AUSTRALIA’S Minister for Climate Change, Penny Wong, recently suggested that most of the global warming since 1960, about 85 percent, has happened in the oceans and that change in ocean heat content is thus the most appropriate measure of global warming.
In my previous post, working from first principles, I determined a discrepancy of 9:1 in the rate of warming from Australian government data relative to IPCC findings. In reviewing these calculations I now realise I made a significant error. I had wrongly assumed that the claimed positive feedback from water vapour was proportional to the carbon dioxide concentration. This is not correct, the claimed positive feedback is proportional to the temperature rise and that change does make a difference to the calculations and needs to be corrected. The revised calculations still show a paradox although only about 3:1.
I had calculated the heating sensitivity of Earth (kappa) by differentiating Stefan’s law for a temperature of 255K and this came out as 0.266C/watt/m2. That figure is very much in keeping with the findings of others for example Soden and Held (2006) 0.25C/w/m2 , Hansen et al (1984) 0.26C/w/m2 , Bony et al (2006) 0.263C/w/m2 , Colman (2003) 0.30C/w/m2 , Kiehl (1992) 0.305C/w/m2 . For a 3C rise, kappa predicts the additional retained heat is 3/0.266 = 11.3 watts/m2 for doubling of carbon dioxide. A significant fraction of this 11.3 watts/m2 comes from the claimed positive feedback effect of rising water vapour. My error occurred in calculating a current retained heat of 11.3 * 0.45 = 5.1 watts/m2 in 2006 (0.45 doublings of carbon dioxide) because we have not seen the full equilibrium rise in temperature (otherwise there would be no net energy flow into the oceans) therefore we will not be experiencing all the claimed positive feedback from water vapour. That means my figure of 5.1 watts/m2 is too high.
I repeat the calculations more accurately below.
If the feedback is proportional to the temperature, (water vapour increases exponentially with temperature but its effect is logarithmic therefore the effect will be the logarithm of an exponential which is linear) then it is indeed valid to allow for the positive feedback by adjusting the heating sensitivity of Earth rather than calculating the positive feedback explicitly in watts/m2. In short, instead of using kappa (the sensitivity without feedbacks) use lambda the sensitivity with feedbacks factored in. This is the approach adopted by many other scientists.
Popular reporting suggests a temperature rise between now and 2070 of 3C. In fact checking back to the IPCC 4th assessment report what is actually claimed is that a doubling of carbon dioxide leads to an increase of 3C which is somewhat different to popular reports. Doubling carbon dioxide leads to a direct increase in retained energy of about 3.7 watts/m2 which would mean a value for lambda of 0.81 (3/3.7).
So how much heating has occurred? The temperature of the planet has been going up and down all the time. By selecting an appropriate reference year one can claim almost any warming one desires. However several sources all claim that AGW only started around the end of the second world war and temperature changes prior to that time were of natural origin. For example from Wikipedia;
“The Intergovernmental Panel on Climate Change concludes that increasing greenhouse gas concentrations resulting from human activity such as fossil fuel burning and deforestation are responsible for most of the observed temperature increase since the middle of the 20th century. The IPCC also concludes that natural phenomena such as solar variation and volcanoes produced most of the warming from pre-industrial times to 1950 and had a small cooling effect afterwards. These basic conclusions have been endorsed by more than 45 scientific societies and academies of science”.
http://www.grida.no/publications/other/ipcc%5Ftar/?src=/CLIMATE/IPCC_TAR/wg1/005.htm shows 0.4C warming since about 1950 although I shows the temperature at that time changing by 0.2C in 5 years so the exact point chosen makes a large difference.
http://www.pnas.org/content/103/39/14288/F1.large.jpg shows between 0.4C and 0.5C
http://data.giss.nasa.gov/gistemp/2005/ shows about 0.4C since 1945
I also note that the government paper specifically talks about ocean heating since 1960 further reinforcing this point. In fact their data shows no ocean heating prior to 1975.
Using a temperature rise of 0.4C, and a value of lambda of 0.81 the extra energy radiated away from earth accounts for between 0.4/0.81 = 0.49 watts/m2 . But IPCC claim that the direct effect of the rise in carbon dioxide in 2006 (the report was released in Feb 2007) was an increase in carbon dioxide forcing of 1.66 watts/m2 and a total impact from all direct factors (ie: excluding feedbacks) of 1.6 watts/m2 . This means that 1.6 – 0.49 watts/m2 or 1.11 watts/m2 of the total forcing must have gone into heating the Earth. But the retained energy calculated from the government paper was 0.32 watts/m2 into the oceans (representing 85% of the total) for a planetary total of 0.32/0.85 = 0.38 watts/m2. 1.11 versus 0.38 is still a discrepancy of 3 times although smaller than my previous claim of 9 times.
Carrying out the calculation the other way round, if 0.38 watts/m2 is being retained, then 1.6-0.38 = 1.22 watts/m2 must be being radiated. If that was happening with an 0.4C rise lambda would have to be 0.4/1.22 = 0.328 C/watt/m2 . A figure of lambda = 0.328 and kappa = 0.266 still suggests a small amount of positive feedback (lambda is greater than kappa) but far less than that claimed by AGW supporters. A sensitivity of 0.328 would suggest an equilibrium temperature rise for doubling of carbon dioxide of 3.7 * 0.328 = 1.2C. However in 2070 carbon dioxide will still be rising and the planet will still be warming, we will not be at equilibrium. We could reasonably expect the same level of energy to be flowing into heating the earth as at present (about 0.38 watts/m2). In that case the actual rise for doubling carbon dioxide would be (3.7 – 0.38)* 0.328 = 1.09C. Since we are currently seeing 0.4C, that would mean a further rise between now and 2070 of 0.69C which is a far cry from the popularly reported 3C.
All this of course assumes that the starting data is correct. In fact there are reports that the oceans have been cooling now for some years and that the steep rise shown since 1998 is an artifact arising from the change to the Argo buoys. These two factors would reduce the 0.32 watts/m2 figure significantly. Also, there is significant dispute over the justification for the corrections applied to the raw temperature data which result in the claimed 0.4C rise. The satellite data from UAH shows far less warming. If these concerns have substance, then the impact of rising carbon dioxide is even smaller suggesting that the net feedback is in fact negative not positive and the temperature rise between now and 2070 would be less and possibly substantially less than 0.69C.
I apologise to readers for my error in the previous article and hope this sets the record straight.
Read Part 1 here: http://jennifermarohasy.com/blog/2009/07/a-climate-change-paradox/