RealClimate recently hosted a guest post by Barry Bickmore about some of Christopher Monckton’s claims. It included this passage about Monckton’s claim that CO2 concentration isn’t rising exponentially, but only linearly:

In other words, the slope keeps getting larger in an exponential trend, but stays the same in a linear trend. Monckton is right that you can do that sort of statistical test, but Tamino actually applied Monckton’s test to the Mauna Loa observatory CO2 data since about 1968 and found that the 10-year slope in the data has been pretty continuously rising, including over the last several years.

The reference is to this post in which I produced this graph:

Monckton himself commented on the RealClimate post, saying this:

It is suggested that we did the test incorrectly, because a climate-extremist performed a similar test on the Mauna Loa CO2 concentration dataset and came up with a different result. However, as our detractors ought to have realized, the Mauna Loa dataset, taken from a single location intermittently perturbed by regional volcanic activity, is not the same dataset as the NOAA global dataset that we used. Accordingly, we are unimpressed by their reliance upon an entirely different dataset.

Wow! He used a different dataset! That changes everything!!

Or does it? Let’s do the same analysis using the NOAA global CO2 dataset Monckton refers to. You can get it here.

There’s nothing new here except the dataset. Computing linear trend rates over moving 10-year intervals gives this result:

It’s clear. The rate of CO2 increase has gone up during the time span covered by the NOAA global data set. Including recently. But wait — is that result significant? Let’s add (2-sigma) error bars to the results:

Why yes, the increase is significant.

One wonders, why would you use the NOAA dataset when the Mauna Loa data set covers a longer time span? Maybe the two datasets give meaningfully different results? Let’s compare:

Nope. Not really different. Let’s add the error bars.

Nope. Not really different.

Referring to the Mauna Loa data, Monckton said it was “taken from a single location intermittently perturbed by regional volcanic activity.” Now, if you’re familiar with CO2 concentration data (which you should be if you’re going to pontificate on the subject), you know that the regional differences are much smaller than the growth over time. You’d also know that the Mauna Loa atmospheric observatory takes great pains to avoid contamination of their data by regional volcanic activity. Heck, if you really knew what you were talking about you’d already know that the Mauna Loa data is a very high-quality dataset, that it agrees extremely well with worldwide averages, and that it can be used as a suitable estimate of the global average.

But it looks like Chris Monckton doesn’t know these things. I guess he doesn’t really know this subject very well.

By the way. If you want to know whether or not the growth in atmospheric CO2 is exponential, there’s an easier way. Log-transform the data. Here’s a plot of log(CO2) concentration using the NOAA global data:

Let’s fit a straight line by linear regression:

It sure looks like log(CO2) has increased faster than linear, i.e., that CO2 concentration has increased faster than exponential. We can test this by fitting a quadratic curve to the residuals from our linear fit:

Sho’nuff. CO2 has increased faster than exponential. Even using the shorter NOAA global dataset. And yes, the result is statisically significant.

### 75 responses to “Mo’ Better Monckey Business”

1. Tamino, excellent work as always.

Is there a way of determining whether or not the difference between the NOAA and Mauna Loa data is statistically significant (the growth in the NOAA data is ever so slightly lower since 1990– which is probably one of the reasons Monckton chose it ), and at which level of confidence? I strongly suspect the difference is not stat. sig.

Going by your time series data it looks like the correlation coefficient between the two datasets ought to be awfully high. Either way Monckton is clearly out to lunch.

Now, I’m sure Monckton is going to try and sue you too now for showing him up. Sigh.

I hope I’m wrong, but is he does, FWIW, you have my support Tamino.

Oxburgh recommended that the CRU work more closely with statisticians, while that may be true, it seems that the ‘skeptics’ need to actually start working with statisticians, period.

2. One lie at a time….

3. Boy, that’s a shock.

Be careful, or you may have His Nibs call you (as he has unnamed others) “sinister” or “pot-bellied” or a “tax-gobbler” or an “enviro-loony” or a “Kool-aid slurper” or even a “zombie”–or he could get really, really serious and write about this noble forum (as he has about unnamed others) that:

“. . .You’ll find precious little science on the zombie websites. They specialize in global whingeing ad hominem, rather than scientific argument ad rem. The frenetic personal assaults have become so self-evidently ludicrous. . .”

And that would be–what?

A badge of honor? Consistent? Hypocritical?

4. Tamino – actually, the “exponential” rise in CO2 is (nominally) from a pre-industrial baseline, so in your plot of log(CO2) it might be better to subtract off the 270 ppm or whatever appropriate for that. Once you’re past doubling the two “exponential” rises are pretty much the same, but before that it ought to have a different curvature, and thankfully we’re not close to doubling yet.

5. Didactylos

Colour me confused. The dataset you link to starts in 1980. Your first global graph starts in 1989. But then at the end, you switch to a global dataset that starts in 1959 – which is kind of coincidentally when the Mauna Loa data starts.

Is there some mislabelling going on?

For extra confusion, your original graph only shows Mauna Loa data from 1969 onwards.

[Response: The first several graphs are not CO2 concentration. They’re the rate of increase of CO2 estimated by linear regression over 10-year time spans. The x-axis is therefore labelled “Ending year” and refers to the ending year of the 10-year span for which the trend rate has been computed.]

