A mathematical model of atmospheric retention of man-made CO2 emissions

Rust and Thijsse have previously shown that changes in global annual average temperature anomalies T(ti) compiled by the Climatic Research Unit 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 to compute average values of γ(t) on suitably chosen time subintervals. The final result is an estimate of γ(t) with enough accuracy to establish the connection between emissions from fossil fuel use and land use changes and increases in global average annual temperature anomalies.