Alan Siddons on Radiative Equilibrium
Posted by jennifer, August 16th, 2008 - under Uncategorized.
Tags: Climate & Climate Change
Radiative equilibrium is one of the foundation stones of radiative forcing theory. But it is not a law of physics, only a rather archaic and untested supposition found in climatology textbooks alone.
“For the Earth to neither warm or cool, the incoming radiation must balance the outgoing.”
Not really.
It’s best to regard radiant energy simply as a finite power source — indeed, that power is expressed as watts per square meter. An object is said to “cool” by radiating, yet this would seem to imply that restricting its radiation will make it get hotter and hotter. That’s the very premise of greenhouse theory, of course, that by disturbing outgoing radiance any magnitude of temperature gain is possible. But this is easy to test.
Confine a lightbulb inside an infrared barrier (like a globular mirror) and electrically feed one watt to it. After a while, will it be generating the heat of a thousand watt bulb? No.
When its temperature is consistent with the input, further heating stops.
It’s like water seeking its own level. Lacking any means to radiate to its surroundings, the lightbulb merely gets as hot as a watt of power can make it, which is not much hotter than what it would be in the open. If not, we’d be able to generate incredible temperatures very cheaply. Just confine, wait, and release.
Conservation of energy: it’s not just a phrase. The theory of radiative equilibrium arose early in the 19th century, before the laws of thermodynamics were understood.
From The Analytical Theory of Heat:
The radiation of the sun in which the planet is incessantly plunged, penetrates the air, the earth, and the waters; its elements are divided, change direction in every way, and, penetrating the mass of the globe, would raise its temperature more and more, if the heat acquired were not exactly balanced by that which escapes in rays from all points of the surface and expands through the sky. — Joseph Fourier (1768-1830)
Alan Siddons
Holden, Massachusetts
Er, no.
(pedantic mode on)
Consider that something grows, proportional with time as well with quantity. In such a simple model growth takes place exponentially as a function of the time.
This can also be formulated as dy = a y dt, so y’ = a y and y(t) = y(0) e at.
That’s why the curve is also called a GROWTH CURVE.
The exponential function grows faster than each polynomial (in x), and we can prove that in the Limit as x goes to infinity (x^a/e^x) = 0
The curve y = 0.0423exp(0.0045x) R^0.9951 is actually an exponential line of best fit to each and every NOAA global mean monthly pCO2 (ppmv) from January 1980 to June 2008! i.e. N = 342. Each and every month is expressed to 7 significant figures e.g. 2008.458, and each and every pCO2 (ppmv) is expressed to 5 significant figures e.g. 385.68
(pedantic mode off)
Congratulations, I never never ever seen anyone so comprehensively disprove their own thesis.
Essentially you are saying that a light bulb (or the earth) can only take so much energy before it reaches equilibrium, put in more energy and it >disappears<
You’ve single handedly broken the law of conservation of energy!
Perhaps you are thinking of a rechargeeable battery? But look – when it’s fully charged it can’t store any more energy and – wait for it – it gets hot!
Have you actually tried this light bulb experiment? there are a number of possibilities:
1) Your IR reflectors cannot be perfect and there are other routes for energy to escape (e.g. conduction) – as the temperature rises more heat WILL escape.
2) The filament’s resistance rises with temperature, it will accept less energy per unit time unless you keep ramping up the voltage.
3) The filament will get hotter until it melts.
But assume you /can/ pump more energy into you box, one way. Basically the contents will get hotter and hotter and it will get harder and harder to pump more energy in.
Eventually you open the box, and with a large bang the contained plasma (for that is what the superheated contents now are) explodes outwards releasing ALL the energy you put in.
But seriously, if you really belive what you posted, you are sad.
Gordon,
no, you still don’t get it.
The value “1″ does *not* come from multiplying of 0.03 with 38 (which makes no sense whatsoever). Spencer’s use of “1 part-per-100000 in 5 years” is just a another way of saying 2 ppm/year which is the current mean increase per year (http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html#global). Why he uses this weird terminology instead of just ppm/year, I don’t know, but it sounds like rhetorics to make it seem small.
