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 fundamentally set by the prescribed autocorrelation structure of the prior fluxes, rather than by atmospheric transport processes alone. 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. Simplified observing system simulation experiments corroborate these diagnostic findings: under the current sparse surface network in East Asia, a relatively longer correlation length (e.g., 600 km) is better than a short length (e.g., 100 km). This process-oriented perspective offers practically useful mechanistic insights for reconciling inversion results, optimizing observing networks, and strengthening carbon budget assessments.
Fan et al. (Wed,) studied this question.