Remaining carbon budgets (RCBs) are crucial for informing climate policy, representing the cumulative future CO2 emissions consistent with limiting global warming to a specified level (e.g., the Paris Agreement goals). However, existing RCB estimates vary widely due to differing methodologies and underlying assumptions. Most studies only account for a subset of relevant uncertainties, often omitting key processes like permafrost thaw or future scenario uncertainty. The IPCC Special Report on Global Warming of 1.5 °C (SR1.5) offered a segmented framework, calculating RCBs directly from TCRE, anthropogenic warming, and the temperature response to non-CO2 emissions. While SR1.5 addressed several uncertainty sources, these were assessed individually, not integrated into a single RCB distribution. This study aims to quantify the distribution of TCRE and RCBs by integrating both geophysical and socioeconomic uncertainties, thereby providing a more comprehensive and robust estimate.

Numerous studies have attempted to estimate remaining carbon budgets, resulting in a wide range of estimates due to different approaches and assumptions. The IPCC's Fifth Assessment Report (AR5) and the subsequent Special Report on Global Warming of 1.5°C (SR1.5) provided significant advancements in understanding and quantifying the uncertainties in carbon budget estimations. However, a key knowledge gap existed regarding the integration of geophysical and socioeconomic uncertainties into a single, comprehensive estimate. Previous studies often treated these uncertainties separately, limiting the accuracy and robustness of the resulting RCB estimates. This research builds upon the existing literature by introducing a more holistic framework that explicitly incorporates both types of uncertainties, thereby improving the reliability and precision of the remaining carbon budget estimations.

This study quantifies the distribution of TCRE and RCBs using a framework that separates the effects of individual uncertain factors while estimating their combined impact. The framework uses five input parameters and their respective distributions: 1. **Anthropogenic warming to date (ΔTanth):** Derived from observation-based data (HadCRUT-CW, GISTEMP, and Berkeley Earth datasets). 2. **Cumulative historical CO2 emissions (E):** Derived from the Global Carbon Project's estimates. 3. **Current non-CO2 fraction of total anthropogenic forcing (finc):** Estimated from observationally-constrained model simulations using the FaIR emulator. 4. **Unrealised warming from past CO2 emissions (ΔTZEC):** Incorporates the Zero-Emission Commitment (ZEC) values from the ZECMIP project to account for warming beyond the TCRE in net-zero scenarios. 5. **Non-CO2 fraction of total anthropogenic forcing at net-zero CO2 emissions (ffc):** Captures future non-CO2 forcing uncertainty, varying with the forcing response to specified non-CO2 emissions and socioeconomic pathway uncertainty. The TCRE is expressed as a function of ΔTanth, finc, and E (Equation 1). The total carbon budget (TCB) is then derived (Equation 2), considering ΔTZEC and ffc. The RCB is calculated by subtracting historical CO2 emissions from the TCB (Equation 3). Distributions of TCRE and RCBs are obtained by randomly sampling the input distributions. The impact of socioeconomic uncertainty is assessed by adjusting the relationship between finc and ffc to reflect variations in non-CO2 forcing across SR1.5 scenarios. Geophysical uncertainty is represented quantitatively by probability distributions reflecting current scientific knowledge, while socioeconomic uncertainty is treated separately given its dependence on human decisions.

The study yielded a median TCRE estimate of 0.44 °C per 1000 GtCO2, with a 5–95% range of 0.32–0.62 °C. This range is narrower than previous assessments, particularly at lower TCRE values, reflecting stronger observational constraints. The TCRE distribution is most sensitive to uncertainty in the current non-CO2 forcing (finc), highlighting the importance of better constraining aerosol forcing. The median RCB for a 1.5 °C warming target from 2020 is 440 GtCO2, with a 67% probability of remaining below 1.5 °C at 230 GtCO2. This is lower than SR1.5 estimates, due to explicitly representing a broader range of geophysical uncertainties. Integrating geophysical uncertainties resulted in a narrower RCB distribution compared to SR1.5. The study finds a 17% chance the 1.5 °C RCB is already exceeded. Analysis of socioeconomic uncertainty shows that the median 1.5 °C RCB can shift by ±170 GtCO2 based on future non-CO2 forcing scenarios, demonstrating the significant impact of mitigation choices on the remaining budget. The results underscore the importance of rapid reductions in both CO2 and non-CO2 emissions to limit warming to the goals outlined in the Paris Agreement.

This study's integrated approach provides a more constrained and comprehensive estimate of the remaining carbon budget compared to previous assessments. The narrower uncertainty range in the RCB highlights the value of combining observational constraints with a more complete representation of uncertainties. The significant impact of socioeconomic uncertainty emphasizes the crucial role of human choices in determining the effectiveness of climate mitigation efforts. While the study's results underscore the urgency for rapid emissions reductions, the remaining uncertainties highlight the need for continued research and monitoring.

This research presents a novel framework for estimating the remaining carbon budget that integrates geophysical and socioeconomic uncertainties. The resulting narrower uncertainty range compared to previous estimates provides a more robust assessment of the remaining emissions consistent with various temperature targets. The findings emphasize the critical need for swift and substantial reductions in both CO2 and non-CO2 emissions to meet the Paris Agreement goals. Future research should focus on further refining the understanding and quantification of uncertainties, especially regarding aerosol forcing and the impact of non-linear climate responses at higher warming levels.

The study relies on several assumptions, including the constancy of TCRE across warming levels, the complete reflection of relevant feedbacks in observational data, and the linear proportionality between temperature response and effective radiative forcing. While supported by existing literature, these assumptions may introduce limitations, particularly at higher warming levels or longer timescales. The framework does not explicitly consider potential non-linear responses or tipping points in the climate system. The separation of geophysical and socioeconomic uncertainty is a simplification, as the two are inherently intertwined.