment, claiming “essential equivalence” is a stretch.
6.Some terminology (e.g., “information transfer”, “resonance”) is physically intuitive but metaphorical. Consider briefly restating these concepts in strictly statistical terms when first introduced.
Citation: https://doi.org/10.5194/egusphere-2026-615-RC1 -
RC2: 'Comment on egusphere-2026-615', Anonymous Referee #2, 10 Mar 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-615/egusphere-2026-615-RC2-supplement.pdf
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AC1: 'Comment on egusphere-2026-615', Ying Li, 26 Apr 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-615/egusphere-2026-615-AC1-supplement.pdf
Peer review completion
Journal article(s) based on this preprint
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Shidong Fan
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(13870 KB) - Metadata XML
-
Supplement
(15407 KB) - BibTeX
- EndNote
- Final revised paper
The study addresses a critical knowledge gap in top-down atmospheric inversions: the internal “information transfer” mechanism by which pointwise observations are translated into flux estimates. This paper introduces a paradigm shift in understanding atmospheric CO2 inversions by moving beyond the traditional view of the prior covariance matrix B as a static statistical assumption. While the community has long recognized that B is important, this study is the first to mechanistically dissect how B fundamentally governs the spatial resolution, detection sensitivity, and cross-contamination risks of the entire inversion system, using a perturbation-response strategy with high-resolution 500-member simulations in the Ensemble Kalman Filter (EnKF) framework. It explained how correlated and uncorrelated flux components, respectively, amplify or suppress observational influence. The paper is generally well structured and clearly written. I recommend publication after minor revisions addressing the points below.
1. The study relies on a 500-member ensemble to minimize noise in remote areas. Is 500 members the “convergence point” where spurious correlations become negligible for the 27km resolution used?
2. Table 1: In the “Perturbation variance” column, “40% of mean” is used. Ensure it is clear whether this refers to the standard deviation or the variance itself.
3. In Section 3.1.1 (Line 222), it is mentioned that negative correlations occasionally arise and may be attributed to “negative diffusivity”. Please discuss briefly the effects on the Kalman gain calculation.
4. It is suggested that following observation-based short correlation lengths (e.g., <100 km) is not recommended, for sparse observation networks. Please clarify if the “600 km” recommendation is specific to the East Asian domain or a general rule of thumb for any region with similar station density? Furthermore, some emphasis is needed to avoid interpreting this as an observationally derived or physically “true” correlation length.
5. The comparison between EnKF and 4D-Var in the discussion is entirely theoretical. Without running an actual 4D-Var experiment, claiming “essential equivalence” is a stretch.
6.Some terminology (e.g., “information transfer”, “resonance”) is physically intuitive but metaphorical. Consider briefly restating these concepts in strictly statistical terms when first introduced.