Sometimes we hear that science is "self-correcting". To be "self-correcting", however, individual people have to step up to the plate now and then and actual do the work. To the extent that the term "science" includes the work of Mann et al., then analysis of MBH98 Figure 7 , which was actually the culmination of MBH98, is part of the "self-correcting" process. For all the sniping against blogs, we’ve seen a nice use of blogs over the past few days in exposing MBH98 Figure 7.
Chefen put the issue on the table, pointing out that the partial correlation coefficients simply didn’t tie together. I brought this to the attention of readers here. Jean S was able to decode Mann-speak and derive a graph that matched Mann’s (which I’ve now also been able to replicate.) Our replicating the Mann figure doesn’t mean that Mann was "right" and Chefen was "wrong" to point out the discrepancy. The difference identified by Chefen pointed to something potentially unstable in the results. Mann said that his results were "robust" – one of his favorite words" to different choices of window length (he used a 200-year window in the illustration), specifically mentioning that the conclusions were robust to a 100-year window. So Jean S ran the results for a 100-year window. I’ve replicated these results. Jean S’s script is here; mine is here.
It is inconceivable to me that any person could describe what you are about to see as "robust". For example, were a Nature referee presented with the 100 year graphs and asked to endorse the claim of "robustness", I do not believe that the claim would be accepted. But decide for yourselves.
Here’s how Mann described the construction of Figure 7:
We estimate the response of the climate to the three forcings based on an evolving multivariate regression method (Fig. 7). This time-dependent correlation approach generalizes on previous studies of (fixed) correlations between long-term Northern Hemisphere temperature records and possible forcing agents lLean et al 1995; Crowley and Kim, 1996]. Normalized regression (that is, correlation) coefficients r are simultaneously estimated between each of the three forcing series and the NH series from 1610 to 1995 in a 200-year moving window. The first calculated value centred at 1710 is based on data from 1610 to 1809, and the last value, centred at 1895, is based on data from 1796 to 1995″¢’¬?that is, the most recent 200 years. A window width of 200 yr was chosen to ensure that any given window contains enough samples to provide good signal-to-noise ratios in correlation estimates. Nonetheless, all of the important conclusions drawn below are robust to choosing other reasonable (for example, 100-year) window widths.
First, here is Jean S’s replication of MBH98 Figure 7.
Figure 1 : Jean S: solid – emulation; dash-dot lines from MBH98. Blue: CO2, green: solar, red: volcanic. There is no moving averages (smoothing) used here. Jean S: "Those are simply partial correlation coefficients in moving windows plotted such that the year corresponds to center of the window." SM – I think that Jean S and I are using "partial correlation coefficient" in different ways. Since our replication graphs are the same, underneath the algebra and terminology, we’re doing the same thing. I’ve haven’t tried to reconcile the terminology yet.
Now here is my version of the same thing expressed a little differently. Here I’ve shown in black – MBH98; blue – the regression coefficients from normalized multiple regression – Jean S’s partial coefficients; red – "partial correlation coefficients" a la Chefen. Like Jean S, I’ve obviously replicated the archived reconstruction. An interesting point here – I’ve simply used CO2 values without logging. I think that the CO2 curve is so smooth that logging must not make any difference. The blue version overprints the black version – so if you can’t tell the difference, it’s because the replication is exact.
200-year window
Figure 2. SM Emulation. Black – MBH98; blue – emulation using regression coefficients from normalized multiple regression – renormalized in each window; red – partial correlation coefficients.
100 Year Window
Remember Mann’s claim quoted above: "all of the important conclusions drawn below are robust to choosing other reasonable (for example, 100-year) window widths." Let’s look at the results using a 100-year window. First here is Jean S’s version/
Figure 3. Jean S – 100 year window, as Figure 1 above.
Now here is my version, arriving at virtually identical results as Jean S, again expressed a little differently.
Black- MBH98 archived; red – partial correlation coefficients; blue- OLS regression coefficients from regression of scaled series. 100 -year window for latter two.
I hardly need editorialize about some of the key points. Observe that the solar coefficient for some reason goes to negative relationships in the 19th century and then increases dramatically in the 20th century with values exceeding that of the CO2 coefficient. Now let’s see the "conclusions" which are supposedly "robust" to the use of 100 year windows.
The first conclusion is the significance of the correlation coefficients. As an editorial aside, didn’t Mann tell us that calculating correlation coefficients would be a "silly and incorrect thing" to do. And didn’t Wahl and Ammann agree with that? Oh well. Mann:
We test the significance of the correlation coefficients (r) relative to a null hypothesis of random correlation arising from natural climate variability, taking into account the reduced degrees of freedom in the correlations owing to substantial trends and low frequency variability in the NH series. The reduced degrees of freedom are modelled in terms of first-order markovian “Åred noise’ correlation structure of the data series, described by the lag-one autocorrelation coefficient r during a 200-year window…For (positive) correlations with both CO2 and solar irradiance, the confidence levels are both approximately 0.24 (90%), 0.31 (95%), 0.41 (99%), while for the “Åwhiter’, relatively trendless, DVI index, the confidence levels for (negative) correlations are somewhat lower (-0.16, -0.20, -0.27 respectively). A one-sided significance test is used in each case because the physical nature of the forcing dictates a unique expected sign to the correlations (positive for CO2 and solar irradiance variations, negative for the DVI fluctuations).
