Guest post by William M. Briggs professional statistician
It is statistically appropriate to point to this year’s frigidity as evidence that the theory of man-made global warming is suspect.
Sure is cold out there, unusually so. By “unusual,” I mean the temperature is on the low end of the observed temperatures from previous winters.
Of course, we don’t have any more than about 100 years of reliable measurements, so it’s possible that the freeze we’re experiencing now isn’t as unusual as we suspect. But, anyway, it still sure is cold.
If you recall, a lot of global warming models predicted it would be hot and not cold, and to risk redundancy, it sure is cold. Does this dissonance between the models’ predictions and what is actually happening mean that those models are wrong?
No. But it sure as ice doesn’t mean that they are right.
Here’s the thing: No matter how cold the winter is, no matter how much snow falls, the global warming models will not be disproved. In technical language, they cannot be falsified by the observations.
Another way to say this is that the winter we’re seeing is consistent with what the models have been predicting. Again — does this consistency mean that the models are right and that the theories of man-made warming are true?
No.
Consistency is such a weak criterion that almost any imaginable theory of climate will produce predictions that are consistent with observations. The term is probabilistic: It means that what actually happens had to have some chance of occurring according to a model. If global warming climate models said, “It is impossible that this winter will see temperatures below X,” and temperatures did, in fact, drop below this threshold, then the models would be inconsistent with the observations. The model would be falsified.
But global warming climate models never make statements like that. They say that any temperature is possible, even if this possibility is low. Certain temperatures have probabilities as low as you like, but they are never precisely zero. (To anticipate an objection: “that number was practically zero” is logically equivalent to “she was practically a virgin.”)
Man-made global warming is just one of many possible theories of climate. Another is the Business-as-Usual Theory (BUT), which states that whatever happened last year will more or less happen this year, and so on into the future.
The winter we’re seeing is consistent with the BUT, which like the man-made global warming theory, never says any temperature is impossible. Further, BUT is corroborated more strongly by this winter than is the man-made warming theory. BUT’s predictions are closer to what we actually see.
“Stop right there, Briggs! You’re making the classical mistake of confusing weather with climate. The global warming models make predictions of climate and not weather. This winter doesn’t mean anything!”
I am not making that mistake, and it is you who are confused. Weather is climate. More specifically, aggregations of weather are climate. Means, averages, and distributions of daily weather comprise climate. That is, climate is a statistical phenomenon and depends for its existence on defining a reference time frame.
For instance, if “climate” is defined as the yearly mean temperature, then this year’s cold winter will produce a yearly mean temperature that is colder than average (as long as the coming summer isn’t abnormally hot: winter, of course, overlaps two calendar years and a hot summer can balance out a cold winter in the yearly mean).
So it is appropriate to point to this year’s frigidity as evidence that the theory of man-made global warming is suspect. If “climate” is defined as the decadal mean temperature, then this year’s cold winter will push the decadal mean lower. And it is still acceptable to point to this year’s winter as evidence against the man-made global warming theory.
Just as it was appropriate when the media trumpeted each and every “record setting high!” as evidence for that theory.
The difference is that one day’s temperature has little influence on a yearly mean — it is just one out of 365 other numbers that make up the average. One day’s temperature is thus weak evidence for or against any theory of climate.
But a slew of months with higher- or lower-than-average temperatures will push that yearly mean higher or lower. A season’s mean temperature is stronger evidence for or against any climate theory than is a day’s.
Back in the 1990s, when the yearly mean temperatures were increasing, this was touted as evidence for the man-made global warming — but those years’ temperatures also corroborated the Business-as-Usual theory. Which theory was better?
For the past decade, we have had a string of years with mostly decreasing temperatures. This is strong evidence against the man-made global warming theory, but pretty good testimony for the BUT. So far, the BUT theory is winning on points (there are other climate theories the BUT doesn’t beat). This doesn’t mean that BUT is true and that the man-made global warming theory is false, but it does suggest that this is so.
You can’t have it both ways. It is a mistake to extol evidence that supports the man-made global warming theory and to cry foul when presented with evidence which weakens that theory.
That so many do this says more about their desires than it does about any theory of climate.
