Much of what’s wrong with the online discussion of global warming is revealed by a recent reader comment on RealClimate.
Greg Goodman thinks that he’s taking climate scientists to school — he actually “lectures” the RealClimate readership about their supposed need to “dig a bit deeper” into the data on Arctic sea ice (both extent and area). He shows a graph based on some analysis which — unbeknownst to him — actually reveals that he doesn’t know what the hell he’s doing. He thinks he has established the presence of “cyclic variations” of which the climate science community is ignorant, and concludes that climate scientists are missing “important clues” about “internal fluctuations” which, of course, those inadequate computer models just can’t handle.
One would be hard pressed to find a more clear-cut example of hubris.
Climate scientists who study sea ice have been all over the data, every piece of it, but instead of making the mistakes Goodman makes they’ve been as careful and rigorous as their expertise and experience allow. They have certainly dug a whole helluva lot deeper than Greg Goodman has, or probably is capable of. It’s Goodman who needs to go back to school.
Goodman links to this graph:
Then he says this:
We only hear about run-away melting in Artic ice but looking at all the daily data available for over 30 years now we also see there are strong “unforced” cyclic variations up there too.This plot is rate of change so the zero line represents neither loss not gain.
The media tend to focus on one day per year in September. Scientists need to dig a bit deeper. What is happening up there is a lot more interesting than simple melting.
Thorough investigation of the daily satellite ice data could give important clues to a better understanding of the “internal” fluctuations in the climate system: the part that, so far, models have trouble reproducing.
According to his own graph, here’s what he did. He took sea ice anomaly values (both extent and area), differenced them to estimate the instantaneous rate of change, then applied a Gaussian filter to smooth the result. It seems quite similar to what he does in this blog post. Let’s take one of the data sets he uses, daily data for Arctic sea ice area from Cryosphere Today, and try to reproduce the procedure. Letting 
It’s not exactly the same as Goodman’s result — for one thing, I didn’t cut off the first and last half-intervals or so like Goodman did — but it’s pretty damn close, I figure I’m on the right track so far. The 360-day smooth certainly does show, to the eye, the apparent “5.42y cyclic variation” which Goodman seems to regard as meaningful. Let’s focus our attention on the 360-day Gaussian filter result, and on that apparent “unforced cyclic variation.”
I can even subject the result to Fourier analysis, which gives this:
That peak just to the left of frequency 0.2 cycles/year corresponds to a period 5.4 years. If we assume the noise in these data are white noise, then it’s statistically significant. If we assume the noise is red noise, it’s still statistically significant. Here, by the way, is the amplitude spectrum (rather than power spectrum) for this data set (the power spectrum is proportional to the square of the amplitude spectrum):
Isn’t the peak at period 5.4 years pretty convincing evidence cyclic variation?
No. It’s not.
The noise in this data set isn’t white. And it isn’t red. For lack of a better term, I’ll call it “green” noise — because it doesn’t give a flat spectrum, it doesn’t emphasize low frequencies or high frequencies, it emphasizes medium freuencies.
Let’s compute the spectrum of the actual data — sea ice area anomaly. It looks like this (click the graph for a larger, clearer view):
It’s dominated by very low-frequency response. This isn’t due to periodic (or pseudoperiodic) behavior, it’s because of the long-term trend. The dashed lines show 90%, 95%, and 99% confidence limits in the presence of red noise. There is one significant pseudo-periodic frequency, very near 1 cycle/year. This is because the spectrum of the area data (not area anomaly) is dominated by a 1-cycle/year fluctuation (the seasonal cycle) but that cycle isn’t constant, it shows year-to-year fluctuations as well as amplitude modulation (the size of the annual cycle has increased). So the spectrum of the area data shows broadband response near 1 cycle/year, and that of the anomalies shows residual broadband response after the “average annual cycle” has been removed.
It’s easier to look for other influences in an amplitude spectrum:
The dashed red line shows frequency 1/5.4 cycle/year, and rather clearly, it’s not exactly meaningful.
This is what the data show.
How, then, does that 5.4-year period pop out in the Fourier spectrum of the filtered velocity data? There are actually two filters applied to the data. One is a derivative filter, which transforms anomaly to anomaly velocity. This has two effects. For one thing, it multiplies the Fourier amplitude by the frequency, which tends to exaggerate high frequencies while suppressing low frequencies. For another thing, most Fourier analysis programs (mine included, and Greg Goodman’s too I’ll bet) de-mean the data before analysis, i.e., they subtract the average value. Subtracting the average value from the velocity data is equivalent to subtracting the linear trend from the original data, i.e., de-trending (linearly) the data. So, the Fourier spectrum of the derivative-filter data is the frequency multiplied by the Fourier transform of the de-trended data.
The second filter is a Gaussian smooth. This is a mathematical operation known as convolution. If you know your Fourier analysis, you know that the Fourier amplitude of the convolution of two functions (in this case, the velocity data and the Gaussian filter) is equal to the product of their Fourier amplitudes.
What happens if we de-trend (linearly) the anomaly data (not velocity!), then compute its Fourier transform (amplitude spectrum), then multiply by the frequency, then multiply by the Fourier transform of a Gaussian filter (which happens also to be a Gaussian). The multiplier itself — frequency times a Gaussian (which is the factor by which the Fourier amplitude is attenuated) — looks like this:
Note that it has little effect on frequencies near about 0.2 cycle/year, but practically eliminates both low and high frequencies. When we multiply that by the Fourier amplitude of the de-trended anomaly (not velocity!) data, then compare that to the amplitude spectrum we got for the velocity data itself, we see that they’re very similar:
Here’s what happened. The Fourier transform of the data does not support the existence of a 5.4-year cyclic variation. In fact it shows nothing at all near frequency 0.2 cycles/year except the ubiquitous ups-and-downs that all Fourier spectra show. But when we kill everything not near about 0.2 cycles/year, we’re left with a spectrum with a single tall peak at frequency 1/5.4 cycles/year (period 5.4 years).
