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.