Climate change sceptics 'wrong'

[Andre]

I guess I just beat Ivan by posting this.

Cimate change sceptics 'wrong'
By Richard Black
BBC environment correspondent

Some say any warming that is measured is due to urbanisation
A major argument used by sceptics of global warming is flawed, a UK Met Office study in Nature magazine says.
This argument maintains that much recorded climate data is inherently unreliable because of where weather instruments are situated.

Most are in or near cities, which produce their own heat; so the rapid warming measured over the last century could be just a record of urbanisation.

The Met Office believes its study shows this "urban heat island" idea is wrong.

The analysis has been done by Dr David Parker. He used data for the last 50 years to create two separate graphs. One plots temperatures observed on calm nights, the other on windy nights.

If the urban heat island hypothesis is correct, he says, instruments should have recorded a bigger temperature rise for calm nights than for windy ones - because wind blows excess heat away from cities and away from the measuring instruments.

Opposing sides

But there is no difference between the curves. "It helps to answer the critics," Dr Parker told BBC News. ...cont

The abstract is http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v432/n7015/abs/432290a_fs.html.

Nature 432, 290 (18 November 2004); doi:10.1038/432290a

Climate: Large-scale warming is not urban
DAVID E. PARKER
Hadley Centre, Meteorological Office, Exeter EX1 3PB, UK

Controversy has persisted over the influence of urban warming on reported large-scale surface-air temperature trends. Urban heat islands occur mainly at night and are reduced in windy conditions. Here we show that, globally, temperatures over land have risen as much on windy nights as on calm nights, indicating that the observed overall warming is not a consequence of urban development.

Sounds like water is boiling at o degrees Celsius.
Some background on
urban heat island effect. (All not true anymore?!).

Anyone want to comment?

 

[Locrian]

Very interesting. I've thought a lot about how good an argument I think this is. I find it odd that windy nights showed no significant change at all. The correlations are very close to perfect. I wonder what affect suburban sprawl has on this.

In any case, this paper is enough to make me uncomfortable with the "urban heat not global warming" argument personally.

 

[Locrian]

Heh, by the way, the next article in the journal:

"Early peak in Antarctic oscillation index" by Julie M. Jones,Martin Widmann

This positive Antarctic oscillation index and large positive trend during a period before ozonedepleting chemicals were released into the atmosphere and before marked anthropogenic warming, together with the later negative trend, indicate that natural forcing factors or internal mechanisms in the climate system must also strongly influence the state of the Antarctic oscillation.

So many things to consider :/

 

[Andre]

Well I haven't seen the actual study but I could think of a few considerations.

This is another way of looking at urban heat island effect:

scroll down to the middle, fig 13 and comment

 

[Locrian]

I don't understand that figure well.

After averaging the means of the trends in each county, counties of similar population

But the population would have been changing. California grew by an awful lot between 1940 and 1996. What population did they use? The final one? Why would a high population lead to a higher rate of temperature increase (which is what is plotted)? Why not simply a higher temperature and hold?

My training as a physicist has equiped me with some problem solving skills (or so I'd like to think!) but in much of this debate I find there is a great deal of information I need to understand what is being discussed.

 

[Andre]

California grew by an awful lot between 1940 and 1996.

That's exactly the point. And the idea of the Urban Heat Island effect is that the temperature rising trend measured at a certain station is actually caused by the growth of the city, increasing the urban heat island effect.

The graph is not documented very well so we have to guess it would be logical to put in the current population.

 

[Andre]

Take for instance http://home.wanadoo.nl/bijkerk/Louisville.jpg . The upper blue one is the average yearly temperature of Louisville Kentucky, presently at close to one million inhabitants. So the trend is a cooling of 0.7 mK/year or 0,07 degrees per century.

Now the second pink plot below is the average temp of Shelbyville, a rural station only a distance of 46 kilometer (30 miles) away from Louisville with a cooling trend of 0,6 degrees per century. We see a absolute difference close to two degrees, that could be explained at least partly with the urban heat island effect, whilst the growing trend of Louisville would explain why the trends diverge and why Sherbyville cools quicker than Louisville.