Why don’t you try and listen to the people who spends precious time trying to explain your flaws in claiming “~97% of the CO2 in the atmosphere is from natural sources”?
I’ll give it another try. The number 3% does not represent the *level* of atmospheric CO2 attributed to human emissions, but rather the percentage of *emissions* of CO2. And since nature absorbs about as much as it emits, it doesn’t contribute to any increase of the CO2 level. The human emissions, on the other hand, just adds to the total amount.
So to summarize the different percentage values; about 3% of the yearly *emissions* are attributed to human activity. About 100% of the yearly *increase of atmospheric* is from these “human” emissions (since nature absorbs about as much as it emits). And about 36% of the total amount of atmospheric CO2 is “human” (the increase from pre-industrial levels of ~280 ppm to today’s 380 ppm being from “human” emissions).
It’s also interesting to note how you, after failing to admit you were wrong, insits on “putting the calculator away”.
Finally, I’d be careful not to talk about errors made by Hansen and at the same time put so much faith in Spencer & Christy, as if they had not done major errors (http://www.realclimate.org/index.php/archives/2005/11/more-satellite-stuff).
Steve, you’re not being pedantic, you’re being imprecise.
“Consider that something grows, proportional with time as well with quantity. In such a simple model growth takes place exponentially as a function of the time.”
This sentence translates to a different differential equation:
y’(t) = a*t*y(t)
Note the proportionality with time. The solution of this is *not* the exponential function. I know what you meant to say, but you didn’t write it that way.
I know about the exponential function, thank you very much. The dispute is not about the exponential function anyway, and its limit behavior is not relevant to the discussion. Nobody denied that this exponential function might be a good fit for the data. The dispute was about usage of “rate of change” and “rate of growth”, and their relation to derivatives and growth factors. This confusion is what you ridiculed Chris’ math skills over. Your last post doesn’t address this at all though, and in fact continues to be imprecise.
“exponential line”
There is no such thing. “Line” has a rather precise meaning in a mathematical context. Lines are straight, not “exponential”.
But I suppose this post won’t get you to admit even the possibility that you might have been wrong to ridicule Chris over this issue. It’ll probably just help escalate the pedantry even further. I hope I’m wrong though.
“You had been one of the few I could disagree with in a constructive fashion, but now you too have succumbed to the viciousness that seems to infest this blog.”
What it means they have nothing to say, and respond in the only way they have left, abuse. In other words Chris, (not that you’re here any more), you won. They just don’t have the guts to admit it.
“Thus, if the incoming flux rate exceeds the outgoing flux rate, then the level builds up until the outgoing flux rate is once again equal to the incoming flux rate, and equilibrium is re-established.”
Magic happens!
The fact that, at night, a cubic meter of air is heated by OLR is definitive proof that radiative equilibrium does not exist in that region.
As the emissivity of green leaves exceeds that of H2O & CO2 vapor by 3 orders of magnitude at STP the region cannot radiatively heat the ground even if slightly hotter and can do so only via conduction.
Couple of (minor) points.
(1) Due to the lack of an adequate number of global staions and and insufficient number of measurements per year at the existing suite of stations, NOAA will not ‘certify’ a global mean CO2 value prior to January 1980. This is why Mauna Loa data was used as a proxy for the global means prior to 1980. So, sorry Chris – data prior to 1980 (IPCC or not) is not adequate to measure global mean trends according to NOAA.
(2) Let’s look at theis question of ‘rates’ (no matter how loosely or tightly ‘defined’). NOAA have issued an update with very slight amendments to their global monthly mean CO2 levels since the data file I last downloaded. A linear fit to the period January 1980 to June 2008 is: y = 1.6239x – 2879.0745 R^2 = 0.9809 (n=342). The mean CO2 level over this period was 359.4518 ppmv so the average linear growth ‘rate’ was 1.6239*100/359.4518 = 0.4518%/year if you will. An exponential fit to the same period is: y = 0.0445exp(0.004500x) R^2 = 0.9829 (n=342) so the exponential (instantaneous) growth rate was 0.4500%/year i.e. closely similr to what I posted before.
