Reduction in Earth’s carbon budget imbalance

Domain: earth_science
Published: 2025-07-24
Editorial outcome: minor_revision

Abstract
The Global Carbon Project (GCP) compiles an updated global carbon budget each year, synthesizing state-of-the-art estimates of anthropogenic CO2 emissions, land and ocean sinks, and the atmospheric CO2 growth rate. The residual between these terms, referred to as the global carbon budget imbalance, reflects the aggregate inaccuracies of the individual component estimates. Growth rates derived from marine boundary layer (MBL) surface flask mixing ratio observations are assumed to be highly accurate. Hence, land and ocean sink estimates from process models are viewed as the primary source of the imbalance. Here we show that substantial discrepancies arise when marine boundary layer growth rate estimates are used to represent the whole atmosphere. Correcting for this discrepancy using atmospheric flux inversion estimates reduces the 0.76 petagrams of carbon per year (PgC yr−1) root-mean-square (RMS) imbalance (from the 2023 GCP report) by up to 25%. Further investigation into the imbalance metric between the 2017 and 2023 GCP reports shows a reduction in imbalance resulting from updates to each carbon budget component, leading to a 16% overall reduction. These reductions provide quantitative evidence of improvements in process models and inventory emission estimates, driven by enhanced forcing data and the inclusion of new carbon cycle processes. Overall, we report a 37% reduction in the root-mean-square imbalance, from 0.91 to 0.57 PgC yr−1, between the 2017 and 2023 GCP reports by combining process model and inventory improvements with atmospheric growth rate corrections. Our findings indicate that land and ocean process models are more accurate than previously believed and that the scientific understanding of Earth’s carbon cycle is improving.

Introduction
Accurate quantification of anthropogenic carbon dioxide (CO2) emissions and their redistribution among Earth’s major carbon reservoirs (atmosphere, oceans, and terrestrial biosphere) is essential for tracking mitigation progress, informing climate policy, and projecting future climate trajectories1–3. As global temperatures rise and the impacts of climate change intensify, the scientific community is refining observational and modeling tools to constrain each component of the carbon cycle. The Paris Agreement’s five-year Global Stocktake further heightens this urgency by requiring transparent, robust assessments of carbon sources and sinks to underpin effective policy-making. Yet persistent, poorly understood variability within the natural carbon cycle still hamper the verification of reported emission reductions under international accords.

Over the past decade, researchers have addressed these shortcomings by acquiring higher-quality observations and activity data, expanding model ensembles, refining parameterizations, and incorporating previously omitted processes—such as cement carbonation and coupled nitrogen–phosphorus dynamics—into land and ocean carbon models4–7. These advances, which we collectively term bottom-up improvements, improve the process models (land and ocean uptake) and inventories (anthropogenic emissions) that underpin contemporary carbon budgets. Although such improvements should, in principle, reduce component-level errors, quantitative evidence of an overall gain in accuracy remains elusive.

CO2 is emitted into the atmosphere due to fossil fuel combustion, industrial processes, and land-use changes. Natural sinks partially offset these emissions with ~25% uptake by oceans and 30% uptake by terrestrial ecosystems, with the remaining 45% accumulating in the atmosphere7. On a global scale, a mass balance exists between annual emissions, sinks, and the CO2 annual growth rate in the atmosphere. The residual imbalance, B I, quantifies our inability to close the budget of fluxes across the Earth’s carbon cycle pools:

B I = E F + E L − S O − S L − S C − G A (1)

All quantities on the equation’s right-hand side denote the component flux estimates in petagram carbon per year (PgC yr−1). E F represents fossil fuel and industrial process emissions, E L denotes land-use change emissions, S O and S L are the oceanic and land uptake, respectively, and S C symbolizes cement carbonation5. G A denotes the atmospheric growth rate of CO2 8, caused by differences between emissions and sinks. The imbalance quantifies the sum of errors in all flux components on the right-hand side, serving as a metric for data imperfections and gaps in our understanding of the contemporary carbon cycle.

Growth rates derived from marine boundary layer (MBL) surface flask (sometimes referred to as in situ measurements) mixing ratio measurements are typically considered highly accurate. Consequently, the budget imbalance has often been attributed primarily to inaccuracies in other components, particularly land and ocean sinks3,7–9. However, the atmospheric growth rate is not directly measured in units of mass change (PgC yr−1) but is derived from mixing ratio measurement changes (ppm yr−1) assuming instantaneous mixing of the fluxes throughout the whole atmosphere. Although surface flask measurements of atmospheric mixing ratios are very accurate and precise, errors are introduced in estimating the whole-atmosphere growth rate due to the sparsity of the MBL surface flask measurement data and methodological assumptions7,10.

Here, we investigate the evolution of collective accuracy using the carbon-budget imbalance reported annually by the Global Carbon Project (GCP). We also quantify the error introduced when the MBL CO2 growth rate is used as a proxy for the whole-atmosphere growth rate. We find that accounting for the discrepancy between MBL and whole-atmosphere growth rates markedly reduces the root-mean-square (RMS) of the annual imbalance time series relative to the values reported in recent GCP Carbon Budget assessments. We further assess the impact of updates to individual budget components between the 2017 and 2023 GCP reports, demonstrating that the overall accuracy of Earth’s carbon-budget components has improved over this period.

Results
Whole-atmosphere growth rate correction
The GCP uses growth rate estimates from the US National Oceanic and Atmospheric Administration (NOAA) Global Monitoring Laboratory, calculated from CO2 mixing ratio observations of well-mixed background air at MBL surface measurement stations. These growth rate estimates serve as the benchmark for most scientific and agency assessments. NOAA estimates the growth rate by smoothing data over time for each MBL station and then averaging it across latitude bands11. GCP converts NOAA growth rate (ppm yr−1) values into the whole-atmosphere mass change (PgC yr−1) using a conversion factor12 of 2.124 PgC ppm−1. This conversion assumes instantaneous mixing—an approximation that introduces errors from finite and varying atmospheric transport timescales and sparse spatiotemporal sampling of MBL observations10. Although the troposphere, which contains about 80% of atmospheric molecules, mixes well within a year, the stratosphere exchanges air slowly with the troposphere over a period ranging from 2–4 years13,14.

Observed stratospheric CO2 mixing ratios are 3–5 ppm lower than tropospheric values, reflecting slow stratosphere–troposphere exchange14,15. Consequently, surface-driven CO2 increases lag in the stratosphere, creating a deficit relative to tropospheric values (see Methods). The GCP acknowledges that using a constant conversion factor of 2.124 PgC ppm−1, an approximation that assumes instantaneous whole-atmosphere mixing, introduces a non-negligible source of uncertainty7. The error introduced by using constant conversion factors to calculate whole-atmosphere growth rates from MBL data can be broken into two errors: troposphere-sampling error and stratosphere-troposphere exchange (STE) error. The troposphere-sampling error reflects a representativeness error due to the sparsity of MBL sites.

To account for the MBL growth rate discrepancies, we compute the whole-atmosphere CO2 growth rate using two atmospheric flux inversion models: Copernicus Atmosphere Monitoring Service (CAMS)16 and Jena CarboScope (CS)17. These models optimize emissions and sinks from the oceans and land surfaces to match mixing ratio measurements at surface sites (including many MBL sites) while incorporating STE and additional atmospheric transport and sampling effects through numerical simulations nudged to meteorological reanalysis data (see Methods). Thus, the global integral of the annual net CO2 optimized surface fluxes provides the whole-atmospheric growth rate. Alternatively, to isolate the impact of STE, we employ a simple two-box model representing the troposphere and stratosphere, assuming a 2 year STE timescale (see Methods). This model assumes MBL-derived rates perfectly represent tropospheric growth, isolating only the STE error. The Inverse models (CAMS and Jena CS) account for both troposphere sampling and STE-related errors, while the box model only accounts for the STE-related errors. Note that neither the inversions nor the box models are free of errors. However, we hypothesize that the improvements from accounting for large-scale transport effects like STE and sampling should be more significant, overall leading to a better growth rate estimate and thus reducing the imbalance.

Figure 1 presents various growth rate estimates alongside the corresponding changes in the imbalance reported by GCP in 2023. The long-term mean imbalance does not change after our corrections, but the influence of those corrections is strong during years with pronounced inter-annual variability. This is expected because the STE adjustment acts as a lagged temporal smoother on MBL growth rates when converting them to whole-atmosphere values (see Methods). Because its magnitude depends on the past values of tropospheric mixing ratios, it damps extremes and nudges annual values toward the mean (see Supplementary Section 1).

Two illustrative cases of the impact of growth rate correction are the peak imbalance of +1.7 PgC yr−1 in 1991 and the trough imbalance of −1.5 PgC yr−1 in 1998. These years coincide with the Mount Pinatubo eruption and a strong El Niño, respectively. These events induced sharp perturbations to the carbon cycle and have historically challenged bottom-up models. For 1991, the high imbalance has been linked to an underestimation of the land-sink response, likely due to a lack of representation of diffuse-radiation effects following the volcanic aerosol injection18,19. Our revised growth-rate estimate raises the previously low MBL value in 1991, and lowers the high value in 1998, producing a small but meaningful reduction in both imbalance extremes (CAMS imbalance for 1991 = +1.17 PgC yr−1 and 1998 = −0.87 PgC yr−1). While these years remain prominent anomalies even after the correction, the diminished residual suggests that process models may be more skillful against such climatic shocks than previously assumed.

The annually varying corrections to the growth rate required to account for the STE effect cannot be captured by a single, time-invariant conversion factor. In particular, the widely used 2.124 PgC ppm−1 factor12, derived under the assumptions of a fixed atmospheric mass and uniform, instantaneous mixing, systematically over-estimates high MBL growth years and under-estimates low MBL growth years (see Supplementary Section 1), biasing flux estimates wherever growth rates deviate from the long-term average.

The RMS imbalance in the GCP 2023 report is 0.76 PgC yr−1 for the period of 1985–2016. Applying the box-model-based STE correction reduces the RMS imbalance by 11% (from 0.76 PgC yr−1) to 0.67 PgC yr−1. The atmospheric inversion corrections from Jena CS and CAMS reduce the RMS imbalance by 24% and 25%, leading to imbalances of 0.58 PgC yr−1 for Jena CS and 0.57 PgC yr−1 for CAMS. A stronger improvement from inversions compared to box model is expected because inversions account for additional atmospheric transport dynamics and atmospheric sampling effects.

The whole-atmosphere corrections are significant relative to the budget imbalance, which aggregates the errors of all components. The growth rate correction terms themselves have RMS magnitudes of 0.16, 0.36, and 0.37 PgC yr−1 for the box-model, CAMS, and Jena CS estimates, respectively. For context, the largest of these correction RMS values is 49% of the GCP-2023 RMS imbalance of 0.76 PgC yr−1. These improvements demonstrate that uncertainties in the atmospheric growth rate account for a substantial share of the total imbalance error. The large improvement in the imbalance due to the growth rate corrections also shows that bottom-up models are more accurate than previously perceived, based on the assumption that the imbalance was primarily caused by errors in these bottom-up models.

