Sense and sensitivity

By Christopher Monckton of Brenchley

Reed Coray’s post here on Boxing Day, commenting on my post of 6 December, questions whether the IPCC and science textbooks are right that without any greenhouse gases the Earth’s surface temperature would be 33 Kelvin cooler than today’s 288 K. He says the temperature might be only 9 K cooler.

The textbook surface temperature of 255 K in the absence of any greenhouse effect is subject to three admittedly artificial assumptions: that solar output remains constant at about 1362 Watts per square meter, taking no account of the early-faint-Sun paradox; that the Earth’s emissivity is unity, though it is actually a little less; and that today’s Earth’s albedo or reflectance of 0.3 would remain unchanged, even in the absence of the clouds that are its chief cause.

These three assumptions are justifiable provided that the objective is solely to determine the warming effect of the presence as opposed to absence of greenhouse gases. They would not be justifiable if the objective were to determine the true surface temperature of the naked lithosphere at the dawn of the Earth. My post of 6 December addressed only the first objective. The second objective was irrelevant to my purpose, which was to determine a value for the system climate sensitivity – the amount of warming in response to the entire existing greenhouse effect.

Since Mr. Coray makes rather heavy weather of a simple calculation, here is how it is done. According to recent satellite measurements, 1362 Watts per square meter of total solar irradiance arrives at the top of the atmosphere. Since the Earth presents a disk to this insolation but is actually a sphere, this value is divided by 4 (the ratio of the surface area of a disk to that of a sphere), giving 340.5 Watts per square meter, and is also reduced by 30% to allow for the fraction harmlessly reflected to space, giving a characteristic-emission flux of 238.4 Watts per square meter.

The fundamental equation of radiative transfer, one of the few proven results in climatological physics, states that the radiative flux absorbed by (and accordingly emitted by) the characteristic-emission surface of an astronomical body is equal to the product of three parameters: the emissivity of that surface (here, as usual, taken as unity), the Stefan-Boltzmann constant (0.0000000567), and the fourth power of temperature. Accordingly, under  the three assumptions stated earlier, the Earth’s characteristic-emission temperature is 254.6 K, or about 33.4 K cooler than today’s 288 K. It’s as simple as that.

The “characteristic-emission” surface of an astronomical body is defined as that surface at which the incoming and outgoing fluxes of solar radiation are identical. In the absence of greenhouse gases, the actual rocky surface of the Earth would be its characteristic-emission surface. As greenhouse gases are added to the atmosphere and cause warming, the altitude of the characteristic-emission surface rises.

The characteristic-emission surface is now approximately 5 km above the Earth’s surface, its altitude varying inversely with latitude: but its temperature, by definition, remains 254.6 K or thereby. At least over the next few centuries, the atmospheric temperature lapse-rate (its decline with altitude) will remain near-constant at about 6.5 K per km, so that the temperature of the Earth’s surface will rise as greenhouse gases warm the atmosphere, even though the temperature of the characteristic-emission surface will remain invariant.

It is for this reason that Kiehl & Trenberth, in their iconic papers of 1997 and 2008 on the Earth’s radiation budget, are wrong to assume that (subject only to the effects of thermal convection and evapo-transpiration) there is a strict Stefan-Boltzmann relation between temperature and incident irradiance at the Earth’s surface. If they were right in this assumption, climate sensitivity would be little more than one-fifth of what they would like us to believe it is.

So, how do we determine the system sensitivity from the 33.4 K of “global warming” caused by the presence (as opposed to the total absence) of all the greenhouse gases in the atmosphere? We go to Table 3 of Kiehl & Trenberth (1997), which tells us that the total radiative forcing from the top five greenhouse gases (H2O, CO2, CH4, N2O and stratospheric O3) is 101[86, 125] Watts per square meter. Divide 33.4 K by this interval of forcings. The resultant system sensitivity parameter, after just about all temperature feedbacks since the dawn of the Earth have acted, is 0.33[0.27, 0.39] Kelvin per Watt per square meter.

Multiply this system sensitivity parameter by 3.7 Watts per square meter, which is the IPCC’s value for the radiative forcing from a doubling of the concentration of CO2 in the atmosphere (obtained not by measurement but by inter-comparison between three radiative-transfer models: see Myhre et al., 1998). The system sensitivity emerges. It is just 1.2[1.0, 1.4] K per CO2 doubling, not the 3.3[2.0, 4.5] K imagined by the IPCC.