In case you’re wondering why the “convolved spectrum” is noticeably different from the spectrum of the velocity data, that’s because what I just plotted is the product of a continuous convolution with the spectrum of the original (not velocity!) data. But the data are discrete, not continuous, so we should really compute the discrete convolution and the discrete spectrum. If we compute the discrete spectrum of the velocity data (which means, only at the “Fourier frequencies” rather than oversampled), and compare that to the “convolved spectrum,” we see that they’re the same at the Fourier frequencies:
No, there’s no evidence of a 5.4-year periodicity in Arctic sea ice area anomaly. But if you kill everything in the Fourier spectrum except a narrow frequency range, whatever humps happen to exist in that frequency range will stick out like a sore thumb, and give you the false impression that you’ve identified strong “unforced” cyclic variations. You haven’t.
It’s one thing to play around with different analysis methods, compute derivatives, apply filters, computer Fourier spectra, and suggest what you consider interesting possibilities. Heck, that’s science. But when you operate under the misconception that you know a lot more about data analysis than you do — when you declare “strong” cycles where there’s no evidence of them — and when you then proceed to scold the scientists who have actually spent their lives studying the data you think you understand better than they do, then you’re guilty of hubris.
And that’s much of what’s wrong with the online discussion of global warming. People look at some data and try to understand it, but they’re in way over their heads and haven’t a clue about what they don’t know. Then, instead of inquiring whether or not they might have gone wrong and how — as they should — they declare that the real experts are missing something.
In fact, this seems to infest just about everybody in the fake “skeptic” camp. Even those with absolutely no clue about how to analyze or understand data (you know who you are) will proclaim that they understand it better than the experts who’ve spent a lifetime working on it. And those who do have some knowledge — I’ll bet Greg Goodman is a pretty smart guy and sure as hell knows a lot more than, say, Anthony Watts — might be even more dangerous. Often, they’re less inclined to doubt their own conclusions, more inclined to think they know better than those who really do know.
Maybe Greg Goodman is a smart, open-minded guy who will realize that he went astray. Maybe he’ll conclude (as he should) that he’s in over his head. He needs to do two things. First, he needs to accept that his analysis isn’t right. Second, he needs to admit (to himself) that he’s nowhere near as savvy about data analysis in general, and Fourier analysis specifically, as he thought he was. Who knows, he might even have an epiphany and impress the hell out of all of us. That would be an incredibly admirable thing to do.
As for Fourier analysis, he should buy — and read — my next book. It’ll be out in about a month, and it’s about Fourier analysis and its application to time series.
But whatever approach Greg Goodman takes to extend his knowledge, he needs to get back to school.
Open Mind 
Maybe even *study* your next book.
When it comes to statitistical analysis, I’m quite devoid of hubris and I think I’ll need a few re-reads of this excellent post to fully grok this.
Ooh, looking forward to your next book!
Creationists do ths even more often than climate deniers.
“That’s not a transitional fossil. I don’t care what actual scientists say, I read a book by Gish and it says that only crocoducks show transition.”
I think it’s more prevalent among them because of the volume of creationist books that are out there.
Silly boy: Don’t you know that once you have established that species B represents a state between species A and species C you’ve only shown the need for TWO transitional fossils rather than the original one? And so ad infinitum?
I like that – we should call it “Xeno’s fossil”.
Here’s his “analysis” of Lunar-solar influence on Sea Surface Temperature:
on a blog where he was subsequently banned.
Apparently “the author has a graduate degree in applied physics, professional experience in spectroscopy, electronics and software engineering, including 3-D computer modelling of scattering of e-m radiation in the Earth’s atmosphere”
Maybe you could untangle the convolutions….
Actually this kind of thing isn’t even beyond a Californian physics professor publishing in Nature, like Richard Muller… to his credit he knew how to stand corrected, though on another matter.
Dunning-Kruger applies often.
God save us from retired physicists/engineers with too much time on their hands! They frequently have mountains of hubris leading to embarrassing displays of ’emeritus-ness’.
(and I say this as a physcicist)
Given the duration of the interval between the time stamp of Goodman’s original comment on the RC thread and the arrival of this comprehensive response (i.e. the ‘flash to bang’ time), I think Tamino should be declared ‘Whack’a Moler’ of the month.
And of course, whether you know what you are doing or not, you need to thoroughly test your results to see that they are consistent with everything else you know to be true.
It is very easy to accept your own results without checking their ramifications.
I won’t even attempt to discuss on this site, because the editorial policy makes that an impossibly sensored , one sided process. But I thank Tamino for taking a proper look at the data.
Had my post been a full article, I would have discussed the processing. That is not possible or useful in a blog comment.
I intent to write this up more full soon and I will take into account Tamino’s legitimate points. Criticism is always useful in science.
My main point in my brief comment here is that we need to be looking at all the data not obsessing about one day in September if we want to get a true impression of variations in Arctic ice cover.
So thanks to Tamino for highlighting the issue.
[Response: I quite agree that all the data deserve study. Your implication (in your comment at RealClimate) that climate scientists aren’t already doing that was not only mistaken, it was offensive. Before you claim to see further than others, find out what they’ve seen. My guess: the fraction of the published literature on sea ice changes that you’ve studied is close to zero.
Also: don’t underestimate the importance of that one day in September.]
“I won’t even attempt to discuss on this site, because the editorial policy makes that an impossibly sensored , one sided process.”
So you say nothing of substance because Tamino will “sensor” you if you do? I suspect he’d be delighted, instead, if you tried to answer the critique — and I think that you know that too. Weak dodge.
“My main point in my brief comment here is that we need to be looking at all the data not obsessing about one day in September if we want to get a true impression of variations in Arctic ice cover.”
And here you confirm, as Tamino guessed, that you know zero about what Arctic scientists have been doing. It isn’t obsessing about one day in September.
[Response: In fact he did respond in greater substance, but your comments were in moderation at the same time.