(3) Now Chris asserts that the the ‘rate of increase’ has increased markedly. So let us look at (say) the last 10 years from July 1997 to June 2008. A linear fit to the period July 1997 to June 2008 is: y = 2.0012x – 3634.6 R^2 = 0.9408 n=132. The mean CO2 level over this period was 373.8594 ppmv so the average linear growth ‘rate’ was 2.0012*100/373.8594 = 0.5353%/year if you will. An exponential fit to the same period is: y = 0.0083exp(0.005300x) R^2 = 0.9406 n=132 so the exponential (instantaneous) growth rate was 0.5300%/year.
(4) So in all fairness it certainly looks as though, in comparison to the average rate of growth in CO2 over the the last of the last 28.5 years from January 1980 to June 2008, for the last ten years July 1997 – June 2008 be it measured ‘linearly’ as an average or exponentially as instantaneous, CO2 has indeed risen at a faster (higher) rate over the last 10 years of that period.
(5) Oh damn! I’m so sorry. I completely forgot. It is all a complete and utter muck up. Perceived trends over the last 10 years don’t count and can’t be used, can they! Their use is of course completely invalid on correctly extrapolated and appropriately trended global warming timescales. Silly, silly me. Please forget everything I wrote above. It is unreservedly withdrawn.
“Silly, silly me. Please forget everything I wrote above. It is unreservedly withdrawn.”
Noted, and minuted.
Steve, still comparing apples and oranges, I see. Let me try one last time to show why you never should ridicule anyone’s math skills again. I apologize to everybody else reading this, but it appears I’m really going to have to spell this out:
linear fit:
y1(t) = 1.6239*t – 2879.0745 ppmv.
y1′(t) = 1.6239 ppvm/year
So according to this model, CO2 levels increase at a constant rate of 1.6239 ppmv/year.
exponential fit:
y2(t) = 0.0445*exp(0.0045*t)
y2′(t) = 0.0045*0.0445*exp(0.0045*t)
According to this model, CO2 levels increase at a growing rate, from 1.4830 ppmv/year in 1980 to 1.6821 ppmv/year in 2008.
You could express these rates into percentages relative to the quantity of the current year if you want, in the following way:
p(t)=(y’(t)/y(t))*100%
Linear fit:
p1(t)=(1.6239/(1.6239*t – 2879.0745))*100% = 100%/(t – 1772.938) which decreases from 0.4829%/year in 1980 to 0.4254%/year in 2008.
Exponential fit:
p2(t) = 0.45%/year, which is constant (as expected for exponential growth).
You can also express the rates as percentages relative to the average of the function over a time period. The average of a function over a period (t_start, t_end) is determined by integrating the function over this interval and dividing by the length of the interval.
P(t) = 100%*y’(t)/avg
avg = (Y(2008)-Y(1980))/(2008-1980), where Y(t) is the primitive function of y(t).
For the linear model, we get:
P1(t) = 0.4524%/year, which is a constant, as expected.
For the exponential model, we get:
P2(t) = 5.701*10^-5*exp(0.0045*t), which increases from 0.4222% in 1980 to 0.4789% in 2008.
By now it should be clear what you did wrong in your last post: you compared a percentage relative to the current quantity for the exponential model with a percentage relative to the average quantity for the linear model.
It should now also be clear that the exponential function grows at a constant rate if by “rate” you mean “growth percentage relative to the quantity in the current year”, but at an increasing rate if by “rate” you mean “change in quantity per year” or even “percentage of change relative to the average quantity”. Both views are valid, and both views are useful. What you should not do, however, is confuse them as you did.
