Guest Post by Ira Glickstein
The Unified Theory of Climate post is exciting and could shake the world of Climate Science to its roots. I would love it if the conventional understanding of the Atmospheric “Greenhouse” Effect (GHE) presented by the Official Climate Team could be overturned, and that would be the case if the theory of Ned Nikolov and Karl Zeller, both PhDs, turns out to be scientifically correct.
Sadly, it seems to me they have made some basic mistakes that, among other faults, confuse cause and effect. I appreciate that WUWT is open to new ideas, and I support the decision to publish this theory, along with both positive and negative comments by readers.
Correlation does not prove causation. For example, the more policemen directing traffic, the worse the jam is. Yes, when the police and tow trucks first respond to an accident they may slow the traffic down a bit until the disabled automobiles are removed. However, there is no doubt the original cause of the jam was the accident, and the reason police presence is generally proportional to the severity of the jam level is that more or fewer are ordered to respond. Thus, Accident >>CAUSES>> Traffic Jam >>CAUSES>> Police is the correct interpretation.
Al Gore made a similar error when, in his infamous movie An Inconvenient Truth, he made a big deal about the undoubted corrrelation in the Ice Core record between CO2 levels and Temperature without mentioning the equally apparent fact that Temperatures increase and decrease hundreds of years before CO2 levels follow suit.
While it is true that rising CO2 levels do have a positive feedback that contributes to slightly increased Temperatures, the primary direction of causation is Temperature >>CAUSES>> CO2. The proof is in the fact that, in each Glacial cycle, Temperatures begin their rapid decline precisely when CO2 levels are at their highest, and rapid Temperature increase is initiated exactly when CO2 levels are their lowest. Thus, Something Else >>CAUSES>> Temperature>>CAUSES>> CO2. Further proof may be had by placing an open can of carbonated beverage in the refigerator and another on the table, and noting that the “fizz” (CO2) outgasses more rapidly from the can at room temperature.
Moving on to Nikolov, the claim appears to be that the pressure of the Atmosphere is the main cause of temperature changes on Earth. The basic claim is PRESSURE >>CAUSES>>TEMPERATURE.
PV = nRT
Given a gas in a container, the above formula allows us to calculate the effect of changes to the following variables: Pressure (P), Volume (V), Temperature (T, in Kelvins), and Number of molecules (n). (R is a constant.)
The figure shows two cases involving a sealed, non-insulated container, with a Volume, V, of air:
(A) Store that container of air in the ambient cool Temperature Tr of a refrigerator. Then, increase the Number n of molecules in the container by pumping in more air. the Pressure (P) within the container will increase. Due to the work done to compress the air in the fixed volume container, the Temperature within the container will also increase from (Tr) to some higher value. But, please note, when we stop increasing n, both P and T in the container will stabilize. Then, as the container, warmed by the work we did compressing the air, radiates, conducts, and convects that heat to the cool interior of the refrigerator, the Temperature slowly decreases back to the original Tr.
(B) We take a similar container from the cool refrigerator at Temperature Tr and place it on a kitchen chair, where the ambient Temperature Tk is higher. The container is warmed by radiation, conduction and convection and the Temperature rises asymptotically towards Tk. The Pressure P rises slowly and stabilizes at some higher level. Please note the pressure remains high forever so long as the temperature remains elevated.
In case (A) Pressure >>CAUSES A TEMPORARY>> increase in Temperature.
In case (B) Temperature >>CAUSES A PERMANENT>> increase in Pressure.
I do not believe any reader will disagree with this highly simplified thought experiment. Of course, the Nikolov theory is far more complex, but, I believe it amounts to confusing the cause, namely radiation from the Sun and Downwelling Long-Wave Infrared (LW DWIR) from the so-called “Greenhouse” gases (GHG) in the Atmosphere with the effect, Atmospheric pressure.
Some Red Flags in the Unified Theory
1) According to Nikolov, our Atmosphere
“… boosts Earth’s surface temperature not by 18K—33K as currently assumed, but by 133K!”
