Physicist Luboš Motl of The Reference Frame demonstrates how easy it is to show that there is: No statistically significant warming since 1995
First, since it wasn’t in his original post, here is the UAH data plotted:
By: Luboš Motl
Because there has been some confusion – and maybe deliberate confusion – among some (alarmist) commenters about the non-existence of a statistically significant warming trend since 1995, i.e. in the last fifteen years, let me dedicate a full article to this issue.
I will use the UAH temperatures whose final 2009 figures are de facto known by now (with a sufficient accuracy) because UAH publishes the daily temperatures, too:
Mathematica can calculate the confidence intervals for the slope (warming trend) by concise commands. But I will calculate the standard error of the slope manually.
x = Table[i, {i, 1995, 2009}]
y = {0.11, 0.02, 0.05, 0.51, 0.04, 0.04, 0.2, 0.31, 0.28, 0.19, 0.34, 0.26, 0.28, 0.05, 0.26};
data = Transpose[{x, y}]
(* *)
n = 15
xAV = Total[x]/n
yAV = Total[y]/n
xmav = x - xAV;
ymav = y - yAV;
lmf = LinearModelFit[data, xvar, xvar];
Normal[lmf]
(* *)
(* http://stattrek.com/AP-Statistics-4/Estimate-Slope.aspx?Tutorial=AP *)
;slopeError = Sqrt[Total[ymav^2]/(n - 2)]/Sqrt[Total[xmav^2]]
The UAH 1995-2009 slope was calculated to be 0.95 °C per century. And the standard deviation of this figure, calculated via the standard formula on this page, is 0.88 °C/century. So this suggests that the positivity of the slope is just a 1-sigma result – a noise. Can we be more rigorous about it? You bet.
Mathematica actually has compact functions that can tell you the confidence intervals for the slope:
lmf = LinearModelFit[data, xvar, xvar, ConfidenceLevel -> .95]; lmf["ParameterConfidenceIntervals"]
The 99% confidence interval is (-1.59, +3.49) in °C/century. Similarly, the 95% confidence interval for the slope is (-0.87, 2.8) in °C/century. On the other hand, the 90% confidence interval is (-0.54, 2.44) in °C/century. All these intervals contain both negative and positive numbers. No conclusion about the slope can be made on either 99%, 95%, and not even 90% confidence level.
Only the 72% confidence interval for the slope touches zero. It means that the probability that the underlying slope is negative equals 1/2 of the rest, i.e. a substantial 14%.
We can only say that it is “somewhat more likely than not” that the underlying trend in 1995-2009 was a warming trend rather than a cooling trend. Saying that the warming since 1995 was “very likely” is already way too ambitious a goal that the data don’t support.
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philincalifornia (20:11:00) :
the IPCC makes the simple error of assuming 100 years is an absolute, and fail to distinguish between atmospheric half life and aerial residence, hence the problem of the “missing sink”, though that was invalidated by Segalstaad in 1992 and 1998. Essenhigh (2009) gave us a clearer equation in explaining that c02 is part of a non-static exchange where 1/5th of c02 is exchanged between various pools depending on its temperature dependence and relatively quick equilibrium.
what are we talking about co2 for anyway? It has F*** all to do with the climate.
Tom P (06:09:54) :
Quite honestly, no-one knows how long a co2 molecule stays in the air. It could be a day or less to 7 years. The rest is just speculation. Not sure where this talk of decay comes from – surely we mean rate of increase? There are 38,000GT of c02 in the oceans, afterall, although oceans regulate aerial c02 content
David Middleton says:
The terms are sometimes used a little carelessly. Of the major gases that this is computed for, I think it is only for CO2 that this distinction is important because most of the other gases are removed from the atmosphere by chemical reactions (or deposition). CO2 is fairly unique in having large exchanges between the atmosphere and other reservoirs.
And, a perturbation of CO2 really had a halflife of only a few years, CO2 levels would be a heck of a lot lower. That is why you have to understand the full nature of the carbon cycle, which is not characterized by a single decay time.
Land use factors need to be included in cumulative emissions too. Besides which, that result is very sensitive to exactly where you start the cumulative emissions curve. Since good modern measurements have been available, the rise in the atmospheric levels as a fraction of emissions has been quite constant with around 40-50% of the excess CO2 remaining in the atmosphere.
