Atmospheric Retention of Man-made CO2 Emissions

Rust and Thijsse [9, 11] have shown that global annual average temperature anomalies T (ti) vary linearly with atmospheric CO2 concentrations c(ti). The c(ti) can be related to man-made CO2 emissions F (ti) by a linear regression model whose solution vector gives the unknown retention fractions γ(ti) of the F (ti) in the atmosphere. Gaps in the c(ti) record make the system underdetermined, but the constraints 0 ≤ γ(ti) ≤ 1 make estimation tractable. The γ(ti) are estimated by two methods: (1) assuming a finite harmonic expansion for γ(t), and (2) using a constrained least squares algorithm [8] to compute average values of γ(t) on suitably chosen time subintervals. The two methods give consistent results and show that γ(t) declined non-monotonically from ≈ 0.6 in 1850 to ≈ 0.4 in 2000. 1 Atmospheric CO2 and Global Temperatures The upper plot in Figure 1 shows an optimal regression spline [11] fit c(t) to the record of atmospheric CO2 concentrations obtained by combining atmospheric measurements at the South Pole [5] with reconstructions from Antarctic ice cores [1, 7]. Although the latter display larger random variations than the former, the two records are consistent in the years where they overlap. The spline c(t) was used to model the Climatic Research Unit’s record [4] of annual average global surface temperature anomalies shown in the lower plot. The solid curve was obtained by fitting the model T (t) = T0 + η [c(t)− 277.04] + A sin [