If, as Nikolov claims, the Atmosphere boosts the surface temperature by 133K, then, absent the Atmosphere the Earth would be 288K – 133K = 155K. This is contradicted by the fact that the Moon, which has no Atmosphere and is at the same distance from the Sun as our Earth, has an average temperature of about 250K. Yes, the albedo of the Moon is 0.12 and that of the Earth is 0.3, but that difference would make the Moon only about 8K cooler than an Atmosphere-free Earth, not 95K cooler! Impossible!
2) In the following quote from Nikolov, NTE is “Atmospheric Near-Surface Thermal Enhancement” and SPGB is a “Standard Planetary Gray Body”
NTE should not be confused with an actual energy, however, since it only defines the relative (fractional) increase of a planet’s surface temperature above that of a SPGB. Pressure by itself is not a source of energy! Instead, it enhances (amplifies) the energy supplied by an external source such as the Sun through density-dependent rates of molecular collision. This relative enhancement only manifests as an actual energy in the presence of external heating. [Emphasis added]
This, it seems to me, is an admission that the source of energy for their “Atmospheric Near-Surface Thermal Enhancement” process comes from the Sun, and, therefore, their “Enhancement” is as they admit, not “actual energy”. I would add the energy that would otherwise be lost to space (DW LWIR) to the energy from the Sun, eliminating any need for the “Thermal Enhancement” provided by Atmospheric pressure.
3) As we know when investigating financial misconduct, follow the money. Well, in Climate Science we follow the Energy. We know from actual measurements (see my Visualizing the “Greenhouse” Effect – Emission-Spectra) the radiative energy and spectra of Upwelling Long-Wave Infrared (UW LWIR), from the Surface to the so-called “greenhouse” gases (GHG) in the Atmosphere, and the Downwelling (DW LWIR) from those gases back to the Surface.
The only heed Nikolov seems to give to GHG and those measured radiative energies is that they are insufficient to raise the temperature of the Surface by 133K.
… our atmosphere boosts Earth’s surface temperature not by 18K—33K as currently assumed, but by 133K! This raises the question: Can a handful of trace gases which amount to less than 0.5% of atmospheric mass trap enough radiant heat to cause such a huge thermal enhancement at the surface? Thermodynamics tells us that this not possible.
Of course not! Which is why the conventional explanation of the GHE is that the GHE raises the temperature by only about 33K (or perhaps a bit less -or more- but only a bit and definitely not 100K!).
4) Nikolov notes that, based on “interplanetary data in Table 1” (Mercury, Venus, Earth, Moon, Mars, Europe, Titan, Triton):
… we discovered that NTE was strongly related to total surface pressure through a nearly perfect regression fit…
Of course, one would expect planets and moons in our Solar system to have some similarities.
“… the atmosphere does not act as a ‘blanket’ reducing the surface infrared cooling to space as maintained by the current GH theory, but is in and of itself a source of extra energy through pressure. This makes the GH effect a thermodynamic phenomenon, not a radiative one as presently assumed!
I just cannot square this assertion with the clear measurements of UW and DW LWIR, and the fact that the wavelengths involved are exactly those of water vapor, carbon dioxide, and other GHGs.
Equation (7) allows us to derive a simple yet robust formula for predicting a planet’s mean surface temperature as a function of only two variables – TOA solar irradiance and mean atmospheric surface pressure,…”
Yes, TOA solar irradiance would be expected to be important in predicting mean surface temperature, but mean atmospheric surface pressure, it seems to me, would more likely be a result than a cause of temperature. But, I could be wrong.
Conclusion
I, as much as anyone else here at WUWT, would love to see the Official Climate Team put in its proper place. I think climate (CO2) sensitivity is less than the IPCC 2ºC to 4.5ºC, and most likely below 1ºC. The Nikolov Unified Climate Theory goes in the direction of reducing climate sensitivity, apparently even making it negative, but, much as I would like to accept it, I remain unconvinced. Nevertheless, I congratulate Nikolov and Zeller for having the courage and tenacity to put this theory forward. Perhaps it will trigger some other alternative theory that will be more successful.
