Guest essay by Mike Jonas
This article is the third in a series of four articles.
Part 1 of the series (Part 1) is here
Part 2 of the series (Part 2) is here
In Part 1, simple mathematical formulae were developed to emulate the carbon dioxide (CO2.) contribution to global temperature change, as represented in the computer climate models.
In Part 2, the formulae were used to have a look at the Medieval Warming Period (MWP) and Little Ice Age (LIA).
Part 3 uses the formulae to have a look at the longer term – at the period used to great effect by Al Gore in his film An Inconvenient Truth.
Note : This article does not say anything new, or claim to find any new results. It has all been said many times before. But by using simple formulae that emulate the internal workings of the computer climate models, it allows the CO2 and non-CO2 components of global temperature change to be quantified using a spreadsheet  instead of a sophisticated climate model.
Please note : In this article, all temperatures referred to are deg C anomalies unless otherwise stated.
In An Inconvenient Truth, Al Gore showed graphs of temperature and CO2 for the last 400,000 years. The data is available from studies of ice cores at Vostok in Antarctica  , and it looks like this:
Al Gore presented the graphs of temperature and CO2 separately, but the correlation between temperature and CO2 is perhaps easier to see if they are presented in a single graph, as in Figure 1.
There is a well-known connection between temperature and CO2 : as temperature rises, the oceans release CO2 into the atmosphere , thus a rising temperature causes rising levels of CO2. The result is clearly visible in Figure 1, with CO2 following some years after the temperature changes.
But what about the connection the other way, ie, CO2 warming the ocean? After referring to this time lag (“CO2 starts to rise about 800 years (600-1000 years) after Antarctic temperature”) RealClimate  puts it this way :
<blockquote>All that the lag shows is that CO2 did not cause the first 800 years of warming, out of the 5000 year trend. The other 4200 years of warming could in fact have been caused by CO2, as far as we can tell from this ice core data.
The 4200 years of warming make up about 5/6 of the total warming. So CO2 could have caused the last 5/6 of the warming, but could not have caused the first 1/6 of the warming.</blockquote>
Well, the formulae established in Part 1 can be used to test this idea.
Applying the formulae established in Part 1 to the Vostok data gives the following picture of the CO2 and non-CO2 contributions to global temperature :
Before discussing this picture, some caveats are needed:
· The temperature range in Figure 2 is much greater than the temperature range used to establish the formulae. This makes the formulae unreliable over the period in Figure 2, as addressed in the following dot points.
· The basic formulae used, namely
Rcy = 5.35 * ln(Cy/C0) – j * ((T0+Tcy-1)^4 – T0^4)
δTcy = k * Rcy
(see Part 1) make no reference to the ice-free ocean area, but it is implicitly built in.
· As the temperature falls and sea ice area increases, the oceans’ influence on global temperature decreases, so CO2’s influence decreases too. (Extreme example : at 100% sea ice, ECS is zero). This means that CO2’s influence will in practice be less than as shown in Figure 2. Equilibrium climate sensitivity (ECS) will be lower at lower temperatures and the time taken to reach equilibrium will be longer.
· Similarly, at higher temperatures than today’s ECS will be higher, but since the average area of sea-ice is currently only a small proportion of the ocean surface (20m in 360m sq km) the increase in ECS would be very small.
· What the factors are that cause these major temperature changes is unimportant. The distinction in Figure 2 is between CO2 and non-CO2. All of the CO2 feedbacks claimed by the IPCC are built into the formulae and are accounted for fully in Figure 2. All the rest of the temperature change is non-CO2 regardless of the actual mechanisms, and regardless of whether those mechanisms are built into the computer climate models.
· At the low temperatures, it is possible that the CO2 feedbacks change too. Whether they increase or decrease is not known, but given that the oceans’ influence is lower at the low temperatures, and given that the feedbacks apply to radiative forcing (not just CO2 radiative forcing) and that non-CO2 radiative forcings must have been operating to produce the low temperatures in the first place, it is reasonable to assume that CO2’s overall contribution, including the feedbacks, is actually lower than as shown in Figure 2.
