Proc. Natl. Acad. Sci. USA
Vol. 94, pp. 83708377, August 1997
Colloquium Paper
This paper was presented at a colloquium entitled Carbon Dioxide and Climate Change, organized by Charles D. Keeling, held Nov. 1315, 1995, at the National Academy of Sciences, Irvine, CA.
Dependence of global temperatures on atmospheric CO_{2} and solar irradiance
DAVID J. THOMSON
Mathematics of Communications Research Department, Bell Laboratories, Murray Hill, NJ 07974
ABSTRACT Changes in global average temperatures and of the seasonal cycle are strongly coupled to the concentration of atmospheric CO_{2}. I estimate transfer functions from changes in atmospheric CO_{2} and from changes in solar irradiance to hemispheric temperatures that have been corrected for the effects of precession. They show that changes from CO_{2} over the last century are about three times larger than those from changes in solar irradiance. The increase in global average temperature during the last century is at least 20 times the SD of the residual temperature series left when the effects of CO_{2} and changes in solar irradiance are subtracted.
Although it is generally conceded that the average surface temperature of the Earth has increased by about 0.6°C during the last century, there is little agreement on the cause of this warming. The primary cause of this disagreement is uncertainty about the relative contribution to this warming of atmospheric CO_{2} and changes in solar irradiance. The purpose of this paper is to describe some data analysis that may help to discriminate between solar and CO_{2} effects, and to give estimates of the relative magnitudes of these two effects. The difference between analysis such as those described in ref. 1 and those here is that this data analysis is based on deseasonalized temperature time series where the effects of precession were included. * The detection of precession in instrumental temperature series and the necessity of including it when removing the annual cycle from temperature data was demonstrated in ref. 2. I also describe some of the statistical peculiarities and limitations of these data series and suggest where better data are needed.
The paper begins with a discussion of the data being analyzed and, to delineate the issues, presents some ordinary leastsquares fits of the temperature data with atmospheric CO_{2} concentration and changes in solar irradiance. I next discuss the mathematical methods used and describe some statistical properties of the various data series. This is followed by some simple estimates of the transfer functions between fossil fuel consumption and atmospheric CO_{2} levels and from CO_{2} levels and changes in solar irradiance to temperature. The penultimate section summarizes recent findings on destabilization of the annual cycle, followed by conclusions.
In these analyses I do not directly take into account the effects of stratospheric aerosols nor various internal feedback mechanisms such as cloud cover. Stratospheric aerosols are generally believed ( 3 , 4 ) to result in cooling, so their omission makes the estimates for sensitivity conservative. Similarly, while a detailed understanding of internal feedback mechanisms, such as water vapor, is necessary to predict temperature changes from first principles, one may use measurements to assess the general climate response to forcing without having to consider the internal feedbacks explicitly, much as one can design a filter using operational amplifiers without detailed consideration of the quantum mechanics, or even current flow, in the individual transistors in the amplifiers.
The estimates given here depend neither on general circulation models nor on the assumptions that underlie such models. The transfer functions are estimated directly from observations of temperature and CO_{2} and, for solar irradiance, a physically based proxy data series.
Data Sources and Preparation
For measurements of surface air temperature I use the lowpass filtered JonesWigley Land plus Marine data ( 5 ) shown in figures 9 and 10 of ref. 2. The bandwidth of the lowpass filter was 0.5 cycle/year so the Nyquist rate is one sample per year. These series differ from the ones usually seen in two important aspects: First, I replaced the standard deseasonalizing procedure used to produce temperature anomaly series with a projection filter separation into lowpass, annual, and highfrequency components so, implicitly, the usual boxcar runningmean smoother has been replaced with a lowpass filter. Second, instead of assuming a constant amplitude climatology with a period of 1 calendar year, I allowed the phase of the annual components to track the observed phase. Thus, the significant changes in the annual cycle caused by the changing balance between direct insolation, periodic at one cycle per tropical year, and transported heat, periodic at one cycle per anomalistic year, has been removed from the data, eliminating the spurious monthly trends associated with temperature anomaly series ( 2 , 6 ). Note that, although the timeresolution of these series is one year, the series is as smooth as that given by the usual boxcar procedure at decadescale resolution. The Global temperature series used here is the arithmetic average of the Northern and Southern Hemisphere series. The Northern Hemisphere, Southern Hemisphere, and Global series are denoted by T_{n}(t), T_{s}(t), and T_{g}(t) respectively, with t the Gregorian calendar date.
In this paper I use the average temperature over the 65 years from 1854 to 1918 as a base reference. There are several reasons to prefer this period to the usual 19511980 reference period. First, based on the sunspot record, solar activity in the 18541918 period appears to be representative of the 245year available record and 65 years covers most of the 88year Gleisberg cycle ( 7 ). Second, median fossil fuel consumption in this period was only about 6% of the current rate and the

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* 
Briefly, the annual temperature cycle at a given latitude consists of direct insolation plus transport effects. The direct insolation components vary with the tropical year, the time from equinox to equinox, 365.2422 days, while the net radiation received by earth and hence the mean transport vary as the anomalistic year, the time from perihelion to perihelion, or 365.2596 days. Precession, loosely defined, is the change in the longitude of perihelion measured from the vernal equinox. 