Completely ludicrous. You selectively believe data that tells you what you want to believe and ignore the wealth of data and theory that contradict it.
P Wilson (16:54:28) :
philincalifornia (20:11:00) :
the IPCC makes the simple error of assuming 100 years is an absolute, etc. etc.
Yes I have noticed that this disgusting semantic argument that has resulted in this strange set of warmist comments. This is nothing to do with science, but rather is related to the mechanism used to pervert the scientific literature in order to make fake headlines that trick people of voting age into believing their s#!t.
The argument (one of them) is that a carbon atom from burned oil or coal that is sequestered into a xylan or cellulose molecule in a big fat log and sits on, or under the ground for ten to a hundred years is an anthropogenic carbon atom, so that represents the [insert believable-to-dupe phrase] lifetime of an anthropogenic carbon atom in the atmosphere (as nasty carbon dioxide, of course).
So why, when I note that the coal and oil carbon atoms were already in the atmosphere once, and ask why they don’t quote a lifetime/residence time/half-life of tens of millions of years, or even billions of years, I get no answer.
Here’s the answer – 100 years is the maximum number that the sheeple will believe. 1000 years has been tried and accepted in the “peer”-reviewed literature, but nobody in the real world is that fricking stupid (well they are actually, but is it a voting majority ??).
I’ve already proposed the Shore Uncertainty Principle, which is that if some of the things that Joel argues for were true (e.g. 100- 1000 year “residence time” of CO2, in the way scientists think of this, in the atmosphere), he would not be here to post about it.
See also David Middleton (15:00:57) :
I nominate this statement for Winner of the Psychological Projection Comment of the
YearDecade:The endless hairsplitting arguments by the alarmist crowd over what the residence time and persistence of CO2 means is simply an attempt to wiggle out of the fact that with short CO2 persistence times, the entire CO2=CAGW conjecture implodes.
But there isn’t much wiggle room. The above ground atomic bomb tests in the South Pacific in the 1950’s created new carbon isotopes that were easily identifiable. This allowed tracking of CO2, from the detonation until the CO2 was re-absorbed by the ocean and biosphere. The CO2 persistence was found to be on the order of ≈10 years.
A century-scale CO2 persistence would allow for a high climate sensitivity number, meaning that a fast rise in CO2 would result in a fast rise in global temperature. In fact, that is the IPCC’s computer modeled conclusion. Unfortunately for the IPCC’s politicians, the planet disagrees.
But a short, decade-scale CO2 persistence requires a much lower climate sensitivity number. That means that the effect of CO2 on the climate can be disregarded for all practical purposes; its tiny to non-existent effect is inconsequential, and can safely be ignored.
The IPCC’s political appointees have no choice in the matter: they must claim a century-scale CO2 persistence. With a short CO2 residence time, they have no reasonable argument why they should not be disbanded. So against all the empirical evidence, the IPCC continues to falsely claim that the average CO2 molecule persists in the atmosphere for a century or more. Conclusion: sucks to be them.
WHEN we see seasonal variations (in the hemisphere) of measureable CO2 percentage changes (due to uptake by plant biota)? And the lifetime is ‘quoted’ as a century?
Horse hockey! Not all of it CERTAINLY!?
.
.
Joel Shore (17:47:28)
“The terms are sometimes used a little carelessly”
that ranks as the understatement of the year. Incompetence is the correct word. However, given that no-one is measuring co2 exchanges, or rates of exchange, which is well nigh impossible, it is surprising, given that oceans have been very warm over the 20th-21st century that there isn’t well over 400ppm of c02. It proves that nature, specifically oceans are very adept at maintaining aerial c02 at around 0.04%. The carbon cycle – as a complete cycle – takes several hundred years at a time
Phil in California: I’m baffled how the concept of decay came into the c02 ratio. Anyway, even taking Anthro c02 as a given, what is often not understood is that if 50% of it stays in the air (from a day to several years) it is less that 1.5% of total c02 – as that ratio of anthro c02 to natural c02 is measurably the same since 1850, then a years prior c02 would dissolve against the ration of oceanic natural emission -yet nature always does the balancing trick. Atmospheric scientists don’t know what happens to co2 or why with any certainty. To say it is removed from the atmosphere is a careless comment – it fluctuates diurnally and seasonally at the very least – particularly during winter when its slightly elevated as nature puts billions of tons into the atmosphere through decay.