And I understand his suspicion of censorship, since I did censor some of his comments on a previous thread. But when I post on a specific person’s claims, I do not censor that person’s replies (unless they’re obscene or utterly irrelevant).]
Looking at the data means thinking about the result. There is nothing on God’s white Earth that would make you think there is a 5.4 year cycle in the Arctic ice pack, therefore there is an error in your analysis. It might be subtle, but it is wrong.
One trap that many technical people can easily fall into – DK sort of – is the fallacy that because they are ‘good at maths’, that they are therefore equally good at every branch of maths. I think I am quite capable in some areas of maths but I know for certain that I am cr@p in other areas – I followed some of Tamino’s post then he lost me.
Different areas of science or other technical professions may require the use of particular branches of math. But unless you actually spend your working life continually across all of maths, you may well be quite rusty on the stuff you haven’t done much of for years. Just because you can make Partial Differential Eqns sit up and dance the Cha Cha doesn’t mean you are the real deal on Statistics as well.
I’m no scientist and to be frank, though it started well, I don’t think I’ll ever understand all that you’ve written in the post, Tamino, but I often spot blatant errors in fake-sceptic blog posts and comments (though I wouldn’t know enough to spot Goodman’s errors). What I do see clearly is that errors on fake-sceptic sites are rarely questioned by other fake sceptics; even when it’s clear that there are regulars on those sites who will see the error they just keep quiet. For instance I’ve noticed that when Anthony Watts posts questionable material on his site he often does not pass comment; he just posts it as ‘interesting’ and needing further analysis (‘going quiet’ seems to be a gaming tactic for Watts).
It therefore becomes clear that for most fake-sceptic sites their raison d’être is to obscure the facts and confuse the un-knowledgeable; so there anything goes. These are characteristics that will never be seen on the genuine—and truly sceptic—climate science sites, where questioning and jumping on errors is all part of the learning process for all the open-minded that go there.
If Goodman truly wanted to develop understanding of what’s happening in the Arctic, he’d have presented his post in the form of a question and welcomed feedback (especially when commenting on a science site like Real Climate, frequented by climate experts, always leaving yourself an opportunity to climb down is a great learning maxim). Instead Goodman’s approach is to burn his boats at the outset with the very climate scientists whose input he clearly desperately needs. Now, having backed himself into a corner speaking tactically, he’ll need to defend it like a cornered rat, or—taking a leaf out of the Watts book—he’ll just go quiet. He’ll need big balls to admit his errors.
“Convolution”
— by Horatio Algeranon
Convolution
Is con volition
Warming skeptic
Constitution
As Bolonius said in Hamlet, “Though this be cycle madness, yet there is method in it.”
High pass filter + low pass filter leaves only the bit in the middle. Nice one.
Both spectroscopy and electronic engineering use lots of convolutions, he should have spotted this.
He actually needs to do three things: the two you suggested, plus learn about the physical processes so he doesn’t keep fooling himself that he can approach the subject only from an index.
[i]The whole problem with the world is that fools and fanatics are always so certain of themselves, and wise people so full of doubts[/i]
http://www.prosebeforehos.com/quote-of-the-day/12/28/bertrand-russell-quote-fools-fanatics-wise-men/
Of course, some of us are foolish enough to use the wrong brackets in a blog comment and still full of doubt..
;-)
How about that. Bertrand Russell preempted some of Dunning and Kruger.
Perhaps it deserves to be renamed as the Russell-Dunning-Kruger Effect.
Thanks tamino. I have always been wary of the conclusions of the cyclomaniacs because they seem to be able to pull un physical cycles out of thin air. There always seem to be a large number of cycles, they seize on some which suit them and ignore other cycles of similar intensity.
This article gives me a better understanding how these cycles can be generated by simple noise in the system.
[Response: “Cyclomaniacs”? I’m adding that to my lingo.]
It doesn’t hurt that cyclomania is a real mental disorder.
Apparently, it’s some sort of “bipolar disorder’, which might explain the obsession with explaining polar ice behavior with cycles.
“Cyclomania”
— by Horatio Algeranon
Cyclomania
Truth distorter
Legerdemainia
Bipolar Disorder
Ever since Orssengo’s primary school level nonsense started at Deltoid I’ve thought of them as mortal siners…
Mortal siners?
I’d hate to take this thread off on a tangent, but I guess that those who repeatedly sign their name to (say) ludicrous op-eds in the WSJ, often without realising what’s in the op-ed let alone being able to engage in substantive discussion of the claims, are co-siners?
[ducks and runs for cover]
I like that first clause–in retrospect…
or cozeners . . .
No, not “or”: “are”.
Since we now know that the ideas purported by alchemy are invalid, and you can’t turned lead into gold, the New Alchemy has become looking for cycles in the climate data to prove it’s all natural, and nothing to do with us.
Maybe Greg could look at *all the relevant data* and ask himself a very simple question: how could a 5.4 year cycle in the sea ice area/extent account for us *losing 80% of the arctic ice volume* since just 1979? Typical fake skeptic tactic: when looking for the source of a pungent odour, concentrate on the squirrel in the room while ignoring the elephant.
Goodman does not make the claim, but the underlying theme of cycle-mania seems to be the idea that somehow cycles are responsible for the trends.
At least a multidecade (eg, 65-year) cycle has a chance of mimicking the trends (in ice loss and warming) we have seen over recent decades.
But a 5.4 year cycle? That would be very high level mathgicturbation indeed (especially if your procedure removes the trend to begin with!)
But maybe there’s a school for that.
If not, there’s always thecircus
A neo-Keplerian? Going in circles? Say it ain’t so!
Subtle put-downs and instructions about “how you really would be doing your science if you knew what you were doing” are often an indicator that somebody has wandered in over their heads without realizing it. Not always, but often. The key skill in internet discussions, I think, is zeroing in as quickly as possible on the likelihood of that being the case. Otherwise these folks will be more than happy to burn up your time with their arguments. They want attention in the end.