The 200-year window has kept the solar coefficient in the positive range, while the 100-year window has the solar coefficient going from positive to negative. The volcanic coefficient is negative in the 200-year window, but its sign changes in the 100-year window. In fact, the sign of even the CO2 coefficient changes in both windows. I haven’t checked the correlation coefficients for significance yet. But my intuition is that the negative correlation coefficient for solar in the 19th century will prove "significant", which makes you wonder how realistic Mann’s significance testing us. Anyway on to the next conclusion:
The correlation statistics indicate highly significant detection of solar irradiance forcing in the NH series during the “ÅMaunder Minimum’ of solar activity from the mid-seventeenth to early eighteenth century which corresponds to an especially cold period. In turn, the steady increase in solar irradiance from the early nineteenth century through to the mid-twentieth century coincides with the general warming over the period, showing peak correlation during the mid-nineteenth century. The regression against solar irradiance indicates a sensitivity to changes in the “Åsolar constant’ of ,0.1 KW-1m-2, which is consistent with recent model based studies [42].
If you go back and look at the 200-year window, you see the rationalization for the bolded remark. There is a sort of local maximum to the solar regression coefficient in the mid-19th century. Now look at the 100-year window. The situation is exactly the opposite. You reach a maximum negative regression coefficient in the 19th century. What a crock. Going on:
Greenhouse forcing, on the other hand, shows no sign of significance until a large positive correlation sharply emerges as the moving window slides into the twentieth century. The partial correlation with CO2 indeed dominates over that of solar irradiance for the most recent 200-year interval, as increases in temperature and CO2 simultaneously accelerate through to the end of 1995, while solar irradiance levels off after the mid-twentieth century.
Using the 100-year window supposedly "robust", again, this is simply not true. You see increases in the regression coefficients of both solar and CO2 in the 20th century, with solar values actually out-stripping CO2 values. In these calculations, Mann has, by the way "grafted" the 1980-1995 instrumental record onto the proxy record up to 1980 and used the grafted values in calculation of the coefficients. Again, the reported conclusion is simply not true for the 100-year window. Next:
Explosive volcanism exhibits the expected marginally significant negative correlation with temperature during much of 1610–1995 period, most pronounced in the 200-year window centred near 1830 which includes the most explosive volcanic events.
Once again, going to a 100-year window, the conclusions don’t hold up. You get positive "correlations" at the beginning of the graph and again in the early 20th century. From this "analysis", Mann then concludes:
It is reasonable to infer that greenhouse-gas forcing is now the dominant external forcing of the climate system.
This is the analysis. I kid you not. Let’s suppose that a 3rd year student handed in this analysis – what grade would it get just as statistics? You probably wouldn’t fail a phys ed student in a state university who was taking a required statistics course, especially if he played on the basketball team. How about a Ph. D. student at an Ivy League university?
The other remarkable thing about this analysis is that this is so easy to do. In this case, Mann archived the data. Anyone – including me – could have done this analysis at any point in the past 6 years. It could have been done by our phys ed student mentioned above. One presumes that no one ever has or else the topic would have emerged before now. So score one for the blogs.
Climate Audit 
101 Comments
Very good. Congratulations from the cheerleaders. It piques one’s interest in other attribution studies and whether they have adequately dealt with colinearity. I suspect McKitrick, Kaufmann and others have done a much better job. Oh right, they are not on the right team.
A note about logging the CO2. If you do it, you’ll find that there is a very good linear relationship between CO2 and ln(CO2/CO2_ref), so you can use either with no problems in this analysis. The CO2 values are serendipitously such that it falls in a narrow enough region of the ln() to make it a good linear approximation.
Where can I download the archived Mann data?
Thanks
JK
If I understand some of the comments over the last five days, one discovery that struck me was that both the solar record as well as the CO2 record are highly correlated with the temperature record. It was also noted that solar and CO2 are correlated with each other.
There have been suggestions, especially from ice core data, that temperature changes predate changes in CO2. With regard to the solar and CO2 data, it could be that increased solar activity causes warming, which then releases more CO2 due to plant growth and warming oceans. Whatever the reason, if there is causality going from solar to temperature to CO2, then maybe all of the signal processessing and statistical expertise that is involved on this site could attempt to model the causation involved with these variables, say with the use of Granger causality methods. This might result in a model that is superior to the one used by Mann.
Don’t want to get into the rights or wrongs of Granger causality but these and other methods have been used by McKitrick, Kaufmann and others. There are a whole range of results using stochastic modeller that seem in a different camp to the CGCM modellers.
David (#4) I understand that Steve M. does not want to present an alternative reconstruction. But if there is a causal relationship between solar and CO2, then it would be good to demonstrate that fact, and causality analysis seems like the way to go, given the data that are available.