Cooling? Certainly. There are several places in the world where nobody believes in global warming, because it's getting so cold. This will show up quickly if you play with that station link.

The world champion urban heat effect is likely to be http://home.wanadoo.nl/bijkerk/tokyo.JPG as can be seen by it's closest rural neighbors

 

[Andre]

Actually we could also make a plot of warming trend against population of a city. Of course we cannot pick a random spot on the globe. We need lots of long active weather stations in a confined area with a common climate and with cities with populations in several orders of magnitude like a few million, few hunderd thousend, few ten thousend and rural stations. I think only the USA would qualify. I'm looking around a bit to see which areas would be suitable.

Those look good as data sources:

Dallas
St Louis
Washington DC
Toronto - Niagara falls
Atlanta
Kansas City
Chicago

I'll let the list grow and then somebody could randomly pick one and see if we can find the same relationship between population and warming trend as fig 13 halfway down

 

[Locrian]

I think Atlanta would be interesting (I only live a couple of hours from there). I used the link you provided and have started making excell graphs but haven't had time to finish.

 

[Locrian]

I did Atlanta and Newnan. Between 1920 and present Atlanta plainly increases in average temperature until it obviously surpases newnan.

So this paper in nature seems to refute something that is plainly obvious. I'm not sure what to think about that.

 

[Andre]

Okay I'll compose a population - trend comparison for the nearest stations, the 3 rural, 4 medium sized and two large cities, Birmingham and Atlanta. Coming up soon.

Actually for the same period of interest 1950 - present

 

[Andre]

Now, that didn't take too long. Did it.

Here is the warming trend versus the population for the Atlanta area.

http://home.wanadoo.nl/bijkerk/Atlanta-trend.JPG

Data and spreadshead available for cross check.
Using a logaritmic scale I had to give the rural stations an arbitrary population of 1000.

And the result is pretty much as expected.

Edit

http://home.wanadoo.nl/bijkerk/atlanta2.jpg shows the station name, the population in thousends (rural arbitrary: 1) and the warming trend in degrees K per year.

 

[Andre]

So this paper in nature seems to refute something that is plainly obvious.

Exactly, And I find that very scary.

Remember Mann et al (MBH1999) did the same with the Little Ice Age and the Medieval Warming Period, by creating the hockeystick. And a fierce battle followed to protect the myth of anthropogenic global warming. It's finally broken now (well I think it is - there are still people believing that the world is flat).

But what is happening to mankind? One tends to philosophize about an obvious need to invent less sound scientific methods, just to serve an idiology?

 

[Andre]

As we infer from the http://home.wanadoo.nl/bijkerk/atlanta2.jpg , there are two stations not behaving according the assumed trend. Gainsville is too hot for it's modest size and Birmingham is too cool for it's considerable size. I have no idea of the reality living in Germany/Holland but a few reasons could be thought of. Gainsville could have emerged out of nothing in a few decades, having a much stronger growth as normal, alternately the weather station could have been smothered by new close by buildings and fences etc, increasing direct warming factors.

As for the too cool Birmingham. Did the city not expand that much the last few decades? or is the met station in or close to a big park, acting as a pseudo rural environment?

There must be people around who could tell.

 

[Locrian]

I'm not sure where the met station is, or I'd drive over there myself and see :D

Birmingham experienced white flight in the '60s through 80's unheard of in most other places. The greater birmingham area has been growing by leaps and bounds over the past 40 years. Downtown has been stagnant for decades. If the met station is downtown there is no reason to expect urban heating to have increased the temperature there for decades. If the met station is in Hoover then something odd is going on.

It's also worth keeping in mind that birmingham is a series of hills that each traps heat. We've had a lot of problems with ozone and other pollutants that may skew the data.

How should I find out where the met station is here?

 

[Andre]

Try the telephone directory?

Shall we do another city this weekend and which one?

 

[pebrew]

This is the kind of thread I like.

As we infer from the http://home.wanadoo.nl/bijkerk/atlanta2.jpg , there are two stations not behaving according the assumed trend. Gainsville is too hot for it's modest size and Birmingham is too cool for it's considerable size. I have no idea of the reality living in Germany/Holland but a few reasons could be thought of. Gainsville could have emerged out of nothing in a few decades, having a much stronger growth as normal, alternately the weather station could have been smothered by new close by buildings and fences etc, increasing direct warming factors.