6. Didactylos

Okay, so I should have remembered why the rate graphs start 10 years after the data. But the graphs at the end are Mauna Loa, not global.

7. David B. Benson

Here are the differences, lnCO2(d)-lnCO2(d-1) of decadal averages of lnCO2 (the forcing):
```1880s 0.014 1890s 0.007 1900s 0.009 1910s 0.013 1920s 0.012 1930s 0.014 1940s 0.004 1950s 0.009 1960s 0.022 1970s 0.033 1980s 0.043 1990s 0.042 2000s 0.050```
so CO2 increased about exponentially through the 1930s, then experienced little growth in the 1940s and after that is clearly superexponential.

The data is from Law Dome and then the Keeling curve (Mauna Loa) the fit between these two sets of data (during the period of overlap) is supurb, year by year.

• David B Benson, I know of no address at which to reach you. Please contact me at ronbroberg over at the yahoo.com place. I would like to talk to you about your CO2/AMO model.

Thanks, Ron

8. CM

Well squashed.
Why did the growth rate dip 1991-1997? Do we know?

9. Michael Hauber

Off topic:

any chance you can provide expert statistical comment on the Russian heat wave and the question Michael Tobis has asked about whether this could have been at all possible without global warming?

My gut feel is that the event is so freakish that even with global warming it is highly improbable. If you define global warming as a gradual 0.02 degree increase each year, then you shouldn’t really expect heat records to be broken by several degrees? According to Accuweather Jim Andrews July in Moscow was 3 degrees warmer than the previous record.

This follows the Australian heatwave in August last year which was 1 degree above the prevous August record. Both these heatwaves are tied to the 2009/2010 El Nino with Australia one of the first areas to feel the warming, and northern NH one of the last.

Or does red noise + the large number of places on the globe where heat records can be set lead us to predict that such heat records should be set from time to time?

10. > 1991-1997
“The Former Soviet Union presents a special case. The collapse of the Russian economy that accompanied the collapse of Communism led to a decline in oil consumption of more than 50 percent over the 1991-98 period.”
http://www.eia.doe.gov/pub/oil_gas/petroleum/analysis_publications/oil_market_basics/demand_text.htm

• CM

[slaps forehead] Of course. Thanks, Hank.

11. Monckton:

1) He is ignorant about data analyis
– or –
2) He is deliberately trying to mislead

#2 is far more likely because his many “mistakes” have been pointed out to him repeatedly and yet he is still “making mistakes”.

If so much were not at stake we could just laugh him off. Thanks for the post, Tamino, we can always (Vis)count on you to set the record straight.

12. Horatio Algeranon

Referring to the Mauna Loa data, Monckton said it was “taken from a single location intermittently perturbed by regional volcanic activity.”

From Monckton’s brain??

13. Jacob Mack

Tamino solid post. I appreciate the work you put into this.

14. Derecho64

Most awesome demolition (as usual), Tamino.

If Monkeyton had a shred of integrity, he’d apologize most profusely for his scurrilous attacks and threats against Abraham, Mandia, et.al., since he’s been shown to be a fraud and a liar many times.

Of course, we know he has no integrity nor interest in the truth, so he persists. He’s quite the piece of, ahhh, “work”.

15. Lamont

“It is suggested that we did the test incorrectly, because a climate-extremist performed a similar test…”

Unfortunately, mathematics itself has a well-known climate-extremist bias, so it cannot be trusted…

16. Andrew Dodds

The guy went to the same college as me.. the shame..

(OTOH, he didn’t do a science degree, but Classics.)

17. Martin Heimann

Tamino,

you made a mistake: you have to take the logarithm of the excess CO2 above the preindustrial concentration (~280ppm). If you subtract 280 ppm prior to taking the logarithm, you will see that the concentration rose quite closely exponential over the 50 years of the record, but not faster. In fact, over the last 20 years the growthrate has slightly declined as compared to the average growthrate over the entire 50 years.

As to the representativity of Mauna Loa: you can take also the 50 years of data from the South Pole – or even better the average of the two.

Cheers

Martin, that makes no sense. The post is looking only at yearly deltas, so the starting point makes no difference.

And in recent years, it is the 2nd derivative that has decreased, not the slope.

• Gavin's Pussycat

Ray, look closer. At the end of the post tamino works with log(CO2). What Martin is arguing is that you should look at log(CO2-CO2(pre-ind)). Then the curve will be close to exponential [haven’t checked], as one might have guessed from the compound-interest behaviour of production processes and installed means of production — at least over the several decades time scale.

19. Monckton said it was “taken from a single location intermittently perturbed by regional volcanic activity.”

I think this is an excellent example of Monckton’s modus operandi, of how he is bringing his humanist education to bear. That sentence is carefully crafted to be factually correct, yet utterly misleading his audience about the relevant facts. There are whiffs of volcanic CO2 drifting up Mauna Loa. Never mind, that the scientists are careful to sort those contaminations out. It is a single location, never mind, that local variations don’t matter much, as is well known and as you have demonstrated yet again in your post.

You’d also know that the Mauna Loa atmospheric observatory takes great pains to avoid contamination of their data by regional volcanic activity.

You are correcting a point, that will likely be the impression left with the audience. However, Monckton never by the letter of the word claimed that the Mauna Loa record is contaminated. He left the audience to use its “common sense” and make that connection. Devious, yet effective. Abominable, too.

20. Martin Heimann

Ray:
