Surprising stability of recent global carbon cycling enables improved fossil fuel emission verification

Independent verification of reported fossil fuel emissions from atmospheric observations is essential for tracking progress under the Paris Agreement. Verification by closing the global carbon budget is hampered by substantial, unexplained interannual-to-decadal variability captured as a budget imbalance δ in F = AGR − LU + B + O + δ. On interannual timescales, land biosphere exchange dominates this uncertainty and is strongly influenced by climate variability (notably ENSO), with ocean variability being much smaller. This study asks whether a simple model leveraging spatially and seasonally resolved temperature sensitivities of land carbon exchange, together with a CO2-dependent long-term sink term, can explain most of the observed variability and thereby tighten constraints on fossil fuel emission verification.

Prior work documents unexplained decadal features in atmospheric CO2 growth, including the 1940s low AGR (linked to wartime land-use changes and/or global cooling), mid-1980s anomalies, and a post-2002 slowdown attributed to enhanced terrestrial uptake during the warming hiatus and ongoing CO2 fertilization. Two modelling approaches dominate: (1) dynamic global vegetation models and (2) global linear regressions against climate indices (tropical land temperature, ENSO). Both leave considerable residual variability, in part due to spatial heterogeneity and seasonal dependence of temperature sensitivity. Rödenbeck et al. developed the NEE-T inversion to derive seasonally and spatially resolved temperature sensitivities of land carbon fluxes from atmospheric CO2, showing predictive skill and suggesting apparent sensitivity changes often reflect spatial patterns of warming rather than ecosystem change. Studies also highlight roles of soil moisture and ENSO in interannual land flux variability, with ocean variability being about 80% smaller and temporally distinct.

The authors build a simple regression model of annual net land carbon exchange: B_net,mod = a × Γ + b × CO2 + c. Here Γ is a weighted spatial average of land temperature anomalies, Γ = Σ_i γ_i T_i, where γ_i are seasonally resolved local temperature sensitivities from the CarboScope NEE-T inversion (run sEXTocNEET_v2021) that repeat annually and are normalized by month. Monthly Berkeley Earth land temperatures are regridded to the inversion grid and decadally detrended using a causal exponential moving average with a 2.5-year time constant, representing exchange with a fast-turnover pool. The CO2 term uses the monthly de-seasonalized average of Mauna Loa and South Pole records (merged with Law Dome ice core data pre-1958 for extensions). The constant c absorbs the (assumed constant over the regression period) global mean land-use flux and offsets from non-zero preindustrial values of a × Γ and b × CO2. Ocean uptake O_mod is computed monthly using the Joos et al. pulse-response ocean model (HILDA HS+LS parameters), driven by atmospheric CO2 history, spun up from 1800, and rescaled to match the GCP integrated 1800–2021 ocean sink (176.03 GtC). Annual values are obtained by averaging monthly outputs. Reported fossil fuel and industrial emissions (including cement carbonation) F_rep are from the Global Carbon Project 2021; Carbon Monitor monthly emissions (from 2019) are rescaled to illustrate COVID-19 impacts. Coefficients a, b, c are obtained by linear regression to the residual land sink consistent with the carbon budget: B_net,res = F_rep − O_mod − AGR_obs − B_net,mod + ε, where AGR_obs is the atmospheric growth rate computed as a 12-month centred difference of the MLO–SPO mean CO2. Parameter uncertainties are estimated by jackknifing over M=12 non-overlapping five-year blocks (1960–2020). Predictive performance (generalization error) is assessed by cross-validation using the same block scheme, reporting RMSE on interannual and, after 10-year moving-average smoothing, decadal timescales. Additional sensitivity tests include: alternative predictors for Γ (unweighted tropical land temperature, Niño 3.4 index with 4-month lag), allowing lags up to 12 months, inclusion of stratospheric aerosol optical depth (SAOD) to account for volcanic effects, exclusion of Pinatubo years (1991–1993), and replacing O_mod with the mean GCP ocean sink estimate. The GCP budget imbalance is analysed in parallel and represented as an AR(1) process for verification benchmarking.

