An integrated approach to quantifying uncertainties in the remaining carbon budget

Remaining carbon budgets (RCBs) represent the future cumulative CO2 emissions compatible with limiting global warming to specified levels (e.g., the Paris Agreement). Prior estimates vary widely due to differing definitions and incomplete treatment of uncertainties. The IPCC SR1.5 assessed RCBs using a segmented framework based on TCRE, anthropogenic warming to date, and non-CO2 responses from emulators, while discussing additional uncertainties separately. A key gap is how combined geophysical and socioeconomic uncertainties shape the full distribution of RCBs. This study quantifies the distribution of TCRE and RCBs by integrating observational constraints and model-based information, explicitly distinguishing geophysical (physical and biogeochemical processes) from socioeconomic (human decision-dependent) uncertainties, and providing both factor-specific effects and combined uncertainty impacts on TCRE and RCB distributions.

SR1.5 provided a prominent recent assessment using a segmented budget framework and considered uncertainties in historical temperatures, emissions, non-CO2 forcing/response, TCRE distribution shape, and under-represented feedbacks, but did not combine them into a single RCB distribution. Numerous studies have estimated TCRE and RCBs using models and observations, finding approximate proportionality between cumulative CO2 and warming and exploring feedbacks (e.g., aerosols, carbon cycle, permafrost) and scenario dependencies. However, integrated treatment of geophysical and socioeconomic uncertainties remained limited. This work builds on SR1.5 and prior TCRE literature by consolidating uncertainties into unified TCRE and RCB distributions and by explicitly quantifying the impact of future non-CO2 scenario choices on RCBs.

Framework and definitions: The RCB for a temperature limit ΔT_lim is expressed in terms of five inputs: anthropogenic warming to date (ΔT_anth), cumulative historical CO2 emissions (E), the current non-CO2 fraction of total anthropogenic forcing (f_inc), unrealised warming after net-zero from past CO2 emissions (ΔT_ZEC), and the future non-CO2 forcing fraction at net-zero (f_fc). Geophysical uncertainties are represented with probability distributions; socioeconomic uncertainty (future non-CO2 pathways) is represented via scenario-based offsets rather than formal probabilities. Core relationships:

• TCRE = ΔT_anth × (1 − f_inc) / E
• Total carbon budget (TCB) from pre-industrial to net-zero for a limit ΔT_lim: TCB = E × (ΔT_lim − ΔT_ZEC) × (1 − f_fc) / ΔT_anth
• Remaining carbon budget (RCB) from present (subtracting historical E): RCB = E × ((ΔT_lim − ΔT_ZEC)/ΔT_anth − 1) Parameterization and input distributions (main case):
• ΔT_anth (2019 relative to 1850–1900): median 1.18 °C; 5–95% range 1.05–1.41 °C (derived by removing natural variability/forcing using a statistical model and averaging three spatially complete datasets: HadCRUT-CW, GISTEMP, Berkeley Earth).
• E (cumulative CO2, 1870–2019): median 2350 GtCO2; 5–95% 1960–2745 GtCO2 (Gaussian fit to Global Carbon Budget 2019).
• f_inc (historical non-CO2 forcing fraction; mean 1990–2019): median 0.14; 5–95% −0.11 to 0.33 (from FaIR emulator with updated aerosol, CO2, CH4 forcings, constrained by observations).
• f_fc (future non-CO2 forcing fraction; 30-year mean before net-zero): linked linearly to f_inc across net-zero scenarios: f_fc = 0.308 × f_inc + 0.14 + offset. Main case uses offset = 0 to represent geophysically consistent future forcing. Socioeconomic scenario uncertainty is explored with intercept offsets ±0.05 (reflecting the 5–95% spread across individual scenario fits) to shift median RCB without changing geophysical uncertainty.
• ΔT_ZEC (Zero-Emission Commitment, 50 years after zero emissions): median 0 °C; 5–95% −0.30 to 0.30 °C (based on ZECMIP; mean adjusted to 0 considering permafrost feedbacks). Target: ΔT_lim = 1.5 °C (also explored 1.75 and 2.0 °C in Supplementary Material). Sampling: Empirical or normal input distributions were sampled assuming uncorrelated uncertainties to obtain TCRE and RCB distributions. FaIR emulator was run for 411 net-zero CO2 scenarios with a 1000-member perturbed-parameter ensemble (climate sensitivity, carbon cycle, forcing), constrained to observed warming, to estimate f_inc and f_fc distributions and their relationship. Assumptions include proportionality of temperature to effective radiative forcing for estimating non-CO2 warming fractions and inclusion of ZEC to account for transient-to-equilibrium effects, permafrost feedbacks, and pattern effects around the time of net-zero emissions.