I was commenting on the last three graphs of Tamino’s post where he takes the log of the CO2 concentration (not the yearly deltas!). Likewise, the argument of David Benson is also not correct – he has to take the logarithm of the excess CO2 (i.e. CO2 – 280ppm) and then compute the deltas over each decade.

BTW: I’m not defending Monckton at all, just when showing that he’s wrong one has to use good science… In any case, why should the CO2 rise exponentially at all? We know that the emissions are not perfectly rising exponentially and also the carbon sinks on land and in the ocean are not expected to exponentially suck up more CO2 with time.

[Response: It was Monckton who defined the terms of his claim — that CO2 increase was not exponential but linear. I showed definitively that it’s faster than linear, in fact it’s faster than exponential. There was nothing scientifically wrong with my demonstration of his error.

If you want to characterize the increase in CO2 concentration as a baseline plus exponential increase, that’s probably a good model — but it doesn’t seem to have much to do with the subject of this post: Monckton’s claims.

I’d emphasize that the actual increase is neither linear nor, strictly speaking, exponential (even referred to a baseline). It’s a much more complicated function of emissions, which, as you state, are also not increasing in strictly exponential fashion. Exponential models are just models. Monckton’s use of a linear model to extrapolate forward to the year 2100 is demonstrably foolish.]

21. Alexandre

Great post, as usual.

I wish those WUWT folks knew some maths to grasp something like this.

22. dhogaza

Michael Hauber:

My gut feel is that the event is so freakish that even with global warming it is highly improbable. If you define global warming as a gradual 0.02 degree increase each year, then you shouldn’t really expect heat records to be broken by several degrees?

Remember that this global rise includes that part of the earth covered by water (70% of it). Average temperatures in the interior of continents will rise more drastically on average.

But it’s still not enough to account for what’s happened. The Moscow heat wave’s been driven by a very unusual configuration of the jet stream, as I understand it. The jet stream’s been doing some odd things in recent years, and I think a very good question is whether or not warming is driving the configuration into states not seen before, or are being seen more frequently than before …

• TrueSceptic

The Jet Stream is a subject I’d like to know a lot more about. Apparently its shift north or south during the summer makes all the difference between a warm sunny summer and a cool wet one in the UK. I take it that there is no real understanding of what causes these shifts, or our weather forecasters wouldn’t be getting their barbecues put out by downpours so often?

23. Didactylos

Tamino, you say “Here’s a plot of log(CO2) concentration using the NOAA global data:” – it still looks an awful lot like Mauna Loa to me. It starts in 1959. What else can it be?

You obviously intended to show global data, because you say “CO2 has increased faster than exponential. Even using the shorter NOAA global dataset.” Did you use the wrong images? Is it a WordPress caching issue?

Sorry to harp on, but trivial errors distract from the point and give ammunition to the deniers. Or if I’m mistaken (again), please let me know.

I quickly repeated your test using the actual global data, and I got the same result with a lot less certainty. Which is completely unsurprising with only half the data!

[Response: That is indeed the Mauna Loa data. The gaffe is entirely mine.]

Martin,
The % increase is itself increasing with a linear trend–that means a faster than exponential rise in CO2.

25. David B. Benson

Martin Heimann | August 10, 2010 at 3:34 pm — Nope. The CO2 forcing formula is
http://en.wikipedia.org/wiki/Svante_Arrhenius#Greenhouse_effect
which is then, of course, proportional to
lnCO2(now) – lnCO2(then)
so taking first differences for different “now” decades the constant “then” term cancels.

26. David

>My gut feel is that the event is so freakish that even with global warming it is highly improbable.

I suspect a key factor that we are missing in analysis of extreme events is that we are changing the PDF of weather patterns as the planet warms. One thing we expect is that a warming world will on average have more sluggish weather patterns (as evaporation scales linearly in temperature but water vapour holding capacity scales exponentially) – my “instinct” is that we will find ourselves locked in more frequent long-lasting weather regimes likes those seen in Russia this year. There are other things going on including the reduction in summertime relative humidity over land and the summer drying of continental interiors.

There is some great science here for someone with the time..

27. dhogaza

I suspect a key factor that we are missing in analysis of extreme events is that we are changing the PDF of weather patterns as the planet warms.

Jet stream in the northern hemisphere (which, after all, is where it is).

It’s been doing unusual shit the past few years.

28. dhogaza

TrueSceptic:

The Jet Stream is a subject I’d like to know a lot more about. Apparently its shift north or south during the summer makes all the difference between a warm sunny summer and a cool wet one in the UK. I take it that there is no real understanding of what causes these shifts, or our weather forecasters wouldn’t be getting their barbecues put out by downpours so often?

If I were 35+ years younger, thinking of trying to understand what global warming means for the northern hemisphere, I’d say this is a topic ripe for exploration.

It’s being watched, though, for instance this is a tidbit.

• This–ultimately a Reuters story, apparently–is in today’s news (127 similar stories, according to Google.)

http://www.ottawacitizen.com/news/Floods+fires+landslides+called+evidence+warming/3383518/story.html

• Deech56

Pretty good until the last sentence. The jet stream story is interesting (and as an aside – why don’t press releases have a link to the article they are touting?).