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UPDATE: This thread is closed – see the newest one “A matter of some Gravity” where the discussion continues.
Why do I still hold a conviction that the N&Z / Selbring descriptions of the greenhouse effect as being gravity / pressure dependent were well known 50 years ago ?
Certainly it is the impression I had held since my schooldays until AGW introduced the issue of atmospheric composition as being relevant some 20 years ago.
The widespread apparent ignorance over this critical issue also reminds me of many heated discussions with AGW proponents over the past few years which hinged upon their apparent ignorance as regards the thermal effects of the phase changes of water and especially the peculiar nature of latent heat and of evaporation as a powerful net cooling process.
Taking just those two points together as lapses into ignorance due to past knowledge having been forgotten explains the entire AGW kerfuffle as a sad decline in scientific education over the past half century.
We have too many people knowing a lot about very little and not enough people knowing a little about a lot. The advantage of the latter group is the ability to put varied scientific concepts into a wider picture which is exactly what we need to do in order to get a grip on climate variability and to avoid daft misapprehensions such as AGW.
Willis Eschenbach says:
December 30, 2011 at 11:23 am
“When a guy starts raving about “relatively enhanced energy”, I tune out and go read some actual science.”
Now why being so hostile, Eschenbach?
It is funny how certain groups of scientists refuse to understand what others write, just because they arent using the exact wording of the other “camp”. A human trait, I suspect.
Maybe you need some more time to ponder on it.
Bart says:
Your statement is completely wrong. The ideal gas law contains pressure, temperature, and number density of molecules. So, in fact, the pressure does not uniquely determine the temperature.
jae says:
Yeah, Willis! Are you going to let some minor little thing like the fact that their theory violates conservation of energy stand in the way of the fact that they can do a 4-free-parameter fit (which they never actually show) to what essentially amounts to 4 significantly-different-than-zero data points for data wrongly calculated? 😉
Yeah…Once you take away the fact that the surface emits 390 W/m^2 while the Earth and its atmosphere absorb only 240 W/m^2, the measured absorption spectra of the various greenhouse gases, the measured radiation from the atmosphere at the earth’s surface, and the measured spectra of the Earth’s emissions as seen from space with “bites” taken out of them at just the wavelengths that are expected, there is hardly any empirical evidence left for the radiative atmospheric greenhouse effect!
Man, Willis is clearly one biased dude! It’s good we have clear, unbiased thinkers like jae here to put things in perspective!
@Konrad Hartmann:
Thank you and well done. Should you get flamed for your crude apparatus, take comfort in the knowledge that you’re the first on the scene with actual scientific discovery. It doesn’t matter whether you prove or disprove anything at all. What matters is that the result contributes knowledge and is therefore a sign as to a way forward.
Here’s a conjecture to work with. Take two containers and fill them with different quantities of dry nitrogen. Put them in the sun hanging from strings. Let them both reach a steady state temperature. My conjecture is that the container with the most molecules is the one that reaches the highest steady state temperature differential over ambient.
More collisions (in higher density container) for same energy content (of each molecule) leads to higher pressure doesn’t it? With higher pressure induced by the dynamic energy environment out there in your back yard the temperature has to be higher in the container with the most critters.
Joel Shore says:
January 1, 2012 at 6:20 am
“So, in fact, the pressure does not uniquely determine the temperature.”
You are right. In Ira’s artificial setup, there is a reservoir of additional gas molecules upon which to draw from the outside. I was sloppy in not pointing out that, in a planetary system, there is no such reservoir.
@Willis Eschenbach, passim
Everything you have written about the nonsensical ‘Unified Theory of Climate’ is spot on.
Anyone with any sense would not even bother to get beyond the ridiculously pompous title.