Most real signals have a wide spread of frequencies involved, with peaks scattered through the spectra. Cyclic behavior, such as the 1/year Tamino points out, displays higher energies at those particular frequencies.
However, given a Fourier spectra with any texture whatsoever (even from white noise), apply arbitrary bandpass filtering (as per Goodman, differencing followed by Gaussian), and you can emphasize whatever “cyclic” frequency you desire – simply by removing everything else, hiding the real behavior of the signal by discarding it.
Cherry-picking: the fallacy of suppressed or incomplete evidence. Goodmans comment is a horribly clear example.
In my article on sea surface temperature I did raise precisely the issue of derivative being a kind of high pass filter and why I used a guassian to remove noise. Thanks for the tip but I am aware of that.
Since this has got more attention than I expect I’ll have to write it up more fully.
Tamino’s frequency response plot shows that the frequencies that my filter lets through would be roughly 3 years to 30 years which, for a data set that is barely longer, does not seem unreasonable. Presenting it as a frequency plot with the scale he has chosen means the section covering 1 year to 2 year periods ( 1.0 to 0.5 on his scale ) fills half the graph and makes it look like I’m chopping out nearly everything which clearly I’m not.
[Response: The information content of a Fourier transform is evenly distributed in frequency space.]
I’m keeping 3 to 30 years and removing anything shorter than 2 years as weather ‘noise’. Doesn’t look like data fraud to me but does merit a full write up explaining the choices made.
[Response: Again you severely overestimate your understanding of what you’re doing.
You are not “keeping 3 to 30 years and removing anything shorter than 2 years as weather ‘noise’.” You are attenuating the response at every frequency. And since the spectral power is proportional to the square of the amplitude, it turns out that a 30-year period is reduced to only 10% of its actual signal power, and a 3-year period to only 16% of its signal power, relative to the least attenuated frequency. You have artificially deflated the response of everything not near the peak in the attenuation curve (at period 2pi for a 1-year Gaussian smooth).]
I’m not sure where the word “velocity” comes from in this context. I’m looking at rate of change of ice coverage since that seems to be a matter that a lot of people are concerned about.
[Response: The word “velocity” is nothing more than a convenient term for “rate of change.”]
Tamino agrees with me that looking at all the data is important. So there’s no controversy there. He has reworked my rate of change graph and got pretty much the same thing. So, I thank him again for his attention to the subject. Again we are in agreement.
So whether the 5.4 year cycle is meaningful or a case of “cyclomania” is a valid question worthy of consideration. What else can we see in this plot?
[Response: Of course whether or not the purported 5.4-year cycle is meaningful is a valid question worthy of consideration. Unfortunately, you haven’t studied the data correctly to answer it. I have. It isn’t.
What’s offensive is that you convinced yourself that climate scientists studying Arctic sea ice hadn’t considered any of this, hadn’t studied the data other than “one day in September”, and felt qualified to scold them about missing important “cyclic variations” which it turns out aren’t real.]
Well from 1997 to 2007 there was clearly an increasingly negative rate of change. In more common language there was a period of significant and accelerating melting. That would be cause for reasonable concern.
Now what we see since 2007 is a general return towards zero rate of change. ie the alarming acceleration of ice loss up to taht point had ended.
Note, this does not mean recovery of where ice was 30 years ago but it means ice coverage is stabilising.
Now that is not something that gets much press. So I’m sure an objective, processional climate scientist like Tamino will find that of interest.
[Response: It doesn’t get much press because it isn’t true.
I guess I’ll have to do yet another post on Arctic sea ice. Perhaps you’d like to go first, presenting your evidence that “ice coverage is stabilising”?
And by the way, I’m not a climate scientist.]
Greg Goodman – If your bandpass filter were even slightly different, you might emphasize (by filtering out everything else) a peak at 0.22, or 0.14, or 0.58/year, or just about anything else in the spectra.
If your results could be wildly different based on your filtering, they are not robust results, but rather the artifacts of your processing.
This is exactly the same error that sank McLean et al 2009 (http://www.auscsc.org.au/images/PDF/influenceofenso.pdf), where they claimed a link between ENSO and global warming. Their methods include both a smoothing and derivative – the end result being a bandpass filter. Foster et al 2010 (http://www.cgd.ucar.edu/staff/trenbert/trenberth.papers/2009JD012960.pdf) demonstrated that their entire set of results and conclusions were based upon their band-pass filter emphasizing 2-6 years, erroneously damping or removing everything else, including the long term trend.
I strongly suggest you read those two papers, and consider the mistakes McLean et al made. Frequency filtering can be tricky – it really pays to be aware of the effects of these operations, ensuring before applying filters that you are not throwing the baby out with the bathwater, inadvertently removing the actual signals.
—
That said – you really should consider the attitude with which you approach the discussion. Your comment at RealClimate, indicating shortsightedness on the part of everyone else, was over the top.
Thanks for the links to the papers, it seems Grant is essentially using the same criticism here.
This is exactly the same error ? No. I did not use crappy running mean filters that distort the data with negative lobes in its freq response. Neither did I use points separated by 12 months to calculate the differential.
[Response: But you did make exactly the same mistake. Diminish both low- and high-frequency response, then declare the mid-frequency behavior to be meaningful.
And for your information, I’m not especially fond of running-mean filters but they do have their uses. Your characterizing them as “crappy” sounds a bit like someone trying too hard to avoid facing his own mistakes.]
Greg Goodman – A bandpass filter is just that – reducing both high and low frequencies, emphasizing those in the pass region. That’s the effect of your derivative/smoothing filter.
It doesn’t matter what the exact form of the bandpass filter is – all that changes is which portions of the spectrum you are emphasizing, which you are dropping. If you are tossing the strongest parts of the signal, you are (inadvertently, I hope) making a mistake – that was McLeans mistake, and you are doing much the same.