• dhogaza

Thanks, Kevin, one snippet from the story:

The disasters have all been driven by a “supercharged jet stream,” meteorologists say. The jet stream, a vast ring of high-speed winds, has split in two with one section heading north over Russia and the other going south over the Himalayas into Pakistan. In Russia the stream is inhaling the heat and spreading it quickly, causing fires. However, in Pakistan it is “supercharging” the monsoon.

So, will a warming climate make such shifts more frequent? Make them the usual summer pattern rather than a highly unusual one?

We’re gonna find out …

• Timothy Chase

The article mentions the “bifurcation” of a supercharged jet stream.

It is my understanding that higher temperatures result in an increase in the rate of evaporation, by roughly 8% per degree Centigrade or a factor of 2 for each 10 degrees Centigrade. Since given an increase in the rate of evaporation the system will move to a new quasi-equilibrium where there is a higher absolute humidity but this new quasi-equilibrium will be established quite rapidly (having a characteristic time period of roughly 10 days), I would assume that at that point the rate of evaporation and the rate of precipitation will be roughly equal even though the rate of evaporation is still at the new higher level. This being the case the rate at which water is circulated through the atmosphere will increase, increasing the rate of air circulation. As such air circulation will be more energetic, as it becomes more energetic, involving higher wind speeds, this will tend to result in the breakdown of laminar flow, or alternatively, turbulence. And as such, we should expect more branching to occur in terms of atmospheric circulation.

Now my question: is the branching that has occurred in jet stream flow simply an instance of this increased turbulence — due to greater energy, or alternatively, higher wind speeds? Or is there some other largely unrelaed mechanism involved?

29. Nick Dearth

OT (sort of), but any thoughts on this post from Willis Eschenbach on temp adjustments for Nepal?

The problem I have with calling the Moscow fires evidence for global warming is that the events themselves are WEATHER–or at least weather related. I think the only way you could really call them weather is maybe by doing some sort of extreme-value analysis. Ask: “What is the likelihood that this event was produced by the distribution of weather events characteristic of the climate baseline?”

• gss_000

Completely agree with this post. I’ve been listening to how media has been covering this and the huge iceberg that broke off from the Arctic and I have to say that I’ve been impressed with how well many experts have made sure that people understand these events are more “weather” events unless a pattern occurs. Hopefully this starts hammering home with the general public.

While in my gut I wouldn’t be surprise if global warming has made these events more likely and we’ll see more, it’s better if the dialogue emphasizes how you can’t conclude anything from one event. Otherwise, the deniers will crow with another big winter storm.

• Didactylos

I remember Tamino analysing how unusual the Australian heatwave was. And undoubtedly such heatwaves are more common in a warming world – but saying “caused by global warming” does indeed cause all sorts of problems with the nitpicking crowd.

I think the best compromise is to say global warming contributed to the heatwaves. It’s a nice media soundbite, and it doesn’t mischaracterise the science.

• Timothy Chase

Didactylos wrote, “I think the best compromise is to say global warming contributed to the heatwaves. It’s a nice media soundbite, and it doesn’t mischaracterise the science.”

“Likely contributed” to the individual heat waves. But I believe you may may draw a stronger conclusion with regard to trends or extreme events.

Although in the case of the trends there is still the question of the extent to which a given trend is actually a trend. For example, global temperature over fifteen years for example vs. arctic sea ice extent minima — where in the case of the latter even the claim that the overall trend is very towards accelerating decline is justified by the evidence.

Likewise there is the question of the extent to which other factors may be contributing to the trend. For example, an increase in regional fires where a given climate oscillation may be involved. Or in the case of sea ice extent minima our understanding of the physical mechanism that is involved may make a stronger conclusion regarding the role of global warming warranted.
*
With respect to individual heatwaves and the like, there will always be of causal factors. We live in a noisy universe where things interact and where there will always be more than one causal factor except when the cause is the thing itself.

For example, an individual forest fire will not be caused by the forest having dried out, but the forest having dried out and the lightning strike that might ultimately go back to a butterfly. Or more likely someone dropping a cigarette thats still lit in the wrong place — which in part might be the result of low levels of serotonin, what they had for breakfast or a careless word. And it has already been pointed out that human practices involving the clearing brush (or failing to do so) or of preventing smaller forest fires and thus permitting more combustible material to accumulate may be a major factor even in terms of the trend both in North America and Siberia.
*
However, in the case of the heatwave in Western Europe in the summer of 2003 we can say (according to at least one paper) global warming has doubled the likelihood of such a heat wave occurring during any given year. This would suggest that either there was a fifty percent chance that global warming was the cause of the heat wave or given the earlier analysis, that global warming is very likely a causal factor in the heat wave, perhaps even the greatest contributing factor.