I did say “a model that is superior to Mann’s.” I agree that it need not be a “climate reconstruction.” When Mann says that CO2 is more highly correlated with temp than solar, he is not taking account of the interrelationship between solar and CO2. Analyzing that relationship is the sense in which I meant that the result would be “superior” to Mann.
#5. I don’t see how you could draw any conclusions from this data set. I was backtracking some discussion of solar-climate correlations prior to this issue arising and will post up some interesting comments from IPCC SAR. Needless to say, the issue has some history which is distinct from trying to “get rid of the MWP”,
“I don’t see how you could draw any conclusions from this data set.” That is also one of the implications of the analyses of MM, Gefen and David Stockwell. The “temperature” data derived by Mann is noise — a random walk with positive drift (the errors summed up have a positive mean). The correlations with CO2, solar etc are likely spurious, as Steve has emphasized repeatedly. It seems that every piece of analysis in MBH98 is a joke and a disgrace to the journal that published it. It is of course even more of a disgrace to the IPCC for touting it so shamelessly without any due diligence. It will be unbelievable if they do not disown the “Hockey stick” representation of temperature in the next IPCC report given the analysis that has been conducted in the meantime. Perhaps it would be good thing, however, if they “soldier on” in denial and the next report leaves them even more open to the ridicule they deserve.
Presumably the NAS Panel are aware of developments at this site and Chefen’s.
#9. I doubt it. Why don’t you write and tell them? They should hear from someone other than us.
Re: 8
Peter,
Based on what I read in the 2nd order draft of the 4th AR, the IPCC is still riding their hockey stick into the sunset.
Re 8. I beg to differ in some small respects. I think the random reconstruction that I think you are referring to, shows that the null hypothesis is hockey stick shaped. Thus only departures from this shape are significant, and the finding of an upright portion of the hockey stick shape per se is tautological. Not that it needs tree-ring data for support anyway. I haven’t done any tests to see if the other series diverge from the other aspects of the hockey stick null. There is no correlation with CO2 with temperature over the 1000 year span. As to solar, there are enough ups and downs in unison to be very significant. Even with LTP series it is likely not spurious. Thanks for the clarifying suggestions.
In the spliced reconstuction, the bristlecones lose their weight in the final portion, but there’s a direct correlation betwen bristlecone growth and CO2. I suspect that there’s a direct correlation between solar and some proxies as the Jacoby treeline proxies only show the “Jacoby signal” if they are south facing.
Very good analysis, but a friendly piece of advice, you may want to dial back the Mann-targetted rhetoric a little. He surely deserves lambasting, but if you target his science and let the stupidity of it all rub off on him implicitly, you will likely turn off less people from reading your posts. Those who are new to this blog may not know the history and may feel that some of your comments are a bit harsh. It’s not that you aren’t polite, but it’s still fairly obvious that you are peeved at Mann. I would be too. But the less you show it, the better for a neutral audience, I’m sure after showing them enough of the MBH98 idiocy they will come to the correct conclusion themselves.
Steve. There seems to be an error in your script.
Line 15 should be: dimnames(corrs)[[2]][1:3]
The link to Jean S’s script doesn’t seem to work.
Fixed the link and will edit the script.
Nicholas, you’re probably right about the tone. I write a lot of stuff straight to air and it tends to be more contentious. When I was writing business letters and wrote something that was fun and amusing, I made a point of waiting a day because I knew that anything amusing wouldn’t help whatever the situation was.
Aside from the misrepresentations, I think that there is a valid point in the triviality of the regression analysis. What he’s done is amultiple regression of temperature against 3 series, without any analysis of residuals or anything. It just seems so trivial and not a very good analysis – even if it were right. I think that there’s something along those liens that’s worth saying without appearing to pile on.
Steve:
What strikes me a lot recently is not only that many of these studies use such simplistic methods and make so many assumptions, but also that there seem to be a number of choices of ways to perform certain statistical analyses, and they don’t seem to explain the rationale they use for selecting which method.
Not only do I feel that they aren’t familiar enough with research which explains how do know which method is appropriate for which circumstance, I’m worried that they in fact try different methods and pick the one which gives them the outcome they are looking for (either subconsciously or consciously, I don’t know). Really, what’s to stop someone from trying different autocorrelation tests, or different correlation coefficient calculation methods with different window sizes, and not report the results, except for the one which has favourable results?
It’s very worrying and I think the answer really should be that the papers get a lot more scrutiny from experts such as yourself. I also think the scientists should be held to higher standards in the sense of explaining WHY they do certain calcuations, not just how they do it and what the results are.
But I guess the point of my previous comment is that, as the “underdog”, you will get more traction if you’re ultra-polite and ultra-neutral in terms of the politics, and just expose the scientific and mathematical flaws. You’ve certainly done a good job on the political neutrality front. If you can be as calm and authoritative as possible, you will be more likely to change peoples’ minds and get them to think that maybe scientists who disagree with you have human foibles too and could actually be wrong.
Steve, I’m having some trouble with the terminology:
1) I think I understand that that the black line (MBH) and blue line (emulation) are “regression coefficients from normalized multiple regression”. Mann states (or implies) that these are equivalent to “correlation coefficients”.