Observe that this result is near-identical to the textbook sensitivity to a doubling of CO2 concentration where temperature feedbacks are absent or sum to zero. From this circumstance, it is legitimate to deduce that temperature feedbacks may well in fact sum to zero or thereby, as measurements by Lindzen & Choi (2009, 2011) and Spencer & Braswell (2010. 2011) have compellingly demonstrated.

Therefore, the IPCC’s assumption that strongly net-positive feedbacks approximately triple the pre-feedback climate sensitivity appears to be incorrect. And, if Mr. Coray were right to say that the warming caused by all of the greenhouse gases is just 9 K rather than 33 K, then the system sensitivity would of course be still lower than the 1.2 K we have determined above.

This simple method of determining the system climate sensitivity is quite robust. It depends upon just three parameters: the textbook value of 33.4 K for the “global warming” that arises from the presence as opposed to the absence of the greenhouse gases in the atmosphere; Kiehl & Trenberth’s value of around 101 Watts per square meter for the total radiative forcing from the top five greenhouse gases (taking all other greenhouse gases into account would actually lower the system sensitivity still further); and the IPCC’s own current value of 3.7 Watts per square meter for the radiative forcing from a doubling of atmospheric CO2 concentration.

However, it is necessary also to demonstrate that the climate sensitivity of the industrial era since 1750 is similar to the system sensitivity – i.e., that there exist no special conditions today that constitute a significant departure from the happily low system sensitivity that has prevailed, on average, since the first wisps of the Earth’s atmosphere formed.

Thanks to the recent bombshell result of the Carbon Dioxide Information and Analysis Center in the US (Blasing, 2011), the industrial-era sensitivity may now be as simply and as robustly demonstrated as the system sensitivity. Dr. Blasing has estimated that manmade forcings from all greenhouse gases since 1750 are as much as 3.1 Watts per square meter, from which we must deduct 1.1 Watts per square meter to allow for manmade negative radiative forcings, notably including the soot and other particulate aerosols that act as little parasols sheltering us from the Sun.

The net manmade forcing since 1750, therefore, is about 2 Watts per square meter. According to Hansen (1984), there had been 0.5 K of “global warming” since 1750, and there has been another 0.3 K of warming since 1984, making 0.8 K in all. We can check this by calculating the least-squares linear-regression trend on the Central England Temperature Record since 1750, which shows 0.9 K of warming. So 0.8 K warming since 1750 is in the right ballpark.

The IPCC says that we caused between half and all of the warming since 1750 – i.e. 0.6[0.4, 0.8] K. Divide this interval by the net industrial-era anthropogenic forcing of 2 Watts per square meter, and multiply by 3.7 Watts per square meter as before, and the industrial-era sensitivity is 1.1[0.7, 1.5] K, which neatly and remarkably embraces the system sensitivity of 1.2[1.0, 1.4] K. So the industrial-era sensitivity is near-identical to the low and harmless system sensitivity.

Will the IPCC take any notice of fundamental results such as these that are at odds with its core assumption of a climate sensitivity thrice what we have here shown it to be? I have seen the first draft of the chapter on climate sensitivity and, as in previous reports, the IPCC either sneeringly dismisses or altogether ignores the growing body of data, results and papers pointing to low sensitivity. It confines its analysis only to those results that confirm its prejudice in favor of very high sensitivity.

In Durban I had the chance to discuss the indications of low climate sensitivity with influential delegates from the US and other key nations. I asked one senior US delegate whether his officials had told him – for instance – that sea level has been rising over the past eight years at a rate equivalent to just 2 inches per century. He had not been told, and was furious that he had been misled into thinking that sea level was rising at a dangerous rate.

Having gained his attention, I outlined the grounds for suspecting low climate sensitivity and asked him whether he had been told that there was a growing body of credible and robust evidence that climate sensitivity is small, harmless, and even beneficial. He had not been told that either. Now he and other delegates are beginning to ask the right questions. If the IPCC adheres to its present draft and fails to deal with arguments such as that which I have sketched here, the nations of the world will no longer heed it. It must fairly consider both sides of the sensitivity question, or die.