And presumably heat waves on the scale that we are seeing in Russia occur only once in a thousand years. Given that it is on a scale which is greater and more severe than what we saw in Europe of 2003 and how infrequent such events would be in the absence of global warming, the role played by global warming is likely even greater.
*
But given the brevity of time and the focus of individual members of one’s audience, weaker language may be more advisable than stronger language — and as always the ability to cite technical literature. As a matter of strategy I would use weaker language where I might be immediately challenged and when actually challenged you could suggest that the stronger language may be warranted and cite the evidence and analysis that warrants the stronger conclusion.

• Gavin's Pussycat

I think a proper expression would be “a taste of things to come”.

“If you liked this heat wave/drought/superstorm…, you’ll love the 22nd century!”–Brought to you by the Exx Mob

??

• Andrew Dodds

From what I’ve read, there was also the matter of basically the entire Russian forestry service getting sacked. According to the principals of lassiez-faire economics, a government service was not required because private landowners would ensure that fires on their property would not get out of control.

• dhogaza

While true, under the current conditions I’d say a major blowup would’ve happened anyway. Think 1988 and the Yellowstone Fire, much of the western US was in flames that year which limited the resources available to control the fire. But the fire managers were adamant that more resources would not have made much of a difference. Also, anti-conservation types used this to argue against the limited “let it burn” policy adopted by agencies in the 1980s, despite the fact that this fire was fought vigorously from day 1. The lodgepole forest of Yellowstone was a largely even-age forest when it blew up, due to an earlier fire two or three centuries earlier (this subspecies of lodgepole has cones that don’t release their seeds unless exposed to heat high enough to melt the waxy pitch that holds the cones intact).

Here are some Yellowstone fire facts from the NPS:

– The summer of 1988 was the driest in the Park’s recorded history.

– More than 793,000 acres (36% of the park) were affected by fire.

– Fires begun outside of the park burned more than half the total acreage.

– Humans caused 9 fires; lightning caused 42 fires.

-About 300 large mammals, primary elk, perished.

\$120 million was spent and 25,000 people participated in this firefighting effort, the largest in U.S. history.

This huge effort saved human life and property, but had little impact on the fires themselves.

– Rain and snow finally stopped the advance of the fires in September.

I’ve bolded two pertinent factoids. My guess is that the russian fires are larger and at least as impossible to control than the Yellowestone Fire.

I’m not, however, arguing that the Russian sacking of their forestry service was wise, not at all. When it comes to resource management, I’m as far from libertarian as you can get.

But, the reality is, when it comes to wildfire, shit happens.

31. Tamino,

It looks like you try to be an honest statistician but still you make the typical mistake of only doing the analysis carefully which you find favourable prior to starting the investigation. Your exponential fit analysis is correct, but if you would be honest, you would do the linear fit analysis with equal care and you would compare the results.

If indeed the exponential fit is in any way “better” (I leave it to you to define “better” in a sensible way) than the linear, you would have every right to say so. However you did not do the linear fit analysis, presumably because prior to starting this investigation you already decided that the answer must be exponential.

If you would have performed both analysis you would have found that in the time range the data is taken on the best exponential and best linear fits are almost indistinguishable. I did this little exercise and the result is here:

Click to access co24.pdf

And for more comments on the same issue see http://stufffromallaround.wordpress.com/2010/08/11/9/

[Response: First, if you were an honest investigator you’d have noticed that this post isn’t about finding the best model for CO2 growth. It’s about demonstrating the folly of Chris Monckton’s claims. Which is pretty obvious.

Second, if you think I’ve made a mistake that’s one thing, but to accuse me of dishonesty is despicable behavior on your part. Shame on you.

Third: you so totally screwed up your analysis. The exponential model fits way better than the linear. I leave it as an exercise for you, to find out why.]

32. Several people pointed out the need to subtract the pre-industrial value. Then again one can repeat both fits, linear and exponential, the result is here:

Click to access co2_subtr.pdf

[Response: Your mistake has nothing to do with failing to subtract a pre-industrial value. You just plain got it wrong. Don’t bother us again until you figure out why, admit your mistake, and apologize for accusing me of dishonesty.]

33. Tamino,

First: you did make a claim: “CO2 has increased faster than exponential.” This is what I’m talking about. I don’t really care about Monckton.

Second: I apologize for accusing you of dishonesty. Still, the fact still stands that you only did one analysis correctly (call it X), which I’m claiming is not enough. Reason: if you do a second analysis (call it Y) correctly and you find that it passes the same statistical tests as X then you should not claim that “CO2 has increased according to X”. You should say “the data for the CO2 increase can not distinguish between model X and model Y”.

Third: no, I did not so screw up my analysis.

[Response: Yes you did screw up your analysis. Big time. The linear model isn’t nearly as good as the exponential model.

Don’t bother us again until you realize your mistake.]

34. Tamino,

Your attitude of “no, you are wrong” does not sound scientific at all. What do you expect? A conversion of the form

“You are wrong.”
“No, you are wrong.”
“No, you are wrong.”