Improvements in process models and inventories
The GCP carbon budget estimates are updated annually to incorporate data re-evaluation and developments in process understanding, and the use of larger model ensembles7. Consequently, inaccuracies in budget components and the resulting imbalance are expected to decrease over time. We analyze changes in budget components between the 2017 and 2023 GCP reports to test this hypothesis. To identify the components causing the imbalance RMS reduction, we calculate an imbalance due to a component change between the 2017 and 2023 reports (see Methods), leaving other components unchanged.

Figure 2 shows the time series of carbon-flux components and the MBL CO2 growth rate from the 2017 and 2023 GCP reports7,8. All components exhibit changes between the 2017 and 2023 estimates, with the largest RMS differences observed in the land-use change (0.23 PgC yr−1), the land sink (0.25 PgC yr−1), and the ocean sink (0.22 PgC yr−1). Fossil-fuel emissions and the MBL growth rate also change notably, with RMS differences of 0.13 PgC yr−1 and 0.07 PgC yr−1, respectively.

A few reasons for the changes in the component estimates are as follows: The GCP ocean sink estimates changed between the 2017 and 2023 reports, with GCP 2023 using a combination of process models and data-driven (fCO2-based20) approaches (as shown in Fig. 2). NOAA MBL flask measurements were recalibrated to the 2019 WMO scale and the derived growth-rate estimates from these recalibrated mixing ratio measurement data were first used in the GCP 2021 report6,21. The growth rates can also change due to stabilization-latency effects in the NOAA MBL time series, which introduce a latency before convergence to the final growth rates levels (see Figure 9 of ref. 10). Beginning with the 2020 GCP report22, the cement-carbonation sink was included after its substantial role in atmospheric CO2 removal was recognized5. Between the 2017 report, in which it was not reported (i.e., assumed zero), and the 2023 report, the RMS difference in this sink is 0.11 PgC yr−1, underscoring its significance.

Figure 3 presents the imbalance RMS change between the two reports. The 16% reduction in the imbalance (from 0.91 to 0.76 PgC yr−1) indicates a significant decrease in the sum of errors. This reduction in imbalance is comparable to the whole-atmospheric growth rate correction when applied to the 2017 GCP report, which results in an RMS imbalance of 0.77 PgC yr−1 when using the CAMS flux inversion (see Supplementary Fig. 1). Note that applying the growth rate correction yields a smaller percentage reduction for the 2017 GCP report (a 15% drop from a 0.91 PgC yr−1 baseline) than for the 2023 GCP report (a 25% drop from a 0.76 PgC yr−1 baseline). This occurs because the total error variance, which mostly determines the RMS of the budget imbalance, is effectively the quadrature sum of variances from multiple error sources (error variances combine in quadrature if independent). Consequently, while a growth rate correction reduces the variance component associated with the growth rate, its fractional impact on the overall RMS is smaller when the initial RMS imbalance (and thus the total underlying error variance) is large due to other substantial uncorrected error components. Therefore, as bottom-up emission and sink estimates continue to improve, growth rate errors will account for an increasingly dominant share of the residual budget imbalance, underscoring the need for further refinement of observational and modeling constraints on global CO2 growth rates.

The colored crosses (and the “+“ signs) in Fig. 3 show the RMS imbalance impact due to different component updates (see Methods). We find that all carbon budget component updates lead to an imbalance reduction. This shows that the component estimates have individually improved, and the imbalance improvement is not due to a compensatory effect where the improvement of one component offsets the worsening of another.

The causes of improving estimates or error reduction can be broken into four broad effects: (1) standard error reduction due to an increase in ensemble size, (2) improvement in process representations, (3) forcing data improvement, and (4) model resolution improvement. The process level improvements stem from numerous individual advancements (see Table 3 of Friedlingstein et al.7, Table S1 of Le Quéré et al.8, and Sitch et al.4). Fossil fuel emission estimates have likely improved due to additional effect of the availability of better emission activity data from emerging economies23.

The carbon budget imbalance analysis presented here can serve as a diagnostic for attributing overall budget improvements to specific component changes. For instance, substituting land sink estimates in the GCP 2023 budget with those from only the six models accounting for diffuse radiation effects yields an RMS imbalance of 0.72 PgC yr−1, a notable reduction from the 0.80 PgC yr−1 obtained using the multi-model mean from the fourteen models omitting this process (all other GCP 2023 components held constant). We also test whether increases in model ensemble sizes are a driver of the observed imbalance reduction between the 2017 and 2023 GCP reports, as larger ensembles might theoretically reduce the standard error of the multi-model mean. However, our tests indicate that, for both land and ocean sinks, expanding the ensemble size does not, in itself, lead to a reduction in the budget imbalance. The RMS imbalance for GCP 2023 using only the land sink models present in the 2017 ensemble is 0.758 PgC yr−1, closely aligned with the 0.762 PgC yr−1 RMS imbalance using the full GCP 2023 land model ensemble; a similar outcome is observed for ocean sink estimates. While a complete imbalance attribution of all changes between the 2017 and 2023 GCP reports is not undertaken here, the budget imbalance analysis presented here can be utilized in future investigations to quantify the influence of individual modifications.

We also perform a suite of sensitivity tests (see Supplementary Section 2) to check that the declining RMS budget imbalance reported here reflects genuine component estimate improvements. We find consistent imbalance reductions across three independent periods (1960–1984, 1985–2004, and 2005–2016), further corroborating that these advances arise from better forcing data and refined process representations. In Supplementary Section 3, we discuss how the carbon budget imbalance (the net effect of all actual component errors) relates to the GCP-reported uncertainty estimates for these components.

Methods
We analyze the global carbon budget imbalance from 1985 through 2016. The primary baseline budgets are taken from the GCP 20178 and GCP 20237 reports. The analysis starts in 1985. For inversion-based growth rates, this allows for a sufficient spin-up period (e.g., CAMS begins in 1979), accounting for typical stratosphere-troposphere exchange (STE) timescales of 2–4 years. We estimate the whole-atmosphere growth rate from a box model and as the global, annual integral of the net surface CO2 fluxes optimized by the CAMS and Jena CS atmospheric inversion systems. The whole-atmosphere growth rate is theoretically equal to the net fluxes, which are mainly due to surface emissions and sinks, except for a minor contribution from CO oxidation.

Atmospheric inversions
CAMS. The CO2 atmospheric inversion of the operational Copernicus Atmosphere Monitoring Service (CAMS) assimilates atmospheric mixing ratio observations (surface air-sample measurements) in the LMDz atmospheric transport model. During the assimilation process, the LMDz model is inverted in a variational framework to yield statistically optimal CO2 surface emissions and sinks at weekly and grid-point scales. For CAMS version v22r1 used here, available surface air-sample measurements at 159 sites between January 1979 and March 2023 were assimilated; the model resolution was 79 layers in the vertical, 1.27° in latitude and 2.5° in longitude. More details on the inversion system can be found in Chevallier et al.16, and references therein.

Jena CarboScope (CS). Atmospheric tracer transport in the Jena CarboScope inversions is simulated by the TM3 atmospheric chemical transport model at a resolution of ~4° in latitude by 5° in longitude, with 19 vertical layers driven by meteorological fields from the NCEP (National Centers for Environmental Prediction) reanalysis. The run “s76_v2023” of the Jena CarboScope employed here uses 8 atmospheric CO2 measurement sites that span its estimation period from 1976 to 2022. CarboScope uses a fossil-fuel CO2 emission prior from GridFED, an ocean CO2 exchange prior based on the interpolation of SOCAT pCO2 data. In contrast to the CarboScope run used in the GCP 2023 report, the run s76_v2023 used here has explicit interannual degrees of freedom (i.e., no regression against predictor variables). For more details on the setup, see Appendix A of17, with slight updates described on the website of CarboScope24.

Although the two inversions differ in aspects such as the number of assimilated measurement-site networks and vertical model resolution, they both incorporate data from a common core MBL network. This MBL network provides the primary observational constraint for estimating the annual global CO2 growth rate in these inversions. Both inversions are designed to track the global CO2 growth rate while also capturing key transport processes, including stratosphere-troposphere exchange.

To demonstrate that the inversions not only reproduce the MBL observations but also capture large-scale transport effects—such as the slow stratosphere–troposphere exchange—we compare the CAMS-inversion–simulated CO2 mole fractions against NOAA MBL observations (Supplementary Fig. 2)25 and AirCore profiles (Supplementary Fig. 3)26. Our analysis shows that the optimized CAMS fields reproduce the MBL mixing ratio measurements and resolve the stratosphere–troposphere CO2 mixing ratio gradient observed by AirCore.

Two-box model
To isolate the impact of stratosphere-troposphere exchange (STE) on the inferred whole-atmosphere CO2 growth rate, we employ a two-box model representing the troposphere and stratosphere. This model simulates the exchange of CO2 between these two reservoirs, where air is exchanged carrying the CO2 mixing ratio of its box of origin. The net rate of CO2 mixing ratio change in each box is driven by the difference in their respective CO2 mixing ratios, modulated by a characteristic exchange timescale.

Let C tropo(t) and C strato(t) denote the mean CO2 mixing ratios (in ppm) in the troposphere and stratosphere, respectively, at time t. We use K atm = 2.124 PgC ppm−1 as the conversion factor representing the CO2 mass required to raise the mean atmospheric mixing ratio by 1 ppm12. The troposphere is assumed to contain a fraction f tropo = 0.8 of the total atmospheric air mass, and the stratosphere a fraction f strato = 0.213.

The model dynamics are described by the following system of ordinary differential equations:

dC strato(t) / dt = (C tropo(t) − C strato(t)) / τ (2)

dC tropo(t) / dt = (E net(t) / (f tropo * K atm)) − (f strato * (C tropo(t) − C strato(t)) / (f tropo * τ)) (3)

Here, τ is the characteristic exchange timescale between the two boxes, representing the e-folding time for stratospheric mixing ratio adjustment (i.e., the stratospheric air residence time). E net(t) (in PgC yr−1) denotes the net CO2 flux (from surface sources/sinks and atmospheric chemical production) entering the troposphere. The factor f strato / f tropo in Eq. 3 ensures CO2 mass conservation during exchange between the reservoirs with differing air masses.

Our objective is to estimate E net(t), which serves as the box-model derived whole-atmosphere CO2 growth rate (G box A), based on observed tropospheric CO2 changes. Rearranging Eq. 3 yields:

E net(t) = f tropo * K atm * [dC tropo(t) / dt + (f strato / f tropo) * (C tropo(t) − C strato(t)) / τ] (4)

We first estimate the time series of tropospheric CO2 mixing ratio C tropo(t) using the annual CO2 growth rates from the GCP 2023 report as dC tropo(t) / dt and the initial condition C tropo(0) = 280 ppm in the year 1750 (t=0). The stratospheric CO2 mixing ratio can also be expressed analytically as:

C strato(t) = e−t/τ * C strato(0) + (1/τ) * ∫ (from 0 to t) C tropo(s) ds (5)

C strato(t) is then obtained by numerically integrating Eq. 5 initialized with C strato(0) = 280 ppm. This formulation shows that C strato(t) depends on its initial state and past tropospheric mixing ratios. It is an exponentially weighted moving average of tropospheric mixing ratios with characteristic timescale τ. This “stratospheric memory” effect imposes a lagged temporal smoothing when inferring whole-atmosphere growth rate from tropospheric CO2 changes. With C tropo(t), its derivative dC tropo(t) / dt, and the calculated C strato(t) (using scipy.integrate module in Python for Eq. 5), we compute E net(t) using Eq. 4.