As for the too cool Birmingham. Did the city not expand that much the last few decades? or is the met station in or close to a big park, acting as a pseudo rural environment?

There must be people around who could tell.

Those are nice plots you put together, but I have to say that atlanta trend-line looks to be pretty statistically unconvincing. And the three to the far left are all that's tilting it. All having remained the same population they could all be related in another way (similar area, geography, topography, ruralness, etc) that could also result in a group like that. Gainesville and Birmingham are outliers compared to the expected result, but with so little data and so much variance those two could be the only ones displaying the true result, one that was unexpected. Theres just not enough data, too much variance, and too little knowledge of other factors (like the smog, or geographic differences). But I'm very interested in the idea of doing these plots. Though I can't help but feel like this must have been done and published somewhere before. right?

anyway, if you do another one, i'd suggest somewhere where there is minimal geographic/topographic diffferences among the data collection sites. maybe oklahoma, nebraska, or somewhere nice and flat like those would be good.

 

[Andre]

Of course essence is that those three are rural, devoid of any direct Urban Heat Effect, as long as it's not too close to a city.

And yes of course, there is so much clutter in inhomogenous areas. Nevertheless it would be interesting to see if my speculations could be retrodictions of abnormal factors around those weather stations of Gainesville and Birmingham.

Oklahoma next then, although I have no idea yet about enough variation in the urbanisation.

 

[Andre]

Okay here is the same story for http://home.wanadoo.nl/bijkerk/oklahoma.jpg . I guess it's the same definite maybe.

I used only the four closest rural station (Pauls valley, Geary, Meeker and Kingfisher) for oklahoma city and all the towns on the page.
It occurs to me that I compare apples with oranges. What should be compared is the trend in temperature rise versus the trend in population growth. A city that doesn't grow should not have a different trend. A city that shrinks should be losing urban heat effect. So if anybody has historical data about town sizes in those areas as of 1950 then we would be in business.

Nevertheless, that highest warmer, Ponca city, (+0.0153 degK/year) bugged me, so I http://home.wanadoo.nl/bijkerk/ponca.jpg , Perry (+0,0008 degK/year) and Newkirk (minus 0.0192 degK/year) and indeed it's weird. The area is not warming, but Ponca city certainly is, much more than you would expect. It appears that the last hotter spike years (1998-2001) make the difference. Compare the spikes against 1954-1956 when all three were about identical. Now is that Urban heat effect?

 

[Locrian]

Shall we do another city this weekend and which one?

I have the same feeling I used to get when I'd skip class

 

[Locrian]

It occurs to me that I compare apples with oranges. What should be compared is the trend in temperature rise versus the trend in population growth. A city that doesn't grow should not have a different trend. A city that shrinks should be losing urban heat effect. So if anybody has historical data about town sizes in those areas as of 1950 then we would be in business.

This was my problem with the graph given in that link; it seemed to be comparing things that didn't need to be compared. Also, the more I think about urban heating, the more difficult I feel measuring it is. There are places in the Northeast I recently visited that are experiencing large growths in population but are not experiencing deforestation - the areas are suburban and every effort is made to keep the wildlife the way it is. I can also imagine a large area that is deforested and strip mined that has virtually no people. I suspect the vast amount of rock and large number of machines at an area like that may cause some "urban heating" even though there is virtually no population. Am I right in thinking processes like this may confuse the issue?

I find it not suprising the trend lines are not always clear and simple.

 

[Seafang]

So then climate change is Confirmed?

Quite a statement; that climate change skeptics are wrong; that implies that climate change is confirmed as real. Well we all knew that.

The argument about heat islands is pretty irrlevant, all though it does point out a problem, with the meausred 'DATA'. But the problem with the so-called data on global mean temperature, is that no system exists or has ever existed for measuring the global mean temperature.
So what was the value of the global mean temperature at zero hours GMT (or UT if you like) on July 4th 2000.

Oh you didn't happen to measure it then; well then what was it at some time epoch when you DID measure it.