2 ) What then is the red line (described as “partial correlation coefficients a la Chefen”)?
re #19: 2) I think they are just normal correlation coefficients. At least I get similar graphs when doing that and I think that is pretty much what Chefen calculated. I think it is interesting here that Mann suddenly decides to use partial coefficients as for the level of maturity in the rest of paper, it would have been more fit to use just plain correlation coefficients. Maybe it has something to do with the shape of Solar-curve, maybe not 😉
Not only do I feel that they aren’t familiar enough with research which explains how do know which method is appropriate for which circumstance, I’m worried that they in fact try different methods and pick the one which gives them the outcome they are looking for (either subconsciously or consciously, I don’t know). Really, what’s to stop someone from trying different autocorrelation tests, or different correlation coefficient calculation methods with different window sizes, and not report the results, except for the one which has favourable results?
Exactly my words. However, in the case of MBH98, I am pretty certain that you can safely omit the sub-prefix question. The thing I would like to know is if this applies only to M, or if it applies also to B and H. If I were B or H, I would pretty soon make the decision if I will stand by the paper all the way to the bitter end or maybe take some distance and maybe save some of my reputation. And I’m not kidding here: during my professional career I’ve read hundreds of “bad” papers, but I have never seen a paper like this where one can not trust a single word. Everything in MBH98 seems to be different from what they appear to be in the first (or even tenth) reading.
MBH98 is truly a work of art, and I’m uncertain if I could come up something even remotely as good as that even if I tried. This topic is a prime example: after crafting a reconstruction they were looking for, they glorify it by matching it nicely to known forcings. To do that they need not only to select a method not used previously but also carefully select the window size. After that they write a smoke-screen by stating that this cherry picking is “robust” just to make sure that nobody would actually try it.
they don’t seem to explain the rationale they use for selecting which method
It seems like every time in MBH98 they DO explain something (like the window width), this is something one should really replicate and test. Especially if the word “robust” is used.
Jean S, There is evidence of crafting in many details, controversy about which preceded your interest.
For example, there was a discrepancy between the tree ring sites to have been used and the ones actually used. We noticed this in a small way in MM03 – 5 series said to have been used and not used were noted in that article. MM03 resulted in Mann making his private FTP directory on MBH98 public. It turned out that about 35 series said to have been used were not actually used, but of course this “didn’t matter”, whereas not using the bristlecones or downweighting the bristlecones was “throwing out data”. In connection with that, there was an odd email from Hughes to Mann preserved at Mann’s FTP site:
ftp://holocene.evsc.edu/pub/MBH98/TREE/VAGANOV/ORIG/malcolm_29-JUL-97
In our complaint to Nature, we noted that these “purposes” were not stated in the Methodological Description and asked what they were. Needless to say, we got a belligerent evasion.
The discrepancies were acknolwedged in the Corrigendum, but the explanation for the discrepancies provided in the Corrigendum was also false. I checked the excuse against original data and fonud the quality control tests said to account for the discrepancies did not explain them. Nature knew this but didn’t care. The Mann corrigendum was not externally peer reviewed and the new SI to the corrigendum was not neither peer reviewed nor even reviewed by Nature editors.
In passing, while I was doing the quality control for this check, I noticed that several Jacoby chronologies archived at WDCP did not match the measurement data. I notified D’Arrigo of this, who said that she would correct the chronologies, but they remain uncorrected 2 years later.
You should re-read some of my correspondence with Jacoby. Their northern treeline composite resulted from the selection of the 10 “most temperature sensitive” sites from 36 collected. He only archived these 10. He refused to provide the other 10. The autocorrelation in Jacoby series is huge. If you pick 10 of 36 series from similarly autocorrelated red noise, you get a HS and the Jacoby NH reconstruction is pretty well median. I was going to srite that up in a paper, but got distracted by other interesting issues. The excuses were fun. Look at the Jacoby category and the early posts. I got a communication from a field worker who said that field workers were very conscious of the need to find the “Jacoby signal” and even joked about it.
malcolm_29-JUL-97
Dear Steve,
We often hear or read that there is a consensus among
“scientists” that the earth is warming due to human
activity. Yet nowhere do I recall any evidence being
presented of this alleged consensus; in fact, the few
polls of scientists I have seen on this topic suggest
to me that the so-called skeptics are in the majority.
I am a statistician and this irks me a great deal. In
my world, you can’t believe something just because you
feel like it.
Best regards,
Kevin Gray
Re #23, you could try counting the number of contributors to the various IPCC reports – but that’s a number you wouldn’t like?
#24: Peter, would you care to comment also the very topic of this post? I’d like to hear your view on this latest turn and if it affects anyway on your view on MBH98.
I’m also curious about Tim Lambert’s efforts in replication/comments. Why not even Carl’s (maybe I learn a few new words) 🙂
Re #25, yup, it’s just another personnalised swipe at MBH 98.