A STE time τ of 2 years was implemented in the box model. The simulated CO2 mixing ratios and the resulting stratosphere-troposphere mixing ratio difference from this box model are shown in Supplementary Fig. 4. This simulated difference aligns well with observed differences from AirCore profiles and CAMS 3D mole fraction field data. Sensitivity tests assessing the influence of varying τ on the budget imbalance reduction are presented in Supplementary Table 1.

Individual component’s imbalance impact
To isolate the impact of updates to an individual carbon budget component C on the overall budget imbalance, we recalculate the imbalance time series by starting with the budget imbalance from the 2017 GCP report (B IM,17) and effectively substitute the 2017 estimate of component C (C 17) with its 2023 estimate (C 23), while keeping all other components at their 2017 values.

The resulting imbalance due to the update in the component C, denoted B IM,C, is calculated as:

B IM,C = B IM,17 + δ C * (C 23 − C 17) (6)

Here, C 17 and C 23 are the multi-model mean estimates for component C from the 2017 and 2023 GCP reports, respectively. The factor δ C is +1 if component C is a source term in Eq. 1 (i.e., fossil emissions E F or land-use change emissions E L). Conversely, δ C is −1 if component C is a sink term (ocean sink S O, land sink S L, cement carbonation S C) or the atmospheric growth rate (G A), assuming these sink/growth values are positive numbers in the component data. The term (C 23 − C 17) represents the change in the estimate of component C between the two reports.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper shows that a better representation of the atmospheric growth rate of CO2 reduces the imbalance of the Earth\ncarbon budget computed annualy by the Global Carbon Project (GCP). GCP uses a simple conversion factor to transform\nNOAA’s estimated growth rate of CO2 (based on marine boundary layer CO2 mixing ratios measurements) into a whole-\natmosphere (troposhere+stratosphere) CO2 mass change.\nThe authors argue that this simple assumption does not correctly take into account the troposhere sampling error (low\nnumber of measuring sites) and supposes that the troposphere and stratosphere mix well within a year, although the\nstratosphere-troposhere exchange (STE) of CO2 happens at longer time scales (2 to 4 years).\nThey use a simple 2-box model to compute the timeseries of STE and 2 inversion models (CAMS and Jena CarboScope) to\ncompute 3 versions of the whole atmosphere growth rates (Ga) and deduce the yearly imbalance of the global carbon cycle\nusing GCP data.\nThese 3 versions of the Ga tend to reduce this imbalance, and in particular the root mean square of the time series of the\nimbalance.\nThe authors deduce from this that the process-based model representing the carbon cycling in the oceans, and on land have\nimproved and that they are not anymore a main source of error in the Earth carbon budget.\nThe paper is very clearly written, presents important and interesting results and I have only minor comments.\nFirst, I would add in the summary and conclusions the importance of the forcing data. The component models are forced with\natmospheric data that play a role in the model accuracy. The authors mention the forcing at some point in the text, but it\nshould be included also in the abstract.\nSecond, there is a discussion on how modellers could fine-tune their models so that the improvement seen is not due to the\nmodel improvement but to fine-tuning. I find this section a bit long and not bringing much to the main message , saying that\nthe imbalance is reduced when calculating the whole atmospheric growth rate in a more precise way. Also, it feels like a\nresponse to a former reviewer. The authors could reformulate in a more positive way.\nNote : the pdf I downloaded doesn’t have any line numbers. It is therefore difficult to describe what should be modified.\np2 1st paragraph : the authors give percentage of uptake of Carbon by the different components – they should add a\nreference\np3 2d paragraph : replace « significantly reduces the root-mean-square (RMS) imbalance .. » by « significantly reduces the\nroot-mean-square (RMS) of the annual imbalance time series »\np4 3rd paragraph : I don’t see how Figure S2 shows that the STE correction on the MBL growth rate serves as a lagged\ntempporal smoother\np6 3rd paragraph : « NOAA MBL growth rate estimates were recalibrated …. GCP 2021 report » weird sentence, rephrase\np 6 paragraph 5 « Fire simulation and suppression » : strange wording : did the author mean « simulation of fire ignition and\nsuppression » ?\np7 Figure 2 caption : land-use change is a positive flux not a negative one !\nP 8 1st paragraph : I don’t see how process modelers could fine tune their model using the temporal average of the residual\nof other carbon budget components. When they run the GCP simulations, they don’t have the results of the other\ncomponents, since these are usually being run at the same time by separate groups.\nP9 last sentence : replace « future climate predictions » by « future climate projections » if the authors think about long term\nclimate simulations (not decadal ones).\nPS2 1.2 : define Cstrato and Ctropo, GMBL\nI’d also want to know a little more on how E(t) is estimated.\nPS2 1.3 C23 and C17 are the men estimates for component C : but estimates of what ?", "reviewer_2": "Key results\nThe key messages from this manuscript are the substantial discrepancies in the marine boundary layer growth rate\nestimates in representing the whole atmosphere. The authors use inversion models to suggest that the MBL-based\nestimates are off. The manuscript also documents a 16% overall reduction in the global carbon budget imbalance\nbetween2017 and 2023 due to improvements in the individual budget component estimates.\nValidity\nWhile I appreciate the alternative approaches to estimating the growth of whole atmosphere CO2 inventory, I did not see any\nevidence that these alternative approaches are more accurate. A reduction in the global budget imbalance, is not in itself\nproof that the alternative estimates are more accurate. I think it is fair to say that these estimates suggest that the reported\nuncertainty on the atmospheric inventory is underestimated, but I would like to see independent proof from observations that\nthese estimates are more accurate.\nSignificance\nIf the authors could demonstrate that the revised inventories are more accurate, that would be a significant improvement to\nthe global carbon budget. The second component of the manuscript that investigates a progressive improvement in the\nuncertainties of the other budget components is certainly interesting, if not terribly surprising. I would hope that the models\nhave improved over the last decade. I suppose this is worth reporting, but I did not find this work to be particularly inspiring or\nnovel.\nData and methodology\nThis manuscript relies heavily on the annual GCP reports. While the GCP provides extensive documentation on the\ncomponents of their analyses, I did not go in and confirm all of the data they compiled. I see no problems with the\nmethodology, but more the interpretation that a different model is inherently better because it reduces the imbalance. One\ncan get a seemingly better answer for the wrong reason. I would feel better with independent observational proof.\nAnalytical approach\nAS described previously, I have concerns over the analytical approach.\nSuggested improvements\nI suggest the authors focus on the larger uncertainties in the atmospheric inventory estimates or find additional observations\nthat support one of the inventory approaches.\nClarity and context\nThe article is well written and clear, although it seems to be making two different points. It is not clear exactly how the\nalternative atmospheric inventory ties to the improved flux estimates in the other parts of the budget. It almost looks like\nneither topic was quite enough for a manuscript, so they stuck both together to have enough for an article.\nReferences\nReferences seem adequate.", "reviewer_3": "Pandey et al present work to better understand the imbalance in the global carbon budget as evaluated through the series of\nbudgets produced by the Global Carbon Project. This work focusses on an unexplored contribution to the imbalance,\nspecifically that due to the representation of the atmospheric growth rate of CO2. While the imbalance is discussed, for\nexample, in Sec 3.9.2 of the 2023 Global Carbon budget paper by Friedlingstein et al. (https://doi.org/10.5194/essd-15-5301-\n2023) the atmospheric term is not covered in that discussion. As such, this paper presents a helpful contribution, given the\nimportance of a high-quality carbon budget for tracking carbon mitigation efforts.\nWhile the results presented appear important to document, I have some concerns about whether the paper, as currently\nstructured, allows the reader to easily assess the importance. My impression is that there has been some attempt to present\nthis as relating to a generic carbon budget, but it is effectively providing analysis of the specific series of carbon budgets\nproduced through the Global Carbon Project. If a reader is unfamiliar with those budgets, I wonder how the paper would read\nwithout that context. For example, it is almost half-way through the abstract before the Global Carbon Project is mentioned. It\nmight be better for the abstract to begin with this information such as ‘Each year the Global Carbon Project collates and\nupdates a global carbon budget to encapsulate state-of-the-art …’ and then introduce the imbalance. Likewise, in the\nintroduction, I think that some/most of paragraph 3 would be better before paragraph 2. I would also suggest that the\nintroduction needs more than the first sentence to provide the rationale for this work – I thought the last paragraph of the\nConclusions provided a stronger ‘why’ than the start of the introduction.\nThe article has two main sections. The first covers the improvement to the atmospheric growth rate. The second part\nexplores whether there have been improvements in other terms in the carbon budget over time, as represented by their\ncontribution to the carbon budget imbalance. The comparative contribution provides useful context for each section, though\nthe analysis is mostly independent across the two main sections.\nOther comments\nP2, final paragraph, line 4: perhaps ‘mixing ratio’ rather than ‘concentration’\nP3, final paragraph, line 6: suggest adding an extra sentence such as ‘Thus the annual net optimised flux provides a direct\nestimate of atmospheric growth rate.’ Also perhaps ‘Alternatively’ instead of ‘Additionally’.\nP3, final paragraph, line 9: suggest moving ‘Inverse models’ sentence to after the following sentence i.e. ‘The box model only addresses … MBL growth rate’ compared with inverse models that account for both ….\nP4, second paragraph, discussion of 1991 and 1998 imbalances. I think this result is overstated given that even with the\nalternate growth rate estimate, these imbalances remain some of the largest. Perhaps rephrase as ‘Our corrections slightly\nincrease the low … and slightly decrease the high … resulting in a small imbalance reduction …’ and ‘possibly more robust\nthan previously assumed.’\nP4, third paragraph, last line. Perhaps ‘as assumed’ rather than ‘as proposed’\nP4, fourth paragraph. It wasn’t clear to me whether it was useful quoting the RMS values for the corrections (i.e. 0.18, 0.36,\n0.37) as I think these just distract from the RMS imbalance which is what the reader needs to focus on.\nP6, paragraph 2. Figure 2 is introduced but not discussed. If it is worth including in the paper then the main features in the\nfigure need to be highlighted for the reader.\nP6, paragraphs 3-5. These paragraphs seem like a missed opportunity. Many reasons are provided for why improvements\nare seen in the budget components but it does not appear as though any of these have been tested, at least in the context\nof this study.