For a start, the 'globe' is a three dimensional object and each point in that three dimensioned space has its own temperature at any particular time. Too complicated for you; well let's simplify it then and say we only care about what the MGT is at a fixed 3 metres abover sea level. To figure out what that is, all you need to know is the temperature at every point on Earth three metres above sea level at whatever point in time you want to compute the average. Then you simply integrate the temperature times area element over the whole Earth until you arrive at the average for the whole Earth at that particular time instant. If you do this on a mid summer day, you could find temperatures as high as +135 F in some desert areas in Arabia, and you simultaneously could find temperatures as low as -125 F in central Antarctica where it wouod be winter night. So your map of instantaneous global temperature will have as much as a 260 F peak to peak range.

Well of course no-one knows what the temperature is at every point on Earth at three metres above sea level so the best you can do is take temperature samples at various points. Aha! a sampled data system. We measure a few temperture samples and we use those samples to recreate the continuous data field of global temperature. Of course the Nyquist sampling theorem requires that in order to recreate that field accurately, we must take at least one sample in each half cycle of the highest spatial frequency component of the original continuous data function, or else the reconstructed field from the samples will suffer from spectrum folding and aliassing errors. Now given that the P-P range can be 260 F and we are seeking to show changes with time as small as 1 deg F over a century, we have to reconstruct the continuous data function with considerable accuracy.

Now I am aware of examples of very high spatial frequencies in the temperature map. All I have to do is look at the local evening news weather report, and they will report the temperatures at points spaced by just a few miles, and that data will reveal cyclic (spatial) variations over distances of 5-10 Km or less. And they are only reporting max and min temperatures, so the continuous time data could be even more variable.

Suffice it to say, that no global measuring grid exists that can record the simultaneous temperatures all over the globe at grid spacings of the order of 5 Km or less; or even 50 Km for that matter. In fact the array of temperature measuring stations is so sparse, that the set of data recorded at those locations cannot possibly reproduce the continuous temperature function all over the globe without extremely serious aliassing errors. If the Nyquist violation was very mild, say only one sample per complete cycle of spatial temperature at the highest frequency, then the aliassed spectrum will be folded all the way back to zero frequency, whci I may remind you is what the true average or DC value of the data is. The actual Nyquist violation is so gross, that the spectrum folds way back to negative spatial frequencies, and the aliassing errors at zero frequency will be huge.

In short, such a sampling plan cannot possibly recreate the temperature continuous map with sufficient accuracy to determine the average or DC value of the function.

So NOBODY knows what the mean global temperature is at any point in time even for the limited case of a single level of 3 metres above sea level, let alone for the real three dimensional globe.

And that is just the spatial problem.

We know for sure that the temperature at anyone point on Earth will rise and fall with at least a 24 hour cycle time, but in practice for most of the globe, the variations of temperature with time, are far more rapid, and sometimes temperatures can change by 20 degrees F in a matter of minutes.

So just repeat the same argument as above but this time for a temporal map of the global temperatures, and you will quickly realize that any measured data we might have is also grossly in error because of temporal aliassing errors.

So altogether, nobody has any credible knowledge of what the mean global temperature is, or ever has been; not close neough to detect a one degree F shift in 100 years in a function that has a 260 F P-P possible amplitude.

Climate models being run on computers, that I have seen, don't even cover half of the possible P-P range of the function.

And don't look to the central limit theorem to buy you out of a Nyquist violation problem.

In any case, even if we knew what the mean global temperature was, and has been, it is a pretty irrelevant number. For one thing, the problem of 'global warming' or 'global cooling', or 'global climate change', is more a question of the balance of heat flows, into and out of the earth. To a first approximation the Earth behaves like a near black body; well a gray body anyway, and the radiated power goes more like the 4th power of the temperature, so heat flow is not a linear function of temperature, so mean temperature tells us nothing about the heat flow balance. The tropical areas directly under their local noon sun, are much hotter than the polar areas in perpetual night, so the radiation from those tropical areas is very much higher than for the colder polar night regions, so a knowledge of the mean temperature over the whole globe, tells us nothing about the current heat balance between arriving solar spectrum energy, and the reflected and re-radiated Infra Red radiation from the earth.