Tamino has examined the full spectra above, along with a significance estimation. Your bandpass filter highlights a portion of the spectrum that fails to meet significance criteria. And even a slight change in your filter would highlight a different miniscule and insignificant frequency. I completely agree with Taminos analysis; your filtering has damped and discarded the highest energy, significant portions of the signal, among them decadal trends.
Meaning your results are far more a function of your methods than the underlying characteristics of the data.
“Note, this does not mean recovery of where ice was 30 years ago but it means ice coverage is stabilising.” Did Goodman really write that?
The raw data may be worth a look to see what all the fuss is about.
Here it is, abet in a monthly form. The red trace is the rolling annual average. The pink is the averaged derivative of that trace. Any sign of a 5.42y cycle? Any sign of the ice coverage stabilising?
As cyclomania is a real psychiatric diagnosis, perhaps it’d be more specific to adopt the very recently suggested term
Epicyclomania
Given the ice context, maybe “Icycle-mania” would work too.
or just “icyclomania”
That fits – the afflicted often tend to go to epic lengths to defend their beliefs…
Do I get any credit for the term?
Just out of interest: there are already signs that Arctic sea ice is cracking up, several weeks before the melt starts. Do look out for a new record in 2013? http://www.sierraclub.ca/en/blog/paul-beckwith/bad-news-arctic-icecap-cracking
[Response: It doesn’t get much press because it isn’t true.
I guess I’ll have to do yet another post on Arctic sea ice. Perhaps you’d like to go first, presenting your evidence that “ice coverage is stabilising”?]
Well it may save both of us some time if you can explain why you disagree with what I said so far in that respect (leaving aside the presence or not of any cycles). A rate of change of zero means no change, neither loss nor gain of ice. Your reworking of my graph runs closer to the end of the data and shows even more clearly than mine that rate of change is approaching zero.
I’m not inferring the future or making predictions but it is currently approaching zero. The maximum rate of loss was around 2007. Since then there was a brief period of recovery (positive rate of change, ie ice gain) and a lesser and diminishing rate of loss.
So do you disagree with either of my observations:
1) the magnitude of rate of change of ice area is currently diminishing.
2) the acceleration in the loss of ice seen between 1997 and 2007 has ended and we are now seeing deceleration of ice loss.
[And by the way, I’m not a climate scientist.]
What is your area of expertise? There does not seem to be any information about you here.
[Response: Does this mean that the Gaussian-filtered derivative-filtered data is your entire case for “ice coverage is stabilising”?]
http://journals.ametsoc.org/doi/abs/10.1175/1520-0485(1980)010%3C2100%3ASDAOPS%3E2.0.CO%3B2
The anomalies can be described by stochastic forcing. One should repeat this filtering exercise with a random Markov process as a null model to test the significance…
Tamino, as an author on at least one peer reviewed paper on climate, you qualify as a “climate scientist”.
[Response: I disagree. I’m hardly qualified to tell the real experts what they’ve been missing, although I feel free to suggest ideas.]
Greg, you should try your procedure on artificial data consisting of a linear trend plus noise. As Tamino has pointed out before, this is a very easy way to sidestep complex questions of statistical significance.
[Response: But not white noise.]
> Response: I disagree.
Yep. Being confident to work with climate scientists in a multidisciplinary setting is not the same as being one myself. For me, the more I consort with climatologists, the more I grasp the vastness of what I still have to learn….
OK, I tried it : start with gaussian noise, take differences, apply gaussian smoothing. Result : I discovered cycles.
Clearly, in 5 minutes of work, I’ve uncovered a fundamental flaw in the random number generator written by those dolts who created Matlab. What other explanation could there be ?
Humour :-)
Tamino: [Response: Does this mean that the Gaussian-filtered derivative-filtered data is your entire case for “ice coverage is stabilising”?]
Does that mean you are avoiding answering?
I have noted that we agree on certain points which is a good start. I’m trying to see where we differ on reading the rate of change plot that we both have produced to be essentially the same. I’ll ask my two simple questions again. I’ll hope you’ll be able to give a simple, clear reply.
So do you disagree with either of my observations:
1) the magnitude of rate of change of ice area is currently diminishing.
2) the acceleration in the loss of ice seen between 1997 and 2007 has ended and we are now seeing deceleration of ice loss.
[Response: I disagree with both “observations.”
Is the Gaussian-filtered derivative-filtered data your entire case for “ice coverage is stabilising”? A simple “yes” or “no” is appropriate.]
Greg Goodman,
Unfortunately, you are ignoring–among many other things–physics. Of course ice “recovers” in the arctic in the Winter. It’s fricking freezing in the winter in the Arctic. Ice freezes when it is freezing! So an annual average of coverage is not meaningful. If you were looking at VOLUME, and saw something, you might have something. I’m betting you’ll see more or less monotonic decline.
Then, too, 2007 was an exceptionally large year of melt–of course there had to be some recovery after it–all you’ve done is apply the cherry-picking the denialists do for temperature in the realm of ice. Congratulations on opening new frontiers in denial.
Ah, you’ve got there bud. I have to admit that I deliberately cherry-picked ALL the available data from the most detailed daily dataset I could find.
If I was to be honest about it , I clearly would have picked all the data that did not exist and included that as well.
My bad.
[Response: What you cherry-picked is “since 2007.”
If you have anything to back up your claim other than the graph you’ve shown, let’s see what ya got. You’ve got a blog, so post about it. Then I’ll be happy to respond. Let us know how long it’ll take you.]
Sorry. the climate cherry picked that one. I’ve shown all the available data and made an observation about an obvious difference in pattern during the period 1997-2007.
Others can judge whether I’m seeing flying pigs by looking for themselves.
[Response: No, we’re not gonna play back-and-forth games. You have three options:
1. If you have further evidence that “ice coverage is stabilising,” show it.
2. If you don’t, say so.
3. Go away and leave the adults alone.]
The Dunning-Kruger is strong in this one.
No.