Reposted from: http://pajamasmedia.com/blog/actually-weather-is-climate/
with permission from the author. Visit his website: http://wmbriggs.com/blog/
suggest that since CO2 concentrations appear to lag warming by about 800/1000 years, may be the observed increase in measured CO2 during the last 100 years is nothing more than the signature of the MWP or Roman warm period
maybe yes maybe no. There are multiple cycles at play, each with its own latency. Solar energy has lots of shortwave, and so penetrates the ocean up to 300 meters. a 1 watt/m2 rms increase in solar would take 36 years to increase 300 meters of ocean 1 degree…. so yeah, that could set in motion all kinds of things that may not show up for decades or centuries. But greenhouse effect is all longwave which only penetrates the first few mm of water where the resulting heat would promote evaporation into the atmosphere…so CO2 variation ought to be much shorter term than solar, methinks.
davidmhoffer (06:13:15) :
Yes, you are missing the fact that in order to get a 3c rise from 3.7 watts, the climate models incorporate positive feedbacks which supposedly add to this value
I included that. CO2 doubling = 3.7. Positive feedback from water vaper = 7.4 watts. IPCC mentions other feedbacks, NONE of which are in the same order of magnitude as those two. Now earth isn’t an ideal black body, but with radiance increasing commensurate with temperature raised to power of FOUR…. the negative feedback from plane old physics ALONE is larger than the temp change the IPCC claims is possible. so either I missed something else, or their claim is WAY over stated.
David
You haven’t missed anything. The ~3.7 w/m2 CO2 forcing refers to the forcing at the TOA (top of the atmosphere). This does not map 1-to-1 to surface forcing. There is some amplification at the surface (even ignoring feedbacks).
I can probably show this with a simple model but I’ll need about 20 mins to think it through. If you’re interested I’ll give it a go. It’ll be a good exercise for me.
Davidmhoffer
Re: TOA/Surface forcing
I’ve come up with a crude calculation which I hope illustrates the amplification of the TOA forcing at the surface.
Let G be the amount of energy emitted from the earth’s surface.
Let A be the amount of energy emitted from the atmosphere.
Another way of thinking of A is that it is the amount of energy that is transmitted through the atmosphere.
If there were no absorbing gases in the atmosphere then we would have the trivial result that: A = G, i.e. all energy emitted from the surface is emitted directly to space.
But we do have absorbing gases in the atmosphere. If T is the Transmission factor (i.e. the proportion of G which is transmitted) then the amount of energy emitted to space from the atmosphere is given by
A = G x T (i) so that
240 = 390 x T
i.e. T = ~0.62 or ~62% of G is transmitted
If CO2 doubles, outgoing energy would be reduced by 4 w/m2 (again using easy numbers) so the energy emitted (transmitted) from the atmosphere, i.e. A = 236. Substituting this new value into (i) we have
236 = 390 x T or T = 236/390 = ~0.605
Now only 60.5% is transmitted. But the earth still needs to get rid of 240 w/m2 which means the surface will need to warm. To find out by how much we can rearrange (i) as follows
G = A/T i.e.
G = 240/0.605 =~397 w/m2 which is an increase of ~7 w/m2 compared to a 4 w/m2 forcing at the TOA. The 1.7 factor (deltaG/deltaA) looks to be pretty consistent with the numbers mentioned in earlier posts, so we have some confidence that the explanation is valid.
illuminating. But still doesn’t quite work…but my wife insists we are leaving for dinner now so my follow up question will not be posted until the AM.
The claim that the climate isn’t weather is like saying that food isn’t strawberries. …and then arguing that strawberries aren’t food.
davidmhoffer (15:03:08) :
illuminating. But still doesn’t quite work…but my wife insists we are leaving for dinner now so my follow up question will not be posted until the AM.
I’ll look forward to it. But as I’m in the UK and I’m not sure which US timezone you live in – I’m not sure when I’ll read it.
The real problem is that they had falsified data and the “warming is man made” by GISS and CRU. Is this climate or weather?
“G = 240/0.605 =~397 w/m2 which is an increase of ~7 w/m2 compared to a 4 w/m2 forcing at the TOA.”
Once again, no, no, and most emphatically, NO.
