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.
Frank Lee MeiDere says: December 28, 2011 at 10:41 pm “but can’t we figure the Earth’s temperature minus greenhouse gasses (sic) by looking at the Moon?” Frank, I think that part of the problem is that the lack of a moderating effect from an atmosphere means that the moon’s surface temperature fluctuates wildly between day and night and at different latitudes. There is considerable relief on the moon’s surface, so some regions are mostly in shade and remain colder than those which receive full sunlight. All this makes it harder to come up with a close estimate of the moon’s mean surface T than it is on earth, which has a much smaller range.
According to Nikolov and Zeller (see Table 1 in their paper via links above) the moon’s ‘mean’ surface temperature is 154.3K, but it’s not clear where they got this figure from or how meaningful it is.
Something semi-related, but something I don’t think you would have seen before – How the 33C Greenhouse Effect (using the questionable assumptions) works out according to Latitude.
At the North Pole, the Greenhouse Effect (including temperature distribution from the equator to the poles) is actually 80C. At the equator, it is as low as 22C. The area-weighted average is still 33C but higher latitudes have a bigger impact.
http://img40.imageshack.us/img40/4605/greenhousebylatitudec.png
In terms of Watts/m2, there is less differential by latitude (and a lower value at the South Pole than might be expected, perhaps related to the average 2 km high altitude).
http://img440.imageshack.us/img440/7808/greenhousebylatitudewm2.png
Hopefully you were able to fold in the proper geometry of the emission-absorption area as I tried to comment over at JoNova’s blog. The absorption surface is no a disk the diameter of the Earth, but a hemisphere (more area to absorb) with an absorption function that is highest where the Sun’s rays hit full on, and then drops as you move to the day-night terminator.
The emission surface is the entire 4pi surface. So the absorption area is a fraction of the emission area. I find it interesting that the equations I have seen do not address this difference in radiative and absorbing surface area, and the net solar flux as a function of angle of incidence.
Off topic now, I found what appears to be actual CRUTEM1 temperature computations by CRU generated in 2007. The data are in regional data sets in order to calibrate tree rings. When plotted they show no significant modern warming, even though the represent much of the Northern Hemisphere. How the regions were combined seems a bid dodgy, and some of the regions seem to have been slightly warmed over the period of the temp record (which is strange, since the data is supposedly regional anomalies against a regional norm???).
Anyway, it is mildly interesting for folks who might be interested. Data is from the Climategate 1 dump.
Frank Lee MeiDere says:
December 29, 2011 at 1:31 am
….
Yes, I’d heard rumours that the Moon was somewhat lacking in atmosphere. I was under the impression we were talking about the effect of ALL greenhouse gasses, not just CO2. … and frankly, I’m sick of seeing such childish displays to honest enquiries.
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Well, yes. I thought that answer was a bit inappropriate myself. However, someone did answer your question in a less juvenile fashion. Because the moon rotates much more slowly than the Earth, the areas exposed to sunlight get very hot. And because emission varies with the fourth power of temperature, the very hot areas return more heat to space compared to a more rapidly rotating planet where the temperatures are more moderate. Since energy in has to equal energy out, the moon will, on average, be a bit colder than the more rapidly rotating Earth
Plausible? For sure. Correct? Quite possibly
In the above post I should have made clear the fact that the lapse rate can be fully explained for an atmosphere free of GHG molecules using thermodynamics rather than radiation. Euler equations are required and Prof Claes Johnson documents the proof in “Climate Thermodynamics.” Section 5: http://www.nada.kth.se/~cgjoh/atmothermo.pdf
Because of this, I repeat that absolutely no component of the lapse rate needs to be attributed to any greenhouse gas.
A further point which I shall be including in my book relates to the thermal “momentum” of the whole Earth beneath the surface, including the core and all energy generated in the core, mantle and crust. I am fully aware that there is only a very minute net flow of thermal energy from beneath the surface and I am not saying this causes any warming. The fact that it is an outward flow is actually a good thing, because it means thermal energy from the Sun is not flowing back into the crust at this stage in history.
The thermal energy we are talking about in the core etc obviously totally eclipses all that in the oceans, land surfaces and atmosphere. I maintain that it thus provides a stabilising effect for long-term climate. The reason goes like this: if the surface were to somehow rise by, say, five degrees in the next 200 years or so, then it would be necessary for the whole (near linear) plot of temperatures from the core to the surface to be raised by 5 degrees at the surface end. The existing levels have come about over millions, perhaps billions of years and they would take some significant “shaking” to alter that underground temperature gradient. Clearly a huge inward flow of thermal energy would be required to fill in the gap under the new (raised) temperature plot. This energy would far eclipse the energy required just to raise the oceans etc by five degrees. Hence, that energy would not in fact raise the oceans by anywhere near five degrees, because the vast majority of it would be needed to raise the underground temperatures.