\nFor example, the fourth paragraph notes that ensemble size likely reduces standard errors. Given the GCP makes all the\nindividual model data available, is it possible to recalculate the 2023 imbalance using the same ensemble size as 2017 to\ntest this hypothesis?\nSupplementary 2.0.3 discusses recalculating the ocean sink estimate with or without the data-based estimates, so the\nimpact of this change has been quantified but it does not appear to be mentioned in the main text. Was that intended? It\ncould be included in this section.\nThe process representation changes are probably harder to robustly assess due to the smaller numbers of models making\nany given change, but it would be helpful to provide any evidence that the highlighted changes make a difference. For\nexample, do the 5 out of 20 models that account for the diffuse radiation effect give smaller 1991 imbalances than the other\nmodels or than they did in 2017 when the effect wasn’t accounted for?\nP8, first and second paragraphs. Given that the SD results are so close to those for the RMS, I think these paragraphs could\nbe reduced with most of the information just presented in the supplementary material.\nP8, Conclusions, line 3. The 37% decrease combines both the 2017 to 2023 change and the growth rate correction. If\npossible, it might be useful to also apply the growth rate correction to the 2017 dataset to give another measure of the impact\nof the growth rate correction compared to other improvements.\nFigure 1. The means of the timeseries plotted on the right-hand side of the figure are so close together that it is possibly not\nworth including them. In this case the final sentence of the figure caption can be removed.\nFigure 2. It may help the reader if the y-axis range was more similar between components. For example, the differences in\nthe cement sink, land use change and ocean sink are visually exaggerated by the smaller ranges for these components.\nSuggest adding ‘(dashed)’ after 2017 and ‘(solid)’ after 2023 in the figure caption. Is the ocean sink the GCP reported value,\nor the model-only recalculation described in the supplementary 2.0.3?\nFigure 3. Given the single component update calculations are done relative to the 2017 case, perhaps the coloured crosses\nwould be better plotted on the left-hand side of the figure in the GCP 2017 column. If an atmospheric growth rate correction\nwas also done in the 2017 case, additional triangles could also be included in the 2017 column.\nSupplementary material\n1.1.1 and 1.1.2: It is interesting that the two inversions use very different numbers of atmospheric measurement sites. Is this\nworth mentioning in the text? I note that there is no discussion in the text or supplementary about differences in the growth\nrate estimates between the two inversions.\n1.2. It would be helpful to note in this section what exchange time is being used for the analysis in the main paper and in\nFigure S1. Is it 3 years?\n2.0.2, second last sentence is not clear to me. Please explain more clearly how the figure demonstrates these points.\n2.0.3. As noted earlier, this section is not referenced in the main text\n2.0.5 Given the small difference in the SD results compared to the RMS results, the second paragraph and Table S3 are\nprobably not needed.\n2.1 Since I did not notice this referenced in the main text, is it needed in supplementary or should it have been referenced in\nthe main text?\nFigure S2. I found this figure difficult to interpret. Perhaps including some description of the colour scheme for the dots in the\nfigure caption would help."}, "author_response": "We thank the reviewers for their thoughtful and constructive comments. We have\nprovided a detailed point-by-point response to each reviewer’s comment (italics) below,\nand all changes made to the manuscript (in blue text) have been highlighted in blue.\nReviewer #1 (Remarks to the Author):\nReviewer: This paper shows that a better representation of the atmospheric growth rate\nof CO2 reduces the imbalance of the Earth carbon budget computed annualy by the\nGlobal Carbon Project (GCP). GCP uses a simple conversion factor to transform\nNOAA’s estimated growth rate of CO2 (based on marine boundary layer CO2 mixing\nratios measurements) into a whole-atmosphere (troposhere+stratosphere) CO2 mass\nchange.\nThe authors argue that this simple assumption does not correctly take into account the\ntroposhere sampling error (low number of measuring sites) and supposes that the\ntroposphere and stratosphere mix well within a year, although the stratosphere-\ntroposhere exchange (STE) of CO2 happens at longer time scales (2 to 4 years).\nThey use a simple 2-box model to compute the timeseries of STE and 2 inversion\nmodels (CAMS and Jena CarboScope) to compute 3 versions of the whole atmosphere\ngrowth rates (Ga) and deduce the yearly imbalance of the global carbon cycle using\nGCP data.\nThese 3 versions of the Ga tend to reduce this imbalance, and in particular the root\nmean square of the time series of the imbalance.\nThe authors deduce from this that the process-based model representing the carbon\ncycling in the oceans, and on land have improved and that they are not anymore a main\nsource of error in the Earth carbon budget.\nThe paper is very clearly written, presents important and interesting results and I have\nonly minor comments.\nReviewer: First, I would add in the summary and conclusions the importance of the\nforcing data. The component models are forced with atmospheric data that play a role in\nthe model accuracy. The authors mention the forcing at some point in the text, but it\nshould be included also in the abstract.\nResponse: We have added text about the importance of the forcing data in improving\nthe bottom-up models.\nAbstract:\nThese reductions provide quantitative evidence of improvements in process models and\ninventory emission estimates, driven by enhanced forcing data….\nIntroduction:\n\"The improvements in bottom-up models are likely due to the combined effects of\nenhanced meteorological and other forcing data, improved process understanding, and\nincreased model resolution.\nMain text:\nThe improvements in component estimates are primarily driven by improved process\nunderstanding and availability of better forcing and inventory data.\nReviewer: Second, there is a discussion on how modellers could fine-tune their models\nso that the improvement seen is not due to the model improvement but to fine-tuning. I\nfind this section a bit long and not bringing much to the main message, saying that the\nimbalance is reduced when calculating the whole atmospheric growth rate in a more\nprecise way. Also, it feels like a response to a former reviewer. The authors could\nreformulate in a more positive way.\nResponse: We have revised the text to address the reviewer’s concern. The Sensitivity\nTests section has been moved to the Supplementary Information. Here is the revised\ntext in the Supplementary Information:\nProcess models often require adjustment of initial-condition parameters to ensure that\nresiduals among the carbon-flux components are globally consistent over long periods.\nFor example, terrestrial biosphere models may adjust their initial carbon‑pool sizes until\nthe multi‑decadal mean of emissions−ocean sink−MBL growth rate approaches zero.\nCommunity syntheses, such as the GCP, reinforce this coherence through their\nmodel‑selection process; for instance, the GCP accepts only ocean‑sink models that\nreproduce the early‑1990s observational constraint of approximately 2.2± 0.7; PgC/yr\n(Friedlingstein et al. 2023). Consequently, a near‑zero mean imbalance does not imply\nnegligible model error. Rather, the year‑to‑year SD of the imbalance provides a more\nindependent yardstick of model improvement, gauging each component’s ability to\ncapture inter‑annual variability while remaining insensitive to shared mean biases.\nReviewer: Note: the pdf I downloaded doesn’t have any line numbers. It is therefore\ndifficult to describe what should be modified. p2 1st paragraph : the authors give\npercentage of uptake of Carbon by the different components – they should add a\nreference\nResponse: We have added references to the GCP 2023 report.\nReviewer: p3 2d paragraph : replace « significantly reduces the root-mean-square\n(RMS) imbalance .. » by « significantly reduces the root-mean-square (RMS) of the\nannual imbalance time series »\nResponse: Done.\nReviewer: p4 3rd paragraph : I don’t see how Figure S2 shows that the STE correction\non the MBL growth rate serves as a lagged tempporal smoother\nResponse: We agree with the reviewer that Figure S2 alone does not explicitly\ndemonstrate how the STE correction on the MBL growth rate functions as a lagged\ntemporal smoother. To provide a clearer explanation, we have now incorporated the\nanalytical solution of the two-box model into the Methods section (Section 1.2, \"Two-box\nmodel\" ):\nOur objective is to estimate 𝐸 (𝑡), which serves as the box-model derived whole-\nnet\natmosphere CO growth rate (𝐺box), based on observed tropospheric CO changes.\n2 𝐴 2\nRearranging Equation 3 yields:\n𝐸 (𝑡) = 𝑓 𝐾 [\nd𝐶tropo (𝑡)\n+ \n𝑓strato 𝐶tropo (𝑡)−𝐶strato (𝑡)\n] …….. (4)\nnet tropo atm\nd𝑡 𝑓tropo 𝜏\nTo implement this, we first derive the time series of tropospheric CO mixing ratio,\n2\n𝐶 (𝑡). We use that the annual MBL CO growth rates from the GCP 2023 report as\ntropo 2\nd𝐶tropo (𝑡)\n. We start with the initial condition 𝐶 (0) = 280 ppm in the year 1750 (𝑡 = 0).\ntropo\nd𝑡\nThe solution can also be expressed analytically as:\n𝐶 (𝑡) = 𝑒−𝑡/𝜏[𝐶 (0)+∫\nt𝑒𝑠/𝜏\n𝐶 (𝑠)𝑑𝑠] ……..(5)\nstrato strato 0 𝜏 tropo\nThe stratospheric mixing ratio, 𝐶 (𝑡), is then obtained by numerically integrating\nstrato\nEquation 5 initialized with 𝐶 (0) = 280 ppm. This formulation shows that 𝐶 (𝑡)\nstrato strato\ndepends on its initial state and all past tropospheric mixing ratios, acting as an\nexponentially weighted moving average with characteristic timescale 𝜏. This\n\"stratospheric memory\" effect means that STE imposes a lagged temporal smoothing\nwhen inferring fluxes from tropospheric CO changes. With 𝐶 (𝑡), its derivative\n2 tropo\nd𝐶tropo (𝑡)\n(taken from GCP MBL growth rates), and the calculated 𝐶 (𝑡) (using\nstrato\nd𝑡\nscipy.integrate module in Python for Equation 5), we compute 𝐸 (𝑡) using Equation 4\nnet\nvia numerical integration.\nReviewer: p6 3rd paragraph : « NOAA MBL growth rate estimates were recalibrated\n…. GCP 2021 report » weird sentence, rephrase\nResponse: We have rewritten the sentence.\nNOAA MBL flask measurements were recalibrated to the 2019 WMO scale and the\nderived growth‑rate estimates from these recalibrated mixing ratio measurement data\nwere first used in the GCP 2021 report (Hall et al. 2021; Friedlingstein et al. 2022).\nReviewer: p 6 paragraph 5 « Fire simulation and suppression » : strange wording : did\nthe author mean « simulation of fire ignition and suppression » ?\nResponse: We have changed the wording to \"simulation of fire ignition and\nsuppression\".\nReviewer: p7 Figure 2 caption : land-use change is a positive flux not a negative one !\nResponse: We have corrected the caption to indicate that land-use change is a positive\nflux.\nReviewer: P 8 1st paragraph : I don’t see how process modelers could fine tune their\nmodel using the temporal average of the residual of other carbon budget components.\nWhen they run the GCP simulations, they don’t have the results of the other\ncomponents, since these are usually being run at the same time by separate groups.\nResponse: We have modified text to make this clear. See our response to the earlier\ncomment of the reviewer on this matter.\nReviewer: P9 last sentence : replace « future climate predictions » by « future climate\nprojections » if the authors think about long term climate simulations (not decadal ones).\nResponse: Done\nReviewer: PS2 1.2 : define Cstrato and Ctropo, GMBL\nI’d also want to know a little more on how E(t) is estimated.