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.
Spector @ur momisugly January 1, 12:35 am
Yes, right, according to Trenberth et al! Sorry, but I posted this comment on the wrong thread. It was addressed to Tim Folkerts and was intended to grab his attention after many earlier “exchanges” on the Trenberth thingy. I also wanted to seek Tim’s expertise as an outspoken physicist, on Item B, concerning his claim that with a transparent atmosphere of N2, the lapse rate would be ~10C/Km.
Oh well, since it is a topic touched on here by Christopher Monckton, let’s open it:
1) So the lapse rate would be higher than the generally accepted ~6.5 C/Km in the real atmosphere.
2) If all surface radiation at 255K escapes directly to space, and the N2 loses heat, (thermal energy) with altitude, what is the mechanism by which that heat is lost?
I’d appreciate some advice.
B F-J, it loses temperature as it rises by adiabatic expansion, no loss of heat.
Spector says:
“Temperatures all over the Earth will rise (or fall) until the net energy flowing out is also 1.222e7 watts or about 239.5 W/m² on average. The Stefan-Boltzmann law characteristic temperature for this particular energy flow per square meter is about 255 degrees K. (Technically, power in watts is a measure of energy flow in joules per second.)
This surface flow may be forced to increase if there are a wavelength selective blocking agents in the atmosphere that only allow a fraction of the full surface energy flow to escape to outer space but do not interfere with most of the solar energy coming in. The blocked surface radiation energy is returned to the closed system.”
I agree with your answer but for the final sentence.
However, I do not understand where Trenberth et al think that 390 watts is emitted from the earths surface.
I do not think that black body theory allows for a black body to receive 239 watts and emit 390 watts.
With respect to the final sentence, heat energy travels from hot to cold, increased insulation, (CO2 maybe) reduces the rate of transmission, (energy flow rate).
If the amount of energy leaving the earth is reduced by increased insulation, the surface temperature will rise.
This increased temperature increases the temperature gradient between the surface and space, increasing the heat energy flow rate, which is dependent only upon temperature gradient and insulation value, lets call it thermal conductivity.
Thermal conductivity increases with increasing temperature.
This would give ‘elasticity’ to the system, reducing sensitivity to changes atmospheric properties.
I do not know if any of the climate models model the variability of thermal conductivity of atmospheric gases.
“Steve Richards says:
January 2, 2012 at 1:45 am
”
For 288k, emissions are in the infrared. There, the emissivity of the Earth’s surface is pretty close to 1.0 (over 0.95). An object with emissivity of about 1 will radiate about 390 W from every square meter of its surface if the surface temperature is at 288k. Stefan’s law is about emission, not absorption. While it was originally determined by observation, it is actually the integrated result over direction and wavelength (or frequency) of Planck’s law.
Planck’s law too is about emission, not absorption. The 239W/m^2 from the Sun is radiation emitted from an object at 6000k which peaks in the visible light spectrum. If it were closer, we’d receive far more power than that. The emissivity of the Earth at visible light wavelengths is much less than 1. Since the Earth is not at 6000k (at least on the surface), this does not come into play.
The clear sky atmosphere close to the ground tends to be close to the 288k value. However, it is a gas, not a liquid or solid so it emits and absorbs in a spectrum characteristic of the constituents where a solid or liquid will offer a continuum. The Planck blackbody spectra is actually an indication of the energy states that are filled at a given temperature. The spectrum emitted by gas is this spectrum times the blackbody continuum where the spectrum is the liklihood of an interaction (abosrption) at a given energy (given wavelength/frequency) – call it the emissivity as a function of wavelength (or frequency) if you like. The blackbody continuum is indicative of the liklihood or amount of material that actually has that much energy available to be emitted. The product of the two is the emission spectra for a gas.
If you have a low lying optically thick cloud, then those tiny water droplets will provide a continuum radiating downward like a black body at the temperature of the cloud base.
Things get even more fun as both the concentration of a particular gas and the total atmospheric pressure will affect the spectrum of a gas. At extremely low pressure, one gets a very narrow and very strong spectral line. As pressures rise, the line gets wider but not as tall. If there is a continuum going through, the low pressure situation will absorb a very narrow portion of the total power (assuming the temperature is low enough so that there is little emission going on at this very narrow line. As pressure goes up, the line broadens and there is more continuum radiation that can be absorbed by the molecules present even though there is less chance of absorbing any particular wavelength photon in a given distance of travel. Of course if the gas is at the same temperature as the black body emitter (surface), the re-emission will occur at the same rate as the absorption and there will neither be an absorption line nor an emission line.
Steve Richards says:
This number can be derived from both direct empirical data and from the average temperature of the Earth plus the fact that the emissivity of most terrestrial surfaces in the mid and far infrared is very close to 1.
You are wrong. The relationship you might be thinking about is that emissivity at a given wavelength has to equal absorptivity at a given wavelength. The amount a blackbody receives depends not only on it but on what radiation is incident on it from elsewhere.
Or, perhaps you think there should be energy balance for the system to neither cool nor heat. There you are correct…but the energy balance has to include all energy flows and has to be restricted to one particular object or system. (Hence, for example, all energy flows at the surface of the Earth balance…and likewise, it is true, that the rate of energy being absorbed by the Earth-atmosphere system has to balance the rate energy is emitted by the system if it is neither cooling nor heating.)
Your statements are a little confused here because we are not talking about conduction. The only significant communication of energy between the Earth and space is via radiation.