…….

Do you really think this would be useful? At the moment your responses seem to indicate that your attitude is pretty much the above, although you have been given clear scientific arguments and I have apologized for the personal aspects (since I didn’t know they would offend you, once you made it clear that they do, I apologized).

[Response: You called me dishonest. Now you say you didn’t know I’d be offended. Hmmm…

And you did so based on a bungled analysis. And you still don’t see it.

I try real hard to be genuinely helpful to people, I even try to learn from those who correct my mistakes (although I’m not as good at that). But in your case I made an exception. No, I didn’t expect my comments to be helpful to you, nor am I inclined to do so. Figure it out for yourself.]

• Timothy Chase

Speaking for myself, I try my best to appreciate it when someone corrects me and they are right to do so. But when someone “corrects” me when in fact I was correct and they are now the ones who are mistaken I am naturally somewhat annoyed. However, when they “corrected” me and the mistake on their part isn’t entirely innocent a stronger reaction on mine is certainly understandable even though not necessarily advisable. But I believe the latter is to a greater extent than the former a matter of context, individual style and choice.

• Timothy Chase

Anyway, back to the essay…

To my eye, the charts showing how the rate at which the rate of growth in CO2 concentration is increasing over time (and thus the rate at which CO2 concentration is accelerating) looks to be linear, and thus the growth in CO2 concentration looks quadratic. However, after switching the analysis to natural log of CO2 concentration rather than CO2 concentration then calculating the difference between the natural log of CO2 as a function of time and a linear fit, Tamino concludes that the growth in CO2 concentration is faster than exponential.

From the main essay:

It sure looks like log(CO2) has increased faster than linear, i.e., that CO2 concentration has increased faster than exponential. We can test this by fitting a quadratic curve to the residuals from our linear fit:
[chart showing a rather good quadratic fit]

Sho’nuff. CO2 has increased faster than exponential. Even using the shorter NOAA global dataset. And yes, the result is statisically significant.

Wow.

35. Mark One eyeball trivially says that stufffromallaround did stuff up his analysis, because his ‘best exponential fit’ is less than the observations at low x, greater than observations at medium x, and less than observations again at high x. So an exponential curve with a higher coefficient will fit better.

36. Mauna Loa is a Venus Denialist trap for those guys. Look at Plimer for example and Loehle.

37. Michael Hauber

If I look at stufffromallaround’s graph, my impression is that a linear fit to data from 1980 is about as good as an exponential fit.

Of course Monkton’s claim to me seems to be that a linear fit is correct and an exponential fit is wrong, and Tamino quite clearly debunks this by showing that an exponential fit is quite good.

Also if I look at the data from 1960 or so it does look very clear to me that an exponential fit is better than linear. Since 1980 – well if I interpret the 2 sigma bars Tamino drew correctly there has been a statisticaly significant increase in the rate of increase from 1990 to 2009, but also a statistically significant decrease in the emissions rate between the early and late 90s.

The question of whether Co2 is increasing exponentially since say the 80s is interesting because that is when global awareness of climate change began. We can hope that at least some of what we have done to combat climate change may be having an effect and Co2 may not be rising exponentially anymore. For instance renewable energy has been growing for a few a while now. I note that Kyoto was adopted in 1997 which is depressingly near the recent low in Co2 increase rate….

On this question I think its also useful to look at raw Co2 emission figures, and one I found on a quick google search seems to show a clear break away from exponential increase in recent decades:

http://www.pewclimate.org/facts-and-figures/international/historical

However I note fossil fuel emissions is not the only source of Co2 in the atmosphere, and other sources could be maintaining an exponential or faster than exponential increase. Also I would trust the atmospheric Co2 figures to be quite accurate, whereas I expect figures on human Co2 emissions are going to involve some guestimating based on economic data from around the world and could be less accurate.

38. MP

@stufffromallaround,

Did you actually calculate the p-values associated with your reduced Chi-square values? What were the values you used for your dof and variance to calculate your Chi-square statistic?

I get chi-square values 1.17 and 6.19 for exponential and linear fits respectively. I assumed a variance of 1, which is completely arbitrary.

http://en.wikipedia.org/wiki/Goodness_of_fit

This type of ‘modelling’ lacking explicit mechanisms will not tell you anything about future CO2 increase anyway.

39. MP

I calculated it for Mauna Loa

• Sekerob

Speaking of MLO, July 390.09, ppmv almost 2 down from June but still 2.35 ppmv up from last year’s July.

The Exponential curve btw fits something I’ve been charting from the MLO data like a glove … chart 2 and 3 above). The shrimp comment of Monckton on Prof.Abraham reminded me of a snark: He (The good Fishcount) ate one and had more brains in is stomach than between his ears. ;P

I wonder what all the smoke and sooth and aerosol crap from the FSU is going to do when it’s coming down elsewhere. The EU is concerned.

40. Didactylos

Unlike “stufffromallaround”, I’m completely out of my depth here. Bumbling around trying to do what I think is correct, but knowing that statistics simply aren’t my metier.

Nevertheless, I tried the exercise anyway, using the global data. Despite what Nick Barnes suggests, I was unable to get an exponential fit that “looks” better.

This is what I found:

```> anova(flin, fexp)
Analysis of Variance Table

Model 1: mean ~ b0 * (year) + b1
Model 2: mean ~ b0 * exp(b1 * (year - 1980))
Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
1     28     38.688
2     28     26.486  0      0         ```

Clearly, exponential is a much better fit. Equally obvious, debating which is “better” as a model over such a short interval is a fool’s game. Which is why Tamino doesn’t do that, but Monckton thinks it is really important (yet still gets it wrong). Heck, if we’re just playing “fit the elephant”, then a quadratic fit is better than either.

Am I close to right with all this? Am I making any stupid mistakes?

[Response: The guy who admits he’s out of his depth, has supplied the best answer yet.]

41. Brendan Lowstien

Help me understand what definition you use for “exponential”?

I was taught that exponential was a curve starting flat or horizontal and then curving up to the vertical.

For example a vertical bar graph with columns on the x axis showing the values 1, 2, 4, 8, 16, 32, 64, 128, 256, etc…. you know as in a curve.

What about the CO2 increases above even closely resembles that sort of exponential curve? It is a diagonal line then a fall and then another straight rise.

I am not calling you a liar, I am just honestly trying to understand and reduce my own ignorance.

I would greatly appreciate your understanding in helping me to understand.

[Response: The “diagonal line then a fall and then another straight rise” isn’t the CO2 concentration at all. It’s the rate of increase of CO2 concentration over moving 10-year time spans. The actual CO2 concentration is shown in the 2nd- and 3rd-to-last graphs.

“Exponential growth” means that each equal increment of time multiplies the value by the same amount. In the example you give, each new value is twice the previous so that multiplier is 2. When the ratio of successive values is constant, the growth is exponential. It turns out that for CO2 concentration, the ratio of successive values isn’t constant it’s actually increasing — which is why it’s properly described as “faster than exponential.”

Your confusion is probably because you’re used to looking at exponential growth on time scales over which it starts out with modest increase but ends with dramatic increase. But if you look at an exponential graph with the time axis greatly expanded, it’s still perfectly exponential but it no longer has the visual resemblance to “starting flat or horizontal and then curving up to the vertical.” It still curves upward but on shorter time scales its curvature is small enough that it lacks the “explosive increase” that most people associate with exponential growth. Imagine your own example but instead of each value being twice the previous value, it’s 1.005 times the previous value.

Monckton’s claim was that the CO2 concentration is essentially linear, i.e., that the difference between successive values is approximately constant (unlike exponential growth for which the ratio of successive values is approximately constant).]

42. Brendan Lowstien

Thanks for the explanation, I appreciate that. I feel a little less ignorant now. It’s been a long time since math at school ;)

43. For those who hesitate to link extreme, record-breaking weather events to climate change, I recommend this quote from Dr. David Orr, professor of environmental studies and politics at Oberlin:

“‘We really don’t have a name to describe behavior of this sort,” Orr said of the resistance to dealing with climate change.

‘It is criminality beyond any language, concepts or laws that we presently have. It’s criminality that places the entire human enterprise at risk. And we simply have not been able to confront inaction that allows the entire human enterprise to slip into catastrophic failure. It really does beggar the imagination to understand why, given the consensus of the scientific community on this issue, why inaction was the order of the day,” said Orr, conspicuously referring to the failure to address the issue in the past tense.

‘A lot of effort is spent to try to figure out how to cleverly frame issues so as to appeal to people’s self-interest. And I don’t know that that’s always the smart way to do it. I think the smartest way to do it is to tell the truth as best you understand it. And the truth of the matter is, for me personally, all of the events that you’ve mentioned are yet further evidence that climate is rapidly destabilizing. Would any one of those specific events have been likely to happen in the absence of the human influence of climate? I think the answer would have to be no to almost a vanishing point.'”

from this interview: http://www.huffingtonpost.com/2010/08/12/global-weirding-extreme-c_n_680364.html

And by the way, the wildfires are exacerbated by the fact that trees are dying all over the world. Vegetation is being damaged by exposure to toxic greenhouse gas emissions, which is going to cause mass famine well before climate change from CO2 renders the planet uninhabitable.

• Timothy Chase

Gail Zawacki wrote:

For those who hesitate to link extreme, record-breaking weather events to climate change, I recommend this quote from Dr. David Orr, professor of environmental studies and politics at Oberlin:

“‘We really don’t have a name to describe behavior of this sort,'” Orr said of the resistance to dealing with climate change.

I am looking forward to reading the article.

Gail Zawacki wrote:

And by the way, the wildfires are exacerbated by the fact that trees are dying all over the world.

Quite likely. Snow melts earlier in the spring. Water evaporates more quickly after it rains. Oceans warm more slowly than land, meaning that the same relative humidity over the ocean will imply a lower relative humidity over the continental interiors — and thus the drying out of the continental interiors.

Gail Zawacki wrote:

Vegetation is being damaged by exposure to toxic greenhouse gas emissions, which is going to cause mass famine …

Here I would be a little more careful. Tropospheric ozone is damaging to plants. Nitrous oxide and methane? As far as I know neither are damaging to plants.

Carbon dioxide? Plants love it. Denialists will get you on that. It is enough to make a “debate” look like a draw, and for them a draw is a win — as they are only looking to sow doubt, confusion and make an excuse for inaction.

But if plants are heat sensitive they will not enjoy the higher temperatures, and if they are moisture sensitive they will not enjoy being dried out. If they are near the coastline subject to a higher sea level and stronger storm surge, they may not enjoy salt water entering the water table. And they may not take to the occasional torrential rain and flash flood that washes away once rich but now desiccated top soil. All of these will make famine much more common.