\nResponse: We have rewritten the text to define the terms:\nLet 𝐶 (𝑡) and 𝐶 (𝑡) denote the mean CO mixing ratios (in ppm) in the\ntropo strato 2\ntroposphere and stratosphere, respectively, at time 𝑡.\nThe detailed method to estimate E(t) is added to the revised manuscript. See our\nresponse to your earlier comment from the reviewer about “STE correction”.\nReviewer: PS2 1.3 C23 and C17 are the men estimates for component C : but\nestimates of what ?\nResponse: We have rewritten text to clarify:\nHere, 𝐶 and 𝐶 are the multi-model mean estimates for component 𝐶 from the 2017\n17 23\nand 2023 GCP reports, respectively\n---\nReviewer #2 (Remarks to the Author):\nReviewer: Key results\nThe key messages from this manuscript are the substantial discrepancies in the marine\nboundary layer growth rate estimates in representing the whole atmosphere. The\nauthors use inversion models to suggest that the MBL-based estimates are off. The\nmanuscript also documents a 16% overall reduction in the global carbon budget\nimbalance between2017 and 2023 due to improvements in the individual budget\ncomponent estimates.\nValidity\nWhile I appreciate the alternative approaches to estimating the growth of whole\natmosphere CO2 inventory, I did not see any evidence that these alternative\napproaches are more accurate. A reduction in the global budget imbalance, is not in\nitself proof that the alternative estimates are more accurate. I think it is fair to say that\nthese estimates suggest that the reported uncertainty on the atmospheric inventory is\nunderestimated, but I would like to see independent proof from observations that these\nestimates are more accurate….\n…If the authors could demonstrate that the revised inventories are more accurate, that\nwould be a significant improvement to the global carbon budget…\nResponse: We thank the reviewer for highlighting the need for more evidence that our\nwhole-atmosphere CO₂ growth rate (AGR) estimates are more accurate than the\nmarine boundary layer (MBL) series. Below, we clarify why the revised growth rate\nestimates are better founded physically and empirically, and why their use is preferable\nto inflating the MBL growth rate uncertainty.\nThe CO₂ measurement and modelling community is aware that stratospheric-\ntropospheric mixing is an issue. Early observations of stratospheric CO₂ by Georgii et\nal. (1969) using aircraft showed a 3-5 ppm drop in CO₂ concentrations. They noted,\n“The marked decrease of the CO₂ concentration in the lower stratosphere compared\nwith the upper troposphere suggests that, contrary to previous practice, it is wrong to\nassume a constant mixing-ratio of CO₂ in the troposphere and stratosphere.” Global\nCarbon Project (GCP 2023 report) reports also note that, “The fourth factor is the\nuncertainty associated with using the average CO₂ concentration from a surface\nnetwork to approximate the true atmospheric average CO₂ concentration (mass-\nweighted, in three dimensions) as needed to assess the total atmospheric CO₂ burden.\nIn reality, CO₂ variations measured at the stations will not exactly track changes in total\natmospheric burden, with offsets in magnitude and phasing due to vertical and\nhorizontal mixing.”\nSo, the use of instantaneous whole-atmosphere mixing assumption introduces errors.\nHowever, it has been assumed that this error is minor relative to the errors in the rest of\nthe carbon budget components. Nevertheless, a quantitative test of these errors against\nthe errors in other components has never been performed. Recently, Pandey et al. 2024\ninvestigated the whole-atmosphere growth rate errors resulting from using MBL sites\nand found the error to be 0.25 PgC per year (or 0.12 ppm per year) for the period 2015-\n2019. This error includes stratosphere-troposphere exchange errors as well as within-\ntroposphere sampling errors.\nAn atmospheric inversion system produces the whole-atmosphere growth rate, which is\nexactly equal to the sum of the fluxes added over a year. Inversion systems assimilate\nthe observations used to calculate the NOAA MBL growth rate. However, they also\nrepresent 3D atmospheric transport using meteorological data. CAMS, for example,\nassimilates the same NOAA flask data used to produce the NOAA MBL observations,\nbut it also accounts for vertical transport. The vertical gradients of these models are\nvalidated using aircraft and satellite retrievals, explicitly resolve 3-D transport, and\ninclude STE.\nTo address the reviewer’s concern, we validated the simulated model‑fraction field from\nthe CAMS inversion against in situ observations. Using the NOAA Marine Boundary\nLayer Observation Network sites, CAMS reproduces the MBL CO₂ measurements with\nhigh fidelity (SI Figure 7). This agreement demonstrates that CAMS not only employs\nthe same observational constraints as the NOAA MBL calculation but also accurately\nmatches them. As a full atmospheric inversion, CAMS also accounts for transport\nprocesses such as stratosphere–troposphere exchange. To assess this, we compared\nCAMS‑simulated CO₂ mixing‑ratio fields with independent AirCore observations. In\n2016, observed stratospheric air-core profiles are 4-5 ppm lower than the tropospheric\naverage, and CAMS successfully captures this reduction (SI Figure 6) while also\nmatching the NOAA MBL observations well. In summary, CAMS captures the MBL CO2\ngrowth rate and STE transport, and the integration of surface carbon fluxes over a year\nfrom CAMS represents the carbon released to the whole atmosphere, thus, the\natmospheric CO2 growth rate based on CAMS is more accurate.\nThe box-model solution presented here is a simple parametric correction that accounts\nonly for stratosphere–troposphere exchange time. Its primary objective is to simulate\nthe CO₂ mixing ratio difference induced by this exchange. We provide an analytical\nsolution that can be readily applied to NOAA MBL growth rates, yielding a substantial\nAGR correction and a corresponding reduction in the global carbon-budget imbalance.\nThe box model assumes an exchange time of 2 years, based on 80% of the\natmospheric mass residing in the troposphere. To validate this exchange time, we\ncompared the simulated stratosphere–troposphere CO₂ mixing ratio difference with\nAirCore observations and CAMS-simulated 3D mole fraction fields. We extracted the\nCAMS 3D mole fraction fields for 2016 and computed the annual mean CO₂ gradient\nacross the 200 hPa boundary (SI Figure 5). We found a stratosphere–troposphere CO₂\nmixing ratio difference of 4–5 ppm in 2016, which is consistent with both CAMS and the\nAirCore observations, confirming that our chosen exchange timescale for the 200 hPa\nbox is a reasonable estimate. Note that the CAMS mole-fraction fields have already\nbeen validated against NOAA MBL as well as independent aircraft and air-core profiles.\nOverall, the whole-atmospheric conversion error arises from well-understood physical\neffects, the main one being the finite rate of STE. Because the STE bias arises from a\nwell-understood physical process that can be parameterized (box model) or explicitly\nsimulated (inverse models), we argue that these errors that can be corrected for using\nestablished models.\nWe have added or modified the following text and figures to clarify these points:\nIn main text:\nThe GCP uses growth rate estimates from the US National Oceanic and Atmospheric\nAdministration (NOAA) Global Monitoring Laboratory, calculated from CO mixing ratio\n2\nobservations at well-mixed background air at MBL in situ stations. These growth rate estimates\nserve as the benchmark for most scientific and agency assessments. NOAA estimates the growth\nrate by smoothing data over time for each MBL station and then averaging it across latitude\nbands [11]. GCP converts NOAA growth rate (ppm yr−1 ) values into the whole-atmosphere\nmass change (PgC yr−1) using a conversion factor of 2.124 PgC ppm−1 [12]. This conversion\nassumes instantaneous mixing—an approximation that introduces errors from incomplete\ntransport and sparse spatiotemporal sampling of MBL observations [10]. Although the\ntroposphere, which contains about 80% of atmospheric molecules, mixes well within a year, the\nstratosphere exchanges air slowly with the troposphere over a period ranging from 2 to 4 years\n[13,14].\nObserved Stratospheric CO mixing ratios are 3–5 ppm lower than tropospheric values,\n2\nreflecting slow stratosphere–troposphere exchange [14,15]. Consequently, surface-\ndriven CO increases lag in the stratosphere, creating a deficit relative to tropospheric\n2\nvalues (see Methods). The GCP acknowledges that using a constant conversion factor\nof 2.124 PgC ppm −1, an approximation that assumes instantaneous whole-atmosphere\nmixing, introduces a non-negligible source of uncertainty [7]. The error introduced by\nusing constant conversion factors to calculate whole-atmosphere growth rates from\nMBL data can be broken into two errors: troposphere-sampling error and stratosphere-\ntroposphere exchange (STE) error. The troposphere-sampling error reflects a\nrepresentativeness error due to the sparsity of MBL sites.\nTo account for the MBL growth rate discrepancies, we compute the whole-atmosphere\nCO growth rate using two atmospheric flux inversion models: Copernicus Atmosphere\noptimize emissions and sinks from the oceans and land surfaces to match mixing ratio\nmeasurements at in situ surface sites (including many MBL sites) while incorporating\nSTE and additional atmospheric transport and sampling effects through numerical\nsimulations nudged to meteorological reanalysis data (see Methods). Thus, the global\nintegral of the annual net optimized surface fluxes provides the whole atmospheric\ngrowth rate.\nIn Method section:\nFor the primary analysis in this study, an exchange timescale 𝜏 of 2 years was\nimplemented. The simulated CO mixing ratios and the resulting stratosphere-\n2\ntroposphere mixing ratio difference from this box model are depicted in Supplementary\nFigure 4. This simulated difference aligns well with observed differences from AirCore\nprofiles and CAMS 3D mole fraction field data. Sensitivity tests assessing the influence\nof varying 𝜏 on the budget imbalance reduction are presented in Supplementary\nTable 1.\nIn Supplementary Information:\nSI Figure 4: Simulated CO mixing ratios in the troposphere (solid black) and\n2\nstratosphere (dashed black) from a two-box model with a stratosphere–troposphere\nexchange (STE) timescale of 2 years and a stratospheric mass fraction of 0.2. The red\ncurve shows the simulated troposphere–stratosphere mixing ratio difference (right axis).\nMarkers denote 2016 observations of stratosphere-troposphere difference from the\nCAMS inversion 3D mixing ratio field airmass-weighted means (circle), AirCore\nmeasurements (inverted triangle), and CAMS AirCore co-samples (upright triangle). Left\nand right axes give CO mixing ratio and mixing ratio difference in ppm, respectively.\ntroposphere exchange, which is neglected when applying a fixed 2.124 PgC/ppm\nconversion factor to convert the MBL-based growth-rate estimates to whole atmosphere\ngrowth rate.\nSI Figure 2: CO mixing ratios measured at marine boundary layer (MBL) sites (Lan et\n2\nal., 2025) alongside CAMS inverse model simulated mixing ratios. Each panel shows\nobserved CO mixing ratios compared with CAMS posterior simulations. Panel titles\n2\nprovide the NOAA MBL site code and location (latitude, longitude) in parentheses.\nCAMS simulations match observations well, capturing key atmospheric transport\nprocesses such as stratosphere–troposphere exchange and lateral transport. The delta\nvalues (𝛥) in each panel represent the mean and 1 standard deviation of the differences\nbetween observations and model simulations for the respective sites over the shown\nperiod. NOAA MBL site details can be found at https://gml.noaa.gov/ccgg/mbl/map.php.