Rust and Thijsse [Proc. CSC'07 (2007) pp. 10-16], [CiSE, Vol. 10 (2008) pp. 49-59] have shown that global annual average temperature anomalies T(t) vary linearly with atmospheric CO_2 concentrations c(t). The c(t) can be related to man-made CO_2 emissions F(t) by a linear regression model whose solution vector gives the unknown retention fractions gamma(t) of the F(t) in the atmosphere. Gaps in the c(t) record make the system underdetermined, but the constraints 0 <= gamma(t) <= 1 make estimation tractable. The gamma(t) are estimated by two methods: (1) assuming a finite harmonic expansion for gamma(t), and (2) using a constrained least squares algorithm [Pierce and Rust, SIAM J. Sci. Stat. Comput., Vol. 6 (1985) pp. 670-683] to compute average values of gamma(t) on suitably chosen time subintervals. The final result is an estimate of gamma(t) with enough accuracy to firmly establish a simple mathematical relationship between man-made emissions and global warming.
Citation: Mathematics and Computers in Simulation
Pub Type: Journals
atmospherAic CO_2, CO_2 emissions, global Temperatures, global Warming