Now, looking at Figure 2, it is clear that CO2 has little influence on global temperature over this longer timescale. Note also that from about -130,000 to -100,000 CO2’s contribution remains at around its highest level while temperature falls more than 8 degrees. Similarly from about -400,000 to -350,000. In all of the major temperature increases, CO2 contributes no more than about 1/6 of the temperature increase.
In Part 2, there was some room for doubt about whether the Medieval Warm Period (MWP) was global, and attention was drawn to the accusation that climate scientists had tried to get rid of the MWP. With the very high publicity given to An Inconvenient Truth, and with the high reputation of the Vostok data (at least to the kind of accuracy needed here), it seems unlikely that anyone will attempt to “get rid of” the temperature and CO2 changes in the Vostok data. Even getting rid of the 800-year time lag of CO2 behind temperature would make no noticeable difference to Figure 2.
The picture of global temperature and its drivers as presented by the IPCC and the computer climate models is one in which CO2 has been the dominant factor since the start of the industrial age and other factors have had minimal impact. In order to support this picture, the IPCC has sought to portray CO2 as having been an important driver of global temperature in the past.
The idea that CO2 has been an important driver of global temperature over the last 400,000 years is not supported by the evidence.
The idea that CO2 has been the dominant driver of global temperature over the last 400,000 years is laughable.
It is important to recognise that the formulae used here represent the internal workings of the climate models. There is no “climate denial” here, because the whole series of articles is based on the premise that the climate computer models are correct, using the mid-range ECS of 3.2.
Mike Jonas (MA Maths Oxford UK) retired some years ago after nearly 40 years in I.T.
 Historical Isotopic Temperature Record from the Vostok Ice Core
Jouzel, J., C. Lorius, J.R. Petit, C. Genthon, N.I. Barkov, V.M. Kotlyakov, and V.M. Petrov. 1987.Vostok ice core: a continuous isotope temperature record over the last climatic cycle (160,000 years). Nature 329:403-8.
Jouzel, J., N.I. Barkov, J.M. Barnola, M. Bender, J. Chappellaz, C. Genthon, V.M. Kotlyakov, V. Lipenkov, C. Lorius, J.R. Petit, D. Raynaud, G. Raisbeck, C. Ritz, T. Sowers, M. Stievenard, F. Yiou, and P. Yiou. 1993. Extending the Vostok ice-core record of palaeoclimate to the penultimate glacial period. Nature 364:407-12.
Jouzel, J., C. Waelbroeck, B. Malaize, M. Bender, J.R. Petit, M. Stievenard, N.I. Barkov, J.M. Barnola, T. King, V.M. Kotlyakov, V. Lipenkov, C. Lorius, D. Raynaud, C. Ritz, and T. Sowers. 1996. Climatic interpretation of the recently extended Vostok ice records. Climate Dynamics 12:513-521.
Petit, J.R., J. Jouzel, D. Raynaud, N.I. Barkov, J.-M. Barnola, I. Basile, M. Bender, J. Chappellaz, M. Davis, G. Delayque, M. Delmotte, V.M. Kotlyakov, M. Legrand, V.Y. Lipenkov, C. Lorius,
L. Pepin, C. Ritz, E. Saltzman, and M. Stievenard. 1999. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 399: 429-436.
 Historical CO2 Record from the Vostok Ice Core
J.M. Barnola, D. Raynaud, C. Lorius.Laboratoire de Glaciologie et de Geophysique de l’Environnement 38402 Saint Martin d’Heres Cedex, France N. I. Barkov, Arctic and Antarctic Research Institute Beringa Street 38 St. Petersburg 199226, Russia January 2003
 RealClimate What does the lag of CO2 behind temperature in ice cores tell us about global warming? http://www.realclimate.org/index.php/archives/2004/12/co2-in-ice-cores/
 Spreadsheet “Part3” with all data and workings – here.
AR4 – (Fourth IPCC report)
AR5 – (Fifth IPCC report)
CO2 – Carbon Dioxide
CWIS – CO2 warming already in the system
ECS – Equilibrium Climate Sensitivity
IPCC – Intergovernmental Panel on Climate Change
IR – Infra-red (Radiation)
LIA – Little Ice Age
MWP – Medieval Warming Period
SKS – Skeptical Science (skepticalscience.com)
WRI – World Resources Institute