So, let me ask you, Steve: did you attack Chris’ math skills because you didn’t understand that Chris and you could have been referring to different types of “rates” so that his remarks could be interpreted as perfectly consistent? Or did you know, but chose to deliberately misunderstand him so you could ridicule? If the former, you may want to apologize and refrain from commenting on people’s perceived lack of math skills in the future, because yours have been found lacking. If the latter, that of course would make you a troll.
But it’s all just Socratic Irony, right?
Anton said…”I’ll give it another try. The number 3% does not represent the *level* of atmospheric CO2 attributed to human emissions…”
Sorry, Anton…you’re dead wrong. I just had it confirmed in an email from the DOE and they forwarded me to the IPCC source. Here’s the DOE link:
http://www.eia.doe.gov/bookshelf/brochures/greenhouse/Chapter1.htm
and if you read the fine print at the bottom of Figure 2, it will lead you to the IPCC source. The IPCC even states that the amount of anthropogenic CO2 is very small compared to the natural sources.
About realclimate…you show me anyone there with any real expertise in atmospheric physics. The place is full of mathematicians, computer programers and geologists who can’t use proxy data correctly. I was kind to Hansen because I don’t favour ad hominum attacks. Still, he’s an astrophysicist with no formal training in atmospheric physics. He’s been seriously wrong in the past about warming and I personally feel that has something to do with his lack of understanding of the atmosphere at a deep level.
I saw a debate involving Gavin Schmidt where he artfully dodged debating Richard Lindzen. He made a lame speech to the effect that he would not be debating the science and that anyone wanting the facts should contact realclimate. I also read the paper by Glassman, in which he revealed Schmidt’s lack of basics in physics.
Gordon: are you serious? Somebody points out that 3% of CO2 *emissions* are anthropogenic, not 3% of current CO2 *levels*, and you counter by referring to a figure that shows CO2 *fluxes*? A figure that *confirms* that 3% of CO2 *emissions* are anthropogenic? That makes no statement on how much of current CO2 *levels* are anthropogenic?
The figure you refer to even shows there’s a positive net flux into the atmosphere of 4 billion metric tons of CO2 per year, which is less than the human emissions of 7.2. That shows it’s theoretically possible to eliminate the positive net flux by lowering human emissions. This makes it even more puzzling why you chose this figure to support your position.
The figure also shows the current CO2 content of the atmosphere at 760 billion tons. With a net flux 4 billion tons of CO2/year, that amounts to 0.53% per year relative to the current quantity. That doesn’t sound like much, but assuming this net flux stays constant long enough, in 50 years that’s an increase of over 25% compared to now. That’s a significant increase within only a couple of human generations.
Note that this is entirely consistent with Roy Spencer’s number of 1 additional molecule CO2 per 100,000 molecules of air per 5 years: from a baseline of 38/100,000, that evaluates to an increase of 1/38/5*100% = 0.53% per year compared to now as well. It’s just that Roy Spencer presents his numbers in such a way that they *sound* ridiculously small. He wants people to forget we’re talking about billions of tons of CO2 here, but even his numbers can’t deny that the overall levels of CO2 will rise by 25% in just 50 years if they continue to rise at this pace.
Still a big “if”, of course, which leaves enough room for a debate, and there is still some uncertainty about the consequences of such an increase in CO2 levels. But muddling the current numbers isn’t going to help the discussion one bit.
Oh, and Gordon, you may want to put a little less emphasis on people’s credentials and more on the content of their arguments. Such authoritarian reasoning makes you look like a pseudo-skeptic. Besides, I’ve found such reasoning often leads to disqualifying yourself from the debate as well.
Gordon,
this is amazing. You’re still confusing emissions with level, and point me to a figure that very clearly shows what we are trying to tell you: Nature releases a lot of carbon every year, but it also re-absorbs equal amounts (actually, currently even more). Anthropogenic emissions on the other hand are not balanced, which results in atmospheric CO2 level net growth.
From the figure:
- Natural emissions/year: 210.2 gigatonnes carbon.
- Anthropogenic emissions/year: 8.8 gigatonnes carbon.
- Total: 219 gigatonnes carbon.
