Guest essay by Mike Jonas
A look at Equilibrium Climate Sensitivity from a logical perspective.
This article is the fourth in a series of four articles.
Part 1 of the series (Part 1) is here
Part 2 of the series (Part 2) is here
Part 3 of the series (Part 3) 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).
In Part 3, the formulae were used to have a look at the period used in Al Gore’s film An Inconvenient Truth.
Part 4 looks at the major components of equilibrium climate sensitivity (ECS). ECS is key to all of the findings of the IPCC and to the computer climate models.
Note : This article does not say anything new, or claim to find any new results. It has all been said many times before. But it does look at ECS from a logical perspective.
Equilibrium climate sensitivity ( ECS)
Equilibrium climate sensitivity ( ECS), is defined in the fourth IPCC report (AR4) as follows :
In IPCC reports, equilibrium climate sensitivity refers to the equilibrium change in the annual mean global surface temperature following a doubling of the atmospheric equivalent carbon dioxide concentration.
ECS is extremely important. It effectively is the one single factor that determines how much the global climate is warmed by increasing levels of carbon dioxide (CO2).
Anyone who doubts the importance of this in the climate models needs only to read the commentary about CO2 being the “control knob” of climate, see eg.  .
How ECS is estimated
The fourth IPCC report explains how ECS is estimated:
Due to computational constraints, the equilibrium climate sensitivity in a climate model is usually estimated by running an atmospheric general circulation model coupled to a mixed-layer ocean model, because equilibrium climate sensitivity is largely determined by atmospheric processes. Efficient models can be run to equilibrium with a dynamic ocean.
In other words, ECS is estimated by running climate computer models. Now of itself that isn’t as bad as it might sound to those who are already sceptical of climate scientists and the state of climate science. Obviously for complex systems some kind of computer model is needed.
Nevertheless, there is good reason to be concerned about this process. Firstly, computer models of complex systems are notorious for deviating from reality over multiple iterations, and these computer models use a very large number of iterations. Secondly, a lot of the processes cannot be modelled, either because they are not understood (eg. clouds) or are too complex (eg. biochemical processes) or both. For these, the models use parameterisations, which are basically guesses expressed as mathematical formulae. But worst of all, the IPCC reports repeatedly say that these are determined by observation:
The development of parameterisations has become very complex (e.g., (Jakob, 2010)) and is often achieved by developing conceptual models of the process of interest in isolation using observations and comprehensive process-models. [AR5 Box 9.1]
[..] methods for providing probabilistic climate change projections [include methods based on] large model ensembles that provide projections consistent with observations of climate change and their uncertainties. [..] Short-term projections are similarly constrained by observations of recent trends. [AR4 TS.5]
It is therefore common to adjust parameter values [..] in order to optimise model simulation of particular variables or to improve global heat balance. This process is often known as ‘tuning’. [AR4 220.127.116.11]
Results from forward calculations are used for formal detection and attribution analyses. In such studies, a climate model is used to calculate response patterns (‘fi ngerprints’) for individual forcings or sets of forcings, which are then combined linearly to provide the best fit to the observations. [AR4 9.1.3]
The problem here is that observations include temperature measurements and factors that relate to temperature, and many of these can only be used by assuming that they are caused directly or indirectly by CO2. So we have the absurd situation that the climate models supposedly show the 20th century warming to have been caused by CO2, but key elements in the models are themselves based on the implicit assumption that the warming was caused by CO2. In mathematics, that’s the ‘circular logic’ fallacy.
Components of ECS
Well, let’s look further into ECS and how it is arrived at. ECS has three major warming components :
- The warming generated by CO2 itself. This comes from increased downward infra-red radiation (IR) from increased quantities of CO2 in the atmosphere. This was described originally by Arrhenius , and is generally accepted as very solid physics by climate scientists and climate “sceptics” alike. The generally accepted value of this component is 1.2, ie. the forcing from doubled CO2 on its own would raise global temperature by 1.2 degrees.
- Water vapour feedback. The theory is primarily that the increased temperatures caused by increased levels of CO2 will increase the amount of water vapour in the atmosphere . Water vapour is itself a greenhouse gas, so this will cause further warming. (AR4 TS.2)
- Cloud feedback. The hypothesis is that as temperatures rise, clouds change in a way that further increases temperature.
The warming from these components is eventually balanced (“equilibrium”) by the increased rate of heat loss that comes from the higher temperatures.
The IPCC report AR4 quantifies the feedbacks in para 18.104.22.168 :
Using feedback parameters from Figure 8.14, it can be estimated that in the presence of water vapour, lapse rate and surface albedo feedbacks, but in the absence of cloud feedbacks, current GCMs would predict a climate sensitivity (±1 standard deviation) of roughly 1.9°C ± 0.15°C (ignoring spread from radiative forcing differences). The mean and standard deviation of climate sensitivity estimates derived from current GCMs are larger (3.2°C ± 0.7°C) essentially because the GCMs all predict a positive cloud feedback (Figure 8.14) but strongly disagree on its magnitude.