However, in the larger picture, you are correct that if you raise the temperature of the surface of the Earth, more radiation will be emitted to space. And, yes, of course this is included in all the climate models; it defines the whole question that they set out to answer, which is: “If we increase the amount of greenhouse gases by a certain amount so that the Earth is now emitting back out into space less than it is absorbing from the sun, how much does the surface temperature have to increase in order for the emission to increase back to the point where energy balance is restored?”
Phil. @ur momisugly January 1, 8:27 pm
Thanks for that Phil, but I think it is a bit more complicated than that. What’s more, this thread has become a bit stale, and I recommend that you pick-up the discussion at a more recent and more relevant thread here:
http://wattsupwiththat.com/2011/12/29/unified-climate-theory-may-confuse-cause-and-effect/#comment-851158
RE: Steve Richards: (January 2, 2012 at 1:45 am)
REF: [‘. . . This surface flow may be forced to increase if there are a wavelength selective blocking agents in the atmosphere that only allow a fraction of the full surface energy flow to escape to outer space but do not interfere with most of the solar energy coming in. The blocked surface radiation energy is returned to the closed system.’]
“I agree with your answer but for the final sentence.
“However, I do not understand where Trenberth et al think that 390 watts is emitted from the earths surface.
“I do not think that black body theory allows for a black body to receive 239 watts and emit 390 watts.”
Perhaps the word ‘retained’ would have been better than ‘returned’—the atmosphere is part of that closed system. The 239 W/m² is the average power that must be radiated out at the top of the atmosphere. (A minor complication: This is not relative to the actual area at the top of the atmosphere but the equivalent area projected from sea level.) Note that he shows 396 W/m² going up and 333 W/m² radiation coming right back down as seen at sea-level. This indicates that only 63 W/m² is actually leaving the surface. The remaining 176 W/m² headed out is progressively emitted from higher levels of the atmosphere.
That is a good thing. It means the atmosphere has a method of cooling itself so that rising warm air can eventually return to the surface. When I look at the out-going radiation spectrum predicted by MODTRAN, I see a reduced flow around the characteristic bands for CO2 and ozone but not for water vapor. As water molecules are not symmetric, they have magnet-like electric fields and would be solid or liquid in the atmosphere if they were not being knocked apart by other molecules. The strong attraction of these molecules in collisions must allow the emission of odd-wavelength photons that, unlike those produced by CO2 or ozone, are not almost always those exact wavelengths that are most likely to be absorbed by similar molecules in the atmosphere. The atmosphere does not ‘create’ the 176 W/m² flow, rather it is carried up by convection and evaporation or created by solar absorption.
Spector says: January 11, 2012 at 4:19 am
Joel Shore says: January 2, 2012 at 8:27 am.
I still have a sneaky suspicion that there is double accounting on the energy budget.
I am happy with black bodies, thermal opaqueness and the conservation of energy.
What I am not happy with is the concept of back radiation and its use in double accounting
We have a ‘total’ energy input to earth of say 341 W/m-2 (Kiel et al 2007 Fig 1). That is our total energy input to the system (earth surface & atmosphere).
Then, current consensus ‘informs’ us that this energy is transformed into 396 W/m-2 leaving the earths surface.
How, using any scientific or engineering terminology, is this possible.
I am happy converting one energy form into another, I am happy measuring and calculating in joules/watts/amps/volts etc.
I am happy with spectral bands and power loss, absorption, convection and conduction etc.
But, how does a total input of 341 W/m-2 transform into 396 W/m-2.
If Fig 1 is true, I would be able to use a wideband width power meter, sensitive to all of the relevant frequencies and measure 341 W/m-2 from the moon’s surface if aimed at the sun.
Conversely I would be able to spot check the radiation say, leaving the earths surface from a 1000 or more random locations using the same measuring device, mounted a 100m above the surface pointing down and it would read on average 396 W/m-2!
I do not think so.
Can anyone explain how I am wrong please?
I have ignored the remaining alleged earth outputs of 23 + 17 + 80 W/m-2 from fig 1.
The AGW Theory does not refine itself with time. It just becomes dumber and dumber, wilder and wilder. We can now stand by for a raft of ‘ad hominem’ attacks against Lord Monckton from the usual suspects.
RE: Steve Richards says: (January 11, 2012 at 11:28 am)
“. . . But, how does a total input of 341 W/m-2 transform into 396 W/m-2”
First, these are not ‘total’ values, they are average energy flow rates for the whole surface of the Earth. The 341 W/m² comes from the solar constant divided by four because the nominal flat surface area of the Earth is four times the area of the disk of solar radiation that it intercepts. At this point a 30 percent reflection factor is usually applied to reduce the net average outgoing thermal radiant energy to 239 (or 240) W/m² required by conservation of energy.
The 396 W/m² comes from the Trenberth diagram as the assumed average thermal energy that is being radiated from the surface of the Earth. This number is based on the Stefan-Boltzmann formula for radiant energy as a function of the fourth power of temperature and it is an average *energy* value, not an average temperature value.
In order to have temperatures warm enough to radiate that much energy, the atmosphere must be continuously extracting an average of 157 (156) W/m² from that surface radiant energy flow so that the total energy radiated to outer space does not exceed the avreage 239 W/m² energy flow that the Earth is capturing from the sun. That is the greenhouse effect. Note that power in ‘watts’ is energy flow in joules/sec.
Please edit the top of the article in order to add a link to Sense and Sensitivity II – The Sequel article: http://wattsupwiththat.com/2012/01/15/sense-and-sensitivity-ii-the-sequel/
Spector says:
January 18, 2012 at 4:21 am
the atmosphere must be continuously extracting an average of 157 (156) W/m²
Extracting! how? to do what?