For all those jumping in demanding a chapter and verse refutation, it is just not worth it. This post is pure snake oil. You don’t need a mathematical analysis of this ‘paper’ – there is no sense there to analyze in the first place.
Considering all the real good that WUWT has done over the years it is such a pity that arrant nonsense like this post gets published here. Having this stuff kicking around just harms the reputation of the site.
Please, Mr Watts, do not publish any more contributions from Nikolov and Zeller.
jae says:
December 31, 2011 at 6:36 pm
“Facts are, at this point, there is still NO frigging empirical evidence for some silly “radiative atmospheric greenhouse effect.” Period.”
There is, but don’t look for it in daytime when convection is active. I have two thermometers (really), one at the 1 foot level and 1 at the 6 foot level. At night the 1 foot thermometer reads several degrees lower than the 6 foot thermometer, especially under clear skies. In daylight that difference goes away and the 1 foot thermometer tends to read higher.
This new paradigm will be resisted furiously by anybody who thinks they know what they are talking about vis a vis climate, even skeptics. The simple truth is that in daylight hours convection limits maximum temperatures, and at night greenhouse effect limits cooling rates. CO2 has nothing to do with maximum temperatures, but will limit cooling rates in cold, dry climates, so can contribute a small amount of warming in certain regions of the globe.
I will now look at weather charts with a new appreciation. Low pressure, cooler and wetter. High pressure, warmer and dryer. They say that correlation does not prove causation. This statement gives me heartburn every time I see it, but I will save that rant for another time.
For those who are interested – Roy Spencer has a good (IMO) takedown of this theory on his website.
http://www.drroyspencer.com/2011/12/why-atmospheric-pressure-cannot-explain-the-elevated-surface-temperature-of-the-earth/#comment-32626
Cheers, 🙂
From Iras article..
The above is absolutely true in a situation where the variable, Volume (V) in the equation PV = nRT is kept constant by the gas cylinder.
For this to apply to the Earth Atmosphere system, it has to be shown that V is or can be considered to be a constant.
Furthermore, in case (A), P is increased artificially by way of introducing more mass (n), but in our equation PV = nRT as it applies to the Earth Atmosphere system, we assume n is close enough to be a constant. In other words, it is NOT POSSIBLE to increase P in the real world without FIRST changing T.
I think that means case (A) is irrelevant.
Case (B) is mathematically identical to case (A) in that we need to introduce an artificial influence i.e. we are adding value to the equation which results in T staying high, instead of falling as in case (A)
Take the Earth with an atmosphere so whispy thin that whatever influence it has on Earths energy budget can be taken as a constant.
This Earth will reach equilibrium temperature when the out going radiation is equal to the incoming radiation.
Now add enough atmosphere to match that of current Earth. In relation to PV = nRT, we have increased n, we have increased P, R is a constant and according to the authors of the ‘unified theory’, T also increases.
How much it increases depends on how much V changes.
The Earth still reaches thermal equilibrium when the outgoing radiation is equal to incoming radiation. No different to when it had a whispy thin atmosphere. Though now either V or T or both are a higher value.
We know that adding more atmosphere will lead to higher P and higher n in PV = nRT. Since R is a constant, we need to know if V is a constant or close enough to be considered a constant.
If the variability of V is too small (say due to gravity limitations), then T may rise even though both incoming and outgoing radiation hasn’t altered.
If the variance in V is big enough to balance the equation, there is no need for T to rise. According to some, volume V DOES vary enough to keep Ts relatively constant.
In the real Earth Atmosphere system, we know n doesn’t change in the time frames we are interested. And because gravity is constant, V can’t change unless P or T changes. We also know that P can’t change whilst n, V and gravity are constant unless T changes.
This means in the real world, temperature must change first. Whether temperature changes due to changes in solar influx, or changes to the composition of the atmosphere, or changes to the amount of energy released by the oceans during a given time frame, whilst this change is taking place, either P or V or both MUST CHANGE since n and R are constant.