So maybe the Earth is warming; some parts definitely are. Not surprising that it has been generally warmer over the last 40 years or so. After all, 1965, was the year that the highese recorded sunspot numbers in history occurred, and for much of the 20th century to the present, sunspot peak numbers have been generally higher, than at any time since the Maunder minimum of the 17th century.

We know that a warmer ocean holed less CO2 so causing increased atmospheric CO2, and we know that melting permafrost areas which turns those materials into decaying peat bogs, also causes increased CO2 in the atmosphere. Vostok and Dome-C ice cores show that periods of increased global warming are typically followed by periods of higher atmospehric CO2 levels, and there weren't too many SUVs around 730,000 years ago.

So today when increased solar activity would lead us to expect warmer temperatures on earth, we would expect rising atmospheric CO2 levels; exactly as the measurements show.

So climate change skeptics have a right to be skeptical about what is happening, and more importantly why it is happening.

 

[Andre]

Well said Seafang. Well the main relevance of urban heat island effect (good refelections Locrian) is whether or not mcKitrick was right with his hypothesis that the global warming is inverse proportional to the number of weather station. Implying that the closure of many rural weather stations world wide in the 1980-1990 timeframe coincided exactly with the big bend in the hockeystick. For this he got ridiculed until scientific dead would follow.

Anyway if we have patience for some 5-10 years I predict that we will see the same bend in the hockey stick for the USA. Reason? Have seen that the bulk of the rural weatherstation have closed in 2003 and they prevailed well over urban stations. So we are left with prevailing urban stations and the urban heat effect will follow automatically.

 

[Seafang]

Andre, If you have been keeping up with the fortunes of the hockey stick in the popular press, then you are already aware of studies published (in the pop press) within the last month that show that the whole hockey stick hypothesis is based on erroneous mathematics. For one thing, the standard hockey stick 'curve' reveals almost no response to the little ice age or the 17th century Maunder age of no sunspots and no auroras, hence lower ozone formation on Earth (aknown green house gas. Not surprising then that Iceland was surrounded by 100s of miles of frozen sea ice and the Thames river froze all the way up to London. You will recall that the 1620 era was the time of the wicked winters of the Pilgrims and the start of our thanksgiving tradition. Yet this climatically disruptive century hardly shows up on the usual hockey stick which plots the last 30-40 years with disastrously rapid rises. this is also the era when satellite data started to measure the solar constant on a continuous basis, showing the rise and fall of the solar constan with the sunspot cycles. Also the values of the solar constant seem to range from 1364 up to 1374 Watts per meter squared from those satellite measurements, yet optical texts from the 1960s and careful measurements made in the 50s and 60s reported a value more like 1353 Watts per meter squared. Those earlier measurements were certainly made from high altitude balloons and rockets, and their allowance for the residual atmosphere may have been a little off, but it is just as likely to be off one way as another.

If we take the modern satellite data to be accurate, and take 1369 as the mean of all the satellites and drop that by 0.8% we get 1358, which is well above the best value known in the early sixties (1353). Why 0.8% ? Well a 0.8% rise in arriving solar flux, would lead to a 0.2% increase in mean global temperature, which is 1 deg F out of a Rankine temperature of around 516, or precisely 0.2% (thereabouts).

So the observed increase in solar constant since the early 1960s is more than enough to account for a 1 deg F increase in mean global temperature, and that degree is supposed to cover the last century or century and a half, rather than the last half century. Strange that NASA reports Mars too having a global warming problem at the moment.

Don't tell me the two SUVs we put up there are to blame, rather than a warming sun.

 

[Andre]

Seafang,

Discussions are like small row boats, if you both sit at the same side, it topples.

Remains only to find out exactly what caused Mann et al to believe the hockeystick and why the ground stations show lost more warming than the weatherballoon sensors and the satelites.

 

[Seafang]

The problem Andre, with the "ground stations showing lots more warming than the satellites" ;is that all that the ground stations show is that the ground stations show lots more warming of the ground stations than the satellites show of the rough hemisphere they are seeing.

