Uncertainty in an Adapted Analytic CO₂ Flux Inversion Model (AACO₂FIM) under different spatiotemporal coverages

Abstract. We developed an Adapted Analytic CO₂ Flux Inversion Model (AACO₂FIM) by adapting the Integrated Methane Inversion system for CO₂ applications. We applied AACO₂FIM to examine how closely the regulated solution aligns with predefined emission variability patterns described by target scaling factors (SFs) used to generate pseudo-observations, thereby isolating uncertainty arising solely from cost-function minimization under the quasi-linear assumption. To concurrently assess spatiotemporal coverage impacts, we revised the inversion package to incorporate two different coverage configurations: Orbiting Carbon Observatory-2 (OCO-2) tracks (oco2Trks) and an hourly global grid (FullC).

Inversion performance was quantified by the convergence of inverted SFs toward target SFs under varying prior-target mismatches and observational coverages over an 8-day window following a one-month spinup. The ensemble-mean posterior SFs reproduced the target patterns, with convergence controlled by forward-model sensitivity and observational coverage. Baseline cases showed near-exact convergence, whereas larger prior-target differences led to poorer convergence. The oco2Trks inversions produced a shrunk but highly correlated valid inversion domain relative to FullC, and both configurations showed the largest posterior variability coinciding with the highest forward-model sensitivity. Under oco2Trks (<10 % coverage of FullC), the observation-related cost function term required a weight two orders of magnitude larger than that of FullC to achieve the best fit quality. When OCO-2 observations were used as a constraint, the inverted SF variability generally matched the bias patterns between forward-modeled concentrations and OCO-2 measurements.