I’m, clearly, pretty interested in all this climate stuff and
the spectacle of people falling over themselves to slag off certainly climatologistsauditing, but it’s certainly getting tedious and repetitive.#26 (Peter H): Aha, so if I (for example) replicate MBH98’s analysis and say that it is not what they claim, this is your opinion an example of a “personnalised swipe”? Are you also saying that the “Attribution of climate forcings”-part of MBH98 is perfectly OK and scientificly sound?
Jean, I’m saying what I’m saying, read the comments (this for instance, from #21, is not exactly complimentary and has to be wrong “but I have never seen a paper like this where one can not trust a single word.”) and don’t put words in my mouth. Note it’s allways ‘Mann’, note Nicholas’s words. Finally, please point me to a perfect science paper.
Peter, #26. If you are really interested in ‘this climate stuff’, how about forgetting personalities pro or against and address the science?
‘tedious and repetitive’ just suggests that you are going to ignore any analysis of MBH98 because its raising uncomfortable facts and its easier to shout loudly to obscure the issue.
The analyses here seem to me to clearly show that the methodology and data analysis techniques employed in MBH98 are wrong and the conclusions derived from those analyses in that paper cannot be sustained. Do you agree with the analysis done at the start of this thread or not?
If not, why not? please discuss your reasoning as to where Steve’s analysis is in error. If you present that, I and maybe others will perhaps agree with you if we look dispassionately at the rigor of the analysis but at the moment it looks to me like MBH98 is fatally flawed, not because I am prejudiced against Michael Mann (I wouldn’t know him from Adam), but because an analysis of his published work shows up serious procedural, mathematical, statistical and methodological problems that, I agree, invalidate the conclusions those authors came to in their paper. If we could all confine this to the scientific questions, perhaps there would be a little more light and a lot less smoke.
#28 (Peter H): Since you asked it, IMHO, this is damn close.
Peter you are aware that Dr. Lindzen was a lead author are you not? Your assumption that the contributors to the IPCC reports implies they support “the consensus” is silly.
Re #29, yes indeed, which part of the IPCC TAR do you want to start with?
Tedious and repetitive is my opinion. I think it’s getting tedious and repetitive – this place has been banging on about ONE paper for what is now YEARS!
Nothing here raises uncomfortable issues. None of us are going to go back in time, so it’s allways going to be an uncertain science. I take the view that nothing I’ve seen here or eleswhere convinces me that the view that the world has experience neither relatively very hot or cold conditions over the last few millenia is the right conclusion.
People here say the data is noise or random or whatever. I think what that means is it’s not showing much of a warm or cold signal – again, that’s what I think as well. people can say they’ve proved the signals are noise, but until they go back and see that is not something they can prove – hence word like robust (this weeks word to mock I see) I guess. So, CA increasingly becomes a load of maths smoke – I must say the statistics get more and more complex with every passing week.
“If we could all confine this to the scientific questions, perhaps there would be a little more light and a lot less smoke.” indeed, then perhaps you ought to criticise nonsense like this “but I have never seen a paper [MBH98] like this where one can not trust a single word.” and not me?
Re #31, and yours that they don’t is?
nonsense like this “but I have never seen a paper [MBH98] like this where one can not trust a single word.”
Which part of my sentence is nonsense? I have seen hundreds (likely thousands) of science papers, both extremely good , extremely bad and usually something between. But never before I’ve encountered a published paper with so many differences in what is sad and done, in what is implied and what are the actual results, and top of that all simple mathematical things written lengthy with language and terminology no-one seems to be familiar with.
BTW, “robust” has a rather precise meaning in statistics, so MBH98 use of that word for describing things which has nothing to do with any understanding of the word is truly amusing wheather you get it or not.
No, no. not the IPCC TAR (how did I know you would counter with that?). This analysis is new, the IPCC TAR is now 5 years old. How can it address the NEW criticisms of MBH98 that are presented here that have arisen since the IPCC TAR? If you want to argue that the analysis done at the top of this thread is wrong then you need to work through it and show where the flaw in reasoning or logic occurs.
Do you agree or not that THIS analysis shows that MBH98 is flawed and the conclusions in it that were used to justify the conclusions of the IPCC TAR are therefore undermined? The IPCC TAR has nothing at all to say on THIS current analysis of the state of palaeo-reconstructions.
You say its just a load of maths smoke, what sort of argument is that?, is the maths valid or not? (I’m sorry Professor Einstein I can’t possibly understand what you say so it can’t possibly be correct). I say that the maths in this analysis looks valid to me and if I, Steve and others who agree with his analysis are correct, THEREFORE the conclusions of MBH98 are not valid and that has large implications for the conclusions of IPCC TAR.
On your point about criticising nonsense wherever it comes from, there is a whole lot of nonsense written on this site and other sites by contributors – along with an exceptionally high percentage of very rigorous and reasoned posts by Steve McIntyre. ‘Not trust a single word’ in MBH98 is absurd if taken to literal extreme but if what is meant is the methodology, the statistical analysis and conclusions are all found wanting and therefore can’t be trusted in that paper, then yes, I agree with that characterisation.
