ATMOSPHERIC RADIATIVE FORCING (WARMING EFFECT) OF CARBON DIOXIDE AT ANY CONCENTRATION

CALCULATION OF ATMOSPHERIC RADIATIVE FORCING (WARMING EFFECT) OF CARBON DIOXIDE AT ANY CONCENTRATION* by H. Douglas Lightfoot and Orval A. Mamer (Canada) November 8, 2014 Summary for wide circulation This is a scientific paper and such papers are often not readily understood beyond the scientific community. Because the results of this paper are important to the present debate about carbon dioxide emissions, this short summary is prepared for much wider circulation.

Carbon dioxide (CO2) is a warming gas because it captures infrared heat radiation (IR) from the earth and warms the air surrounding it. At a given concentration of CO2, a certain amount of the available IR is absorbed by the CO2. If more CO2 is added, the warming effect of the added CO2 is less per molecule because some of the IR has already been absorbed. At some point, further additions of CO2 will have no warming effect because all of the available IR will have been absorbed Currently, there is general agreement that the relationship between warming and concentration is a logarithm curve, a mathematical curve with a characteristic shape.

This curve works well within the current concentration range of interest of 275 in 1750 to 378 parts per million by volume (ppmv) in 2005. Problems beyond this range limit its usefulness. For example, it does not start at zero and, therefore, does not give actual warming measurements, but only the difference between two concentrations. There are no limits as to where the logarithmic curve is valid and where it is not, and there is no upper limit because the curve continues upwards indefinitely.

To resolve these problems, by trial and error we found a quadratic curve, which has a different characteristic shape from that of the logarithm. It exactly matches the logarithm curve over the range of 275 to 378 ppmv, starts at zero and reaches a limit where the curve becomes horizontal. The fact that the curve starts at zero establishes the warming effect at 378 ppmv as 8.67 watts per square metre (W m-2). The upper limit of concentration where the curve becomes horizontal is calculated exactly by calculus at 654.6 ppmv. We also found a sine curve, which has different characteristic shape again, that does the same as the quadratic, but with a warming effect at 378 ppmv of 7.48 W m-2. Any mathematical curve that meets the restrictions will have warming values close to 8.67 or 7.48 W m-2. *From: ENERGY & ENVIRONMENT, VOLUME 25, NOV 8, 2014, MULTI-SCIENCE PUBLISHING COMPANY LTD 1

The total warming effect of all of the greenhouse gases is 324 W m-2. Thus, CO2 is (8.67/324) = 2.7% of the total. The other greenhouse gases, except for water vapour, account for 0.7%. Therefore, water vapour accounts for (100 – 3.4) ≈ 96% of global warming.

We can confirm this conclusion by calculating the average number of molecules of water vapour for each molecule of CO2 in the atmosphere. The temperature and relative humidity (RH) is readily available for many cities around the globe, and with this information we can calculate the weight of water per kilogram of dry air. Using chemistry we can calculate the number of molecules of water vapour per molecule of CO2 at a concentration of 378 ppmv, the concentration in 2005. At 50% RH and 15oC, the earth’s average temperature, there are 23 molecules of water vapour per molecule of CO2. Therefore, CO2 accounts for (1/23) = 4.3%. Making allowance for the fact that water vapour molecules are more effective than CO2 molecules at absorbing IR, CO2 accounts for 2.7% of global warming. Thus, water vapour accounts for approximately 96% of global warming. This method is scientifically sound and relatively simple for anyone to replicate. The temperature, RH and concentration of CO2 are readily available measured values. Calculation of water vapour as grams per kilogram of dry air is by an easy to use psychrometric chart, which is an accurate tool of heating and ventilating engineers. The chemistry is well known.

The results of these two independent scientific methods agree and show conclusively that CO2 is a very small part of global warming, and that whatever controls the level of water vapour in the atmosphere controls atmospheric temperature.

*From: ENERGY & ENVIRONMENT, VOLUME 25, NOV 8, 2014, MULTI-SCIENCE PUBLISHING COMPANY LTD 2