IR cannot violate the rules simply because someone wishes it to be so. The emission/absorption lines are still quantized and discrete, they only appear as “bands” because the instruments used to measure it do not have sufficient resolution to see the individual lines. If a CO2 molecule radiates energy at 2349cm, the only molecule which will absorb that wavelength is another CO2 molecule. For this calculation to apply, the atmosphere would have to be 100% CO2. Near the surface, much of the transfer of energy between molecules is due to collision induced absorption, so this makes such a simplistic calculation all the more irrelevant.
I’ve been sayin this for years. Averaging daily weather-related temp readings and then coming up with an anomaly over time and calling it anthropogenic climate change as if it were different from the weather-related temperature data it is derived from cannot be supported by this kind of statistical figuring. It is not an explained mechanism. It is not a cause and effect explanation. It is not a correlation of any kind. What would be interesting is to also report median and mode as well as high and low anomaly.
UncertaintyRunAmok (07:19:10) :
“G = 240/0.605 =~397 w/m2 which is an increase of ~7 w/m2 compared to a 4 w/m2 forcing at the TOA.”
Once again, no, no, and most emphatically, NO.
I think if you set up a simple energy balance model you’ll find it’s yes, yes and most emphatically yes.
I agree my explanation is crude but it’s only intended to illustrate the point.
John Finn
I’ll look forward to it. But as I’m in the UK and I’m not sure which US timezone you live in – I’m not sure when I’ll read it.
Time zones being a Canadian invention, and I being in Canada, there’s no need to drag the Americans into it 🙂 I’m Central Time. That said, my follow up question got really complicated and turned into more of a position paper, but please read it as a question:
In brief, I treated the whole planet, atmosphere included, as a Black Body. Your explanation treats the earth land and sea surface as a Black Body with a layer of atmosphere around it. To make up for a deficit of 4 watts at Top of Atmosphere, the Black Body needs to radiate an extra 7 or so. Fair enough as the atmosphere makes for an awful correlation to Black Body since the bulk of the energy spectrum goes right through it. Even then, any energy increases would eventually propagate through the system as a whole making the model valid given sufficient time to achieve equilibrium, but let’s put that aside for a moment.
CO2 molecules make for an excellent Black Body correlation provided that you remember that they are suspended in the atmosphere. So energy captured by a CO2 molecule is radiated in all directions as opposed to the earth Black Body only having one way to go. So energy radiated by a CO2 molecule heated up by LW from the earth can wind up in one of three places. The portion radiated downward will either collide with another molecule in the atmosphere, or earth. The energy radiated sideways or upward will either collide with another molecule in the atmosphere, or escape into space.
So the physics really falls apart again. If all we were looking at was CO2, about 20% of its radiation would be down. To get an extra 4 watts going down you would need to radiate about 20. Of course that’s not fair. The other 80% gets radiated in other directions, some of which escapes into space and some of which hits other molecules. Of the energy that hits other molecules, 20% would be radiated down and 80% would either escape or hit other molecules and so on in a law of diminishing returns. So you still need CO2 to radiate an extra 16 watts or so (guesstimate mine) to raise the over all atmosphere temperature to deliver 4 down. What temperature rise does that require?
In the Troposphere at an average of -20 C, you would need a temperature increase of 4 degrees C to correspond to a 1 degree C rise at earth surface to get 7 watts going out to get back to equilibrium. Even if I over guesstimated by double, we would still need to see Troposphere temperatures varying from mean by over double that of surface temperatures. Amsu-A only has about 10 years of data, but they pretty much track together, suggesting once again that the rise in earth radiance for a given temperature increase would over whelm contribution from CO2. That’s only a 1 degree rise. Since earth radiance goes up with T^4, an exponential rise in CO2 contribution would be required to keep up. Further, how long would it take? The stratosphere has 2500 times as many other molecules as CO2…. So a very long time for the CO2 to heat up the rest of them even if you include conduction as well as radiance. One could, I suppose, calculate the transmission spectrum of CO2 for a given temperature and then determine if molecules beyond the troposphere absorb in that spectrum but not in the one the earth normally radiates at…. But we’re starting to talk pretty thin atmosphere there, so a lot would just escape, and the rest…20% down, 80% sideways or up….
OK, I’m sure I blew it somewhere back there in the logic chain…. But the energy balance doesn’t seem to add up either way. If the whole thing, atmosphere included, is a Black Body, then we’d need to see exponential rises in CO2 contribution to keep up with increased earth radiance? If we look at it as two layers, we would need an exponential rise in CO2 contribution to keep up with earth radiance?