Quite what any of this has to do with climate cooling and warming (largely regional and irregular), remains a stubborn mystery.
kdkd (21:33:36) :
savethesharks:
“The climate models have shown for a long time that early greenhouse gas forced global warming will result in amplified warming in the arctic. It’s very powerful evidence that we have a serious problem, and the repeated challenges by sceptics have been unable to undermine this evidence.”
So c02 during the 30’s must have been well into the 500ppm mark – a russian icebreaker was found floating in free waters 300miles from the North Pole – scientists then were worried about global warming. However, since its only been measured since 1979, nothing of certainly prior to this can be vouchsafed for – even during the holocene optimum or the Medieval Warm period – from which we can infer that it was very probably warmer in the Arctic than the period since 1979 to the present, given the nature of greenland ice cores as proxies -1875 marked the coldest/lowest period of the entire holocene so it is an inappropriate starting point in any case
Smokey (19:08:31) :
“The above ground atomic bomb tests in the South Pacific in the 1950’s created new carbon isotopes that were easily identifiable. This allowed tracking of CO2, from the detonation until the CO2 was re-absorbed by the ocean and biosphere. The CO2 persistence was found to be on the order of ≈10 years.”
… and measurements of the increase in the same isotopes in the ocean have been used to determine the time taken for adsorption and sequestration in the marine environment of many decades and more.
All the available data has been used to validate the analysis that CO2 has a range of sequestration times ranging from a decade or so to many centuries and more depending on all the available processes. Your stubborn insistence on concentrating on just one value is like the sunbather’s who thinks because his sunburn improves after a day or so he can safely ignore any long-term skin damage.
Tom P
“All the available data has been used to validate the analysis that CO2 has a range of sequestration times ranging from a decade or so to many centuries and more depending on all the available processes”
more correctly, it’s circulation, like money circulation. The chances are that if you spend a $1 in your local community, same coin might just come back to you as change somewhere else – but that doesn’t mean it was in the bank accumulating all the time in absence – it could have gone via the hotel, the cinema, the department store, the bank and so forth until it ended in your pocket again, which could have been days or years later. The greatest reservoir is the bank of course – though in co2 terms, oceans contain up to 40,000GT, though oceans are capable of absorbing any amount of co2 – and this process depends on ocean temperatures.
so its uncertain where the long term “skin damage” comes from. If its the radiative effects of c02 then it is so much the factor 3 sunblock in the sahara, and an increase in 2% of this factor 3 won’t do anything to stop sunburn. More of the same sunblock doesn’t increase its effect – you’d need a higher factor of lotion. (Actually, climatologists know more co2 doesn’t mean more heat, so contrive fake equations to make it look like it does)
P Wilson (04:24:03) :
“…oceans are capable of absorbing any amount of co2 – and this process depends on ocean temperatures.”
The ability of the oceans to absorb carbon dioxide is far from infinite – and decreases with temperature.
Your post is certainly on a par with the Luboš Motl’s head article in terms of its scientific worth. Maybe you and him could work up something together here to brighten these dark months?
Thats what I said: Oceans can absorb any amount of c02, but depends on temperature. Des[pite very warm oceans over the 20th-21st the surprise is that there isn’t even more c02 in the atmosphere
@ur momisuglyjoel Shore (17:47:28) :
I agree. The terms are used carelessly. The RT of CO2 has almost nothing to do with its chemical properties. The RT is not really like a half-life; it’s dictated by the ratio of sourcing-to-atmosphere-rate to the sinking-from-atmosphere-rate. It can fairly easily be estimated by dividing the Gt C in the atmosphere by the total annual Gt C emissions to the atmosphere. If the source rate and sink rate were equal, there would be no CO2 in the atmosphere… The RT would be zero,
The RT will be equal to the Gt C Atmosphere / Gt C Source Rate. If CO2 had an RT of 20 years, there would be 20 years’ worth of CO2 emissions in the atmosphere (~2160 ppmv). The RT is a function of source rate / sink rate.
