http://math.nist.gov/~BRust/pubs/MAMERN09/PreprintMAMERN09.pdf 1 Atmospheric CO2 and Global Temperatures The upper plot in Figure 1 shows an optimal regression spline  fit c(t) to the record of atmospheric CO2 concentrations obtained by combining atmospheric measurements at the South Pole  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 Units record  of annual average global surface temperature anomalies shown in the lower plot. The solid curve was obtained by fitting the model T(t) = T0 + [c(t) − 277.04] + Asin 2 (t + ) , with free parameters T0, , A, , and . The constant 277.04 ppmv is the preindustrial CO2 concentration estimated by averaging ice-core measurements for 1647-1764. The corresponding temperature anomaly, estimated by the fit, was T0 = (−0.507 ± .016)◦C. The sinusoid, with = (71.5 ± 2.2) yr and A = (0.099 ± .012)◦C, represents the oscillation discovered by Schlesinger and Ramankutty . It accounts for 8 %of the variance in the record. The baseline T0 + [c(t) − 277.04], with = (0.01039± .00042) ◦C/ppmv, accounts for 77 % of the variance. It indicates a linear relationship between global warming and increasing atmospheric CO2. The total warming since 1856 has been 0.9◦C, and that warming is accelerating.