Always a pleasure to read an article so clearly and simply put.
bucko36 (13:55:44) : I’m confused?? What did he say?????
I think what he said was, whereas it is possible that the AGW Emperor is clothed in the fine garments its learned courtiers are fussing over, it does appear that he is buck naked.
davidmhoffer (12:16:22) :
John Finn
I’ll look forward to it. But as I’m in the UK and I’m not sure which US timezone you live in – I’m not sure when I’ll read it.
Time zones being a Canadian invention, and I being in Canada, there’s no need to drag the Americans into it 🙂 I’m Central Time. That said, my follow up question got really complicated and turned into more of a position paper, but please read it as a question
David
Sorry about my “american” assumption. It’s just that there’s rather a lot of them about – and a good few post on WUWT.
I’ve read your post but will need to go over it again before I could give a reasonable response to your points. However, I’d just like to make the following couple of points of my own.
1. In your original post, you queried the apparent discrepancy between IPCC value of ~18 w/m2 and the CO2 forcing figure (amplified by feedback) of ~11 w/m2. I believe I gave a simple illustration as to why the IPCC use the higher figure. I did not attempt to justify it. However, it does seem reasonable that if an extra 4 w/m2 is to be emitted from the TOA then the surface will need to emit more than 4 w/m2 since some of the extra energy emitted from the surface will be absorbed by the ghgs in the atmosphere.
2. I don’t doubt your 80% : 20% absorption figures but ultimately some goes up and some goes down. OK – 80% is not radiated to the surface (immediately) but some of that 80% will be re-absorbed and 20% of that will be radiated down and 80% radiated elsewhere … and so on. In a column of the atmosphere there is the potential for lots of absorptions and emissions.
If I am able I’ll try and give a more considered response to your post later (I am quite definitely not able at the moment 🙂 )
PS I hoped you enjoyed dinner.
Anthony: Please re-post that hilarious cartoon of the pompous naked emperor walking along under a shade held up by four 18th century flunkies and labeled “IPCC”. It’s so perfect, now more than ever.
Sorry about my “american” assumption. It’s just that there’s rather a lot of them about – and a good few post on WUWT.
no need to apologise, apparently we look like them too 🙂
1. In your original post, you queried the apparent discrepancy between IPCC value of ~18 w/m2 and the CO2 forcing figure (amplified by feedback) of ~11 w/m2. I believe I gave a simple illustration as to why the IPCC use the higher figure. I did not attempt to justify it. However, it does seem reasonable that if an extra 4 w/m2 is to be emitted from the TOA then the surface will need to emit more than 4 w/m2 since some of the extra energy emitted from the surface will be absorbed by the ghgs in the atmosphere.
I wasn’t actually disputing your numbers, I sort of accepted them. In reading your comment above I may have misunderstood though. If IPCC calculates 3.7w/m2 at TOA, there would be amplification at earth surface due to the difference in the area of the TOA sphere vs the seal level sphere – but only about 3%. At end of day though, I don’t think you can calculate baed on the extra energy being modeled as starting at TOA and coming down. It “starts” at earth surface as normal level of earth radiance and goes up. The “normal” amount gets retained and the rest escapes. IPCC claim is double the amount of CO2 and retain an extra 3.7 w/m2 = 1.1 degree temp increase. But at 0 C that would only be enought to sustain about .75 degrees. At 20 C, that would only be enough to sustain 0.64 degrees. At 30 C, it would sustain only .58 degrees. In brief, the warmer it is, the less effect a given change in energy input gets. If I magnify as per your estimate, I still have the same disconnect between the steepness of the two curves, and at some point, radiance MUST over whelm CO2 forcing. At the same time as that is happening, the curve from CO2 forcing has to go the other way. If going from 280 ppm to 560 ppm adds 3.7 watts, does adding another 280 to toal 840 ppm add 7.4 watts? No, it can’t. The last 280 can only capture a certain percentage of what is coming at it, and since the first 560 already got some of it, the last 280 gets the same percentage of a smaller number.
So…as temperature goes up, the effect of a given energy input decreases. As CO2 concentration goes up, the effect on energy input decreases. No?
