In fact I suspect a multivariate correlation analysis would show that the correlation was negative.
Actually there is a slightly postive correlation that is rooted in first principles. But, it is not anything near that used in the global warming hype.
From observed data:
0.27oC change in Earth's surface temperature for CO2 doubling is depicted in the following graphic:
- The upper horizontal redline represents a temperature of 22.8oC at the chart Cambrian CO2 peak of 7000ppm.
- The second and descending redline is a rough approximation of the average peak temperatures connecting similar conditions of albedo and near constant climate factors removing catastrophic events initiating sporadic iceages. The downtrending redline terminates at approximately 21.6oC and today's 320ppm CO2 concentration.
Which appears to merely be a confirmation of what can determined from first principles:
Given:
The temperature of the Earth's surface with an atmosphere is 288oK (+15oC).
and the blackbody temperature of the Earth without atmosphere at 255oK (-18oC)
One may apply the Stefan-Boltzman relation:
E=sT4
where:
E = total amount of radiation emitted by an object per square meter (Watts m-2)
s is a constant called the Stefan-Boltzman constant = 5.67 x 10-8 Watts m-2 K-4
T is the temperature of the object in K
to determine the total GHG radiative forcing necessary to maintain the atmosphere/surface greenhouse temperature at the current 288oK surface temperature of the earth.
Under constant albedo conditions (CO2 does not contribute to earth's albedo) The total flux at the Earth's troposphere/surface system due to greenhouse factors is:
Flux (E288) at the Earth's surface with atmosphere = 5.67*10-8(288oK)4 = 390.08 w/m2
Blackbody flux (E255) without atmosphere = 5.67*10-8(255oK)4 = 279.74 w/m2
==================================================================
difference = 110.34 w/m2
The (natural + anthropogenic) CO2 contribution is 3.6% of atmospheric greenhouse warming. When expressed in terms of overall radiative forcing acting on both atmosphere and surface all radiative flux associated with CO2 must, of necessity, be:
0.036*110.34 w/m2 = 3.97 w/m2
However, CO2 IR flux at surface temperature from CO2 concentrations in the atmosphere is less than half that total CO2 contribution of 3.97w/m2 to the system, (at least half of the CO2 IR flux is radiated and/or scattered by clouds & dust upward to be lost to space and atmospheric heating rather than contributing towards surface warming.)
Re-cycling of Infra-Red Energy
According to Dr Hugh Ellsaesser's IPCC submission, "The direct increase in radiative heating of the lower atmosphere (tropopause level) due to doubling CO2 is 4 wm-2. At the surface it is 0.5 - 1.5 wm-2". Schlesinger & Mitchell (1985), estimated this surface flux at 2 wm-2. Thus, depending on the model, or modeler, the estimates for increased surface flux following a CO2 doubling, varies between +0.5 and +2 wm-2. An above-averaged figure of +1.5 wm-2 will be assumed here for purposes of analysis and comparison.
Doubling the atmospheric CO2 concentration can only add 1.5w/m2 at the surface for a total surface radiative forcing of
390.08+3.97 = 391.58w/m2
Giving us
(391.58/5.67*10-8)0.25-288oK = 0.277oK (C)increase in surface temperature for doubling of atmospheric CO2 concentration.
A result well within any reasonable expectation of our rough graphic estimate of 0.27oC associated with CO2 doubling derived from the paleo CO2-temperature record in my prior replies.