I am using the land-use factor of about 1.5 Gt C/yr and fossil fuel factor of about 6.5 Gt C/yr.
I am using the cumulative emssions that CDIAC (ORNL) publishes. CDIAC’s emssions record starts in 1750. I converted the annual emissions Gt to ppmv and used 277 ppmv (Law Dome) as a starting point for anthropogenic emissions.
When I back 45% of the anthropogenic emissions off the annual number, I wind up with about 370 ppmv for a modern value.
If I back all of the anthropogenic emissions off, I wind up with about 338 ppmv and I get a CO2 curve that mimics Moberg’s temperature reconstruction,
Actually, the only contradictory data are from the ice cores. The plant stomata data can be empirically tested and directly calibrated to moder instrumental CO2 records. The ice core data cannot be empirically tested; nor can they be calibrated to modern instrumental data yet. Furthermore, the AIRS data pretty clearly shows that low- to mid-latitude atmospheric CO2 is 20 to 30 ppmv higher than Antarctica.
The ice core CO2 data are great because they do give us a very long time series. But they do not accurately image decadal and century scale changes in CO2. They are like a long-period moving average.
The Pleistocene ice cores show that CO2 lagged behind temperature changes,
Kouwneberg’s SI CO2 reconstruction shows two CO2 maxima: ~390ppmv @ur momisugly 400 AD and ~320 ppmv @ur momisugly 1300 AD. Those maxima occur ~150 and ~350 years after warming peaks in the GISP2 ice core temperature reconstruction (Alley, 2004).
The instrumental and ice core data show that CO2 lagged behind the warm up from the Little Ice Age.
Ad hoc ergo propter hoc is a logical fallacy. “A” did not necessarily cause “B” just because “B” followed“A”… But… If CO2 consistently follows behind temperature changes… It’s kind of impossible for CO2 to be causing those temperature changes.
Dave Middleton (08:39:51) :
Maybe should should join Wilson and Motl in this proposed article. Your science is at a comparable level.
The residence time is not dependent on the ratio of the source to sink rates, but the ratio of the mass in the system to the sum of the source and sink terms in mass/time. Hence your assertion:
“If the source rate and sink rate were equal, there would be no CO2 in the atmosphere… The RT would be zero”
is nonsense, as a moment’s consideration of the time a water molecule spends in a pipe between your hot-water tank and bath should demonstrate.
Your last paragraph does severe violence to any form of logic. You might assert that because a certain human-induced causality has not been seen in previous natural responses, it’s “kind of impossible”.
But on the same basis you would have to claim that humans are incapable of burning down forests because such causality had indeed not been seen until humans discovered fire.
Tom P
Since the Anthropogenicatmospheric proportion remains constant, then it is no more than 1.5%, (A constant is a constant) if annual emissions are 3% and 50% of this dissolves in reservoirs. The other 50% doesn’t just stay in the atmosphere indefinately – no-one knows what happens to it, and for all we know it could be 0.5% at this moment. No one is measuring it so this atmospheric half life notion – the rate of time required to eliminate c02 down to a theoretically unknown c02 level (hows that for a mathematical paradox) is an arbitrary idea. Nature doesn’t follow these equations, although climatologists do – maybe because they formulate them, or borrow them from physics and mathematics, then quickly fall into fallacy on that basis, quite aside from the fallacy of using isotope tags to determine a ration. That is like taking a drop of water from the ocean to determine how much ocean there is down to the last litre. All we really know is that nature gives an equilibrium of around 0.04% atmospheric c02
It might be apt to put the horse before the cart before jeering at the passenger’s logic, otherwise one has random extrapolation running riot over reason.
What does this have to do with climate cooling and/or climate warming by the way?
P Wilson (10:28:09):
Your reasoning came crashing down in the first sentence. Of course the “Anthropogenicatmospheric proportion” is not a constant – it was much lower before industrialisation.
“It might be apt to put the horse before the cart before jeering at the passenger’s logic, otherwise one has random extrapolation running riot over reason.”
This paints quite a picture! – and maybe gives some insight into your thought processes.
