How Lord Monckton’s Conundrum can be used to calculate maximum climate sensitivity to CO2

Thought Experiment;

Guest post by Bob Irvine

How Lord Monckton’s Conundrum can be used to calculate maximum climate sensitivity to CO2. What follows is a discussion only.


The IPCC defines Equilibrium Climate Sensitivity (ECS) “…as the global average surface warming following a doubling of carbon dioxide concentrations. It is likely to be in the range 2.0C to 4.5C with a best estimate of about 3.0C and is very unlikely to be less than 1.5C.” (Page 12, IPCC AR4 WG1, Summary for Policy Makers)

This implies that positive feedbacks to warming in the earth system enhance an initial ECS, or no feedback response, of about 1.0C to a likely catastrophic ECS of 3.0C.

Every political movement needs a narrative. The catastrophist global warming (CAGW) narrative is outlined by Gavin Schmidt below.

Most readers of this site will be aware of these arguments, but they are worth restating for people trying to feel their way in this debate. 5 of the 6 steps above are reasonable while the alarmists are trying to change our society based solely on step 5. This step 5 is quoted below.

“…the last glacial period is a good example of a large forcing (~7 W/m2 from ice sheets, greenhouse gases, dust and vegetation) giving a large temperature response (~5 ºC) and implying a sensitivity of about 3ºC (with substantial error bars). More formally, you can combine this estimate with others taken from the 20th century, the response to volcanoes, the last millennium, remote sensing etc. to get pretty good constraints on what the number should be. This was done by Annan and Hargreaves (2006), and they come up with, you guessed it, 3ºC.”

The “Real Climate” position above is that a likely ECS of 3.0C can be calculated from the Last Glacial Maxima”, a period when the earth was an ice world with very different albedo and feedbacks. None of the support estimates (i.e. 20th century estimates, volcanoes, the last millennium, remote sensing) quoted stack up. This is particularly true of the now debunked hockey stick shaped temperature history of the last millennium and the failed climate models for the 20th/21st century.

The words, “…you guessed it, …”, show a confected arrogance, and indicate that Gavin knows that he is vulnerable in this area. He is trying to deflect the uninformed reader by implying that the science is settled in this complex area. It is not. Disingenuously, he also forgets to mention that the 3.0C quoted is overwhelmingly made up of extremely uncertain positive feedbacks, as mentioned.

Common sense would tell most people that a massive positive feedback to warming of this magnitude, based on very little evidence, is very unlikely in a relatively stable system such as the earth’s modern climate. Yet, this is the crux of the global warming debate that has been going on now for nearly thirty years. The sceptics generally believe ECS is somewhere between 0.5C and 1.5C while the alarmists believe massive positive feedbacks multiply a mild initial warming by a factor of three.

Positive feedback to warming should not be confused with physical changes that result in changes in the Earth’s albedo. These are normally cyclical and can conceivably result in significant temperature change. They include any cosmic ray or magnetic effect, possible solar cycle effect on clouds and Milankovitch cycles etc.

This discussion addresses this issue and will require some imagination. The reader will be asked to imagine that the sun can be turned on and off at will and that we have access to two planets that can be placed in any orbit we wish and made to rotate on their own axis once every 24 hours.

One, Planet A, an imaginary planet, has no water or ocean and no atmosphere. It is made of hypothetical material and colour such that its emissivity and albedo are exactly the same as the real preindustrial earth at the top of its atmosphere as seen from space approximately as we know it today.

The other planet, Planet B, is the real pre-industrial earth with atmosphere and ocean approximately as we find it today.

The reader will also be asked to imagine that the planet in question attains its equilibrium temperature relatively quickly after the sun has been turned on. This has the advantage of being true relative to the age of the universe.


Equation 1;

Solar (1365w/m2)/4 x (1-Albedo [30 to 35%]) = Emissivity (0.96) x SB Constant x Temperature4 (K4)

From equation 1; Earth’s Temperature as seen from space = 255K

Note; Any preindustrial solar or GHG effect on albedo is included in equation 1.

Equation 2;

Professor Happer calculates equilibrium climate sensitivity to the equivalent of a doubling of CO2 without feedbacks as about 1K. Other estimates for this have been as high as 1.16K. I will use an approximation of 1.1K for this discussion.

This equates with about 10K for all GHG warming without feedbacks in the Earth’s preindustrial atmosphere. The direct radiative effect.

Assumption 1;

That the efficacy a GHG forcing is approximately equal to the Efficacy of the same Solar forcing as stated in the IPCCs AR5 report.

The Experiment;

There are two distinct types of feedback.

1. The first is a feedback that is generic to all types of forcing, and is a reaction to warming of the system, only. This is the only type of feedback generally considered as significant by the IPCC when calculating climate sensitivity. This discussion attempts to put a maximum value on climate sensitivity based solely on this type of feedback. Note; Clouds as a feedback to general warming are included here.

2. The second type of feedback does not depend on warming but is related to the intrinsic nature of the individual forcing. For example, an initial small change in solar forcing may cause physical changes that can amplify any initial warming by changing the earth’s albedo in some way (e.g. Clouds). Similarly greening of the planet by CO2 fertilisation may affect planetary albedo. These possible dampings or amplifications are not a reaction to temperature change but are related to, and unique to the physical nature of each particular forcing.