\nSI Figure 3: Vertical CO profiles from AirCore soundings (black) (Baier et al., 2022)\n2\nand CAMS inversion simulations (orange) for 2016. The figure displays pressure (hPa)\nversus dry-air mole fraction (ppm); the dashed grey line indicates the 200 hPa level,\nused here as an approximate boundary between stratosphere and troposphere. Inset\nboxes report the mean stratosphere–troposphere difference (𝛥) for both datasets. The\nposterior mixing ratio field of the CAMS inversion closely reproduces the MBL\nmeasurements.\nIn addition, our corrections lower the RMS of the imbalance by 25 % (CAMS inversion).\nTo assess whether the 25% reduction in the RMS budget imbalance could plausibly\narise from random variability, we performed an F-test comparing the variances of the\ntwo 32-year time series. The original series, based on the canonical MBL-derived\natmospheric growth rate (AGR), has an RMS of 0.76 Pg C yr⁻¹ (variance = 0.5776 Pg²\nC² yr⁻²), whereas the revised series that incorporates the CAMS whole-atmosphere\nAGR yields an RMS of 0.57 Pg C yr⁻¹ (variance = 0.3249 Pg² C² yr⁻²). Their variance\nratio, F = 0.562, follows an F(31, 31) distribution; the one-sided cumulative probability P(\nF ≤ 0.562 ) = 0.057 indicates only a 5.7% likelihood that a variance—and hence RMS—\nreduction of this magnitude would occur if the two series truly possessed identical noise\ncharacteristics. In other words, there is roughly a one-in-seventeen chance that the\nobserved improvement is due solely to chance, lending quantitative support to our\nconclusion that the revised whole-atmosphere AGR provides a more accurate\nrepresentation of whole atmosphere CO2 growth rates.\nReviewer #2 Comment 2:\n“The second component of the manuscript that investigates a progressive improvement\nin the uncertainties of the other budget components is certainly interesting, if not terribly\nsurprising. I would hope that the models have improved over the last decade. I suppose\nthis is worth reporting, but I did not find this work to be particularly inspiring or novel.”\nResponse: We agree with the reviewer that we expect the models to improve over time.\nOur study seeks to move beyond this general intuition. Specifically, our objective is to\nquantify the magnitude of these advancements and, to delineate the specific\ncomponents responsible for driving them. We believe our detailed investigation offers\ndistinct contributions:\n1. Firstly, we introduce a quantitative benchmark for evaluating community-wide\nprogress. Through a comparative analysis of successive Global Carbon Project\n(GCP) releases, we demonstrate a notable 16% reduction in the 1985–2016\nRMS budget imbalance (from 0.91 to 0.76 Pg C yr⁻¹). To the best of our\nknowledge, this constitutes the first objective, end-to-end metric for assessing\nprogress within the global carbon-budget modeling community.\n2. Secondly, our research provides a component-level attribution of this observed\nnet gain. By propagating each updated term through our analytical framework,\nwe reveal that the improvements are not localized to a single component.\nInstead, they are distributed across multiple elements, including the ocean sink,\nland sink, land-use change emissions, atmospheric growth rate, and fossil-fuel\nemissions.\n3. Thirdly, in response to comments from Reviewer #3, we conducted an additional\nexperiment designed to determine whether the documented gains are\nattributable to enhanced process realism or are merely statistical artifacts. Our\nfindings, derived from substituting the full ensemble of 20 DGVMs with a targeted\nsubset of six models that explicitly incorporate diffuse radiation effects, show a\nfurther reduction in the RMS imbalance to 0.72 Pg C yr⁻¹. Conversely, a simple\nexpansion of the DGVM ensemble size from 15 to 20 models yielded no\ndiscernible improvement. This suggests that the accurate representation of key\nphysical processes is a more critical determinant of model advancement than\nsheer ensemble size.\nReviewer: It is not clear exactly how the alternative atmospheric inventory ties to the\nimproved flux estimates in the other parts of the budget. It almost looks like neither topic\nwas quite enough for a manuscript,\nResponse: The correction of the atmospheric growth rate and the improvement in the\ncarbon budget imbalance from the other components are connected in the context of\nthis study as follows:\n1. Since the atmospheric growth rate is typically considered highly accurate, any\nimbalance in the budget is usually attributed entirely to the other components,\nparticularly the land and ocean sinks. However, our analysis indicates that the\natmospheric growth rate itself carries a significant discrepancy. This suggests\nthat the contribution of errors from the land and ocean sinks to the total budget\nimbalance is smaller than previously thought. Consequently, the estimates for\nthese components are now more accurate than previously. The following text\nfrom manuscript describes it\nThese improvements demonstrate that uncertainties in the atmospheric growth rate\naccount for a substantial share of the total imbalance error. The large improvement\nin the imbalance due to the growth rate corrections also shows that bottom-up\nmodels are more accurate than previously perceived, based on the assumption that\nthe imbalance was primarily caused by errors in these bottom-up models.\n2. Second, the reduction in the carbon budget imbalance between the GCP 2017\nand 2023 reports quantifies the cumulative improvement from updates to all other\nbudget components. This “benchmark” reduction provides a natural yardstick\nagainst which to compare the impact of our whole‑atmosphere growth‑rate\ncorrection. For example, the CAMS model alone lowers the imbalance from 0.76\nto 0.57 Pg C yr⁻¹—an absolute improvement of 0.19 Pg C yr⁻¹—whereas the\naggregate improvement across all models falls from 0.91 to 0.76 Pg C yr⁻¹ (0.15\nPg C yr⁻¹). It is important to recognize that component errors combine in\nquadrature, so the vector sum of individual uncertainties will exceed any single\ncontribution. We have added text to make this point clear:\nText added in main text:\nThis reduction in imbalance is comparable to the whole-atmospheric growth rate\ncorrection when applied to the 2017 GCP report, which results in an imbalance of\n0.77 PgC yr−1using the CAMS flux inversion (See Supplementary Figure 1).\nText added in main text:\nThe atmospheric growth rate correction, when applied to the 2017 GCP report,\nresults in a similar improvement in imbalance to that achieved through the combined\nimprovements in carbon budget components between the GCP 2017 and GCP 2023\nreports.\nReviewer #3 (Remarks to the Author):\nReviewer: Pandey et al present work to better understand the imbalance in the global\ncarbon budget as evaluated through the series of budgets produced by the Global\nCarbon Project. This work focusses on an unexplored contribution to the imbalance,\nspecifically that due to the representation of the atmospheric growth rate of CO2. While\nthe imbalance is discussed, for example, in Sec 3.9.2 of the 2023 Global Carbon budget\npaper by Friedlingstein et al. (https://doi.org/10.5194/essd-15-5301-2023) the\natmospheric term is not covered in that discussion. As such, this paper presents a\nhelpful contribution, given the importance of a high-quality carbon budget for tracking\ncarbon mitigation efforts.\nWhile the results presented appear important to document, I have some concerns about\nwhether the paper, as currently structured, allows the reader to easily assess the\nimportance. My impression is that there has been some attempt to present this as\nrelating to a generic carbon budget, but it is effectively providing analysis of the specific\nseries of carbon budgets produced through the Global Carbon Project. If a reader is\nunfamiliar with those budgets, I wonder how the paper would read without that context.\nFor example, it is almost half-way through the abstract before the Global Carbon Project\nis mentioned. It might be better for the abstract to begin with this information such as\n‘Each year the Global Carbon Project collates and updates a global carbon budget to\nencapsulate state-of-the-art …’ and then introduce the imbalance. Likewise, in the\nintroduction, I think that some/most of paragraph 3 would be better before paragraph 2.\nI would also suggest that the introduction needs more than the first sentence to provide\nthe rationale for this work – I thought the last paragraph of the Conclusions provided a\nstronger ‘why’ than the start of the introduction.\nResponse: We have restructured the Abstract and Introduction. We now begin with a\nclear statement that our study focuses on budgets reported by the GCP.\nAbstract:\n\"The Global Carbon Project (GCP) annually compiles an updated global carbon budget\nthat synthesizes state‑of‑the‑art estimates of anthropogenic CO2 emissions, land and\nocean sinks, and the atmospheric CO_2 growth rate. The residual between these terms,\nreferred to as the global carbon budget imbalance, reflects the aggregate inaccuracies\nof the individual component estimates\"\nWe have also modified the start of the introduction as per the suggestions of the\nreviewer. First two paragraphs of the introduction:\n“Accurate quantification of anthropogenic carbon dioxide (CO_2) emissions and their\nredistribution among Earth’s major carbon reservoirs (atmosphere, oceans, and\nterrestrial biosphere) is essential for tracking mitigation progress, informing climate\npolicy, and projecting future climate trajectories (Schimel and Carroll 2024; Jones et al.\n2023; Peters et al. 2017). As global temperatures rise and the impacts of climate\nchange intensify, the scientific community is refining observational and modelling tools\nto constrain each component of the carbon cycle. The Paris Agreement’s five‑year\nGlobal Stocktake further heightens this urgency by requiring transparent, robust\nassessments of carbon sources and sinks to underpin effective policy‑making. Yet\npersistent, poorly understood variability within the natural carbon cycle still hampers the\nverification of reported emission reductions under international accords.\nOver the past decade, researchers have addressed these shortcomings by acquiring\nhigher‑quality observations and activity data, expanding model ensembles, refining\nparameterizations, and incorporating previously omitted processes—such as cement\ncarbonation and coupled nitrogen–phosphorus dynamics—into land and ocean carbon\nmodels (Sitch et al. 2021; Xi et al. 2016; Hall et al. 2021; Friedlingstein et al. 2023).\nThese advances, which we collectively term “bottom‑up improvements”, improve the\nprocess models (land and ocean uptake) and inventories (anthropogenic emissions)\nthat underpin contemporary carbon budgets. Although such improvements should, in\nprinciple, reduce component‑level errors, unequivocal evidence of an overall gain in\naccuracy remains elusive.”\nLast paragraph of the introduction:\n“Here, we investigate the evolution of collective accuracy using the carbon‑budget\nimbalance reported annually by the Global Carbon Project (GCP). Specifically, we\nquantify the error introduced when the MBL CO_2 growth rate is used as a proxy for the\nglobal mean atmospheric growth rate. We find that accounting for the discrepancy\nbetween MBL and whole‑atmosphere growth rates markedly reduces the\nroot‑mean‑square (RMS) of the annual imbalance time series relative to the values\nreported in recent GCP Carbon Budget assessments. We further assess the impact of\nupdates to individual budget components between the 2017 and 2023 GCP reports,\ndemonstrating that the overall accuracy of Earth’s carbon‑budget components has\nimproved over this period.”\nThe article has two main sections. The first covers the improvement to the atmospheric\ngrowth rate. The second part explores whether there have been improvements in other\nterms in the carbon budget over time, as represented by their contribution to the carbon\nbudget imbalance. The comparative contribution provides useful context for each\nsection, though the analysis is mostly independent across the two main sections.