Old Rocks
Diamond Member
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 [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 Units 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 + [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 [10]. 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.
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 Units 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 + [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 [10]. 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.