So – if CO2 raises the temperature by 1.2 degrees, then water vapour and related changes will raise the temperature a further 0.7 degrees (1.9 – 1.2), and clouds will change in a way that raises temperature another 1.3 degrees (3.2 – 1.9).
Water Vapour Feedback
The atmosphere’s ability to hold water vapour increases with temperature increase. AR4 FAQ3.2 :
a well-established physical law (the Clausius-Clapeyron relation) determines that the water-holding capacity of the atmosphere increases by about 7% for every 1°C rise in temperature.
This leads to increased precipitation :
Our 50-year observed global surface salinity changes, combined with changes from global climate models, present robust evidence of an intensified global water cycle at a rate of 8 ± 5% per degree of surface warming. This rate is double the response projected by current-generation climate models
Wentz et al 2007  indicates that the water cycle increase in the climate models is even lower (1% to 3%).
So – the climate models have far too low a value for the water cycle increase. Why does this matter? An increased water cycle transfers more energy from the surface to the troposphere, thus more energy is lost to space, and hence the temperature is reduced. By placing the water cycle increase at an unrealistically low level, the climate models operate on an unrealistically high feedback, and hence on an unrealistically high ECS.
Support for this analysis also comes from Forster and Gregory  :
There is preliminary evidence of a neutral or even negative longwave feedback in the observations, suggesting that current climate models may not be representing some processes correctly if they give a net positive longwave feedback.
The Cloud Feedback Challenge
The challenge that the cloud feedback hypothesis has to overcome is that no-one really knows how clouds behave or what effect they have on temperature.
The IPCC has a lot to say about clouds in its AR4 report :
TS.4.5 – Cloud feedbacks (particularly from low clouds) remain the largest source of uncertainty.
Box TS.8 – parametrizations are still used to represent unresolved physical processes such as the formation of clouds and precipitation [..] Uncertainty in parametrizations is the primary reason why climate projections differ between different [climate models].
TS.6.4.2 – Large uncertainties remain about how clouds might respond to global climate change.
7.5.2 – Cloud feedbacks remain the largest source of uncertainty in climate sensitivity estimates and the relatively poor simulation of boundary layer clouds in the present climate is a reason for some concern
8 – Executive Summary – important deficiencies remain in the simulation of clouds and tropical precipitation (with their important regional and global impacts).
22.214.171.124 – Outside the polar regions, relatively large [re mean surface temperature] errors are evident in the eastern parts of the tropical ocean basins, a likely symptom of problems in the simulation of low clouds. The extent to which these systematic model errors affect a model’s response to external perturbations is unknown, but may be significant
126.96.36.199.2 – Given that clouds are responsible for about half the outgoing SW radiation, these errors are not surprising, for it is known that cloud processes are among the most difficult to simulate with models
188.8.131.52.1 – The sign of the climate change radiative feedback associated with the combined effects of dynamical and temperature changes on extratropical clouds is still unknown.
That was just a small selection of the IPCC’s statements on the knowledge of clouds – see  for the full set. And they don’t even know how much cloud there is:
184.108.40.206 – the effects of known and unknown artefacts on ISCCP cloud and flux data have not yet been quantified. Other satellite data sets show conflicting decadal changes in total cloud cover [..] In summary, while there is some consistency between ISCCP, ERBS, SAGE II and surface observations of a reduction in high cloud cover during the 1990s relative to the 1980s, there are substantial uncertainties in decadal trends in all data sets and at present there is no clear consensus on changes in total cloudiness over decadal time scales.
Cloud effect on radiation
Clouds affect temperature primarily by intercepting incoming and outgoing radiation. The basic mechanisms are conceptually simple :
In simple terms, there is a very neat symmetry. At Earth’s surface, for a given change in cloud cover, the percentage change in outgoing re-emitted radiation that is direct is the same as the percentage change in incoming absorbed radiation that is direct. Similarly for indirect radiation. So there is no net change.
Now that is indeed over-simplified, but the incoming vs outgoing differences are very subtle (no wonder the climate models have problems with them). The chief differences are
1. Incoming and outgoing radiation contain both shortwave (SW) and longwave or infra-red (IR), but the proportion of IR in outgoing radiation is higher. So clouds can theoretically have a net effect if they affect SW and IR differently. NASA Earth Observatory  gives a good explanation.
2. The distributions of incoming radiation and outgoing radiation are slightly different. They are both greatest at the tropics and least at the poles, but there is a difference. So clouds can theoretically have a net effect if their distribution changes.
Calculation of cloud feedback
From AR4 220.127.116.11 as quoted above, cloud feedback supposedly contributes 1.3°C ± 0.55°C to ECS (to 3.2°C ± 0.7°C from 1.9°C ± 0.15°C). Note that the low end of the range is strongly positive, even though they admit in AR4 18.104.22.168.1 (quoted above) that they don’t even know what sign it has!