\nOther comments:\nReviewer: P2, final paragraph, line 4: perhaps ‘mixing ratio’ rather than ‘concentration’\nResponse: Done.\nReviewer: P3, final paragraph, line 6: suggest adding an extra sentence such as ‘Thus\nthe annual net optimised flux provides a direct estimate of atmospheric growth rate.’\nAlso perhaps ‘Alternatively’ instead of ‘Additionally’.\nP3, final paragraph, line 9: suggest moving ‘Inverse models’ sentence to after the\nfollowing sentence i.e. ‘The box model only addresses … MBL growth rate’ compared\nwith inverse models that account for both ….\nResponse: We have modified the text as per the reviewer's suggestion.\nThus, the global integral of the annual net optimized surface fluxes provides the whole\natmospheric growth rate.\nAlternatively, to isolate the impact of STE, we employ a simple two-box model\nrepresenting the troposphere and stratosphere, assuming a 2-year STE timescale and\nthat MBL-based growth rates accurately represent tropospheric growth (see Methods).\nThis model assumes MBL-derived rates perfectly represent tropospheric growth,\nisolating only the STE error. The Inverse models (CAMS and Jena CS) account for both\ntroposphere sampling and STE-related errors, while the box models only account for the\nSTE-related errors.\nReviewer: P4, second paragraph, discussion of 1991 and 1998 imbalances. I think this\nresult is overstated given that even with the alternate growth rate estimate, these\nimbalances remain some of the largest. Perhaps rephrase as ‘Our corrections slightly\nincrease the low … and slightly decrease the high … resulting in a small imbalance\nreduction …’ and ‘possibly more robust than previously assumed.’\nResponse: We thank the reviewer for this suggestion. In the revised manuscript, we\nhave softened the language to acknowledge that, even after applying the\nwhole‑atmosphere growth‑rate corrections, 1991 and 1998 continue to exhibit some of\nthe largest annual imbalances. The passage now emphasizes that (i) the STE\nadjustment becomes most influential in years with rapid changes in the marine MBL\ngrowth rate, and (ii) the resulting imbalance reductions are modest but indicate that\nprocess models handle extreme events slightly better than previously thought.\nFigure 1 presents various growth rate estimates alongside the corresponding changes\nin the imbalance reported by GCP in 2023. The long‑term mean imbalance does not\nchange after our corrections, but the influence of those corrections is strong during\nyears with pronounced inter‑annual variability. This is expected because the STE\nadjustment acts as a lagged temporal smoother on MBL growth rates when converting\nthem to whole‑atmosphere values (see Methods). Because its magnitude depends on\nthe history of tropospheric anomalies, it damps extremes and nudges annual values\ntoward the mean (see SI Section 1.0.2).\nTwo illustrative cases are the peak imbalance of +1.7 PgC yr−1 in 1991 and the trough of\n−1.5 PgC yr−1 in 1998 (Friedlingstein et al. 2023). These years coincide with the Mount\nPinatubo eruption and a strong El Niño, respectively. These events induced sharp\nperturbations to the carbon cycle and have historically challenged bottom‑up models.\nFor 1991, the high imbalance has been linked to an underestimation of the land‑sink\nresponse, likely due to a lack of representation of diffuse‑radiation effects following the\nvolcanic aerosol injection (Mercado et al. 2009; O’Sullivan et al. 2021). Our revised\ngrowth‑rate estimate raises the previously low MBL value in 1991, and lowers the high\nvalue in 1998, producing a small but meaningful reduction in both imbalance extremes\n(CAMS imbalance for 1991 = +1.17 PgC yr−1 and 1998 = −0.87 PgC yr−1). While these\nyears remain prominent anomalies even after the correction, the diminished residual\nsuggests that process models may be more skillful against such climatic shocks than\npreviously assumed.\nReviewer: P4, third paragraph, last line. Perhaps ‘as assumed’ rather than ‘as\nproposed’\nResponse: Done.\nReviewer: P4, fourth paragraph. It wasn’t clear to me whether it was useful quoting the\nRMS values for the corrections (i.e. 0.18, 0.36, 0.37) as I think these just distract from\nthe RMS imbalance which is what the reader needs to focus on.\nResponse: The RMS values for the corrections are useful for magnitude, allowing the\nreader to compare these errors with other budget component errors. We have added a\nsentence to the revised manuscript to highlight this. We have modified the text to clarify\nthe point:\nThe whole-atmosphere corrections are significant relative to the budget imbalance,\nwhich aggregates the errors of all components. The AGR correction terms themselves\nhave RMS magnitudes of 0.16, 0.36, and 0.37 PgC yr−1 for the box‑model, CAMS,\nand Jena CS estimates, respectively. For context, the largest of these correction RMS\nvalues is 49% of the GCP‑2023 imbalance of 0.76 PgC yr−1. Applying these same\ncorrections to the 2017 GCP report (baseline budget imbalance RMS of 0.91 PgC yr−1;\nSI Fig. 10) yields smaller percentage reductions. This occurs because the total error\nvariance, which determines the RMS imbalance, is effectively a sum of variances from\nmultiple error sources (leading to errors combining in quadrature if independent and\nzero-mean). Consequently, while a fixed AGR correction reduces the variance\ncomponent associated with the growth rate, its fractional impact on the overall RMS is\nsmaller when the initial RMS imbalance (and thus the total underlying error variance) is\nlarge due to other substantial uncorrected error components. Therefore, as bottom‑up\nemission and sink estimates continue to improve, AGR errors will account for an\nincreasingly dominant share of the residual budget imbalance, underscoring the need\nfor further refinement of observational and modelling constraints on global CO growth\n2\nrates (also see Figure 3). These improvements demonstrate that uncertainties in the\natmospheric growth rate account for a substantial share of the total imbalance error.\nThe large improvement in the imbalance due to the growth rate corrections also shows\nthat bottom-up models are more accurate than previously perceived, based on the\nassumption that the imbalance was primarily caused by errors in these bottom-up\nmodels.\nReviewer: P6, paragraph 2. Figure 2 is introduced but not discussed. If it is worth\nincluding in the paper then the main features in the figure need to be highlighted for the\nreader.\nResponse: We have added a discussion of Figure 2 in the revised manuscript.\nFigure 2 shows the time series of carbon‑flux components and the MBL CO growth\n2\nrate from the 2017 and 2023 GCP reports (Corinne Le Quéré et al. 2018; Friedlingstein\net al. 2023). All components exhibit changes between the 2017 and 2023 estimates,\nwith the largest RMS differences observed in the land‑use change (0.23 Pg C yr−1),\nthe land sink (0.25 Pg C yr−1), and the ocean sink (0.22 Pg C yr−1). Fossil‑fuel\nemissions and the MBL growth rate also change notably, with RMS differences of 0.13\nPg C yr−1 and 0.07 Pg C yr−1, respectively.\nNOAA MBL flask measurements were recalibrated to the 2019 WMO scale and the\nderived growth‑rate estimates first adopted in the GCP 2021 report (Hall et al. 2021;\nFriedlingstein et al. 2022). These estimates can also vary due to stabilization effects in\nthe NOAA time series, which introduce a latency before values converge to their final\nlevels (see Fig. 9 of Pandey et al. 2024). Beginning with the 2020 GCP report\n(Friedlingstein et al. 2020), the cement‑carbonation sink was included after its\nsubstantial role in atmospheric CO removal was recognized (Xi et al. 2016). Between\n2\nthe 2017 report, in which it was not reported (i.e., assumed zero), and the 2023 report,\nthe RMS difference in this sink is 0.11 Pg C yr−1, underscoring its significance. The\nGCP ocean sink estimates also changed between the 2017 and 2023 reports, with GCP\n2023 using a combination of process models and data-driven (fCO2-based (Bakker et\nal. 2016)) approaches (shown in Figure 2).\nReviewer: P6, paragraphs 3-5. These paragraphs seem like a missed opportunity.\nMany reasons are provided for why improvements are seen in the budget components\nbut it does not appear as though any of these have been tested, at least in the context\nof this study.\nFor example, the fourth paragraph notes that ensemble size likely reduces standard\nerrors. Given the GCP makes all the individual model data available, is it possible to\nrecalculate the 2023 imbalance using the same ensemble size as 2017 to test this\nhypothesis?\nSupplementary 2.0.3 discusses recalculating the ocean sink estimate with or without the\ndata-based estimates, so the impact of this change has been quantified but it does not\nappear to be mentioned in the main text. Was that intended? It could be included in this\nsection.\nThe process representation changes are probably harder to robustly assess due to the\nsmaller numbers of models making any given change, but it would be helpful to\nincorporatvide any evidence that the highlighted changes make a difference. For\nexample, do the 5 out of 20 models that account for the diffuse radiation effect give\nsmaller 1991 imbalances than the other models or than they did in 2017 when the effect\nwasn’t accounted for?\nResponse: Thank you for this very helpful suggestion. We conducted the tests you\nproposed and added the results into the manuscript.\nThe carbon budget imbalance analysis presented here can serve as a diagnostic for\nattributing overall budget improvements to specific component changes. For instance,\nsubstituting land sink estimates in the GCP 2023 budget with those from only the six\nmodels accounting for diffuse radiation effects yields an RMS imbalance of\n0.72 PgC yr−1, a notable reduction from the 0.80 PgC yr−1 obtained using the multi-model\nmean from the fourteen models omitting this process (all other GCP 2023 components\nheld constant). We also investigated whether increased model ensemble sizes were a\ndriver of the observed imbalance reduction between the 2017 and 2023 GCP reports,\nas larger ensembles might theoretically reduce the standard error of the multi-model\nmean. However, our analysis indicates that, for both land and ocean sinks, merely\nexpanding the ensemble size did not, in itself, lead to a significant reduction in the\nbudget imbalance. For example, the RMS imbalance for GCP 2023 using only the land\nsink models present in the 2017 ensemble was 0.758 PgC yr−1, closely aligned with\n0.762 PgC yr−1 RMS imbalance using the full GCP 2023 land model ensemble; a similar\noutcome was observed for ocean sink estimates. While a complete attribution of all\nchanges between the 2017 and 2023 GCP reports is not undertaken here, the budget\nimbalance analysis presented here can be further utilized in future investigations to\nquantify the influence of individual modifications.\nReviewer: P8, first and second paragraphs. Given that the SD results are so close to\nthose for the RMS, I think these paragraphs could be reduced with most of the\ninformation just presented in the supplementary material.\nResponse: We have moved this section to the supplementary material as per the\nreviewer’s suggestion.\nReviewer: P8, Conclusions, line 3. The 37% decrease combines both the 2017 to 2023\nchange and the growth rate correction. If possible, it might be useful to also apply the\ngrowth rate correction to the 2017 dataset to give another measure of the impact of the\ngrowth rate correction compared to other improvements.\nResponse: We performed the reviewer-recommended test by substituting each\nalternative AGR estimate into both the 2017 and 2023 carbon-budget components. We\nhave added a figure to the SI to showcase the results.