BTW this is not “derivative-filtered data”, I understand your criticism of the MFC paper that was linked by someone above. They were comparing two different data sets and it could be said that they were using (probably unintentionally) the derivative as a filter.
That is not what I am doing here. I am studying the rate of change directly.
Climate forcings are power terms. They do cause neither temperature nor ice. They cause a rate of change of those physical quantities.
Now, could you say _why_ you disagree with my points which would seem to an obvious and uncontroversial reading of the plot that you were able to reproduce.
[Response: Setting aside your misunderstanding of climate forcing, temperature response, and what you did with the data …
You are the one who made the claim that “ice coverage is stabilising.” It’s your responsibility to back it up. Rather than refute what you’ve shown only to have you show something else for me to refute, etc. etc. ad infinitum, the onus is on you to put your cards on the table.
If you have anything to back up that claim other than the graph you’ve shown, let’s see what ya got. You’ve got a blog, so post about it. Then I’ll be happy to respond. Let us know how long it’ll take you.]
Are you saying taking the first difference is not a good approximation to the rate of change?
Or that the 6 month or 12 month gaussian filter is making the data bend to wards zero when really it is doing something else?
Tamino: “It’s your responsibility to back it up. Rather than refute what you’ve shown only to have you show something else for me to refute, etc. etc. ad infinitum, the onus is on you to put your cards on the table.”
At this stage you seem to be spending more effort avoiding the question that it would take to answer it, so I guess we are not going to get any further in meaningful discussion.
Thanks for your comments and criticisms and for taking the time to reproduce my graph.
[Response: The one who has consistently and repeatedly avoided the question “What other evidence do you have?” is most certainly you.
It looks like you don’t have anything else at all to back up your claim, just the graph you produced (and the analysis behind it), but when your bluff is called you run and hide.
If you have more evidence, produce it. If you don’t, say so. Either way I’ll respond, and as is usual when I directly address others’ claims you’ll have full right of uncensored reply.
If, however, you lack the courage to show your evidence, then we’ll all know exactly how reliable your opinion is.]
…and it gets closer to “all” with each additional comment.
Statements like “a brief period of recovery (positive rate of change, ie ice gain) ” [after the huge loss in 2007] are really WUWT caliber (certainly worthy of an invitation, if one has not already been offered)
http://arctic-roos.org/observations/satellite-data/sea-ice/total-icearea-from-1978-2007
http://smg.beta.photobucket.com/user/Chiloe/media/Climate/2011_sea_ice_PIOMAS_min.png.html
Yes, clearly stabilizing.
Not!
Another example of fake skeptics confusing themselves by calculating the derivative. Jeesh.
It’s remarkable how that statement can be both true and false at the same time.
A question, perhaps answered in your next book;
In what circumstances would it be easier to spot a (real) cycle via transformed data rather than directly?
[Response: There aren’t many. In fact, transformations are very likely to lead to you spot “cycles” that aren’t real.
But — if the transformation improved the behavior of the noise, then it would help identify cyclic behavior. If for instance the data are heteroskedastic then a transformation (e.g., the “Box-Cox” transform, a.k.a. “power transform”) might help a lot, by making the noise stationary.]
There is a big impact from the Duning Kruger effect here it seems. The people who doubt the least are the most confident. This bugs me too.
I appreciate leaning a bit of math and having a laugh from reading your blog. Keep it up! Lets hope we can figure put this whole humanity thing before we run out of atmosphere or oil or both.
Glad to see Greg Goodman get spanked. He got a bit of a swelled head when he had some success beating up Vaughan Pratt over at Climate Etc.
The detrenders are very dangerous when it comes to signal processing. A largely monotonic trend will always generates a 1/f^2 profile in the power spectral density. That’s the important part, yet what GG tries to eliminate.
Greg, if you’re still reading, I have to agree with Tamino about the hubris. As if your remark on RealClimate about the scientists not digging deeply enough wasn’t bad enough, the very first thing you say here is “I won’t even attempt to discuss on this site, because the editorial policy makes that an impossibly sensored , one sided process.” Talk about poisoning the well! Hubris.
And then you play this silly game of offering a tidbit but refusing to engage in replying to Tamino’s very reasonable questions. And when others present you with data or analyses which point to flaws in your analysis–putting their cards on the table–you more or less ignore them and huff off with a petulant “At this stage you seem to be spending more effort avoiding the question that it would take to answer it, so I guess we are not going to get any further in meaningful discussion.” Well!
Hubris.
You’re coming across as a bit of an immature, attention-seeking fool, Greg.
[edit]
Tamino [Response: The one who has consistently and repeatedly avoided the question “What other evidence do you have?” is most certainly you.]
Since you are going to go through it with a fine toothed comb (which will be useful), anything I present needs careful explanation and checking before making it public, that will not be done in half an hour or blogged tomorrow.
[Response: Here’s my guess: ya got nothin’ else but you won’t admit it …]
However, that does not prevent you from commenting directly to simple questions about the rate of change plot that we both produced.
[Response: … and you’re genuinely scared since you already got pwned once — so you want me to help you …]
Are you saying taking the first difference is not a good approximation to the rate of change?
Or that the 6 month or 12 month gaussian filter is making the data bend to wards zero when really it is doing something else?
[Response: … because you haven’t got a clue.]
Greg Goodman has actually withdrawn (or more correctly ‘put aside’) his 5.42 year cycle. His present gripe is that we are ignoring what his marvelous graph shows (and don’t forget to ignore the 5.42 year cycle trace). That Tamino has reproduced the graph shows it is a fair representation of the rate of change of SIA. The graph shows “stabalisation” as plain as the nose on your face.
What is this “stabalisation”?. Goodman tells us he observes “1) the magnitude of rate of change of ice area is currently diminishing. 2) the acceleration in the loss of ice seen between 1997 and 2007 has ended and we are now seeing deceleration of ice loss.” and ask for confirmation that we also see it. Are we blind or something?