Peter, try to stay focused on what was said. In #23 Kevin pointed out that the “consensus” is not supported by any poll. You then assert that being a contributor to the IPCC reports implies that all the contributors support the “consensus”. I point out that a well known skeptic, and lead author who does not support the “consensus”, would be included in your count thus making it flawed. So Peter instead of admitting your leap of logic was flawed you respond with this straw man.
Looking at the graphs above and the means by which they were derived reminds me of basic variogram computation in geostatistics.
I wonder if there is a commonality?
Variograms basically determine at what sample spacing, here at what time span, a variable becomes statistically random. In geoscience it is a simple 2d problem, (exploration) and in mining a 3D more complex problem.
It’s simple to compute and Goldensoftware’s Surfer has a neat variogram generating routine.
I haven’t the time right now to do that but someone with some spare time (read incessant commentators) might be interested to do so.
If I remember, I’ll do it in July some-time when I get back from the drilling campaign.
(If the variogram range is 30 years, then that implies that temperatures are statistically random when time spans of greater than 30 years are considered. Time spans less than 30 years and the temperatures have high correlation with time, usually linear, and if non linear all bets are off).
Fun thing to do.
Oh there is one geoscience geostat. problem no one has been able to solve – predicting the diamond grade of beach diamond deposits. In the mining business we don’t bother doing a JORC code compliance because we can’t. It is impossible.
And so is predicting climate.
Anyone needing to comment get me fgserv7747 at fastmail.com.au
Well, I’m inclined to say that there is a “consensus” and that the majority of IPCC contributors firmly support the “consensus”. Politicians should be guided by such a consensus, but scientists should, in the mean time, be examining and cross-examining all the issues and assumptions.
A consensus per se does not make something true. Stock brokers and analysts are professional people who try to do a good job; there was a “consensus” that Enron was a good stock. In 2000, around the same time as IPCC TAR, Enron was voted the best managed company in the US and Andrewe Fastow the Financial Executive of the year.
It’s much easier for a market consensus to be wrong than a consensus of scientists. However many scientists weighing on these issues haven’t studied the details.
Let’s distinguish the quantum of AGW impact of climate from Hockey Team reconstructions if you don’t mind.
In addition to there being a “consensus” on AGW, there is, for example, a probable consensus among IPCC contributors that the Hockey Team view of climate history in the millennium is correct. Does that prove that the Hockey Team is right? Hardly. I question whether any of the IPCC contributors not directly involved have any real idea of the issues. The Hockey Team has been firmly esconced at the heart of IPCC since its beginning – Jones, Briffa, Bradley, etc. As someone hwo knows the ins and outs of these data, as well or better than any one else, including IPCC contributors, if the consensus view proved to be right, it would be almost accidental. The handling of the data doesn’t support reliance on the conclusion – although the conclusion might or might not be right.
Are the estimates of climate sensitivity to 2xCO2, including range, based on better analysis than Hockey Team analysis? I don’t know whether I hope that it is or hope that it isn’t. Doug Hoyt thinks that the estimates are grossly off. Doug may be wrong, but he’s not a fool, and, if he’s wrong, he’s not wrong in a trivial way. Same the other way. How many people have worried through every last inch of the calculations? A lot fewer than the “consensus”.
#37. Louis, I had ore reserve calculations in mind when I started at this. I’ve seen calculations where the area of influence of a high-grade hole was grossly inflated. The use of “cutting factors” in ore reserve calculations is an empirical form of making a “robust” statistic. I’ve lived to my sorrow through a project which fell well short of projected grades.
In one sense, the bristlecones are a “high grade” hole. Mann’s statistical method is, at the end of the day, the equivalent of someone coming up with an “advanced” statistical method to justify overweighting high-grade holes in an ore reserve calculation. This is a viewpoint which others won’t understand in their gut the way that you and I do.
Re 32: Peter, Peter:
“Tedious and repetitive is my opinion. I think it’s getting tedious and repetitive – this place has been banging on about ONE paper for what is now YEARS!”
That’s like OJ’s defence counsel saying “Your Honor, the prosecution goes on and on about this alleged double homicide”.
Then you say:
“People here say the data is noise or random or whatever. I think what that means is it’s not showing much of a warm or cold signal – again, that’s what I think as well. people can say they’ve proved the signals are noise, but until they go back and see that is not something they can prove – hence word like robust (this weeks word to mock I see) I guess. So, CA increasingly becomes a load of maths smoke – I must say the statistics get more and more complex with every passing week.”
Peter, I know you’re a farmer (and all praise to that), but the stats in relation to Fig 7 of MBH are elementary, first year stuff. As Steve remarked, it’s amazing no-one looked at it before.
I’m personally gobsmacked by this one. If I was analysing this data, the first thing I’d do was to look at the correlations of each the three forcings against the reconstructions. Having observed that both Solar and C02 forcings are highly correlated with my temp reconstruction (and inter-correlated to boot), I would be leery of asserting that my correlation coefficients from a multiple regression represent the contribution of the relative forcings to reconstructed (or instrumental) warming.
With Mann’s stats, I’ve always tended to the “incompetent” versus “mendacious” side, but this one makes me wonder.