\nThe AGR correction terms themselves have RMS magnitudes of 0.16, 0.36, and 0.37\nPgC yr−1 for the box‑model, CAMS, and Jena CS estimates, respectively. For context,\nthe largest of these correction RMS values is 49% of the GCP‑2023 imbalance of 0.76\nPgC yr−1. Applying these same corrections to the 2017 GCP report (baseline budget\nimbalance RMS of 0.91 PgC yr−1; SI Fig. 10) yields smaller percentage reductions. This\noccurs because the total error variance, which determines the RMS imbalance, is\neffectively a sum of variances from multiple error sources (leading to errors combining in\nquadrature if independent and zero-mean). Consequently, while a fixed AGR correction\nreduces the variance component associated with the growth rate, its fractional impact\non the overall RMS is smaller when the initial RMS imbalance (and thus the total\nunderlying error variance) is large due to other substantial uncorrected error\ncomponents.\nSI Figure 1: Root‑mean‑square (RMS) carbon–budget imbalance for 1985–2016\n(black) in the 2017 and 2023 GCP assessments, compared with the imbalance\nobtained after replacing the GCP marine‑boundary‑layer atmospheric growth rate\n(AGR) with three alternative estimates—Jena CS (blue), CAMS (orange), and a simple\nbox model (green). Hatched bars show the RMS magnitude of each AGR correction\nitself. The light‑grey shading highlights the 2017 analysis block.\nReviewer: Figure 1. The means of the timeseries plotted on the right-hand side of the\nfigure are so close together that it is possibly not worth including them. In this case the\nfinal sentence of the figure caption can be removed.\nResponse: We have removed the mean markers as per the suggestion of the reviewer.\nReviewer: Figure 2. It may help the reader if the y-axis range was more similar between\ncomponents. For example, the differences in the cement sink, land use change and\nocean sink are visually exaggerated by the smaller ranges for these components.\nSuggest adding ‘(dashed)’ after 2017 and ‘(solid)’ after 2023 in the figure caption. Is the\nocean sink the GCP reported value, or the model-only recalculation described in the\nsupplementary 2.0.3?\nResponse: We have made a note in the figure captions about the different y-axis scales\nof the panels and stated that the RMS values provide a hint of the magnitude\ndifferences. The revised Figure 2 caption:\n“Figure 2: ….. The values in parentheses for each panel label are the respective RMS\nof the difference between the GCP 2017 and 2023 time series, which gives an estimate\nof the magnitude of the changes.”\nWe have added text to clarify that we show the GCP-reported mean values for a\ncomponent in Figure 2.\n“The GCP ocean sink estimates also changed between the 2017 and 2023 reports, with\nGCP 2023 using a combination of process models and data-driven (fCO2-based\n(Bakker et al. 2016)) approaches (shown in Figure 2).\nReviewer: Figure 3. Given the single component update calculations are done relative\nto the 2017 case, perhaps the coloured crosses would be better plotted on the left-hand\nside of the figure in the GCP 2017 column. If an atmospheric growth rate correction was\nalso done in the 2017 case, additional triangles could also be included in the 2017\ncolumn.\nResponse: The reason for plotting these in 2023 is to help the reader understand the\nimpact of these changes on the overall imbalance RMS reduction. For example, it aims\nto answer questions such as whether the 2023 imbalance is reduced due to changes in\njust one component (while the other components remain unchanged or worsen) or if it is\ndue to all components. Therefore, we prefer to keep the component-level correction at\nthe “GCP 2023“ X-axis point.\nSupplementary material\nReviewer 1.1.1 and 1.1.2: It is interesting that the two inversions use very different\nnumbers of atmospheric measurement sites. Is this worth mentioning in the text? I note\nthat there is no discussion in the text or supplementary about differences in the growth\nrate estimates between the two inversions.\nResponse: We have added a text to the revised manuscript to highlight the difference\nin the number of atmospheric measurement sites used by the two inversions. We have\nalso provided a discussion of the difference in the growth rate estimates between the\ntwo inversions in the revised manuscript.\nAlthough the two inversions differ in aspects such as the number of assimilated\nmeasurement-site networks and vertical model resolution, they both incorporate data\nfrom a common core MBL network. This MBL network provides the primary\nobservational constraint for estimating the annual global CO2 growth rate in these\ninversions. Both inversions are designed to track the global CO2 growth rate while also\ncapturing key transport processes, including stratosphere-troposphere exchange.\nReviewer 1.2. It would be helpful to note in this section what exchange time is being\nused for the analysis in the main paper and in Figure S1. Is it 3 years?\nResponse: We have made several additions to the revised manuscript to clearly\nindicate the use of a two-year STE time in the analysis. Please note that we now\nvalidate the use of this exchange time by comparing the differences between observed\nand modeled concentrations in AirCore profiles, as well as through the CAMS\ninversion’s posterior concentrations field.\nA STE time 𝜏 of 2 years was implemented in the box model. The simulated CO mixing\n2\nratios and the resulting stratosphere-troposphere mixing ratio difference from this box\nmodel are depicted in Supplementary Figure 4.\nResponse: 2.0.2, second last sentence is not clear to me. Please explain more clearly\nhow the figure demonstrates these points.\nResponse: We have clarified this point in the revised text.\nIn Equation 4, the deviation between the derivative of tropospheric concentration and\nnet emissions arises from the difference between tropospheric and stratospheric\nconcentration values. The stratospheric concentration is entirely determined by past\ntropospheric concentrations. Therefore, this deviation depends on how the current\ntropospheric concentration for a given year compares with its past values. Hence, The\nestimated conversion factor time series depends on the magnitude of changes in the\nannual MBL CO₂ growth rate. In years with sharp fluctuations in growth rates, the\nconversion factor deviates from the mean, highlighting its sensitivity to higher-order\nvariability in the MBL record.\nReviewer: 2.0.3. As noted earlier, this section is not referenced in the main text.\nResponse: We have linked this section to the main text. It is now included in the\nSensitivity Tests section of the SI, which has been moved from the main text to the SI in\nthe revised manuscript.\nReviewer: 2.0.5 Given the small difference in the SD results compared to the RMS\nresults, the second paragraph and Table S3 are probably not needed.\nResponse: We have removed the second paragraph from the sections and Table S3 as\nper the reviewer's suggestion.\nReviewer: 2.1 Since I did not notice this referenced in the main text, is it needed in\nsupplementary or should it have been referenced in the main text?\nResponse: We have removed this section from the Supporting Information, as we\nagree with the reviewer that it is not necessary to convey the main point of the paper.\nReviewer: Figure S2. I found this figure difficult to interpret. Perhaps including some\ndescription of the color scheme for the dots in the figure caption would help.\nResponse: We have added a description of the color scheme for the dots and\nexpanded the figure caption:\nSI Figure 4: Annual CO conversion factor derived from the two‑box STE model. Shown\n2\nis the factor (Pg C ppm−1) required to convert the MBL CO growth rate (ppm yr−1) to\n2\nthe whole‑atmosphere CO mass growth rate (Pg C yr−1). Point colours denote the\n2\nmagnitude of the corresponding annual MBL growth rate, as indicated by the colour bar.\nThe horizontal dashed line marks the mean conversion factor of 2.128 Pg C ppm−1\n(1900–2017), closely matching the value used in recent GCP assessments. Substantial\ninterannual variability is evident, with larger departures from the mean occurring in\nyears characterised by unusually large positive or negative MBL growth rates.\nReferences:\nBaier, B., Sweeney, C., Newberger, T., Higgs, J., Wolter, S., & NOAA Global Monitoring\nLaboratory. (2021). NOAA AirCore atmospheric sampling system profiles (Version\n20230831) [Data set]. NOAA GML. https://doi.org/10.15138/6AV0-MY81\nGeorgii, H. W., and D. Jost. 1969. “Concentration of CO2 in the Upper Troposphere and\nLower Stratosphere.” Nature 221 (5185): 1040–40. https://doi.org/10.1038/2211040a0.\nMasarie, K. A., and P. P. Tans. 1995. “Extension and integration of atmospheric carbon\ndioxide data into a globally consistent measurement record.” J. Geophys. Res. 100\n(D6). https://doi.org/10.1029/95jd00859.\nPandey, Sudhanshu, John B Miller, Sourish Basu, Junjie Liu, Brad Weir, Brendan\nByrne, Frédéric Chevallier, et al. 2024. “Toward Low-Latency Estimation of Atmospheric\nCO2 Growth Rates Using Satellite Observations: Evaluating Sampling Errors of Satellite\nand In Situ Observing Approaches.” AGU Adv. 5 (4): e2023AV001145.\nhttps://doi.org/https://doi.org/10.1029/2023AV001145.\nFriedlingstein, Pierre, Michael O’Sullivan, Matthew W. Jones, Robbie M. Andrew,\nDorothee C. E. Bakker, Judith Hauck, Peter Landschützer, et al. 2023. “Global Carbon\nBudget 2023.” Earth Syst. Sci. Data 15 (12): 5301–69. https://doi.org/10.5194/essd-15-\n5301-2023.\nBallantyne, A. P., C. B. Alden, J. B. Miller, P. P. Trans, and J. W. C. White. 2012.\n“Increase in observed net carbon dioxide uptake by land and oceans during the past 50\nyears.” Nature 488 (7409): 70–73. https://doi.org/10.1038/nature11299.\nLan, X., J.W. Mund, A.M. Crotwell, K.W. Thoning, E. Moglia, M. Madronich, et al. 2025.\nAtmospheric Carbon Dioxide Dry Air Mole Fractions from the NOAA GML Carbon Cycle\nCooperative Global Air Sampling Network, 1968-2024, Version: 2025-04-26,\nhttps://doi.org/10.15138/wkgj-f215"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors answered all my questions and addressed my comments.\nI am therefore suggesting to accept this revised version of the paper", "reviewer_2": "This is my second review of this manuscript. I appreciate the authors’ thoughtful response to all of the reviewer comments. I\nfeel that they have adequately addressed my concerns and their response to the other reviewers was sufficient. The article is\nsignificantly improved from the previous version. I have no additional concerns that need to be addressed.", "reviewer_3": "I appreciate the work that the authors have done to address my comments on the submitted manuscript and am comfortable\nthat they have dealt with my major concerns.\nI have a few minor comments on the current version of the paper.\nThe atmospheric CO2 measurements used to calculate the growth-rate are referred to as 'in situ' in a number of places\nwithin the text. 'In situ' is usually only used for sites that have an instrument at the site to continually monitor CO2 (e.g.\nhttps://gml.noaa.gov/ccgg/insitu/) whereas much of the network comprises flask sampling. I would suggest avoiding using\nthe term 'in situ'.\nFigure 3 is referenced before Figure 2. This could be avoided if lines 175-191 were moved later in the paper once the 2017\nand 2023 budgets have been compared - perhaps around line 231. A new paragraph could be started to present the\ncomponent imbalances (the colored crosses).\nThe sentence about the ocean sink (lines 224-226) might be better after the sentence (line 213) when the ocean sink is\nmentioned.\nLine 231 - should this be Supplementary Figure 1 rather than 10?\nSupplementary material\nLine 18: suggest adding 'Methods Sec 5.2, ' before 'equation 4'.\nThe SI Figure 5 caption is improved. Perhaps add to the final sentence '... unusually large positive or negative MBL growth\nrate anomalies from a multi-year smooth fit to growth rate.'\nIn relation to both SI Figure 4 and SI Figure 5, I assume the larger interannual variability from around 1960 onwards is when\natmospheric measurements begin while the earlier period is based on ice-core or firn data which is inherently smoother. I\nwonder if this is worth noting somewhere."}, "author_response": ""}]

Decision letter