@Tom P (09:59:08) :
My “bath” and the “hot water pipe” aren’t continuously exchanging water molecules… It’s a one-way trip for the water molecule from the pipe to the bath and then out the drain.
CO2 is continuously being cycled between the biosphere, atmosphere and oceans. Its residence time in the atmosphere is entirely dependent on the ratio of source rate vs sink rate. The atmosphere didn’t just come pre-equipped with a standard CO2 level. There is some CO2 in the atmosphere because the source rate has generally exceded the sink rate by a small amount over the last 600 million years or so. Atmspheric CO2 has fluctuated between ~180 ppmv to ~5000 ppmv during the Phanerozoic Eon because the ratio of source rate to sink rate has varied.
The RT will always be a function of the Gt C (Atmosphere) / Gt C (Source Rate). If there are 800 Gt C in the atmosphere and the source rate is 200 Gt C/ yr… The RT is 4 years. If the C sources suddenly shut off, the 800 Gt C in the atmosphere would be consumed by the sinks in a bit over 4 years.
You are correct. I did make a mistake when I said, “If the source rate and sink rate were equal, there would be no CO2 in the atmosphere… The RT would be zero.” The RT could not become zero unless the sink rate exceeded the source rate for a period of time. If the source rate and sink rate were equal, the RT would stabilize at Gt C (Atmosphere) / Gt C (Source Rate).
Your analysis of my logic is just about as bass-ackwards as it could be. If “B” happens after “A;” “A” might have caused “B.” Post hoc ergo propter hoc dictates that it is a logical fallacy to assume that “A” caused “B”.
The lag time of CO2 behind temperature in the ice cores and plant SI data does not mean that the temperature changes did cause the CO2 changes. The lag time simply opens up the possibility that temperature changes drive CO2 changes. The lag time does make it rather difficult, if not impossible, for the CO2 changes in the Pleistocene ice cores and Holocene SI data to have driven the temperature changes during those time periods.
Your forest fire example is simply a false analogy. No forest has ever burned down prior to a fire starting. Forests do not cause fires to start, irrespective of an anthropogenic cause of the fire itself.
In the Pleistocene, ice core data indicate that CO2 levels appear to have risen and fallen along with temperature changes of glacial-interglacial cycles. The CO2 changes lagged behind the temperature changes. Mankind did not participate in those changes of CO2 concentrations. In the Holocene, plant SI data show that CO2 also rose and fell in a manner that lagged temperature changes. Mankind’s role in the Holocene CO2 changes was also pretty well nonexistent.
About 400 years ago, the Earth started to warm up from the Little Ice Age. About 150 years ago, CO2 levels started to rise significantly. Mankind has had a role in the current CO2 rise. Our annual contribution of CO2 has risen from 0% to about 4% of the total source of CO2. But the warming still started more than 250 years before the CO2 started to rise.
As far as the personal insults go… What is it about you guys? Is there an insult course over at RC? I think I’ve been extremely civil to all but one warmist on this blog. And I only got snarky with him after about four days of steady insults from him.
It seems that for most of you folks, the play book consists of two logical fallacies and then a tirade of insults…
1) Appeal to authority.
2) Argument ad homiem.
3) Vile personal insults.
Apart from Joel Shore, Ferdinand Englebeen and Leif Svalgaard (although he’s not really a warmist), I’m hard-pressed to name any warmists who actually argue the science in a civil and thoughtful manner.
Tom P (02:15:55) :
… and measurements of the increase in the same isotopes in the ocean have been used to determine the time taken for adsorption and sequestration in the marine environment of many decades and more.
———————
… and while there, it causes global warming …. how ??
Or were you switching “catastrophes” ??
David Middleton (11:11:12) :
I said your statement about residence times was nonsense, as you now agree. There’s no need to take this as a “vile personal insult”.
As for the analogy of the forest fire, it has more relevance than you admit. In the past it was almost certainly Milankovitch cycles that initiated the increase in global temperatures, while for forest fires it was generally lightning, both natural causes. The causality is not now reversed, as you suggest, but rather human activity is now an additional option in both cases, whether by increased green-house-gas emissions or careless campfires.