Whatever happened would happen far, far more slowly and permanent variations of the order of five degrees would take perhaps many thousands of years. Now I know there have been variations of the order of 2 to 3 degrees over a few hundred years, but I suggest such variations are probably about the limit of what can be stored by way of extra thermal energy mainly in the oceans. If we are approaching that limit now (after warming since the Little ice Age) then, unless we see thermal energy starting to flow back into the crust, we probably have nothing to worry about because there would already be a significant propensity to start long term cooling – if not quite yet, then probably within 50 years or so based on historic apparent long-term cycles of the order of 900 to 1000 years.
But let me stress, in conclusion, that I am talking about totally natural cycles beyond the control of mankind. Carbon dioxide has absolutely no warming effect because any back radiation does not have the required energy to cause any warming.
The IPCC thought experiment used to establish the 33 K fiction is as follows:
Remove the atmosphere in which case the present -18°C in the upper atmosphere for radiative equilibrium with space of the 240 W/m^2 iR from the Earth’s surface coincides with the surface. +15 – (-18) =33 K!
Unfortunately, it’s wrong. because no clouds and no ice reduces albedo from 0.3 to 0.07. Redo the radiation calculation and you get 0°C. That implies GHG warming of 15 K. However, you still have aerosols in the atmosphere and convection. A modelled estimate is ~9 K.
Note this is a different derivation to the one which the author refers to.
Serious doubts arising: The Daily Mail Global Warming or a New Ice Age?
http://www.dailymail.co.uk/debate/article-2011667/Global-warming-new-ice-age-YOURE-paying-politicians-hysteria.html
Mydogsgotnonose says:
December 29, 2011 at 5:22 am
The IPCC thought experiment used to establish the 33 K fiction is as follows:
Remove the atmosphere in which case the present -18°C in the upper atmosphere for radiative equilibrium with space of the 240 W/m^2 iR from the Earth’s surface coincides with the surface. +15 – (-18) =33 K!
Unfortunately, it’s wrong. because no clouds and no ice reduces albedo from 0.3 to 0.07. Redo the radiation calculation and you get 0°C. That implies GHG warming of 15 K. However, you still have aerosols in the atmosphere and convection. A modelled estimate is ~9 K.
===================
What the AGWScience Fiction propaganda has done is to misuse basic figures to give the appearance that ‘greenhouse gases’ raise the temperature of the Earth from -18%deg;C to 15°C to promote this ‘meme’ that ‘greenhouse gases raise the Earth’s temp’
What they don’t tell you is the -18°C is the figure, standard in this, of the Earth without any atmosphere at all, that is, without the whole of the real greenhouse around Earth of the gaseous atmosphere which is predominantly nitrogen, oxygen and water.
Nitrogen and Oxgen are therefore real greenhouse gases warming the Earth and so part of the reason why the Earth is 15°C and not 33°C colder.
However, if one takes the Water Cycle out of that mass of fluid gaseous ocean above us, weighing down on us at a ton/square ft, that’s how much is on your shoulders.., the temperature would be 67°C.
In other words, the water cycle reduces the temperature of the Earth by 52°C to bring it down to the 15°C.
I know from experience the desert goes from very hot during the day to damn cold at night. So I may be overly simplistic here, but doesn’t the large day/night temperature swing (high temperature during the day, low temperature at night) that occurs in the arid desert give some measurable indication of the contribution GHG’s, especially gaseous H2O, make to the planet’s temperature?
Frank Lee MeiDere says:
December 28, 2011 at 10:41 pm
////////////////////////////////////
Unfortunately NO because:
1. The moon does not have a 1 bar atmosphere devoid of green house gases:
2. The moon does not have or does not have the equivalent of the large thermal reservoirs which we have on Earth, ie., it surface is not 75% composed of water.
3. It rotates only once every ~27.5 days, not once every 24 hours.
These differences make comparison impossible.
@richard_verney
Good points. Thanks.
Perry says:
December 29, 2011 at 1:04 am
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A pity then that your childish answer did not answer his question!
I believe that he was seeking clarification as to how the 288K figure has been assessed and inherent in this is whether there is such a thing as a global average temperature and if so, how do you assess it?
