| 20 Aug 2026
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.
This study by Rong et al. conducted sensitivity test and uncertainty analysis to test the influence on CO2 emision inversions by using an Adapted Analytic CO₂ Flux Inversion Model (AACO₂FIM), this study is useful considering more inversion models are needed to derive global/regional atmospheric inversion flux. But the recent version lacks more detailed description especially for models improvement and setups, besides, the setups of uncertainty test is hard to follow, and it reads more like technical paper. Some revisions are needed before this MS is recommanded for publication.
Some comments are list below:
In the abstract, it should be introduced here what’s new or revised for the Adapted Analytic CO₂ Flux Inversion Model (AACO₂FIM) model that was used to derive CO2 inversion flux in this study. From line 7-12, it reads like only observation CO2 concentration was different, or just CH4 was replaced with CO2 in “Integrated Methane Inversion system” and only sensitivity test was conducted? but in the main text, it sounds like some modifications have been added in the model
Line 12, what does “an hourly global grid (FullC)” mean? Hourly scaling factors on prior CO2 flux at grid cell? Or others?
In introduction section, line 23-56, “carbon-flux” or carbon were frequently used, considering the authors only focused on CO2 flux inversion, it should be quickly moved to CO2 instead of carbon (containing atmospheric CO2 CH4 or dissolved CO2 CH4 in water or soil …), and the nature of the CO2 cycle can be different with CH4 cycle, regarding the sentence of “significant uncertainties persist due to the highly complex nature of the carbon cycle”.
Line 32-34, “Regional models need coarser-grid global inversions for the same time frames to be readily available, highlighting the need for long-term maintenance of both global and regional models chosen by the local community.” But most of regional/local inversion models used output from global models, which is freely available to use and do not need the researchers to independently run or maintain at global scales.
Line 42, “and coefficient γ adjusts the relative weight of the two terms”, the use of different values of γ can bring significantly bias to posterior flux, and how to define the γ for other users, normally use the value of 1 to define equal weight between term-1 and 2?
Line 44, “In term-1, the SF covariance matrix is scaled by the prior error (expressed as a percentage)”, it seems term-1 is not expressed as % in this equation.
The Jacobian matrix is the quantitative relationship between emissions and concentration, which is driven by atmospheric transport models. Here “between the emission SF and the concentration fields” maybe it’s better to change with “between the emission(prior or posterior) and the concentration fields”?
Line 57, “In this study, we replaced methane (CH₄) with carbon dioxide (CO₂) to perform inversions using the Integrated Methane”, the CO2 can be much diurnally varied than CH4, i.e. diurnal anthropogenic CO2 emissions and biological CO2 flux(can be negative in midday and positive at night), whether these factors are considered in the default/revised model?
Line 58, “Besides model development”, what development was conducted here? and I think it’s main highlight of this study for model development instead of following sensitivity test of “the paper aims to assess uncertainty in the inverted emission scaling factor (SF) under both full global coverage (5° longitude × 4° latitude) and the Orbiting Carbon Observatory-2 (OCO-2) coverage.”
Line 76 “here they are applied to optimize a 2D emission field and a 3D concentration field (Meirink et al., 2008).” The inversion was applied to optimize a 2D emission field, and the GEOS-Chem model use the “optimize a 2D emission field” to generate “a 3D concentration field”, the original description reads like Variational methods was also applied to derive a 3D concentration field.
Line 87, “Nonetheless, we chose not to apply the aggregation routine to reduce the number of state vector elements for several reasons. First, aggregation can introduce errors”, it’s known that aggregation error will lead to large bias for emission inversion, and what is the aggregation error by using “73 longitudes × 46 latitudes”? it’s also coarse related to 0.5 o or 1o
Line 92-93, “Observation and transport-related concentration errors were set at 4.0 ppm and 1.0 ppm,
respectively, and the prior uncertainty of 𝐱𝐚 was set to 50%,”, where does these uncertainty extents come from? Please add references or reasons.
Line 144, at global scale for anthropogenic CO2 emissions, the “gas flaring, shipping, and aviation” is relatively small when compared with industrial emission sources, but it seems the authors illustrated too much on gas flaring, shipping, and aviation from line 147 to 159, instead of main anthropogenic categories. I do not think the emission inversion can constrain gas flaring, shipping, and aviation emissions when other components are much larger i.e. ocean flux, main anthropogenic CO2 emissions and biological CO2 flux.
The same comments on 160-163, “Surface correction adjusts emissions to remove CO2 produced by oxidation of other emitted species 160 (e.g., CH4, isoprene, monoterpenes). CH4 sources include 2004 monthly-mean wetland emissions and annual averages for livestock, landfills, rice,and other natural sources (e.g., termites). Isoprene (C5H8) and monoterpenes (C10H16) are tree-emitted biogenic volatile organic compound (BVOCs) (Hantson et al., 2017) that can oxidize to CO2. These” please remember the main sources/sinks of CO2, the authors have illustrated too much that is not important or even have ignorable influence on CO2 emission inversions. I also do not think these above considerations can influence the emission inversion of CO2 from regional to global scales, even small bias on other components (i.e. prior uncertainty, observation coverage, model bias ) can have much larger influence (1000 times) than the settings here.
Line 177, “BBIO_SIB3 refers to a CO2 emission dataset at 3-hourly intervals (2006–2010) derived from the Simple Biosphere Model version 3” the observation and emission constraint period is 2019, but the BBIO_SIB3 is only for 2006-2010? The same question for “residual annual terrestrial exchange (NET_TERR_EXCH),”
Line 192, “3.2. Other data sets” this section lacks the introduction of vertical levels for both satellite-based OCO2 and model simulations, which is important for readers to evaluate
Section 5.3 It’s good to see the γ dependency here, and whether there is any suggestion what value of γ can be chosen for different studies?
Section 6. “below: Fossil fuel emissions from land in the Northern Hemisphere are the largest contributors, typically accounting for over 80% of total emissions at main-emission centers in the Northern Hemisphere; for example, Eastern China can reach 10×10-8 kg/m²/s.”. From my perspective, the comparison of emission flux(Eastern China can reach 10×10-8 kg/m²/s) at coarse spatial resolution is meaningless, because there can be large emission hotspot(i.e. 0.1 o) within the grid cell, the coarse spatial resolution has averaged the large flux values.
Line 463, “applied (SF ≡1.0).”?