So according to their numbers, human emissions are around 4% of the total carbon emissions.
BUT, this is not the same as the *increase*, nor the *level* of CO2 in the atmosphere.
After having included the absorbed amounts, the numbers are:
- Nature net result: -2.2 gigatonnes carbon/year.
- Human net result: +6.2 gigatonnes carbon/year.
- Total net result: +4 gigatonnes added to the atmosphere every year. (which means +2 ppmv CO2)
Please, it’s really not that hard.
“Please, it’s really not that hard.”
As a matter of fact it is much too hard for Climate Science.
Fluences are by definition vector quantities, your arithmetic employed in balance equations is daft.
Look at the Mauna Loa or AIRS daily and nightly data points. The variance is 20ppm at 3km or on the order of 100Gtons for DAILY fluences.
That variance is anticorrelated with a biogenic source.
Spencer’s F-Test of the 13C/12C fraction of the CO2 variance for the seasonal signal and long-term trend shows that they have the same origin:
the oceanic partial pressure.
You boys have nothing on Gordon or Spencer, quit posing.
Beowulff said…”It’s just that Roy Spencer presents his numbers in such a way that they *sound* ridiculously small. He wants people to forget we’re talking about billions of tons of CO2 here, but even his numbers can’t deny that the overall levels of CO2 will rise by 25% in just 50 years if they continue to rise at this pace”.
The numbers ‘are’ ridiculously small compared to the overall CO2 produced naturally. The IPCC even admits that, claiming that anthropogenic CO2 is only a fraction of the natural CO2. I realize that a billion tons sounds like a big number, but compared to the total amount of CO2 released from the land and the ocean, and the gigantic volume of the atmosphere, it’s peanuts.
However, forget the math for a minute and visualize the 1 CO2 molecule contributed by humans and surrounded by 100,000 molecules of air. Seriously, what heat effect is that molecule going to have? If there is a heat effect, it is being done by the 97% of the CO2 molecules contributed by natural means, and that is peanuts.
If you read Spencer further, and you should, rather than reading the mathematician and computer modeler Gavin Schmidt, he claims that greenhouse warming is far more complicated than a molecule of CO2 absorbing and re-emitting heat. It has to do with water vapour transport systems that carry heat high into the atmosphere, where it cools and releases precipitation as rain or snow. Please note the cooling after condensation.
Furthermore, Spencer and Christy have observed such phenomenon directly via satellite but the AGW crowd doesn’t want to hear it. Thay have witnessed a cooling effect by clouds.
The system is so complex it is not clearly understood, yet modelers like Schmidt think they can apply differential equations to it and make predictions. Lindzen, Christy and Spencer, who are bona fide atmospheric physicists, are trying to tell people like Schmidt that they have the signs wrong on their feedbacks.
Instead of Schmidt having the humility of a serious scientists, who would want to know what they are getting at, he derides them. He arrogantly implied that Lindzen, a professor at MIT with over 40 years experience in the atmosphere was ‘old school’ and that his computer driven rhetoric is ready for textbooks. The guy comes across to me as an egomaniac, not a serious scientist. A serious scientist would go to those guys and say, “OK…can you show me where you think my model is wrong”.
So what if the CO2 rises 50% in the next 50 years? It has risen significantly since 1995 and the warming trend has been essentially flat. Not only that, the May 2008 study figured there would be no warming till 2016 because of the Atlantic and Pacific Oscillations, then it would magically start warming again.
Man…I’ve had that kind of pseudo-science up to here. As far as I’m concerned, studies like that are well-placed people justifying their tenure and their funding. They haven’t got a clue as to what is happening.
Anton said “So according to their numbers, human emissions are around 4% of the total carbon emissions. BUT, this is not the same as the *increase*, nor the *level* of CO2 in the atmosphere”.
Anton…I think you are confusing a few things. For one, the current level has been clearly stated by the IPCC as about 380 ppmv, or as Spencer puts it, 38 molecules of CO2 per 100,000 molecules of air.