I would envisage that if I had an IR thermometer and went around my garden pointing it at the surface there would be a 100 (or more) different temperature readings. My garden is only a small area, now consider the changes over a mountain range from valley floor to highest peak, in the confines and open spaces of a town even by the beach where there are significant changes between the sea line and a few hundred metres inshore. We would have no idea as to the average surface temperature of the globe even if we were to increase the number of thermometers used for its assessment a million times.
We say that the average temperature of the Earth is about 15 degC but this could easily be out by several degrees in either direction.
This is one reason why the satellite data is to be preferred at least there is a constant height at which measurements are taken.
Jay Davis says:
December 29, 2011 at 7:02 am
I know from experience the desert goes from very hot during the day to damn cold at night. So I may be overly simplistic here, but doesn’t the large day/night temperature swing (high temperature during the day, low temperature at night) that occurs in the arid desert give some measurable indication of the contribution GHG’s, especially gaseous H2O, make to the planet’s temperature?
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If one is trying to assess the effect of back radiation it is not that simple. Water vapour is a so called GHG, Water vapour also has the ability to store far more latent heat. In dry arid air the latent heat capacity is reduced and the air contains (on a per temp basis) less energy and therefore dissipates its heat far quicker than would be the case with moist air irrespective of the action of any back radiation.
The Viscount is altogether too generous to the IPCC. How in all honesty can any organisation which has filched billions of dollars peddling false science be allowed to retain control of influence of policy makers by just saying: ‘Oh dear, we were wrong, now we’ll agree to the testimony of more skeptical scientists,so everything’s OK now, isn’t it’?
They have been wrong, have been bullies and should be disbanded.
There is a price for failure and the failure has been catastrophic.
If the weasel politicians are too weak: call in Donald Trump. He has no problems saying: ‘You’re fired!’
BASICS
Text: “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”
My comment: Area of a sphere is (4 pi r^2); area of a disc is (pi r^2). But this is for only ONE SIDE of the disc. Should the area factor not be 2 instead of 4? And the insolation 681 W/m^2 instead of 340.5?
IanM
The Earth itself is a warm body, resulting from a combination of radioactive decay, tidal flexing and magnetic field interactions. Annual temperature variations disappear only a few meters below the surface (in most areas) and then the temperature rises with depth. Western Canada has a sedimentary cover that is probably representative of such cover elsewhere, and increases by 1 – 3 C/100 m. The bottom of the oceans is said to be about 4*C, but the geothermal gradient is much higher in the thinner oceanic crust; a huge amount of heat must be lost to the oceans on a constant basis. The “bank” of energy in the top few hundred meters of crustal rock has to be equal to a multiple of that of equivalent volumes of water, given the greater thermal capacity of rock compared to water.
Without surface cooling, the surface of Western Canada would be somewhere in the 18*C/291K range, I estimate, clearly higher than the present average planetary temperature of 14.5*C. None of the 3 assumptions include this background of Earth-heating of the atmosphere. I don’t see this energy flux in any of the Trenberth’s oceanic energy balancing acts, either.
Any comment as to why this aspect of atmospheric heating is not in the discussion?
Thanks to Monckton for the clarity of his argument. The question that still occurs to me is: exactly what is meant by “surface” when we talk of a surface temperature of 288K ? The other questions I am angling toward by this question is: How do we account for the extremely large pool of cold temperatures in the deep ocean when we speak of surface temperature of the earth? Shouldn’t oceans be integrated into what we call surface temperature? I believe it has been reasoned the the cold of the ocean depths derive from the *surface* of polar seas, therefore it seems reasonable to consider them a part of the *surface* temperature of the earth. Presumably the cold of the poles and thus the ocean deeps is still a result of radiative transfer of heat to space from the earth’s polar regions. It should be taken into account. Because the cold of the ocean is so extensive, if it is taken into account as part of surface temperature it lowers sensitivity even more and in a substantial way.
Thanks Richard,
I was being over simplistic with regards to back radiation.
Monckton is correct on the issue of the 255 K estimate for the Earth’s surface temperature in the absence of the greenhouse effect. He is incorrect in his claims about climate sensitivity for the reasons discussed by myself and others in his Dec. 5th thread. (See, e.g., here: http://wattsupwiththat.com/2011/12/05/monckton-on-sensitivity-training-at-durban/#comment-820816 and other comments of mine before and after )
Myrrh: you are confusing lapse rate warming with GHG warming.
Joel Shore; it seems you are assuming 100% thermalisation of the absorbed IR. It can’t happen in my view [Law of Equipartition of Energy].
The absorption must be by second phases, mostly cloud droplets with dissolved CO2 [mainly molecular].
Climate science made a number of serious wrong turnings a long time age. No climate model can predict climate – much of the the physics is completely wrong!