• I do believe all the things you mention will impact vegetation. But there is primarily the ozone, which makes trees and plants more vulnerable to insects, disease, fungus, and weather – all has been documented in published science. And leaves of plants that are being watered in pots have the same characteristic foliar damage from ozone, to the same extent, as plants growing wild.

Ozone results from nitrous oxide mixing with UV radiation. I didn’t mention CO2 specifically, although frankly it seems just as likely that excess CO2 (aka plant food) would ultimately have the same effect on plants that excess calories (aka the American diet) has on obesity with its attendant diabetes, heart disease, and general increased mortality.

Can I answer the deniers with that? Or will they claim fat is good…Maybe they will. Look at Rush…

44. Robert P.

You are confusing nitrous oxide (N2O) with nitric oxide (NO). Nitrous oxide is a long-lived greenhouse gas. It’s highly inert in the lower atmosphere and not, as far as I know, toxic to plants. The compounds that catalyze ozone formation in the lower atmosphere are nitr*ic* oxide, NO, and nitrogen dioxide, NO2. These are short-lived, reactive and toxic, but not significant greenhouse gases.

45. I’m not a scientist so I may well muddle up the chemicals and volatile organic compounds and how they make a toxic chemical soup in the atmosphere. Doesn’t change the fact that something is killing vegetation. It would be a dream come true for me if somebody with expertise would figure out what exactly it is that is causing trees to die. Having said that, I would point you to this however:
“While emissions of nitrous oxide, a precursor compound in ozone, have declined in the United States by about one-third since 1985, the study found that ozone levels had increased by 29 percent over the same period.
The study notes that from 2001 to 2006, ozone precursor emissions in east Asia were up 44 percent, and 55 percent in China.
“The changes we have seen over the past 25 years coincide with when China was transforming itself into an economic powerhouse,” Jaffe said.”

many links to published research at the Basic Premise page on the top of the blog http://www.witsendnj.blogspot.com

46. Jacob Mack

Statisticians also make things up:

http://wattsupwiththat.com/2010/08/14/breaking-new-paper-makes-a-hockey-sticky-wicket-of-mann-et-al-99/#more-23450

McShane and Wyner (2010)

Full of strawmen and improper weighting to say the least.
Figured you may comment on this in the future Tamino, since it allegedly puts all other analysis to rest… such a joke of a paper, however, it is being touted as some sort of great proof.

47. Didactylos

They’re *still* bashing on a decade-old study?

Of course they are. What else can they do? *sigh*

48. Sorry to continue off topic Tamino, but I re-discovered this EPA passage this morning, for Robert P:
“Ozone chemistry in the presence of sunlight, nitrogen oxides (NOx) and volatile organic carbon (VOC) is well understood and a central component of modern air quality models. The chemical formation of O3 in the troposphere results from the oxidation of nitric oxide (NO) to nitrogen dioxide (NO2) by organic (RO2) or hydro-peroxy (HO2) radicals. Photolysis (the chemical process of breaking down molecules into smaller units through the absorption of light) of NO2 yields NO and a ground-state oxygen atom, O(3P), which then reacts with molecular oxygen to form O3 (CD, p.2-2).
Oxidized nitrogen compounds are emitted to the atmosphere mainly as NO, which is oxidized to NO2 which subsequently can be reduced back to NO. Consequently, NO and NO2 are often grouped together into their own family called NOx (CD, p.2-3). Oxidized nitrogen containing compounds are essential to the formation of O3 in the air. There are a large number of oxidized nitrogen containing compounds in the atmosphere including NO, NO2, nitrate (NO3), nitrous acid (HNO2), nitric acid (HNO3), nitrogen pentoxide (N2O5), pernitric acid (HNO4), peroxy acetyl nitrate (PAN) and its homologues, other organic nitrates and particulate nitrate. Collectively these species are referred to as NOy. NOx is considered a good surrogate for NOy and, thus, is commonly monitored and reported (see Table 2-1).

Click to access 2007_07_ozone_staff_paper.pdf

49. Robert P.

Yes, that is a more complete description of the role of nitrogen oxides in ground-level ozone production. NO and NO2 are the major players, but there are others – NO3, HNO2, etc., and they are constantly being converted into one another. Note, though, that *nitrous oxide*, which has the formula *N2O*, is *not* part of any of these chemical mechanisms. It’s an important greenhouse gase precisely because it is relatively unreactive (and hence long lived.)

Atmospheric nitrogen chemistry is horribly complicated, and made more so by the confusing chemical terminology.

50. Greg. Tingey

There’s another one who goes on and ON aboiut “Climategate” in the UK.
A tedious bore called Christopher Booker – he’s a professional journalist, and he is anti-conspiracy, often with good cause, in political matters.
Unfortunately, he now sees conspiracies everywhere ….
You can sample his maunderings on climate here:
http://www.telegraph.co.uk/comment/columnists/christopherbooker/

As one of the many thousands of people in the UK taking phenological readings, for reporting to a mass-observation type of study, I have no time for Booker, but he sways a lot of people.