Given how subtle the effect of clouds is, and given that there is so little known about it, how is this 1.3°C ± 0.55°C cloud feedback calculated?
The answer is given in the IPCC quotes above – they simply guess :
parametrizations are still used to represent unresolved physical processes such as the formation of clouds and precipitation [..] Uncertainty in parametrizations is the primary reason why climate projections differ between different [climate models].
Basically, there is an up-front assumption that virtually all of the 20th-century global warming was caused by CO2 (“How ECS is estimated”, above). In order to satisy that assumption (as quoted above, they call it “tuning”), they have to find about three times as much warming as they can get from CO2 itself (ECS 1.2). They speculate that water vapour contributes a further 0.7 of ECS, although, as explained above, this needs some pretty heroic assumptions about the water cycle. They then fiddle with the cloud parameters until they get the results they desire. The process is not supported by actual physics. That is why the models all differ so much in their treatment of clouds.
An additional curiosity is that an increased water cycle would suggest more clouds, not less, making a high positive cloud feedback even less likely. As NASA Earth Observatory  says:
The balance between the cooling and warming actions of clouds is very close although, overall, averaging the effects of all the clouds around the globe, cooling predominates.
Logically, a cloud feedback of +1.3 degrees looks like a very long stretch indeed.
Climate models’ estimations of ECS are implicitly based on the assumption that the 20th century warming was caused by CO2. Therefore any assertion that the models show that the 20th century warming was caused by CO2 is invalid (circular logic).
In addition, the climate modellers and the IPCC have
(a) used an unrealistically low water cycle, resulting in an unrealistically high value for CO2-driven global warming, and
(b) built on the almost complete lack of knowledge about clouds, in order to claim that clouds add a large amount to CO2-driven global warming.
The reality is that a doubling of CO2 would of itself raise the global temperature by about 1.2 degrees (this part of CO2 science is pretty solid and generally accepted), plus or minus an unknown but probably modest amount of feedback from water vapour etc, and from clouds. Knowledge in this area is so weak that even the sign of the feedback is not known.
In other words, of the mid-range claimed ECS of 3.2 degrees per doubling of CO2, nearly two-thirds is either unrealistic or sheer speculation.
One final point; a delicious irony (mathematically speaking) :
· As shown above, there is an implied assumption in the models that CO2 is the principal driver of global temperature. That assumption is demonstrated very clearly in Part 1, where all of the post-industrial warming is assumed to be caused by CO2.
· But when the results of the models are then compared to past surface temperatures, as was done in Part 2 and Part 3, it is found that CO2 plays little part in temperature change.
So, the assumption that CO2 is the principal driver of global temperature leads to the finding that it isn’t.
Mike Jonas (MA Maths Oxford UK) retired some years ago after nearly 40 years in I.T.
 NASA Earth Observatory, Clouds and Radiation http://earthobservatory.nasa.gov/Features/Clouds/
 Wentz et al, How Much More Rain Will Global Warming Bring?, https://www.sciencemag.org/content/317/5835/233.abstract Science 13 July 2007: Vol. 317 no. 5835 pp. 233-235 DOI: 10.1126/science.1140746
 Durack et al, Ocean Salinities Reveal Strong Global Water Cycle Intensification During 1950 to 2000, http://www.sciencemag.org/content/336/6080/455 Science 27 April 2012: Vol. 336 no. 6080 pp. 455-458 DOI: 10.1126/science.1212222
 The full set of IPCC AR4 statements about clouds is at IPCCOnClouds (PDF)
 Arrhenius, S., 1896: On the influence of carbonic acid in the air upon the temperature on the ground, Philos. Mag., 41, 237–276.
 Lacis ert al, Atmospheric CO2: Principal Control Knob Governing Earth’s Temperature, http://www.sciencemag.org/content/330/6002/356.abstract Science 15 October 2010: Vol. 330 no. 6002 pp. 356-359 DOI: 10.1126/science.1190653
 R B Alley, The biggest control knob: carbon dioxide in Earth’s climate history, http://adsabs.harvard.edu/abs/2009AGUFM.A23A..01A American Geophysical Union, Fall Meeting 2009, abstract #A23A-01
 Piers Mde F. Forster and Jonathan M. Gregory, 2006: The Climate Sensitivity and Its Components Diagnosed from Earth Radiation Budget Data. J. Climate, 19, 39–52. doi: http://dx.doi.org/10.1175/JCLI3611.1 http://journals.ametsoc.org/doi/full/10.1175/JCLI3611.1
AR4 – (Fourth IPCC report)
AR5 – (Fifth IPCC report)
CO2 – Carbon Dioxide
ECS – Equilibrium Climate Sensitivity
IPCC – Intergovernmental Panel on Climate Change
IR – Infra-red (Radiation)
SW – Short Wave (Radiation)