One thing puzzles me about this. It is stated that in the absence of greenhouse gases in the atmosphere, the Earth’s surface temperature should be 255K. I have read an estimate that the atmosphere weighs about five quadrillion tons. We can appreciate this from the fact that air at the surface has a pressure of about 15 pounds per square inch. Boyles Law outlines the relationship between the volume, temperature and pressure of a gas, and indeed, as we ascend above the surface of the Earth, air pressure decreases, as does air temperature. Lord Monckton says that the characteristic emission surface of the atmosphere is at an elevation of 5 kms, and here the temperature is about 255K. Oddly enough, this is the elevation of the center of mass of the atmosphere. How much of the 33K warming at the surface is caused by the greenhouse effect, and how much by pressure?
@Disko Troop
It was precisely that kind of consistent response from the warmists that first set off warning bells for me that something just might be wrong with global warming. I, and many others like me, are not experts in any of these fields, and WUWT is one place we can come to find hard data and open debate. Being able to ask questions is integral to understanding the issues. (Mind you, I do understand a certain exasperation towards those who ask something like, “Who is Phil Jones?” when they could just have easily typed the same words into Google and received an instant and quite understandable response. That, however, wasn’t an issue in this case.)
Doug Proctor says:
December 29, 2011 at 9:23 am
Any comment as to why this aspect of atmospheric heating is not in the discussion?
A while ago I chased the numbers and was convinced that they were too small to make a difference in the argument, 0.08watts/m^2 or so .
HankHenry says:
December 29, 2011 at 12:37 am
The 288.2k is an average value temperature over the Earth required to emit the same amount of power as is being absorbed into the Earth system from the Sun. Note that while Stefan’s formula is T^4, when one deals with very small fractional changes in T it behaves approximately in a linear fashion and one can assume that the power is proportional to the T over that small range of variation.
“Mike McMillan says:
December 29, 2011 at 12:52 am
The characteristic-emission surface is a new concept to me. If it is at 5km, that makes about 75,000 more square miles of disk to receive sunlight, and 300,000 more sq miles of radiative surface. Does that have any effect on the calculations?”
If there actually were a ‘surface’ there that emits a continuum then it would have some small effect. This characteristic emission surface and altitude has no physical meaning or relationship to anything in the realm of reality. Stefan’s law is based on Planck’s law based on black body continuum emissions. Earth’s surface (on average or at a single place) will emit this continuum as will an optically thick cloud top. A gas will emit/absorb based upon a spectrum of lines unless it becomes optically thick at all wavelengths, even between the spectral lines which is not relevent for our atmosphere.
What happens in our system is that for some point on Earth, either the surface or a cloud top of an optically thick cloud, there is emission of black body continuum. The atmosphere above it then absorbs and re-emits spectral lines based on its own temperature and on the gas components. If the atmosphere is cooler than the surface, the re-emission will be less than the absorption. If the atmosphere is warmer than the surface, the re-emission will be greater than what was absorbed and there will be spectral emission lines visible above the blackbody continuum.
Since the temperature of the atmosphere (the lapse rate) is nothing but conservation of energy and the flow of energy by conduction, convection, and radiation, it is not an unchanging constant and will change as the nature of the atmosphere changes. Since space is much colder than Earth’s surface and there is heat transfer to space, the atmosphere will have a lapse rate so there will always be line absorption rather than line emissions. However, this modifies our black body continuum to a complicated mess which is no longer the characteristic radiation curve of a black body. Rather it is a composite of line absorption spectrums and a continuum. Stefan’s law isn’t suitable for working with this at all.
In Stefan’s law, the emissivity factor is an engineering kludge number or fudge factor. By returning to Planck’s law and applying an emissivity factor based on the spectral absorption at each wavelength (or frequency), one can then get an emission curve of a gas for a particular temperature. Note that Kirchoff’s law regarding the equality of emission and absorption power only works when dealing with emissions at the same temperature as the spectrum being absorbed. Obviously, sunlight is coming in with a substantial contribution of visible light and a good deal of that is being absorbed by the Earth yet at roughly 300k (instead of 6000k like the Sun) Earth is emitting no power in the visible light range.
I find myself in an uncomfortable position. I am on the same side of the AGW/CAGW debate as Lord Monckton, and I believe he is one of our more eloquent spokespersons. However, questionable arguments are not limited to proponents of AGC/CAGW. When I come across an argument that I perceive lacks internal consistency, I sometimes document my concerns, and every once in a while submit that documentation for public scrutiny. Such was the case when I read Lord Monckton’s reasoning that greenhouse gases are responsible for an Earth surface temperature difference of 33 K.