Not only that…as late as Nov 8, 2001, 10 of the 15 analysts covering Enron still rated it as a “buy” or “strong buy,” even though the SEC probe was underway, Enron was releasing more and more bad news every week, bankruptcy was a few weeks away, and the stock value had dropped over 80% in less than 3 months.
#38
“cutting factors” ?
Jaysus, another term we need to get a handle on. There is no end to the imagination to deceive….
🙂
But your comment here is slightly out of thread
🙂
Here’s the thing that still gets me: Mann admitted that he was not a statistician, and if I recall correctly neither is Hughes or Bradley. That’s enough to make one concerned that the paper may have some flaws since it is basically a statistical analysis of existing data, however it is the use of novel techniques that really gets my attention. Normally before using a novel technique one publishes a formal proof of the technqiue so that other experts in the field can verify that it is valid. In this case a real statistician would be employed to write up and publish this proof. This has not been done in the case of MBH98 and all the subsequent supporting papers as well. Then they confound the issue by calling their novel techniques by the names of existing, and sometimes similar, well established ones.
Once you understand this basic problem with MBH98, it’s easy to see why it’s so flawed, as proven by Steve, Ross, Jean S., and others. And since MBH98 and it’s unproven novel techniques is the basic foundation for many other climate reconstructions, it makes one wonder if they are also fatally flawed. Especially if you consider that Mann, Bradley, and Hughes are individually authors or coauthors of many of these other papers.
Steve, even your loose version of the term “consensus” is a bit too much. The reason is that the current climate science group is a sort of vocal majority though not necessarily an actual majority (you could probably list on one page all the scientists that are actually heavily researching the topic). Many of the scientists that don’t agree or want more information are just now getting active in their resistance to bad science and policy. So, yes, there is a “consensus” among IPCC climate scientists, but they’re the only ones getting funding, and resulting publications. The rest, like you, are doing this on their own nickel (while simultaneously being accused of being industry lapdogs) and slowly getting the word out that something is not right with the analysis.
Mark
My problem is not with those that have a belief there is a consensus but with those that try to pass off that belief as fact. Where is the poll to support the assertion? And what specifically is the consensus on? A survey by Dennis Bray and Hans von Storch makes for an interesting read considering it post dates the IPCC’s “consensus” claim.
#41. Your point about the need to prove a “novel” method was something that caught the eye of McCullough and Vinod, who mentioned this case in an article on replication. They were very acid when not only was the novel technique not proven on other data, but the methods were not made available in the most copious detail. Mann was not going to be “intimidated” into showing his algorithm.
If you see how mining scams work, you get real cautious about “novel” methods. There are famous cases where people have said that they have new assay methods, which can find gold and platinum in properties where “conventional” methods have failed. Guys would have pages and pages of assays from fly-by-night labs in Utah. When I was younger and more naive, you wonder whether there’s something there, but the guys who were my age always said not to waste a second on these things. Needless to say, if the gold wasn’t there in a conventional assay, it wasn’t there period.
Fascinating, as usual. Has Mann or anyone on the Team replied to this latest screw-up?
I don’t blame Peter for getting tired of defending the indefensible. It’s all so tedious, numbers and all. Why do we even need numbers? Just say what you mean, eh? Be reasonable, we’re all gentlemen, you can trust what we say. Accept the hockey stick up your post hock propter hock and move on.
;^)
Re #32: “this place has been banging on about ONE paper for what is now YEARS!”
Mann’s 1,000 year temperature reconstruction is the most important “scientific” paper backing the AGW cause. If the general public knew what readers of this blog knew it would be all over for Kyoto and the massive funding of climate science would plummet.
The IPCC will resist any recognition of problems as long as they can. They are looking after their self-interest. Just like ExxonMobil does when someone attacks their bread and butter.
Re: 32 Peter,
It sounds to me as if you will not be satisfied until we can prove that something does not exist.
Mann, Bradley, Briffa, Jones, and other authors in in harmonious agreement base their work on statistical manipulations of data. (Often, the data belongs to others. Usually the data is unavailable. It is lost, missplaced, proprietary, or simply held secret, so that others can not verify the results independently.) These authors have made statistics a key factor in their papers, not this blog or any of its participants.
Re Hearnden
Steve regularly posts some remarkable new insight, and as sure as night follows day, along comes Hearnden, who never addresses the import of the original post, but only seeks to sidetrack the debate, to take it off topic.
He is in fact a “spoiler” who’s sole intention is to dilute the intellectual impact of the original posts.
Correct, MarkR. Which is why most of us regulars have stopped feeding the troll.
Feed me, feed me!
OK,
How do you keep a turkey in suspense?
“He is in fact a “spoiler” who’s sole intention is to dilute the intellectual impact of the original posts.”
And paid by the big environmentalist group to do just that.
Re #49: Wrong, Reid, although if this site is the only discussion you ever see of climate issues I can certainly see why you might think that. You should have read the AR4 while you had the chance, but failing that have a look at this.
Re #’55, LOL Sid, what claptrap. As John A might say ‘that would be nice’ but infact nothing could be farther from the truth – OK?
