L. David Roper
6 April, 2016
I recently showed that Earth average temperature lags atmosphere CO2 concentration since 1959 by about 6 years.
In the work reported here I did a linear fit of the Earth average temperature to the atmospheric CO2 concentration from 1959 to 2008. Then I add sunspot numbers to the fit. It is known that an increase in sunspot numbers correlates with a slight increase of solar radiation.
The equation for the fit is T = -3.384 + 0.000587*Sunspots + 0.01001*CO2 . The fit is shown in the following graph:
The chi-square for the fit without using sunspot numbers is 0.5118; using sunspot numbers it is 0.4728, a 7.6% decrease.
Subtracting the fit from the data yields the remainder curve shown in the following graph:
There appears to be an approximate oscillating period of about 0.7 years, but with a non-constant amplitude.
After completing the above work I decided to extend it back to 1880 for which good values for Earth average temperatures are known. To do this I had to find a way to extend the atmospheric CO2 concentration from 1959 back to 1880. I did this by fitting a hyperbolic tangent to the atmospheric CO2 concentration data between 1959 and 2008. The resulting atmospheric CO2 concentration and sunspot numbers are shown in the following graph:
The linear fit of the Earth average temperature to the atmospheric CO2 concentration and both the atmospheric CO2 concentration and the sunspot numbers are shown in the following graph:
The chi-square for the fit without using sunspot numbers is 1.6648; using sunspot numbers it is 1.6365, a 1.6% decrease. So, over this larger yearly range, sunspot numbers do not effect the Earth average temperature very much
The Earth-average-temperature data are fitted well by a linear equation in the atmospheric CO2 concentration, except for an approximate oscillation of period about 0.7 years. Adding a linear term for sunspot numbers inproves the fit, but still leaves the approximate 0.7-years oscillation.
Roper Global-Heating Web Pages
L. David Roper interdisciplinary studies