You’re right about the fact that ‘choosing the suitable time period’ is critical to all arguments in climate change. I noted many times that 1961 – 1990 was not perhaps optimal, but I’m surprised that no debates about this take place regularly. It’s great that you were asked to write this piece, as it adds considerably to the discussions taking place.
What I think people will soon understand and accept is that our earth’s climate has many recurring ‘beats’ and is, therefore, like a Fourier signal with multiple ‘beats’ of different frequency. Each ‘beat’ may be subject to particularly modulations through external or internal factors (solar output, oceanic heat content, winter snow etc etc) and, only by coming to understand those beats and how they integrate, will we start to really understand climate.
When you know there are beats of:
months (lunar);
2-3 years (quasi-biennial oscillation);
5 – 7 years (ENSO)
11 and 22 years (solar/Hale cycle)
20 – 30 years (PDO etc)
50 – 70 years (Gleissberg)
and many more, you’ll see that getting a coherent picture without a few hundred years of rigorous collation of data is going to be tricky.
That’s why folks try short-cuts using proxies. If it works it’s great. But if not? Seems like we finding out right now……..
There’s a few more things which would merit discussion:
1. Any correlation between cold winters and hot summers? 1947 and the early 1980s in the UK come to mind….I hold no position on this one, just interested in other’s experiences around the world…….
2. For farmers, is ‘annual mean temperature’ less important than extremes at the wrong times (late frosts, deluges, droughts etc etc)? Please try to link the debate about food supplies to realities of agriculture……
After 25 years in IPCC ‘warm mode’, perhaps the next 25 years will be in ‘neutral mode’?
1. Any correlation between cold winters and hot summers?
I think this is a much more important question than people realize. For starters, farmers are, as you pointed out, far more governed by the growing season fluctuation than the annual fluctuation. My personal observation is that “less cold” winters are often coupled with “less warm” summers and vice versa. Its hard to find data broken up that way, but what little I’ve seen suggests that. The other reason I think it important is that most long term temperature reconstructions rely on tree ring and other similar data. This assumes that any fluctuation in growing season is mirrored by the non-growing season. The farther north you go, the shorter the growing season and the longer the part of the year that the tree ring data doesn’t measure, so any divergence becomes more significant. Given that the recent controversy has been over tree ring data from Siberia, I just don’t see how it can be considered valid unless studied from that perspective.
“”” UncertaintyRunAmok (07:19:10) :
“G = 240/0.605 =~397 w/m2 which is an increase of ~7 w/m2 compared to a 4 w/m2 forcing at the TOA.”
Once again, no, no, and most emphatically, NO.
IR cannot violate the rules simply because someone wishes it to be so. The emission/absorption lines are still quantized and discrete, they only appear as “bands” because the instruments used to measure it do not have sufficient resolution to see the individual lines. If a CO2 molecule radiates energy at 2349cm, the only molecule which will absorb that wavelength is another CO2 molecule. For this calculation to apply, the atmosphere would have to be 100% CO2. Near the surface, much of the transfer of energy between molecules is due to collision induced absorption, so this makes such a simplistic calculation all the more irrelevant. “””
Well what you say as to the “discrete lines” may be true of the pure gases (CO2) at low temperatures and pressures.
But in practice, the intrinsic line width associated with these lines is substantially broadened by other phenomena, such as the Doppler effect, which will shift the line frequency due to the thermal motion of the CO2 molecule (Temperature broadening) and also due to the collisions between the CO2 and ordinary air molecules.
So how do you know that the observed CO2 spectrum seen through say the bottom 10 meteres of atmosphere, really does show those sharp lines that are calculated. The same of course applies for the main greenhouse gas like H2O
“”” scienceofdoom (21:09:02) :
continuing.. for George E. Smith:
I’d be amazed if Trenberth had got such a basic number wrong- what are you citing?
The averaged value across the globe is 240W/m^2. At a given point at a given time, it is quite possible to be 340W/m^2. “””
Well then be amazed.
The official NOAA chart which evidently is attributed to Trenberth shows an incoming solar radiation component of 342 W/m^2, which gets divvied up in various ways.
Well that may happen on some planet, but not on this one. On Earth, we have a TSI value of about 1366 W/m^2, which is 4 times Trenberth’s number.