Note: I neither agree nor disagree with Lord Monckton’s calculation of the Earth’s “climate sensitivity to CO2” (hereafter refered to simply as climate sensitivity), which I believe is defined as “the change in average Earth surface temperature for a doubling (relative to a specified initial amount of atmospheric CO2) of the amount of atmospheric CO2.” I haven’t given the climate sensitivity problem enough thought to either agree or disagree with Lord Monckton’s analysis. However, regarding climate sensitivity, I want to make three comments. First, if the calculation of climate sensitivity depends on a literal definition of the change in Earth surface temperature in the presence/absence of greenhouse gases, and if the climate sensitivity would be appreciably different for a change of a few degrees K in the value of that temperature difference, then I guess I have to question Lord Monckton’s climate sensitivity values.
Second, I believe a definition of “sensitivity” based on “a doubling” of the independent variable is uncommon. Most definitions of sensitivity use a “derivative” approach—i.e., are expressed in terms of “a change in a dependent variable per change in an independent variable in the limit as the change in the independent variable approaches zero.”
Third, since for whatever reasons the climate science community has elected to use “doubling” in its definition of climate sensitivity, then the numerical value of climate sensitivity is a function of two values of the independent variable (CO2 level) not one value as would be the case for the “derivative”definition of “sensitivity”. It’s true that knowledge of one of the two independent variable values is sufficient to compute the other value of the independent variable; but given the apparent highly non-linear nature of Earth surface temperature as a function of CO2, I believe it is imperative when discussing climate sensitivity to specify one of the two independent variable values.
In his justification for an Earth surface temperature difference with and without greenhouse gases, Lord Monckton wrote {note: text in square brackets [ ] are my thoughts for the purposes of discussing Lord Monckton’s algorithm}: “ According to recent satellite measurements, 1362 Watts per square meter of total solar irradiance arrives at the top of the atmosphere [seems reasonable]. 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 [seems reasonable], and is also reduced by 30% to allow for the fraction harmlessly reflected to space [seems reasonable], , giving a characteristic-emission [I believe that should be characteristic-absorption] 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. [Although I have a few issues with this definition of the characteristic-emission surface which I plan to note in subsequent comments to Lord Monckton’s guest post, for the purposes of this discussion I’ll use Lord Monckton’s definition.] 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 [seems reasonable]. It’s as simple as that.
My question to Lord Monckton is: “What part or parts of the above algorithm is (are) related to greenhouse gases?” The Stefan-Boltzmann constant isn’t. The assumed emissivity of unity isn’t. The temperature to the fourth power rule isn’t. The total solar irradiance of 1362 Watts per square meter isn’t. The divisor of 4 isn’t. This leaves two values that may be dependent on greenhouse gases: (1) the “30%” reflectivity, and (2) the measured Earth surface temperature of 288 K. If both of these values are unrelated to to greenhouse gases, then greenhouse gases become irrelevant to Lord Monckton’s analysis of the 33 K temperature difference; and with equal justification one could claim the temperature difference of 33 K corresponds to the Earth (a) with/without an atmosphere, (b) with/without oxygen, (c) with/without nitrogen, (d) with/without argon, etc.
It is reasonable to assume that the measured temperature of 288 K is dependent on greenhouse gases. However, to varying degrees it is also reasonable to assume that the measured temperature of 288 K is dependent on (a) the total Earth atmosphere, (b) the amount of oxygen in the Earth’s atmosphere, (c) the amount of nitrogen in the Earth’s atmosphere, and (d) the amount of argon in the Earth’s atmosphere, etc. Thus, it is reasonable to conclude that the measured temperature of 288 K is not solely dependent on the presence of greenhouse gases—other phenomena may have affect.
This leaves us with the 30% reflectivity value. If the 30% reflectivity value were valid for an Earth without greenhouse gases (i.e., the albedo of the Earth in the absence of all greenhouse gases was 0.3), then I believe there would be merit in assigning a 33 K temperature difference to greenhouse gases. However, the 30% reflectivity value is highly dependent on clouds which are formed from water vapor which is a greenhouse gas. As I wrote in my previous guest post, to base a temperature difference on two values each of which is related to and depends upon the presence of greenhouse gases and then claim that such a temperature difference represents conditions with and without greenhouse gases is illogical.
Bottom line, the temperature difference of 33 K may be relevant to an analysis of climate sensitivity, and by chance may be the actual difference between the Earth’s surface temperature with and without greenhouse gases; but the temperature difference as computed using Lord Monckton’s algorithm does not represent the Earth surface temperature difference with and without greenhouse gases.