The IPCC claims it was about 280 ppmv in the pre Industrial era, a figure that leaves me skeptical due to the proxy data from which it was derived. In fact all CO2 levels beyond about 1950 are artificially derived. We’re basing the 280 ppmv on polar ice cores. Is it not reasonable to assume the density may have altered by the time the CO2 drifted to the poles? And, as Jaworowski claims, ice at great depth is under tremendous pressure. That, and water being introduced along the way affects the carbon isotopes, and so does the heating from the extraction drill.
The IPCC claims that all of the CO2 increase from 280 ppmv to 380 ppmv is anthropogenically derived, simply because there’s no other explanation. Do you call extracting carbon isotopes from ice in polar regions, and infering a carbon density, a reasonable explanation for anthropogenic changes in CO2 density?
The point to note is that the CO2 density was 280 ppmv then and it is 380 ppmv now. The IPCC is alleging that NOW the balance of emissions of CO2 are 97/3 natural to anthropogenic. Yet, they are claiming that the 100 ppmv increase over about 300 years came totally from anthropogenic sources.
Never mind the distant past for now, since 1990, only 3% of all CO2 emissions were anthropogenic. Half of that 3% is unaccounted for. Is there any reason to assume that remaining 1.5% has changed drastically over the years? 300 years ago, the IPCC maintains 0% of all CO2 emissions was anthropogenic. Between then and now, that 0% has increased to 1.5% of all CO2 emissions, yet the atmosphere has gained 100 ppmv of CO2. Do you not question that increase at all? I sure do. I’d be willing to bet the density of CO2 300 years ago was closer to what it is now than to 280 ppmv.
I understand the exponential nature of the added CO2, it will keep increasing each year. But only 50% of it goes into the atmosphere according to the IPCC. Over time, it gets reabsorbed as well and the absorption of all CO2 is done at a rate of 97.5%. So, they want us to believe, that although the ratio of natural to anthropogenic emissions today are 97/3, that somehow over the past 300 years, only anthropogenic CO2 built up in the atmosphere.
I’ve heard the fancy theories about how emissions of CO2 have been calculated over time, and if that was true, they’d be able to put a gas meter in the air and measure that amount of CO2. But they can’t because they still can’t account for where the CO2 goes. NASA gave up on it because they can’t account for 40% of the anthropogenic emissions.
I’m not talking about how much anthropogenic CO2 is in the atmosphere, I’m talking about what we contribute. Out of that 380 ppmv, we are contributing 1 molecule every 5 years. When that 98.5% of CO2 is reabsorbed, do you think the anthropogenic molecules are labelled, “please don’t reabsorb”?
You can use your calculator all you want, my brain tells me there is something really wrong with the theory. I don’t care if CO2 doubles, or trebles, the history of warming over the past 60 years has shown us that the warming response is minimal. Furthermore, we’ve had about a 33% increase in CO2, according to the IPCC, since 1998, and the warming trend has been flat.
I have always felt that we should cut back on all emissions and I’m all in favour of doing that over time. I don’t see one bit of evidence for doing it now and in a hurry.
“Fluences are by definition vector quantities…”
No, they’re not. Besides, we were talking about flux, not fluence anyway. After this, I fail to see the need to indulge you in your attempt at changing the topic.
Oops, link didn’t work. Fluence: http://en.wikipedia.org/wiki/Fluence
Gordon said:
“However, forget the math for a minute and visualize the 1 CO2 molecule contributed by humans and surrounded by 100,000 molecules of air. Seriously, what heat effect is that molecule going to have?”
See, that’s where you go wrong, and that’s precisely what Spencer hopes for. You want people to work with their gut feelings, and people’s guts are notoriously bad at working with numbers. In fact, clearly many people’s *brains* even have difficulty. So by all means, put your calculator away if you want, but don’t expect other people to do that too.
First mistake: it’s not surrounded by 100,000 molecules of air, you’re conveniently leaving out the 38 molecules of CO2 that are already there. It still doesn’t sound like much, but you’re off by a factor 39 already.