The fact that anyone ground station shows warming, doesn't mean that the whole Earth is warming. The fact that any set of ground stations shows lots more warming of those ground stations still doesn't prove the whole globe is warming. Only when a sufficient number of suitably spaced ground stations simultaneously shows the temperatures over the globe with sufficient spatial resolution to prevent aliassing errors, will it be possible to say the whole globe is warming; don't hold your breath waiting for that situation.

Even the satellites don't show the mean global temperature (at least I don't think so) because the entire globe is not simultaneously monitored; unless there are a lot more monitoring satellites up there than I know about.

If the whole Earth were warming significantly, one might expect the weather to remain pretty much the same, but if some parts get warmer and other parts get cooler, then one would expect the weather to get more severe.

So today's weather is the result of a global temperature spread that could be as much as 260 degrees F. So how much influence would one expect if some regions warm up one degree or even five, compared to the fact that the range is so extreme already.

 

[Seafang]

I believe that around the turn of the 19th century, the 'high arctic'; that region north of +60 latitude, had about 12 weather monitoring stations for all that vast area. I'll leave it to the reader to calculate how much of the Earth's surface area that is.

That number of monitoring ground stations increased up to 80 something by about the mid 1970s, and then for resons unknown to me it has declined so that today it is about 72 stations.

Anybody who thinks 80 stations is enough to correctly map what is happening over that much of the globe should rethink that position.

Anyone who thinks today's 72 stations give the same map that the 12 stations of 1900 gave or the 80 odd of the mid 1970s just doesn't understand the problem.

 

[Locrian]

Andre, If you have been keeping up with the fortunes of the hockey stick in the popular press, then you are already aware of studies published (in the pop press) within the last month that show that the whole hockey stick hypothesis is based on erroneous mathematics.

The problem Andre, with the "ground stations showing lots more warming than the satellites" ;is that all that the ground stations show is that the ground stations show lots more warming of the ground stations than the satellites show of the rough hemisphere they are seeing.

The fact that anyone ground station shows warming, doesn't mean that the whole Earth is warming.

Seafang, these statements lead me to believe you may misunderstand which side of the issue Andre is on. I know he has spent a deal of time saying almost these exact same things repeatedly on the board.

 

[Bystander]

From the links in the original post: BBC,"If the urban heat island hypothesis is correct, he says, instruments should have recorded a bigger temperature rise for calm nights than for windy ones - because wind blows excess heat away from cities and away from the measuring instruments;" and, Nature, "Here we show that, globally, temperatures over land have risen as much on windy nights as on calm nights, indicating that the observed overall warming is not a consequence of urban development."

We have a meteorologist publishing apparently intuitive solutions to problems in heat and mass transport in a peer reviewed rag. Did the review include any chem. E.s? Aeros? Other transport types? Are there problems with the intuitive solutions? Would anyone care to buy a vowel? Stick to the fundamental principles of physics when examining claims for and against GW/AGHW. Parker has taken up space in Nature. Credibly? No. Is Nature more or less credible today than before printing this piece? Not much difference --- Phys. Rev. printed Pons & Fleischman, J. Chem. Phys. has published some laughers, polywater pollution exists in a number of respectable journals --- journals tend to last, authors and bad ideas do not.

 

[Seafang]

Seafang, these statements lead me to believe you may misunderstand which side of the issue Andre is on. I know he has spent a deal of time saying almost these exact same things repeatedly on the board.

Don't get me wrong Locrian; I am not mistaking the gist of Andre's position. If anything I read his posts as implying that he is not grinding on any axe; but letting the chips fall where they may; which is really my position. So I was really trying to support Andre and definitely not being critical of his position.

I would like to pose the following thought experiments to see what you folks think.

Experiment #1:- Wave your magic wand, and instantly remove every single water vapor molecule from the atmosphere; leave everything else intact. Now contemplate what a real physical Earth complete with oceans will do in response to your rash treatment.

Experiment #2:- Unwave your magic wand, and instantly fill the entire Earth's atmosphere with saturated water vapor from ground level to 10-15-whatever Km height all over the globe. Contemplate anew what the real physical Earth will do in response to this action.

Forget all about computer models and Southern oscillations or other climate catastrophe buzz words, and just use plain common sense to see what will happen.

