Tag Archives: CO2 Sensitivity

The Numbers Don’t Work

by James R. Barrante, Ph.D.

The major idea driving the greenhouse gas effect originates with the observation from the late 1800’s that planet Earth is warmer than similar planets of the same size and distance from their star.  The reason given by a number of scientists, including the physical chemist Svante Arrhenius, was that it was because Earth had an atmosphere containing specific gases that could absorb a portion of the infrared light radiated by the planet and return it to the planet.  The Earth receives light from the sun that warms the planet.  In turn, in order to maintain a constant temperature, Earth must radiate a portion of the light back to space.  The wavelengths of light radiated by the planet fall in a band in the infrared region of the light spectrum, controlled by the Earth’s temperature.  Any interference in this process, such as the absorption of this infrared radiation by atmospheric gases,  will upset the energy balance of the planet.

The two major gases able to intercept wavelengths of infrared light radiated by the planet are water vapor (its level varies with climate, so let us assume an average level of about 2%), and carbon dioxide (about 0.04%).  These two gases are known as “greenhouse gases.”  Just from the concentration difference alone, we can see that water vapor is the major player here.  Moreover, water vapor is able to absorb a much wider band of infrared light than is CO2.  Most scientists agree that of the total radiation absorbed, water vapor absorbs about 90%.

Based on calculations made by assuming the planet was a blackbody radiator, it was found that the planet was 33ºC warmer than it should be, supposedly caused by our atmosphere.  Assuming that the two major greenhouse gases are water vapor and carbon dioxide, carbon dioxide would be responsible for 10%, or 3.3ºC, of that warming.  That is, increasing the CO2 in the atmosphere from 0 ppmv (parts per million by volume) to the 1850’s value of 280 ppmv should have raised the temperature of the planet by 3.3ºC.  It is well known that the absorption of light by matter is not linear with concentration, but falls off exponentially or logarithmically.  In the late 19th century, Arrhenius suggested a simple equation to relate the amount of warming by a greenhouse gas to its level in the atmosphere to be

ΔT = T2 – T1  =  ln (C2/C1)

where k is an experimentally determined constant and ln is the natural logarithm.  We can see that this equation is problematic, if the concentration C1 is equal to zero.  So let us modify the equation by choosing some very small level of CO2 to represent zero concentration.  (It turns out that this choice is quite arbitrary, as long as it is very small).  The new equation becomes


Using the original premise that the presence of CO2 in the atmosphere raised the temperature of the globe by 3.3 degrees, we can determine the constant k.

3.3  =  ln (280/1 × 10¯¹º)

k  =  0.115ºC

We are now able to see how global temperature changes with increasing concentration of CO2.  It is clear that if you double the concentration of CO2 in the atmosphere, global temperature will increase by a whopping 0.08°C.  So, increasing the CO2 level from 0 ppmv to 100 ppmv, raised global temperature by 3.2°C; further increasing the level from 100 ppmv to 200 ppmv raised global temperature by 0.08ºC; and further raising the level from 200 ppmv to 300 ppmv raised global temperature by 0.05ºC.

A number of years ago climate scientists announced that the increase in CO2 level from its 1850’s value of 280 ppmv to the present value of about 380 ppmv raised global temperature by 0.8ºC.  Let’s see how that squares with our modified Arrhenius equation.

ΔT  =  0.115 ln (380/280)  =  0.035ºC

Not very good, is it!  Something obviously is wrong!  Whatever the case, it is apparent that associating a 0.8ºC temperature increase in global temperature with an increase in the CO2 level from 280 ppmv to 380 ppmv is not at all consistent with the CO2 and water vapor’s warming the planet by 33ºC as described by the climate-change crowd.  The numbers do not work!




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