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.