If we assume that feedbacks of type 2 are unlikely to raise climate sensitivity to CO2 in any significant way, then a maximum climate sensitivity to CO2 can be calculated with reference to type 1 feedbacks only.

We switch the sun off and place Planet “A” in earths current orbit and make it rotate once every 24 hours. We turn the sun on again and the temperature on the surface of this imaginary planet relatively quickly reaches an equilibrium temperature of 255K (-18C) according to Equation 1.

We then turn off the sun and replace Planet “A” with Planet “B”, the real earth with the earth’s atmosphere and the same albedo and emissivity as Planet “A”. Planet “B” is placed in earth’s orbit and is made to rotate on its axis once every 24 hours as was Planet “A”. The sun is turned on and Planet “B”, with all ingredients in place, relatively quickly reaches an equilibrium temperature 288K (15C) as measured at its surface.

The atmosphere, water vapour and oceans have added approximately 33K (288 – 255). This 33K includes all feedbacks except feedbacks that effect albedo as they have been included on the left-hand side of equation 1 and, therefore are included in the planet “A” calculation. Importantly, this 33K includes the large feedback attributed to the radiative GHG effects of any extra water vapour, which must be shared between the original GHG and solar forcing.

Note that if this extra water vapour forms more clouds, it will increase albedo and reduce climate sensitivity, not increase it.

The important thing here is that the warming effect of the GHG and solar inputs are applied concurrently and instantaneously and are indistinguishable from each other. They produce a temperature without feedbacks (other than albedo changes) of 265K (255K + 10K) on planet “B” according to equations 1 & 2.

With the real atmosphere in place the surface temperature is measured at 288K. The preindustrial type 1 and type 2 feedback factors for solar and GHGs combined cannot be more than 1.09 (288/265).

From equation 2, maximum equilibrium climate sensitivity to CO2 x 2 is approximately 1.2K (1.1 x 1.09).

There are a couple of unlikely but possible reasons why GHG equilibrium sensitivity could be higher than 1.2C.

1. CO2 ECS can be higher if GHGs produce a type 2 feedback that warms the planet more than any similar sized type 2 solar feedback. All type 1 feedbacks apply equally to GHG and solar forcing, by definition. Global greening is a possible type 2 candidate here, but I doubt if this could be significant or swamp any likely cloud changes due to solar activity.

The logic here is that if, GHGs contributed comparatively less per unit than solar, to the cooling effect of the 30% albedo that is included for both planet “A” and “B”, then it is possible CO2 ECS is greater than the 1.2K. This is unlikely.

2. CO2 ECS can, also be higher than 1.2K if the efficacy of GHG forcing is a lot larger than the efficacy of solar forcing. The IPCC does not believe this to be the case.


These large swings in temperature can only be explained by cyclical phenomena. The 33K (288 – 255) atmospheric affect is actually a range from, say 31K to 35K or more.

This range in atmospheric affect over the last few millennia must be driven by natural cycles that affect albedo, as well as ocean cycles that drive internal variability, there is no alternative explanation. Solar cycles, Milankovitch cycles and any other cycle, that change the albedo on the left of equation 1, can have a large effect on temperature and since they are cyclical, these large swings do not affect the overall, long term ECS and it remains low at less than 1.2C.

The cycles mentioned drive both type 1 and type 2 feedbacks, while warming due to CO2 is dominated by type 1 feedbacks. CO2, therefore, has a maximum ECS of about 1.2K.


Sensitivity to CO2 x 2 can be lower than 1.2C if the efficacy of CO2 forcing is significantly lower than the efficacy of a similar sized solar forcing.

The IPCC finds that a forcing that acts on higher latitudes will have higher efficacy possibly because energy flow from the tropics would be slowed. They also found that a forcing acting at a higher altitude will have a lower efficacy, essentially because energy from these areas is returned to space relatively quickly. There are some exceptions related to the various feedbacks.

Here is the relevant quote from the IPCCs 4AR.

“Nearly all studies that examine it find that high latitude forcings have higher efficacies than tropical forcings. Efficacy has also been shown to vary with the vertical distribution of an applied forcing (Hansen et al., 1997; Christiansen, 1999; Joshi et al., 2003; Cook and Highwood, 2004; Roberts and Jones, 2004; Forster and Joshi, 2005; Stuber et al., 2005; Sokolov, 2006). Forcings that predominately affect the upper troposphere are often found to have smaller efficacies compared to those that affect the surface. However, this is not ubiquitous as climate feedbacks (such as cloud and water vapour) will depend on the static stability of the troposphere and hence the sign of the temperature change in the upper troposphere (Govindasamy et al., 2001b; Joshi et al., 2003; Sokolov, 2006).”

Solar forcing acts mainly, anywhere up to tens of meters below the ocean surface and can remain circulating in the oceans for hundreds or even thousands of years. It seems inconceivable to me that this solar forcing can be said by the IPCC to have a similar efficacy to GHG forcing that acts almost totally on the atmosphere, this energy returning relatively quickly to space. In my opinion, the earth should be viewed as a total system, not just an atmosphere. When viewed in this way, it is possible that GHG forcing has a significantly lower efficacy than solar forcing.

via Watts Up With That?

October 28, 2019 at 12:24AM


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