CO2 or Sunspots: Statistical Correlation Chooses

Statistical correlation is a powerful technique with
very many uses. It produces "R squared" a measure of
whether two series of measures trend together.

(Those who are new to statistical correlation and
"R squared" will find a tutorial on the subject he

http://mathworld.wolfram.com/Correlation.html

http://mathworld.wolfram.com/Correla...efficient.html

Item 20 in the above shows R squared for several graphed
relationships.)

When applied to a time series of global mean surface
temperatures and data from prospective global warming
causes covering the same time period, correlation can
help locate the cause of the observed global warming.
Low "R squared" values, those near zero, can, by
themselves, totally rule out a prospective cause.
High "R squared" values indicate that a prospective
cause is very likely, but do not, by themselves,
'prove' something caused the warming. (Experimental
science rarely 'proves' something like a mathematical
proof does.)


Below are directly observed data for global mean surface
temperature, CO2 concentration, and sunspots for the last
50 years. This is as long as the longest directly
observed record of atmospheric CO2 concentration.

The R^2 value for the correlation of CO2 and planetary
surface temperature is 0.78. The simple rising
line showing heating for increasing CO2 explains a
lot of the variance in the global mean temperature.
The relationship between CO2 and global temperature
is very strong and the anthropogenic greenhouse gas
radiative forcing theory is well supported by these
data.

The R^2 value for sunspots and and planetary
surface temperature is very near zero. These data
clearly do not support any relationship between
sunspot numbers and global mean surface temperature
over the last 50 years. It is very unlikely that
sunspots have anything to do with the current
global warming.

This test applies very easily to all other claims for
global warming causes. It will quickly separate the
wheat from the chaff.


-.-. --.- Roger Coppock

=-=-=-=-=-=-= The Data =-=-=-=-=-=-=
The global mean surface "Temp"erature data are the GISS
adjusted J-D yearly land and sea average, available from
NASA at:

http://data.giss.nasa.gov/gistemp/ta...LB.Ts+dSST.txt


The "CO2" data are the yearly averages of the monthly data
from the Keeling curve measured at Mauna Loa, available at:

ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt


"Sunspots" are the yearly averages of the monthly means
in the NOAA NGDC "MONTHLY" file. They are available at
the FTP site accessed through this web page:

http://www.ngdc.noaa.gov/stp/SOLAR/SSN/ssn.html


Year Temp CO2 Sunspots
1958 14.08 315.33 184.5917
1959 14.06 315.98 158.75
1960 13.99 316.91 112.275
1961 14.08 317.65 53.8833
1962 14.04 318.46 37.6
1963 14.08 318.99 27.8917
1964 13.79 319.20 10.2
1965 13.89 320.03 15.0583
1966 13.97 321.37 46.875
1967 14.00 322.18 93.6667
1968 13.96 323.05 105.8917
1969 14.08 324.62 105.5583
1970 14.03 325.68 104.6917
1971 13.90 326.32 66.65
1972 14.00 327.46 68.9333
1973 14.14 329.68 38.15
1974 13.92 330.17 34.4083
1975 13.95 331.14 15.4583
1976 13.84 332.06 12.55
1977 14.13 333.78 27.4833
1978 14.02 335.40 92.6583
1979 14.09 336.78 155.275
1980 14.18 338.70 154.65
1981 14.27 340.11 140.45
1982 14.05 340.98 116.2917
1983 14.26 342.84 66.6333
1984 14.09 344.20 45.85
1985 14.06 345.87 17.9417
1986 14.13 347.19 13.4
1987 14.27 348.98 29.225
1988 14.31 351.45 100
1989 14.19 352.89 157.7917
1990 14.38 354.16 142.2917
1991 14.35 355.48 145.775
1992 14.12 356.27 94.4833
1993 14.14 356.96 54.7333
1994 14.24 358.63 29.8667
1995 14.38 360.63 17.5
1996 14.30 362.37 8.625
1997 14.40 363.47 21.4833
1998 14.57 366.50 64.2083
1999 14.33 368.14 93.175
2000 14.33 369.41 119.5333
2001 14.48 371.07 110.925
2002 14.56 373.16 104.0917
2003 14.55 375.80 63.5667
2004 14.49 377.55 40.4417
2005 14.62 379.75 29.7833
2006 14.54 381.85 15.1833
2007 14.57 383.72 7.5417

=-=-=-=-=-=-= "R" Program Outputs =-=-=-=-=-=-=
The following are outputs of the "R" statistical program:
For information on "R," please see:

http://www.r-project.org/

--------

Call:
lm(formula = Temp ~ CO2, data = aframe)

Residuals:
Min 1Q Median 3Q Max
-0.2316612 -0.0805322 0.0185249 0.0763159 0.1798386

Coefficients:
Estimate Std. Error t value Pr(|t|)
(Intercept) 1.10008e+01 2.41721e-01 45.5103 2.22e-16 ***
CO2 9.24797e-03 7.01018e-04 13.1922 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.101321 on 48 degrees of freedom
Multiple R-Squared: 0.783817, Adjusted R-squared: 0.779313
F-statistic: 174.034 on 1 and 48 DF, p-value: 2.220e-16

--------

Call:
lm(formula = Temp ~ Sunspots, data = aframe)

Residuals:
Min 1Q Median 3Q Max
-0.3909495 -0.1523184 -0.0514594 0.1445919 0.4380756

Coefficients:
Estimate Std. Error t value Pr(|t|)
(Intercept) 1.41804e+01 5.39054e-02 263.06149 2e-16 ***
Sunspots 4.97803e-05 6.18766e-04 0.08045 0.93621
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.217902 on 48 degrees of freedom
Multiple R-Squared: 0.000134823, Adjusted R-squared: -0.0206957
F-statistic: 0.00647235 on 1 and 48 DF, p-value: 0.936213