However these observations need translating for those of us who consider a seasonal ice-free Arctic as inevitable. What we observe is 1) The end of the red Tamino line is negative but it is pointing quite steeply upwards towards zero. 2) 2007 still stands as the year with greatest rate of ice loss and that means there has since been a slower rate of ice loss than there was in 2007.
The problem with saying “Yep. Can’t argue with that.” is Goodman conflates these observations with seeing “the alarming acceleration of ice loss up to taht point (ie 2007) had ended,” that the data suggests “a lesser and diminishing rate of loss,” allowing the conclusion that there is “since 2007 a general return towards zero rate of change” with the most recent data showing “even more clearly … that rate of change is approaching zero,” where a “rate of change of zero means no change, neither loss nor gain of ice.”
Goodman says “I’m not inferring the future or making predictions” but he obviously is. And why not? Do I not predict a future ice-free summer Arctic? The difference is of course that Goodman bases his predictions on denial of the science. In his book, cherry-picking a data-set to show flying pigs is the be-all and end-all of it.
My memory of time series analysis is that before calculating the serial correlation profile for a time series one needs to ensure it is stationary, usually by some kind of differencing. Am I wrong, or is Willis Eschenbach in this post (low down in comments) calculating an AR(1) parameter of 0.75 of undifferenced data? Maybe I misunderstand R code (I’ve never done TSA in R) but specifying the seasonal and AR structure through the c(1,0,1) option isn’t enough, is it? Willis needs to difference the data first, then estimate the auto-regression? Is it really the case, as Willis claims, that sea surface temperatures regularly show an autoregression value of 0.95?
[edit]
[Response: Put up or shut up.]
I’m trying to be charitable here. OK, someone who isn’t very experienced with data dives in to analyze it. That’s fine…even admirable. They find something that seems important and get excited. Now, if they had any sort of understanding how science works, they’d take it and maybe show it to someone with a little more experience, who would school them. However, maybe Greg is an utter neophyte. He moves immediately to trumpet his discovery with a bit of snark toward those silly scientists who are getting so fired up about Summer ice loss.
However, even after being repeatedly “schooled”, he doesn’t see how utterly wrong-headed his analysis is. He doesn’t see the cherrypick. He doesn’t look at the physics–that, yes the world is warming, but the north pole in winter is still cold enough that water will freeze. He doesn’t stop to think how thick the ice might be. He doesn’t think…period. The learning curve does not have a positive slope.
How do you avoid the conclusion that Greg just ain’t that bright?
Response: Here’s my guess: ya got nothin’ else but you won’t admit it …]
[Response: … and you’re genuinely scared since you already got pwned once — so you want me to help you …]
Someone with experience in signal processing and apparently strongly motivated to dismiss what what I’m doing would be “helpful” in the sense of aggressively checking what I’m doing. I certainly don’t expect any more help than that from you.
You have reproduced my rate of change graph, so that was useful.
[Response: … because you haven’t got a clue.]
So yet again, lots of bluster, guessing and gesticulating to avoid commenting on rate of change.
So far you have not got further than “I disagree” and “you haven’t got a clue”
Not very convincing arguments.
1) the magnitude of rate of change of ice area is currently diminishing.
2) the acceleration in the loss of ice seen between 1997 and 2007 has ended and we are now seeing deceleration of ice loss.
Now that would seem to be pretty incontrovertible.
So what is your problem with explaining why you disagree. “Here’s my guess: ” the data shows something you do not wish to recognise ?
[Response: When asked whether the graph you showed, and the analysis behind it, was your entire case for “ice coverage is stabilising,” you said “No.” So I said OK, show us what you’ve got. Since you’ve made a startling claim, it’s hardly unreasonable to require you to show your evidence. Post it on your blog in excruciating detail. Take all the time you need.
But you won’t.
If you actually don’t have further evidence, admit it. Then I’ll be happy to respond. In detail.
But I am not gonna play your “show me where I’m wrong while I pretend to have more evidence that I won’t reveal” game, just so you can continue to argue after you get pwned again. Put up or shut up. Otherwise, stop pestering the adults.]
Yes and according to your analysis that deceleration is only due to a 5.4 year cycle and since it’s due to a cycle, it is only temporary and the long term rate will continue. How does that mean “ice coverage is stabilising”?
Greg Goodman,
Do you agree with me that:-
1) The end of the red Tamino line is negative but it is pointing quite steeply upwards towards zero.
2) 2007 still stands as the year with greatest rate of ice loss and that means there has since been a slower rate of ice loss than there was in 2007?
And if you do, is there anything substantially different between my 1) & 2) and what you are trying to say in your 1) & 2)?
[edit]
[Response: Put up or shut up.]
The idea that the times of “zero rate of change” shown on Goodman’s graph somehow represent “stability” (and that parts of the graph approaching zero rate indicate that ice is “stabilizing”) is just bizarre.
‘Stability” implies that there is no further change (or at least that such change is small and there is a tendency to remain small), but anyone can see that at every point on the graph where the rate was “zero”, it was zero only very briefly, merely “passing through zero” (ie, still changing).
That’s not “stability”, at least not under any normal definition of the term (certainly not under any scientific or engineering definition)
It’s a bit like saying when you are at the top of a very steep hill on a roller coaster, the position of your car is “stabilizing” (approaching “stability”) because it’s speed is approaching zero (imagine that the car slows almost to a stop before it goes over the “plunge of death”. Pretty “stable”, huh?)
But let’s look on the bright side: when ice finally reaches zero cover in late summer, it will have “stabilized” (provided the amount of new ice formed each winter is about the same and that ice does not keep diminishing into winter due to further warming)
Greg, here’s the thing. You are more knowledgeable than I about the nuts and bolts of analysis. But you are missing the forest for the trees.
Because (as Ray says) ice still forms in the winter, the annual cycle amplitude is increasing. That means that the positive rate of change in the freezing season goes up.