• The Weighted-T model reproduces interannual and decadal variability in the global carbon budget with a cross-validated RMSE of 0.50 ± 0.09 GtC yr−1 (interannual) and 0.16 ± 0.04 GtC yr−1 (decadal), explaining about 75 ± 6% of variance in the residual land sink. In contrast, the GCP process-model budget imbalance has RMSE 0.76 ± 0.11 GtC yr−1 (interannual) and 0.36 ± 0.14 GtC yr−1 (decadal).
• Performance gains are strongest on decadal scales (ratio of decadal to interannual RMSE: GCP ≈ 0.36/0.76 vs Weighted-T ≈ 0.16/0.50), aided by non-autocorrelated residuals in the Weighted-T model, which reduces error accumulation.
• The model captures major ENSO-related AGR anomalies (e.g., 1997–1998 El Niño and subsequent La Niña) and decadal features such as stagnating AGR in the 1980s and slow growth in the 1990s–2000s. Performance is poorer immediately after Mount Pinatubo (1991–1993), consistent with unmodelled diffuse-light effects.
• The stability of regression coefficients and repeating local γ_i sensitivities, coupled with homoscedastic, trend-free residuals, indicate surprising stability of global-scale carbon cycle sensitivity to climate and CO2 forcing over 1958–2021. Short-lived pools (~2.5-year turnover) dominate variability across timescales captured by the Γ term; the b × CO2 term represents multi-decadal responses but is not intended for long-term forecasting.
• Emission verification: Over a five-year stocktake, misreporting exceeding about 4.4% (95% confidence, assuming ~10 GtC yr−1 emissions) would be detectable using cumulative discrepancies inferred from AGR, ocean uptake, and the land model; comparable approaches using the GCP budget imbalance would require ~8.8% misreporting. Short-lived annual changes (e.g., ~0.52 GtC decrease in 2020 due to COVID-19) are not detectable.
• Reported and inferred global fossil emissions agree well since 1958 outside the Pinatubo period, with no evidence of misreporting post-2015 Paris Agreement. Extensions to 1900 indicate inferred emissions exceed reports by ~0.59 GtC yr−1 from 1900–1935 and are ~0.3 GtC yr−1 lower in the 1940s, likely reflecting unmodelled variability in land-use emissions rather than ocean variability or input data errors.

By explicitly incorporating spatially and seasonally resolved temperature sensitivities derived from atmospheric inversions, the Weighted-T model addresses the dominant source of budget uncertainty—interannual-to-decadal land biosphere variability—thereby tightening the closure of the global carbon budget. The resulting substantial reduction in unexplained residuals enables more accurate atmospheric verification of reported fossil fuel emissions over the Paris Agreement’s five-year stocktake cycle. The model’s success, despite fixed parameters and annually repeating local sensitivities, supports the view that global carbon cycle sensitivity has been remarkably stable for the past six decades and that apparent changes largely reflect shifts in warming patterns rather than changing ecosystem physiology. The dominance of short-lived terrestrial carbon pools in explaining variability across timescales underscores the importance of fast turnover processes in global carbon exchange. Remaining mismatches during strong volcanic forcing episodes indicate roles for processes like diffuse-light fertilization not represented in the model, and the CO2-trend term, while capturing multi-decadal responses, lacks mechanistic detail for long-term projections.

A simple framework combining a regression-based net land sink model using spatially weighted, seasonally resolved temperature sensitivities with an efficient ocean pulse-response model reproduces key interannual and decadal features of atmospheric CO2 rise since 1960 and provides context back to 1900. It reduces the unexplained carbon budget residual and enables atmospheric verification of reported global fossil emissions to within about 4.4% (95% confidence) over five-year periods. The strong, stable performance with constant parameters suggests no large surprises in recent global carbon cycle dynamics. Discrepancies prior to 1960 likely reflect greater variability in land-use emissions. Future work could explicitly represent volcanic diffuse-light effects, allow time-varying land-use fluxes, and further assess multi-decadal ocean variability to refine verification and historical reconstructions.

• Volcanic effects: The model underperforms after the Mount Pinatubo eruption (1991–1993), likely due to unmodelled diffuse-light impacts on photosynthesis; adding SAOD does not improve the Weighted-T model notably.
• Land-use flux assumption: The land-use term is assumed constant over the regression period; historical extensions suggest time-varying LU emissions likely contribute to early 20th-century discrepancies.
• Fast-pool approximation: Temperature effects are filtered with a 2.5-year turnover assumption, emphasizing short-lived pools; longer-term terrestrial processes are not explicitly represented, and the b × CO2 term is empirical and not suited for long-term forecasting.
• Ocean uptake representation: Although validated, the pulse-response ocean model is a simplification; results are robust to using GCP ocean estimates but still inherit uncertainties.
• Detection limits: The approach cannot detect short-lived annual emission perturbations (e.g., the ~0.52 GtC COVID-19 drop in 2020) and is optimized for multi-year verification windows.
• Input data uncertainties: Early-period reconstructions rely on ice-core CO2 and historical temperature fields, which may introduce additional uncertainties.