If you come up with an outcome for either experiment, that is different from the world you woke up to this morning; please let us know how you got there.

Here's some things to chew on. The CO2 absorption band in the Infra-Red that accounts for the 'greenhouse effect' (so they say) shows nearly total extinction from about14.15 microns to about 15.6 microns with a long edge to around 16.0 microns and a short side edge down to about 13.75 microns (data from the Infra-Red Handbook) and this is for a 300 metre path at sea level.

The Earth's roughly black body radiation at its global mean temperature of 57F, 14C or 287K peaks at 10.1 microns wavelength; well below the onset of CO2 absorption. Remember exactly 25% of black body radiation occurs at wavelengths shorter than the peak.

However, the highest temperatures in the deserts of Arabia and such places can reach +135 F, 57C or 330 K.

330/287=1.15 and raising that to the 4th power gives 1.75, so the hotter regions under the noon sun in summer, can be radiating 75% higher rate than places at the global mean temperature. Even more important, the black body radiation peak at 330 K occurs at 8.78 microns wavelength, so CO2 isn't even close to intercepting very much of that infrared radiation. When you realize that man made heat bodies like tarred parking lots and concrete roads, might reach surface temeperatures higher that 150F (egg cooking temperatures), it is apparent that the IR radiation from the warm regions of the globe is higher than the mean and is spectrally shifted away from the CO2 absorption band, so the tropical regions of the globe under the day sun, are radiating like crazy with much subdued CO2 influence.

The effect is even wilder at the cold end of things. The Antarctic -125 F, -87C, or 186 K lowest temperatures result in an IR BB emission spectrum that peaks at 15.6 microns, smack dab in the middle of the CO2 absorption band, but the radiance is lower than the global mean temperature radiance by (287/186)^4 =5.67 times. So the IR emission rate in the winter antarctic nights is 5.67 times lower than at the global mean temperature, assuming that the IR emissivity of frozen ice at 15.6 microns is the same as the mean Earth emissivity. I don't yet know what the IR emissivity of ice is.

But any way you cut it, the polar regions just aren't radiating much at all, and they do so right in the middle of the CO2 absorption band at 15 microns. Maybe that might explain some of the claim that the polar regions are warming faster than the tropics. Any GHG effect must be much more effective at the poles than it is under the tropic sun.

If you ask me, it is very hard to support the theory that CO2 infrared absorption is responsible for the temperature of the lower atmosphere. Ground conduction directly to the atmopshere followed by convection rules the roost; hot air rises.

I think after you do my two thought experiments with water vapor, you will conclude as I have, that we couldn't change the temperature of this planet by much even if we wanted to; either up or down. That giant swamp cooler that the ocean/atmosphere evaporation sets up is far too powerful a negative feedback machine to allow a little puny CO2 to affect anything.

Incidently if the CO2 15 micron absorption band shows near total extinction in just 300 metres of sea level atmosphere; that suggests that there would be little change if the CO2 is increased by a factor of 10 or even 100; it would still be nearly total extinction for radiation in that band.

In my view the common theory of Green house gases is completely wrong.

Water vapor is the controlling factor (cloud cover), and until we boil off the oceans it will stay in control.

When sea ice melts, it absorbs about 80 calories per gram of ice in just latent heat of melting. When the heated water evaporates, it absorbs another 590 calories per gram or so, and all that huge amount of heat is convected into the upper atmosphere, where it is dumped when water clouds or ice crystal clouds form; there to be radiated to space free form CO2 involvement.

The computer climate models don't account for water vapor and cloud cover because a ten year or thirty year running average of global temperature must run roughshod over the real physics of heat transfer, which all takes place in milliseconds, seconds, minutes and hours.

Tomorrow, the atmopshere will have no memory of the absorption of a 15 micron photon by a CO2 molecule which is immediately transferred to either Nitrogen of Oxygen (Argon too) in the atmospheric collisions which occur. CO2 is one molecule in 2700 in the atmosphere, so it is about 14 molecules in any direction to the next CO2 molecule, so CO2-CO2 collisions are rare and the CO2 molecule is out of the picture in milliseconds.