In a closed system such as that in a gas tank, increasing T by however means will increase pressure only, due to V being constant. If the container was flexible and allowed some expansion (like a balloon), then P will still rise but not as much since V also rises to a new limit.
In an open system like that of the Earth, V only has gravity as a restriction, this means gravity and n (the numbers of molecules) are the key variables in the equation PV = nRT as applied to the Earth Atmosphere system.
.
There was an Israeli paper awhile back using unit root statistical analysis, as developed for economic forecasting, that analyzed temperature data and CO2 . What it showed was that increasing CO2 increased temperatures, but the increase was not permanent.
At the time there was no mechanism by which a temperature increase from increased CO2 could be temporary. By linking surface temperature gravitationally to the black-body temperature at top of atmosphere, such a mechanism is now provided.
The unit root analysis of CO2 provides confirmation that gravity and pressure controls surface temperatures, while increasing GHG leads to increasing convection.
Ira Glickstein, PhD says:
December 31, 2011 at 6:58 pm
Dr. Glickstein (can I call you Ira?), After your lengthy and polite response, you say “Sorry Dan”. I don’t have a dog in this fight – I just want to understand and I appreciate your helping me so please don’t apologize.
So, while I appreciate your opinion, what I was hoping for was a more definitive answer. I think this is probably basic thermodynamics but I’ve retained very little. I think my old textbook is out in the shed somewhere with my disco shoes and I doubt it would do me much good anyway.
Intuitively, it seems reasonable that any gas’s specific heat is higher at higher pressures, simply because you are heating more mass. From what I remember of thermodynamics, when heat is added the temperature goes up, work is done, or (more commonly) a combination. So it seems reasonable to me that a denser gas (higher pressure) will absorb more heat than a less dense gas and hence do more work and/or reach a higher temperature. Konrad’s experimentation seems to imply that this is the case.
But the most important thing is that I believe this is the crux of Drs. Nikolov’s and Zeller’s argument. If it’s not true, then they don’t have a case.
Dan
Bart says:
Bart: You are talking nonsense. If you think you can uniquely determine the temperature from the pressure by using the ideal gas law, then by all means, demonstrate this.
Joel Shore;
Yeah…Once you take away the fact that the surface emits 390 W/m^2 while the Earth and its atmosphere absorb only 240 W/m^2>>>
But Joel…
The whole point is that 390 w/m2 is WRONG!
Demonstrably WRONG!
P = 390 w/m2 is arrived at by taking the “average” temperature T of earth surface of 15 C and calculating P via SB Law. THAT IS A COLOSSAL MATHEMATICAL MISTAKE!
Yes, I’m yelling! With just cause!
P = 5.67 * 10^-8 * T^4
Is that the right equation, or isn’t it?
You CANNOT first average T, and then calculate P!
The ONLY valid mathematical approach is to average T^4 and THEN calculate P!
Joel, please, look at the equations! You cannot dispute what I have just said and get to keep your degree! Ignore your belief system for a moment, JUST DO THE MATH!
Is the average of T converted to T^4 the same as the average of T^4 converted to T?
IT IS NOT AND NO ONE WITH ANY FOUNDATION IN MATH WILL CLAIM OTHERWISE.
Here is a dead simple, easy to understand example that proves my point. Take two data points on earth, one at +30C and one at 0C for an average of 15 C:
D1 = 30C = 303K = 478 w/m2
D2 = 0C = 273K = 315 w/m2
“average” T = 15C
“average” P = 396 w/m2
Where did 390 go?
Let’s make it more obvious and use +40 and – 10C. DO THE MATH!
D1 = 40C = 313K = 544 w/m2
D2 = -10C = 263K = 271 w/m2
“average” T = 15C
“average” P = 408 w/m2
WHERE DID 390 GO?
You’re rebuttal relies on 390 w/m2 squared being right. But given that it is calculate by averaging T and then converting to P, the only way it can POSSIBLY be right is by pure coincidence!
