The global fraction of anthropogenically emitted CO2 that stays in the atmosphere, the CO2 airborne fraction, has been fluctuating around a constant value over the recent period of 1959-2021. The consensus estimate of the airborne fraction is around $44\%$, indicating that approximately $44\%$ of emitted CO2 stays in the atmosphere and the remaining $56\%$ is absorbed by the oceanic and terrestrial biospheres. In this study, we show that the conventional estimator of the airborne fraction suffers from a number of statistical deficiencies, such as non-existence of moments and a non-Gaussian limiting distribution. We formulate a new estimator of the airborne fraction that does not suffer from these deficiencies. We show that the new estimator is superconsistent, has a Gaussian limiting distribution, and is able to reduce estimation uncertainty substantially. Our empirical analysis leads to an estimate of the airborne fraction over 1959-2021 of $47.6\%$ ($\pm 1.1\%$; $1 \sigma$). Hence, our empirical results imply a higher, and better constrained, airborne fraction than the current consensus. Our theoretical results indicate that a conventional analysis of the airborne fraction may be problematic, especially in future low emissions scenarios such as those implied by "net zero" international agreements. Our newly proposed estimator avoids these issues and thus provides a promising approach to future studies of the airborne fraction, especially in low emission scenarios.

翻译：人为排放的二氧化碳中滞留在大气中的全球比例（即二氧化碳大气留存率）在1959-2021年近期时段内围绕恒定值波动。目前学界普遍认为该留存率约为$44\%$，意味着约$44\%$的排放二氧化碳滞留大气，其余$56\%$被海洋和陆地生物圈吸收。本研究表明，传统的大气留存率估计量存在多项统计缺陷，包括矩不存在和极限分布非高斯性等问题。我们提出了一种新型估计量，该估计量不存在上述缺陷。研究发现新估计量具有超一致性、高斯极限分布特征，并能显著降低估计不确定性。实证分析表明，1959-2021年期间的大气留存率为$47.6\%$（$\pm 1.1\%$；$1\sigma$）。因此，我们的实证结果揭示了比当前共识更高且约束更优的大气留存率。理论结果表明，传统大气留存率分析可能存在问题，特别是在未来低排放情景（如国际"净零"协议所隐含的路径）下。我们提出的新型估计量规避了这些问题，为未来大气留存率研究（尤其在低排放情景下）提供了具有前景的研究路径。