It is illogical to reject a human cause for a broad range of phenomena on the basis that such a causality was not exhibited when humans were not present.
As for the current relationship between CO2 and temperature: if the causality is as you suggest, why would smoothly increasing annual CO2 concentrations be the causal result of temperatures that have not been rising steadily year on year? Or to put it another way, as temperatures have indeed stalled for the last eight years, why have CO2 concentrations continued their steady climb?
what creates more CO2 the constant decay of plant and animal mater or the burning of it?
and in the time period that were discusing man has been preventing more forest fires than he has been creating so careless camp fire analigy is a little off base.
Tom P (10:50:29) :
Perhaps you’re missing the point. The anthropogenic aerial fraction of co2 has not increased to 30% since 1850 but has remained constant, so today it is 3-4%/2, since 50% remains airborne whilst 50% doesn’t.
http://wattsupwiththat.com/2009/11/10/bombshell-from-bristol-is-the-airborne-fraction-of-anthropogenic-co2-emissions-increasing-study-says-no/
In other words, the increase of co2 since 1850 has been almost entirely natural, and the anthropgenic part is some 12ppm of the total, as we’re at a multicentennial natural highpoint of c02
Tom P
“It is illogical to reject a human cause for a broad range of phenomena on the basis that such a causality was not exhibited when humans were not present.”
Land use changed, deforestation, cities, urban areas all have their effect on local climates and temperatures. They’re not statistically significant enough globally however, and none of these factors are drivers of global climate change in one direction or the other.
In reply to the question of increasing c02 whilst temperatures level or decrease, the warming of oceans at the equator leads to higher co2 as oceans expel more vapour, heat and co2 – vegetation adds its source, some absorbed elsewhere back into oceans and other reservoirs so that the aerial level of c02 stays at around 0.04%. The lag between temperature and c02 is reputed as around 800-1500 years – which might be due to the fact that a complete ocean cycle is 800 years,or that the MWP was between 800-1000 years ago. Its common that temperature falls whilst co2 rises for a while from those ancient ice lollies, and vice versa. What is clear is that temperature leads the way whilst c02 follows the tmperature trend later
P Wilson (16:43:12) :
“In other words, the increase of co2 since 1850 has been almost entirely natural, and the anthropgenic part is some 12ppm of the total, as we’re at a multicentennial natural highpoint of c02.”
You’ve completely misread the Knorr paper that this article discusses:
http://wattsupwiththat.files.wordpress.com/2009/11/knorr2009_co2_sequestration.pdf
The annual increase in CO2 in the atmosphere is about half the annual rate of emissions. The proportionality between the two is excellent evidence that increase of CO2 can be entirely attributed to anthropogenic emissions – that’s an increase from 280 ppm to nearly 400 ppm CO2 in the atmosphere.
Your subsequent notion that this more than a quarter increase over a few decades is due to a delayed reaction to the MWP a thousand years ago is fanciful to say the least and ignores the very correlation between emissions and atmospheric CO2 that you first pointed out.
the annual rate is 4% so 2% stays airborne, and prior year’s c02 might be absorbed or taken up by reservoirs – over 5 years certainly so – so its safe to assume that if there is no significant increase in the airborne fraction then anthropogenic c02 doesn’t accumulate whilst natural c02 does. Itquite clearly means that if 45% (some 1.8% of all c02) doesn’t accumulate over years – but that most of the previous year’s aerial anthropgenic c02 circulates between oceans, air and land, such that there is never more than 3-4% anthropogenic c02 in the atmosphere. Its reasonable to assume that oceans have emitted a lot of c02 since the pacific climate shift since the late 70’s, and if the ice cores that show a lag of 800-2000 years are reliable a trend, then the same process is happening today. The important question then is: What happened 800-2000 years ago to give this multicentennial increase in c02 percentages?
certainly there has been a large output of c02 since 1850 though proxies from ice cores are not accurate – they show trends but not exact data, and only vague data from ground level that was absorbed in icesheets. What the actual aerial c02 was in france, the USA or China, indeed antarctica 200-100,000 years ago is anyones guess. Why is it not possible for ice to absorb what show years later at 180ppm, whilst aerial c02 up to 100 metres aloft was 350ppm?