Second, there is not just one molecule of CO2, or 39 for that matter (nor are there only 100,000 of air molecules). 4 billion metric tons of extra CO2 per year works out to about 5.47*10^37 additional molecules of CO2 per year. Can you visualize that? Can you imagine that many molecules having at least *some* effect?
It’s not that difficult to see why Spencer preferred to use the 1 in 100,000 per five years number over the 5.47*10^37 molecules per year number. They’re both true in a way, but they both create totally different intuitive responses. That’s why you shouldn’t just trust your intuition in these matters.
You keep focusing on how small the human emissions are compared to the natural emissions. Don’t you understand that this doesn’t matter? It doesn’t matter where the actual molecules of CO2 came from, nature doesn’t care, and radiation doesn’t care. It only matters that there is a *net gain* in the *total amount* of CO2. And since the human contribution is larger than this net gain, it’s likely that without the human contribution, there would not be a positive net gain, and CO2 levels would likely not be rising. It’s really that simple. And remember, all this can be learned from the figure *you* selected to support your position.
Really, if you can’t grasp this simple, basic concept, what point is discussing anything more complicated with you, like thermodynamics and non-linear dynamics? It’s almost like you don’t *want* to understand it.
I’m starting to understand why Chris gave up trying to educate people on this blog on basic science and math… I can only hope that more neutral readers will learn something from all this.
I’m off for vacation, with little to no internet access, giving my SIWOTI syndrome a little rest. So I won’t be back at this thread. Have fun.
Beowulff…I realize you’re off for a holiday but I’ll reply anyway.
The thing you don’t seem to comprehend is how vast the atmosphere is. The human contribution of CO2 is less than 3% of ALL CO2, and ALL CO2 is about 3/100ths of a percent of the atmosphere. That’s the trouble with numbers, you get a large figure and can’t put it in perspective because your brain can’t allow for that.
You’re right about the difference in intuitive responses. Neither my brain nor yours can visualize 5.47*10^37 molecules but they can begin to visualize 1 molecule in relation to 100,000. That’s why I asked you to put your calculator away because you can’t begin to comprehend the numbers anyway.
5.47*10^37 molecules is not a lot in the overall scheme of the atmosphere and I find it really doubtful such a density of CO2 per 100,000 molecules of air could make that much of a difference.
No one’s brain can figure out what is happening to that CO2 or how it is affecting the atmosphere. In fact, no one’s brain can know for sure what the density of CO2 was in the pre Industrial era. Here’s proof of that from an expert on ice core proxy data:
http://www.warwickhughes.com/icecore/zjmar07.pdf
I would think Spencer’s thinking behind the 1 molecule in 100,000 per 5 years comes from his incredulity at the stubbornness of computer modelers who ignore his satellite data. It’s so damned obvious, based on the data, that no net warming has taken place for 10 years and that the tropical tropospheric hot spot has not developed.
The public is mislead by computer model nonsense and someone needs to put things in perspective for them. I think the 1 in 100,000 analogy per 5 years tells it like it is, and explains why no warming has taken place over the past decade.
“No, they’re not. Besides, we were talking about flux, not fluence anyway.”
Pimple on Grendel’s behind: flux, fluxion, fluence, all synonymous to Webster, D. Who cares what Connelley thinks?
Ok, you don’t do vector calculus, few of us do (I did good just to get points for the set up of multivariate problems with Stewart’s equations).
We will take scalar math if you appropriately tag your little CO2 molecules, following Suess, and show us that any change in the atmospheric 13C/12C fraction is due to your–fluxes.
This is exactly what Spencer did and found the seasonal sinusoid (which Keeling thought biogenic) riding on top of the Mauna Loa trend had the same variance, a straight line, as the trend in terms of this ratio using an F-Test.
The trend is the combination of all–fluxes. The seasonal–flux–could be a partition, e.g., a biogenic–flux–drowning out the remaining components of erosion, etc., but the evidence refutes that notion.