Of course!
OK, take a quantity (mass) of air, which we can think of as a certain number M of molecules of O2, N2 and trace gases. Put that quantity M into a container #1 and a similar quantity M into container #2 which has twice the volume of container #1. Allow both to reach temperature equilibrium. The air in #1 has twice the density of that in #2. Since specific heat is related to the heat capacity of a given mass of gas, we heating or cooling exactly the same mass of gas M molecules in #1 as #2, so, to a first approximation, both will take the same amount of energy to heat to a higher temperature and will release the same amount of energy when cooled to a lower temperature. (All this assumes the temperatures are above freezing and not extremely hot, and the pressures involved are between 0.5 and 2 bar).
kwik says:
January 1, 2012 at 6:12 am
Hostile? This is me being bored. I’m bored because I can’t understand the raving. Instead of answering my questions (like what is “relatively enhanced energy”), you want to bitch about my point of view? Come back when you have something to add. Until then, lead, follow, or get out of the way. Complaining about my mental state is meaningless.
w.
THANKS shawnhet for the link! I found it well worth reading. Spencer explains his take on Nikolov’s theory very well, in plain English. There are several comments by Nikolov in that thread along with some productive cross-discussion by other commenters.
Joel Shore says:
January 1, 2012 at 10:13 am
“If you think you can uniquely determine the temperature from the pressure by using the ideal gas law, then by all means, demonstrate this.”
Given n, V, and R, of course you can. What are you thinking?
Yes, Dave, as I have agreed before, the exact method is as you describe it. But, if they average T, rather than T^4, how much does that change results?
You calculated the average (T) vs average (T^4) error correctly, and it amounts to 6 w/m2 out of 390 w/m2, which is only about 1.5% – way “close enough” for Climate Science work.
For L&K to be correct about the GHE-free Effect to be 133K rather than the conventional 33K (i.e, GHE-Free Earth at 155K rather than 255K), the error in the conventional accounting would have to be 100/255 = +39% You have found -1.5%, and in the opposite direction, so now we need to find 39 + 1.5 = 40.5% error in the conventional accounting to make L&K correct.
davidmhoffer says:
For heaven’s sake, David. Everybody in the field already understands the correct way that the average should be done. I alone have mentioned this and Holder’s Inequality probably a thousand times (slight exaggeration). The point is that it does not make a very large difference for Earth-like temperature distributions. You may be able to argue about whether 390 W/m^2 or 396 W/m^2 is a more accurate measure of the emission (and, in fact, I believe this is a large part of the reason why the estimate of the emission did change by a few W/m^2 between Kiehl and Trenberth’s original paper in the late 1990s and the recent update), but it ain’t going to be anywhere close to 240 W/m^2. Another point is that the emissivities of most terrestrial surfaces in the infrared are very close to 1 but not exactly 1. This effect and the difference between the average of T^4 and the (average of T)^4 error act in opposite directions and tend to at least partly cancel each other out.
These considerations are important if you are worried about getting the emission from the Earth down to better than a few W/m^2 but they are of zero importance for what we are talking about.
David: In real science, approximations are always being made. It is useful to assess those approximations and figure out what the potential errors are. But scientists do not go around talking about colossal mathematical mistakes every time someone makes an approximation. That is what people who desperately want the answer to come out a certain way do.
shawnhet says:
While I am not always Roy’s biggest fan, I must say that he has done a very good job in that post. I sort of feel sorry for Roy (and Willis and Ira) having to deal with so many people on their side (in the larger debate about the importance of AGW) who are willing to believe complete and total nonsense! Folks who fall into this category should realize that, while they may convince a few who are similarly confused about the basic science, you make the AGW skeptic community look really, really bad in the eyes of real physical scientists!
