Guest essay by Mike Jonas
This article is the second in a series of four articles.
Part 1 of the series (Part 1) 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.
This article uses the formulae to have a look at the Medieval Warming Period (MWP) and Little Ice Age (LIA).
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.
IPCC Report 1990
The 1990 IPCC Report contained the following graphic :
In later IPCC reports, this graph was missing, and the MWP was either shown as much less significant or not shown at all. Considerable effort has been expended by climate scientists on trying to establish whether the MWP and LIA actually existed globally, or whether they were simply local to Europe and North America. There has also been a lot of discussion about whether climate scientists have tried to “get rid of” the MWP. For example, David Deming’s statement  to the US Senate in 2006 includes :
I had another interesting experience around the time my paper in Science was published. I received an astonishing email from a major researcher in the area of climate change. He said, “We have to get rid of the Medieval Warm Period.”
There is actually a lot of evidence that the MWP existed and that it was global. For example, places outside Europe and North America where evidence of the MWP has been found include Antarctica  , China , Peru , the Pacific Ocean , and many other places .
It is worth noting that, whereas the existence of a global MWP is generally accepted but is disputed in some quarters, the existence of the LIA is generally accepted and there is little or no dispute.
Why get rid of the MWP?
So … why does it matter so much whether the MWP existed, and whether it was global?
The problem that a global MWP poses is that it is incompatible with the climate models, which focus almost exclusively on CO2. The contribution of CO2 to global temperature during the MWP and LIA is easily calculated using the formulae developed in Part 1.
First, the data: CO2 data for this period is from Law Dome in Antarctica .
It is pretty obvious, just looking at the graph, that CO2 would have had little influence during this period, but its contribution can be quantified using the formulae developed in Part 1:
The CO2 contribution is as calculated in climate models, using an Equilibrium Climate Sensitivity (ECS) of 3.2 (including all feedbacks).
Figure 3 shows very clearly why the promoters of the computer climate models were so keen to get rid of the MWP : it demonstrates that the computer climate models are incapable of representing the climate. The impact of CO2 on the whole of the MWP and LIA periods was utterly trivial. CO2 even went in the opposite direction at times – rising while the temperature fell, and vice-versa. The models’ big upturn in CO2 contribution in the 20th century is not reflected in the temperature after 1939.
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 is not supported by the evidence from the MWP and LIA (905 to 1977).
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.
 1990 IPCC Report section 7http://ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_chapter_07.pdf Figure 7.1(c).
 David Deming’s statement to the US Senate Committee on Environment & Public Works. http://www.epw.senate.gov/hearing_statements.cfm?id=266543
 Hemer, M.A. and Harris, P.T. 2003. Sediment core from beneath the Amery Ice Shelf, East Antarctica, suggests mid-Holocene ice-shelf retreat. Geology 31: 127-130. http://geology.gsapubs.org/content/31/2/127.abstract
 Zunli Lu et al. 2012. An ikaite record of late Holocene climate at the Antarctic Peninsula. Earth and Planetary Science Letters. doi:10.1016/j.epsl.2012.01.036 http://www.sciencedirect.com/science/article/pii/S0012821X12000659
 Yan, H., Sun, L., Shao, D., Wang, Y. and Wei, G. 2014. Higher sea surface temperature in the northern South China Sea during the natural warm periods of late Holocene than recent decades. Chinese Science Bulletin 59: 4115-4122. http://link.springer.com/article/10.1007/s11434-014-0317-3
 Thompson et al. 2006 Jun 30. Abrupt tropical climate change: Past and present. doi: 10.1073/pnas.0603900103 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1484420/
 Yair Rosenthal1, Braddock K. Linsley, Delia W. Oppo. Pacific Ocean Heat Content During the Past 10,000 Years. Science 1 November 2013: Vol. 342 no. 6158 pp. 617-621 DOI: 10.1126/science.1240837 http://www.sciencemag.org/content/342/6158/617
 Papers on the MWP as Global Event. https://agwobserver.wordpress.com/2009/09/08/papers-on-the-mwp-as-global-event/
 Ice Core results: Law Dome CO2 and CH4 records of the last 1000 years first published in Etheridge et al., 1996 and 1998. [..]
Etheridge, D.M., L.P. Steele, R.L. Langenfelds, R.J. Francey, J.-M. Barnola, and V.I. Morgan. 1996. Natural and anthropogenic changes in atmospheric CO2 over the last 1000 years from air in Antarctic ice and firn. Journal of Geophysical Research, 101, 4115-4128.
Etheridge, D.M., L.P. Steele, R.J. Francey, and R.L. Langenfelds. 1998. Atmospheric methane between 1000 A.D. and present: evidence of anthropogenic emissions and climatic variability. Journal of Geophysical Research, 103, 15979-15996.Law Dome Ice Core 2000-Year CO2, CH4, and N2O Data. ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/law/law2006.txt
 Spreadsheet “Part2” with all data and workings – Part2 (excel .xlsx file)
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