Evidently he takes into account that only a bit more that half of the earth surface is sunlit at any time; actually about 51-52% because of atmospheric refraction, the sun’s angular diameter and other scattering effects.
The earth surface unfortunately only respoonds to what it sees, and when it sees actually 4 times Trenberth’s figure, arriving at the surface, the heating of the surface is much faster (even four times as fast), and it reaches a higher peak temperature, because of that 4X irradiance. The higher temperature reahced results in a much greater amount of thermal radiation from the ground, and moreover it is spectrally shifted to shorter wavelengths because of the higher surface temperature (Wien’s Displacement Law). Consequently the outgoing LWIR is both greater in intensity than with Trenberth’s model, and also spectrally shifted further away from the CO2 absorption band.
The integrated result is that the earth cools much more in reality than it would if bathed continuously at 1/4 the irradiance. The surface emittance is going to roughly follow a 4th power of T law, while the surface emitted spectral peak emmittance follows more of a 5th power of T law; which is of more interest when figuring GHG (CO2) absorption.
Averaging a function which is highly non-linear, always yields a lower value that the integral of the effects of that non-linear function.
And in Trenberth’s model, the surface irradiance of 198 W/m^2 is the same everywhere including on the noonday sun lit North African Deserts, and at the South Pole during the peak of winter midnight.
Total nonsense.
If they are going to create “Climate models” they should at least model something akin to the planet we live on; which does not enjoy a constant never ending low value solar insolation; but a highly variable and cyclic one which creates totally different physical effects.
“The earth surface unfortunately only respoonds to what it sees, and when it sees actually 4 times Trenberth’s figure”
Sorta only worse. At equatorial region at high noon it would see the whole thing, 1366 watts. Moving north and south from there it would decline to pretty much zero at the poles. during course of day it would start at zero at dawn, surge to max at noon, and fall back to zero at dusk for the duration of the night. At mid latitudes similar curve but with more like a 683 watts/m2 max. Take 30% off for deflected radiation if you like, but the variation in energy input is huge at equator and declines as you approach the poles. Further, your comment on radiation varying with T^4 is right on. A daytime surface temperature increase from 25 C to 35 C would be about 64w/m2 swing in radiance, about what you would see equatorial, but north temperate zone we might see 12 to 22 degrees, which is the same temperature differential, but a radiance increase of only 56w/m2. there is no way that you can just average all those curves out and call it 240 watts across the board.
“”” davidmhoffer (18:28:17) :
But remember that the assertion IS that the logarithm of the CO2 atmospheric abundance matches the rise in mean global surface temperature
I thought that the assertion was that CO2 causes small rise in temp that results in exponential rise in water vapor as max water vapour in atmosphere about doubles for every 10 degree rise in temp, approximately tripling CO2 direct effect? “””
Well actually ANY rise in mean global surface temperature will result in increased H2O in the atmosphere. CO2 has no special dispensation to produce warming that selectively leads to more water vapor. Water vapor itself is perfectly capable of doing that. CO2 is merely a small incremental increase in total atmospheric GHG; which is totally dominated by H2O.
And we have Wentz et al, July 7 , 2007 SCIENCE “How much more rain will Global warming bring ?”
And their measured answer, :- one degr C rise in mean global surface temperature results in 7% increase in total evaporation, total atmospheric water content, and total precipitation. Total precip always has to equal total evap over time, or else we would end up with the oceans over our head, instead of under our feet.
And if this 7% per degree were valid over the whole range of atmospheric moisture from zero upwards, you would expect, the evap/precip and total atmospheric water content to each grow the same. If the rate constant varied widely over a large temperature range, you would still expect evap and precip tyo be equal, but you would not expect atmospheric total water to grow at the same rate; but it does according to Wentz.
As for the GCM view of the situation; they agree that precip equals evap; they’d be silly not to, and it so happens they also agree on the same 7% per degree growth in total atmospheric water. BUT ! according to the GCMs, the rate of increase of evap/precip, is only 1-3%; not 7% as Wentz et al observed on a real planet called earth.
So there is your 3:1 mandatory computer model fudge factor; but more importantly the models are in error from the observation by as much as a factor of 7 : 1.