Bart says:
…Which is demonstrating exactly what I said: that the pressure does not uniquely determine the temperature because you also have to know the number density. (What not having an enclosed box gets you is that you don’t have to know n and V independently, but only need n/V.)
davidmhoffer says:
January 1, 2012 at 11:12 am
David, the 390 can be estimated from the average temperature of the earth. It is also a part of the overall energy budget of the planet, so it can be estimated as a “missing term” in that balance.
However, it also has been measured by satellites. Many satellites. Many times. It always gets measured at about the same, an average of somewhere around 390 w/m2.
So if you wish to say it is wrong, you need to:
1. Locate and understand the satellite records, and
2. Show why they are incorrect.
You are not arguing against theory as you seem to believe, David. You’re arguing against both theory and observations.
w.
PS – I find it hilarious that you say “DO THE MATH!” regarding averaging using T^4 rather than T … but you haven’t done the math for the planet to show your point.
The HadCRUT3 global absolute temperaature data is here (zipped ascii file). I’ve just taken that data, converted it to the equivalent Stefan-Boltzmann radiation temperature, and area averaged the radiation temperatures as you recommend. Care to guess what the average radiation temperature is, using the HadCRUT3 absolute temperature data?
391.6 W/m2.
See, the scientists got there ahead of you … about 390 W/m2 is the answer we get when we do the average the way you recommend.
If I average the temperature in the normal way, on the other hand, and then converted it to S-B radiation temperature in W/m2, the answer is …
385.4 W/m2.
The T^4 average is larger than the T average, which is as we’d expect. as for example the RMS average is greater than the regular average.
In either case, however, Joel Shore’s point is still valid … as you would know if you had just decided to actually DO THE MATH rather than recommend that others do it.
Willis,
Your hostility is palpable, you are throwing the baby out with the bathwater and your math is wrong.
1. My point was to demonstrate that averaging T is mathematically incorrect, which I did.
2. At no time did I make any claims as to what the “right” number should be. As per your own calculations, you have shown a 6.1 w/m2 difference between the two approaches. In the context of the climate debate, 6.1 w/m2 is huge.
3. If you are going to caculate average P from a global data set, then to do it right, one cannot use the average annual T for a given grid cell. “T” for any given grid cell is an annual average derived from the monthly averages derived from the daily averages derived from the hourly averages. Given that daily fluctuations in T are often in the range of 20 degrees, and annual fluctations in T in temperate zones can be in the range of 80 degrees, simply calculating average P from an annualy averaged data set of T is making the exact same mathematical error I was trying to illustrate in the first place.
4. FURTHER to the above, in order to arrive at any meaningful understanding of energy balance, one would have to calculate P by averaging T^4 on an hourly basis and global basis and then trending those values collectivelly over time. Doing the same with average T masks the fact that an increase (for example) of several degrees in the Antarctic could easily be more than off set by a decrease in T in the tropics of just a few tenths of a degree.
I have a lot of respect for you Willis (though it is increasingly clear you have none for me) but in this case you are wrong and you are not being objective.
Ira Glickstein, PhD says:
January 1, 2012 at 11:26 am
Ira, thanks again for bearing with me. I should know better than showing up at a gunfight with only a knife, but here I go again:
You said: “Since specific heat is related to the heat capacity of a given mass of gas, we [are] heating or cooling exactly the same mass of gas M molecules in #1 as #2, so, to a first approximation, both will take the same amount of energy to heat to a higher temperature and will release the same amount of energy when cooled to a lower temperature.”
I do get that both containers have the same heat content if the same amount of energy is added to each (duh). But the same temperature? The authors made reference to the ideal gas law (which of course received a lot of criticism), but here’s where I think it might matter. Using PV=T (n and R are the same for each), you are essentially saying that when adding equal amounts of energy to each container, only the T term is affected. We’re assuming fixed volumes (one twice the other’s), but P can certainly be affected as well. It seems intuitive that the larger container, having less pressure, would manifest a larger portion of the heat input as increased pressure while the smaller container, at higher pressure, would increase temperature faster.
Does this make any sense?
Thanks,
Dan