Connection Between CO2 and Climate Change

Peter Guttorp, University of Washington, Norwegian Computing Center

Fifteen years ago, most scientists had not yet convinced themselves that greenhouse gases led to observable climate change. Indeed, the influence of solar activity was still a viable explanation for the observed increase in average global temperatures, thanks largely to a 1991 Science article by Eigil Friis-Christensen and Knud Lassen that showed temperatures were highly correlated with sunspot numbers.A 1995 Science article by David J. Thomson, titled “The Seasons, Global Temperature, and Precession,” provided the first strong evidence in favor of an observable greenhouse gas effect. Also notable is that the work was based primarily on a careful statistical analysis of the temperature series, rather than on climate models. To me, this paper was the first smoking gun that global warming is connected to the increase of CO2 concentrations in the atmosphere.There have been many works since to substantiate the connections, but an explanation of Thomson’s paper may be helpful to Amstat News readers.The amount of solar radiation reaching the Earth depends on the angle of Earth’s rotation to the ecliptic (the plane of the orbit) and its distance from the Sun (because the Earth’s orbit is elliptical). The former follows the “tropical” year, the time between two vernal equinoxes, which is 365.2442 days and governs seasons. The distance of the Earth from the sun follows the “anomalistic” year, the time between aphelion (farthest point from the sun) in Earth’s orbit, which is currently 365.2596 days.The interaction between these two cycles so close in time yields long temperature cycles, which result in the quarternary ice ages. The shortest of these cycles is about 26,000 years, very long compared to the instrumental record of temperature.Because these cycles are so close in value, one must use statistical tools to study their influences. Complex demodulation, in effect, removes one of the influencing cycles and looks at the remaining spectrum of a quantity, called the “phase.”

Phase of the Jones-Wigley Northern Hemisphere temperature series (solid) with average phase from 156 northerly land stations (dashed) and the line expected if the anomalistic year frequency dominates the tropical yearWhen one removes the influence of the tropical year, the phase should be flat if the dominant frequency is that of the tropical year. If the anomalistic year is dominant, we would expect to see a linear phase in the residuals with slope equal to the inverse of the difference between the frequencies (57.3 arc seconds per year). The figure above shows the phase of the Jones-Wigley Northern Hemisphere temperature series (solid line), the average phase for 156 stations above 23°N (dashed line) and the dotted line with a slope equal to the precession constant (the rate at which the Earth’s axis rotates).The analysis shows that between 1880 and 1920 the dominant frequency in the temperature series is the anomalistic one. To explain the phase diagram after 1920, a statistician would look at the “residuals,” the difference between the predicted (dotted) line and the estimated phase. The figure below shows the residuals, together with a fit to the logarithm of atmospheric CO2 levels.

Since the fit is excellent, we have two possible explanations: Either the CO2 levels are influencing the phase and thus changing the distribution of temperature (i.e., the climate) or there is a common underlying feature driving both the phase change and CO2 levels. No mechanism has been proposed that can do the latter.Graphics reprinted with permission from The American Association for the Advancement of Science