But ice is still declining for all seasons, and if you break that down, you won’t find much evidence of a decrease in rates of decline:
Don’t know if that image will embed or not…
But 7 months of the last year’s data were below their trend lines, and by eyeball, the magnitude of the negative monthly anomalies exceeds the magnitude of the positive ones.
NOT what stabilization of ice loss rates looks like! FWIW, I suspect the problem is likely to be a combination of your analysis conflating seasonal cycle with trend rates, combined with the details of recent variability. (I think Tamino could probably tell us both quite a bit about appropriate ways of significance testing you loss rate graph.)
But as I say, I’m not very knowledgable about TSA.
Image link, in case embed didn’t work:
Well I think it must be pretty obvious to everyone that you can’t say why you disagree you are just refusing to acknowledge what the data shows. Resorting to using editorial control just underlines it.
[Response: It’s obvious to everyone that you’re not interested in acknowledging, or learning from, your mistakes.
I planned all along to show the reason that your interpretation of “what the data shows” is wrong. I simply refuse to get into a never-ending argument with you, so I insisted that you put your cards on the table. Since either you’re lying about having further evidence, or are too cowardly to reveal it, when I do show the error of your ways your right to uncensored reply is forfeit.]
However, this probably established an all time record of your tolerating someone else’s comments and actually discussing something on Open Mind , so at least something was achieved.
I always say if a proposition has merit it will withstand or be improved by criticism. So your comments on the frequency analysis are useful. I will rework it to address those issues.
Not having to divert time to what has become a fruitless non-discussion here will let me get on with the job.
BTW it’s not a bluff, there is more, but since your mind is closed you probably won’t be ‘able’ to see that either.
I don’t expect this to be published , it’s a personal note.
Climate is changing all the time. Be careful not to be in denial when those changes don’t fit your expectations.
Take care now. ;)
Greg,
I am begging with you to listen to reason. Independent of all the errors you are making in interpreting the FTs, what you are looking at is NOT relevant. Consider the physics. The ice could completely melt away in summer–an ice-free Arctic–and as long as it refroze by November and remained so through April, you’d still be left with limited decline year on year.
Couple this with the fact that 2007 was a year of huge melt, and of course you had to see “recovery”. You’ll see the same thing with 2012.
If you want to perform a relevant analysis, look at ice volume rather than coverage or area.
Footnoting previously posted link for those who didn’t bother to click it, that attributes Epicyclomania to Edim
Even if there is a significant 5.4 year cycle, I can’t imagine how that means we can ignore the long term downward trend. You need a very strong capacity for self-delusion to think that it makes a difference.
Not only capacity but a strong need for at least distraction from unfolding reality. Something to get them through another NH summer to where they can point to a record rate of re-freeze for comfort.
It must be awful to view the approach of summer with dread, but I guess that’s likely to get a lot more common in coming years.
Chris O’Neill
I think the 5.42y cycle was (may be even still is) important in the mind of Greg Goodman because he sees his discovery of such a cycle as providing a stick to poke at those laggards climatologists who for all these years would have failed to notice it.
The annual average SIE/SIA is not a smooth curve, explainable by winter freeziness & summer meltiness rather than magical cycles, or magic oscillations for that matter.
Perhaps whatever “more” it is that Greg Goodman has hidden up his sleeve will prove less illusory for him than what he has given here. Even after putting aside his magical cycle, his analytical skills did appear to need a lot of attention.
“1) the magnitude of rate of change of ice area is currently diminishing.
2) the acceleration in the loss of ice seen between 1997 and 2007 has ended and we are now seeing deceleration of ice loss.
Now that would seem to be pretty incontrovertible.”
Call me a contrarian, but that would seem to be entirely controvertible! Both statements are both wrong and irrelevant. Of course, this is why I tried to ask him what he was actually trying to say, as opposed to what he actually said.
Still, now he’s gone, we will never know what he was actually trying to say. And does anybody still care that what he said was entirely controvertible?
It seems to me that the “easy” ice will go first (a fair amount in 2005, even more in 2007) so a reduction in the rate of loss more recently is only to be expected, is it not? When there’s no ice left the rate of loss will be zero, and a dead patient is in a stable condition. At that point Goodman will presumably claim vindication.
Statistics is a fine thing (and I’ve learnt a tremendous amount on the subject from this excellent blog) but not terribly useful in isolation from the physical realities involved.
Ah. You mean like what McIntyre does? Using ‘red’ noise that is overly-persistent, and doesn’t resemble anything found in nature?
Sorry, forgot to include supporting linkies:
The Wegman report sees red (noise) [deepclimate.org]
How Red are my Proxies?[realclimate.org]
Looking for correlations in the rate of change of something as a way of distracting attention from the change itself has become a classic trick for the skeptics. It is (as Tamino) pointed out, the mean value of the rate of change that gives rise to the long term trend, so an oscillation in the rate of change tells you essentially nothing about the long term trend whatsoever, and hence is no basis for claims about whether ice extent has stabilised.
Now if Greg really does think sea ice extent has stabilised, then perhaps he should make a testable prediction of this, such as a prediction for NSIDC September minimum sea ice extent (with error bars)? This is something scientists do (and sometimes statisticians as well)
If the Arctic ever goes completely ice free, the rate of change from year to year will be zero.
Perhaps Mr Goodman would be so kind as to back up his useful (?) work by making a clear, and clearly falsifiable, prediction about future Arctic sea ice. And no, saying that whatever he has discovered (?) will continue wouldn’t count.
Click to access esd-3-173-2012.pdf
“We use statistical methods for nonstationary time
series to test the anthropogenic interpretation of global
warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century. Specifically, the methodology of
polynomial cointegration is used to test AGW since during the observation period (1880–2007) global temperature
and solar irradiance are stationary in 1st differences, whereas
greenhouse gas and aerosol forcings are stationary in 2nd differences.”
Does this make sense? It seems to me that they have no idea of the physical reality.
[Response: No. It’s senseless.]
Thanks.