What temperature rise does a doubling of atmospheric CO2 lead to? Overall, the IPCC says anywhere from about 2 – 6°C, i.e. they don’t know.
Recently the Germany-based European Institute for Climate and Energy (EIKE) posted an essay by Dr. Wolfgang Burkel, who concludes that doubling atmospheric CO2 will lead only to a 0.58°C of warming at the Earth’s surface.
What follows is a translation and summary of his essay.
Dr. Burkel’s calculation method looks at the energy balance directly at the Earth’s surface. Evaporative cooling of additional water vapor is so powerful that only 0.58°C of warming is enough for compensating a doubling of CO2 concentration.
Anthropogeníc Greenhouse Effect Too Weak For A Climate Catastrophe!
By Wolfgang Burkel
The greenhouse effect of CO2 is expressed by the formula: dF = 5.75ln(C/Co).
Figure 1: Logarithmic climate sensitivity of CO2.
Figure 1 shows that a doubling of CO2 concentration delivers an additional radiative forcing of 3.7 W/m², which in turn leads to an atmospheric warming of about 1°C, which is accepted by almost all scientists. The IPCC provides a figure of 1.2°C; Lüdecke and Link  calculate 1.1°C. Other sources provide similar values.
The problems begin when the results are carried over to the Earth’s surface. Suddenly the values diverge immensely. Even within the IPCC itself there is no agreement. See the following chart:
Figure 2: CO2 effect according to the IPCC AR4 2007.
First of all one sees that the values in the table appear as guesses, and are thus alien to any scientific method. The reason for this are the varying estimates of ‘positive feedbacks’, which are built into the politically dominated models. But logic does not support a positive feedback. How should a small warming of the atmosphere lead to a large warming at the Earth’s surface?
Why does one calculate a change in global temperature by taking a detour through the atmosphere? The result is useless because there is no consensus on what it means for the Earth’s surface.
Figure 3: Energy budget at the Earth’s surface and change through the greenhouse effect (in parentheses): Evaporation 84 W/m² (+4); Radiation 45 W/m² (-4) and convection 17 W/m² (+0). Absorbed from the sun 140 W/m² (+/- 0). Earth’s surface temperature: 15°C (+0.58°C).
Figure 3 shows the heat flux as part of the energy budget. What happens in the atmosphere or at the outer edge is insignificant for the energy balance. The energy at the Earth’s surface eventually finds its way out into outer space.
There’s a consensus on the magnitudes of the energy flux: evaporation is 84 W/m², radiation is 45 W/m² and convection is 17 W/m². A change in one is compensated by the others. Anthropogenic greenhouse effect reduces the energy flux from radiation. But then the temperature of the Earth’s surface rises until a new equilibrium gets established.
For calculating the warming, the dependence of the three above-mentioned transport mechanisms on temperature is used.
Evaporation of water removes heat from the Earth’s surface and transports it to the upper atmosphere, where it gets dumped as the vapor condenses. For the stability of the climate, this is of great importance because the evaporation heat is strongly dependent on the Earth’s surface temperature. With an average of 84 W/m², evaporation provides almost 60% of the heat transport from the Earth’s surface towards the upper atmosphere. We know that precipitation on Earth has increased over the last 100 years, and thus transports more heat back to the upper atmosphere, away from the Earth’s surface.
A warming of 1°C increases heat transport due to evaporation back to the upper atmosphere by 7.5%. At 84 W/m², that translates to 6.3 W/m² of additional cooling effect for the Earth’s surface. As we see, evaporation acts as a powerful brake against changes in climate.
About 70% of the long-wave radiation from the Earth’s surface is absorbed by the greenhouse gases. Direct radiation from the Earth’s surface into space is about 45 W/m². This value is reduced somewhat by the higher anthropogenic greenhouse effect. A doubling of atmospheric CO2 concentration results in a radiation reduction of 4 W/m² (as mentioned earlier).
But radiation intensity is proportional to the 4th power of the absolute temperature. A warming of 1°C translates to 1.4%, or 0.63W/m².
There’s also a feedback from additional water vapour in the air. Using Figure 5 below, water vapor at its current concentration delivers a maximum 8 W/m² of radiative forcing.
Figure 5: The effect of greenhouse gases on thermal radiiation.
And with 7.5% more water vapor, this yields an additional radiative forcing of 0.6 W/m². Note that Figure 5 shows that effect of various greenhouse gases greatly depends on the spectrum wavelength.
Figure 5 shows that the effect of CO2 as a greenhouse gas is limited to a narrow long-wave range in the neighborhood of 14 microns, and is for the most part saturated.
Also additional water vapor has only a marginal impact.
As the Earth’s surface temperature rises, warm air travels up and transports heat to the upper atmosphere. Convection provides only about 12% of this outward heat transfer, and thus we will neglect it here.
Tallying it all up
Summary of changes in energy flux resulting from 1°C of warming:
Evaporation: +7.5% = 6.3 W/m²
Radiation: +1.4% = 0.63 W/m²
Feedback through water vapor: 0.6 W/m²
A warming of 1°C of results in an additional cooling effect of a total of 6.33W/m² because of mechanisms that transport heat away from the Earth’s surface and towards the upper atmosphere.
And we already know that doubling the atmospheric CO2 concentration leads to a radiative forcing of only 3.7 W/m², see Figure 6:
Figure 6: Warming as a function of CO2 concentration. Doubling CO2 concentration leads to a radiative warming of 3.7W/m². A 1°C warming leads to a tarnsport mechansim effect of 6.3W/m².
Using Figure 6, the exact value for climate warming is 0.58°C.
How does this figure compare to the current discussion? This figure is in agreement with Lindzen and Choi of MIT . These two scientists quantified the climate sensitivity at 0.5°C using satellite data, i.e. real observations and not dubious computer simulations.
Hermann Harde  found a climate sensitivity of 0.62°C using spectroscopic examinations and model calculations.
The minimal effect of CO2 on climate is not surprising. This is confirmed by both theory and by actual observations and measurements.