“”” davidmhoffer (13:00:56) :
“The earth surface unfortunately only respoonds to what it sees, and when it sees actually 4 times Trenberth’s figure” “””
Well David; you and I seem to be among the few, who seem to understand that you cannot simply average a non-linear function and get the right answer.
If you take a cyclic varying function of the form Y = (1 + a sin 2.pi.t/T) and integrate it over any number of complete cycles of period T, you end up with an integral of 1.000. By extension, any repetitive cyclic variation containing only harmonics of the base period, also integratews to 1.000 over any complete number or cycles of the fundamental.
But if you now raise that expression (1+a.sin2.pi.t/T)^4 and integrate that you ALWAYS get a POSITIVE increase over 1.000 over any complete cyle or multiples. It comes from the integral of the term +6a^2.sin^2(2.pi.t/T). Well there also is another term a^4.Sin^4(2.pi.t/T), but that is usually negligibly small compared to the other term. The remaining two terms in sin^1, and Sin^3 also integrate to zero over any complete cycle.
So the earth’s surface emitted cooling radiation is alsways higher than that computed from the average temperature because of this offset, and that happens twice every day, and on an even larger sacale over the annual cycle.
But when it comes to the effect of this on the GHG absorption, particularly CO2; you have to do it differently, because of the Wien’s Displacement Law; which incidently is not mentioned in that Miskolczi paper.
The surface emitted thermal radiation; approximating a black body spectrum (emissivity modified) has a spectral peak emittance that increases as the 5th power of the temperature; not the 4th power. And it moves to a shorter wavelength since Lambda max . T is a constant. The CO2 absorption band, however stays at pretty much the same wavelength, so it moves further down the tail of the emitted spectrum. BUT !!, ewven thoguh it is further down the tail, the spectral emittance at the CO2 absorption band is still higher than it would be at the lower surface temperature; but when you compare it to the total surface emission over the full spectrum, the CO2 loses effect as the surface emitting temperature increases.
Over earths surface temperature extremes, the thermal emission spectral peak moves from around 8.7-8 microns at the highest temperatures, to around 15.0 at the coldest. This is one of the reasons why one would expect GHG(CO2) warming to be greater at the poles, where the emission temperatures are lower, but the spectrum sits right on the CO2 band.
“”” scienceofdoom (21:09:02) :
continuing.. for George E. Smith:
I’d be amazed if Trenberth had got such a basic number wrong- what are you citing?
The averaged value across the globe is 240W/m^2. At a given point at a given time, it is quite possible to be 340W/m^2. “””
Well SoD, I’m quite familiar with how they get the number they use; it’s just that nobody bothered to inform planet earth about Trenberth’s rule. So Earth does not calculate it’s total incoming solar energy that way, so naturally it gets a different answer. And moreover, there is nowhere in place any system capable of measuring Trenberth’s number; so it is a bit disingenuous to say his number agrees with measurments.
And even though the total surface area of the planet, is about four times the total interception disk, the actual amount of the earth surface that is soalr irradiated at any time (absent cloud cover) is about 51-52% of the total earth surface; not 25%. This comes from a sun angular diameter of about 0.5 deg, and a horizon atmospheric refraction of at least the same order of magnitude at each end of the day. When the sun’s lower limb is sitting on the visible horizon, the entire sun disk is completely below the horizon. Then atmospheric scattering conducts sunlight into the night sky at admittedly a lower level for the duration of morning and evening twilight.
The earth surface takes all of this detail and more into account; but Trenberth’s model does not.
Why not model what earth really does, rather than some “artist’s impression” ?
With regard to Pachauri and the IPCC science y’all may be interested in my E-Mail exchange with him in April and May 2008. see my blog at
http://climatesense-norpag.blogspot.com
Well David; you and I seem to be among the few, who seem to understand that you cannot simply average a non-linear function and get the right answer
That and energy must increase exponentially to achieve a linear temperature increase, claiming expontial increase in future CO2 emmissions due to fossil fuel consumption would run the planet out of oil in 3 years, linear increases in CO2 forcing are impossible since the amount of energy to contain is finite and so incremental CO2 forcing must diminish even if exponential CO2 increases were possible, same rule applies to water vapour….
What I really dont get is how hard it is to get a basic discussion of physics going when even a simple understanding of these issues is 100 times the proof that glacier melting was a fabricated story.