• Observation-based TCRE: median 0.44 °C per 1000 GtCO2; 5–95% 0.32–0.62 °C per 1000 GtCO2. Distribution is right-skewed, with stronger constraint on low TCRE values and a wider upper tail, consistent with potential strong negative aerosol forcing.
• Sensitivity of TCRE uncertainty: Removing uncertainty in f_inc narrows the 5–95% TCRE range by 33%; removing uncertainty in E or ΔT_anth narrows by 13% and 10%, respectively.
• RCB for 1.5 °C (from start of 2020; geophysical uncertainties only): median 440 GtCO2 (≈50% chance of not exceeding 1.5 °C); 33rd percentile (≈67% chance) 230 GtCO2. Overall distribution includes a 17% probability of negative RCB (i.e., budget already exceeded).
• Comparison to SR1.5: Median and 67% budgets are smaller by about 60 GtCO2 and 110 GtCO2, respectively, than SR1.5 (adjusted to 2020), due to integrated treatment of broader geophysical uncertainties.
• Sensitivity of RCB to parameter uncertainties: Uncertainties in f_inc, ΔT_anth, and ΔT_ZEC substantially affect the RCB spread; reducing each to zero increases the 67% RCB from 230 to about 260, 290, and 300 GtCO2, respectively. Uncertainty in historical cumulative emissions E has negligible effect on RCB spread because opposing effects in TCB and already-emitted E largely cancel.
• Socioeconomic uncertainty (future non-CO2 forcing): Applying a ±0.05 intercept offset in the f_fc–f_inc relationship shifts the median 1.5 °C RCB by ∓170 GtCO2 (higher f_fc lowers RCB). Median becomes 270 GtCO2 for +0.05 offset and 610 GtCO2 for −0.05 offset. This is smaller than, but consistent with, the SR1.5 assessed ±250 GtCO2 scenario variation effect.

Integrating key geophysical uncertainties into a unified framework yields a narrower and more robust RCB distribution than earlier assessments that summed separate components. The observation-constrained TCRE aligns with prior ranges but is tighter, especially at low values. The analysis clarifies how present-day aerosol forcing (through f_inc) dominates TCRE uncertainty and, together with ΔT_anth and ΔT_ZEC, shapes the RCB distribution. The negligible influence of E uncertainty on RCB underscores compensating effects between total budget size and already-emitted amounts. Socioeconomic choices governing future non-CO2 emissions materially alter RCBs: increased future non-CO2 forcing (higher f_fc) reduces allowable CO2 emissions, while mitigation of short-lived climate forcers can expand the budget. Results imply that meeting 1.5–2 °C targets requires rapid CO2 reductions to net-zero within decades and concurrent stringent reductions of non-CO2 emissions. The framework provides transparent attribution of uncertainty sources and quantitative sensitivity to scenario choices, informing policy design and prioritization (e.g., aerosol and methane controls).

This study presents an integrated, observation-constrained framework to estimate TCRE and the remaining carbon budget while combining major geophysical uncertainties into a single distribution and explicitly characterizing socioeconomic scenario effects. Key contributions include: a narrowed TCRE range centered at 0.44 °C per 1000 GtCO2; a 1.5 °C RCB of about 440 GtCO2 (median) and 230 GtCO2 (67% chance) from 2020 when considering geophysical uncertainties; and quantification of scenario-driven shifts of ±170 GtCO2 due to future non-CO2 forcing. The results emphasize the need for rapid CO2 emission reductions to reach net-zero around 2040 and strong mitigation of non-CO2 climate forcers. Future research should refine aerosol forcing constraints, improve understanding of pattern effects and long-timescale feedbacks (e.g., permafrost), and continually update budgets with new observations and evolving emissions trajectories.

• Assumes TCRE estimated from present-day observations applies at the time the temperature limit is reached; this holds well up to ~2 °C in models but may weaken at higher warming or under strong non-linearities.
• Assumes feedbacks (including permafrost and wetland methane) are reflected in observational constraints and will not accelerate enough in coming decades to invalidate the TCRE estimate; potential tipping elements at higher warming are not captured.
• Represents CO2-induced temperature at net-zero as TCRE contribution plus an uncertain Zero-Emission Commitment (ΔT_ZEC), capturing transient-to-equilibrium adjustments, permafrost, and pattern effects; possible nonlinearity in forcing–temperature response over time is not explicitly modeled.
• Approximates non-CO2 warming using the non-CO2 forcing fraction and a 30-year averaging window; recognizes a ~15-year lag between forcing fraction changes and realized warming and does not simulate post–net-zero dynamics.
• Treats input uncertainties as uncorrelated for sampling; tail behavior of distributions is more sensitive to this assumption than medians and interquartile ranges.
• Socioeconomic uncertainty in future non-CO2 forcing is represented via a fixed intercept offset (±0.05) rather than a formal probability distribution; additional geophysical uncertainty in the composition of non-CO2 forcing may further shift budgets.
• Best suited for warming targets below 2 °C during this century.