My impression, for what it is worth, is that Peter is one of those who are gravely (and genuinely) concerned about the risks to humanity from AGW, and desparate to do what he can to fix it. He thinks (“believes”) that all of us are “deniers” willing to risk the future of our children. To him, whatever it takes is justified to raise awareness, and to bring about responsible action to fix the problem. The end justifies the means. He trusts those who tell him that we have a real problem, and distrusts those who question those assumptions.
Right Peter??
Humm, Bruce, in a way, though I dislike the implication that I might think you don’t either care, genuinely, about the planet or (below the belt this) your/any children :(.
You used the word believe – and of course you used to discredit me. I’m not religious and I don’t ‘believe’ in that sense, nor do I use the word.
I do distrust and trust certain people – just like everyone else here. It’s just mine are different people. But I am rational in my approach – that the generality of the science points to there will be from some to a lot more warming as we ought to address that rather than pick away endlessly at selected scientific papers.
Re #56: Let me rephrase my comment “The IPCC will resist any recognition of problems as long as they can.”
The IPCC may acknowledge a lack of consensus on Mann’s temperature reconstruction. But they will continue to use the temperature reconstruction as a centerpiece in it’s political summary reports. And most probably the political summary reports will not include any note about the controversy.
Bruce,
The real problem is that people like Peter Hearnden and Steve Bloom really don’t understand the scientific method very well, which becomes obvious when they dismiss (or minimize) the role of replication of results, a cornerstone of the method. You can’t call what you are doing science if you make it impossible for others to reproduce your results, but they just don’t understand how critical that is. It’s also clear that they don’t understand the science and math involved, so they make their decisions based on quantity (number of people that agree/disagree) instead of quality (of the science), since they can’t really judge the quality. That kind of decision making is actually very understandable and probably very common, but the mistake they make is that they go around advocating for the side they have chosen anyway. This is probably because they already held a world view that we are destroying the planet by other means, so it was easy to buy into the AGW fear. Once I understood this I saw that it was useless to attempt to engage them in a debate on the science. This is not intended as an insult to these gentlemen, who I’m sure are sincre, but as an observation to explain their behavior.
donno
Paul P,
Very well put. And we all have situations like that, both in science and in other areas of life. The key point of your message is that while anyone can (and should at times) rely on others to provide their own take on a given subject, going from there to advocating for the providers of such opinions is a mistake. This is where my dislike of messages by Peter Hearndon and apparently Steve Bloom differs from my dislike of those of John Hunter and, I think, Tim Lambert. The former can’t argue the science while the latter refuse to. The former should shut up and the later speak up (at the risk of being wrong; at least at first). Now if Steve M allowed and we got engaged in discussions of politics or religion, say, then for all I know the situations might be reversed. But for a discussion of climate science and the statistics thereof, Hunter and Lambert should engage instead of sniping and Steve B and Peter Hd should stick to an occasional subsidiary point.
What about me, you ask? Well I know some statistics, but nothing to engage the heavy hitters here with. But I do know chemistry, physics and biology (especially biochemistry) so I feel free to engage in discussions involving such subjects and do so. I also know Philosophy of Science pretty well and so engage in discussions like this.
Re #61, well, I’ve not seen ‘lacks the comprehension’ used for a while around here. An unpleasant, if padded, use of it. But, why not just insult the intelligence of anyone who has a contrary view and be done with the waffle? Go on, I dare you, show your true colours!
Dave, likewise, though I’d add your contempt for anyone you think you can belittle (which means most anyone who posts off message here) never ceases to amaze me.
And he does it again.
Peter any individual cannot be an expert on EVERYTHING, becuase someone does not have a complete understanding of a singular issue is not a hit on them. It can be assumed that they are well knowledgable in other areas.
As per usual the point has gone completely over your head, zooming like a 767 in the stratosphere.
Re: 44, 45, “consensus.” I hope that anyone who thinks there is a “scientific consensus” on AGW is familiar with the Subject Index at CO2science.org.
Sid, I understand the scientific method – I can do without it being insutingly made out I don’t. But, to be as insulting as PP was, perhaps you better shut up as well since you clearly don’t understand jack? Get it now? I actually know you’re no fool, but, (the bit you wont admit since it’s off message) neither am I. OK?
All. Please, you either want other views or you need to censor them so you can just talk to those of the same view. What’s it to be?
Pretty sure you need to go back and re-read Peter. NO-ONE is saying we don’t won’t hear opposing views. THe issue is that you are not proposing alternate views, you are distracting from the matter at hand.
And I have no idea about the bit I won’t admit. There is little I won’t admit.
re #64: Peter, let me propose you a couple of simple questions. Suppose I have a temperature reconstruction (maybe published by your favorite hockey team member) for the southern hemisphere (SH), and I calculate the forcing-correlations exactly the same way (with the same forcings data) as they are calculated for the northern hemisphere in MBH98. Now
1) How should the correlation curves look like? Similar to MBH98 or somehow different?
2) If the correlation curves for the SH are completely different (from what you think they should be), what would be your conclusions?
– Peter Hearnden
why should I believe you ? I cannot recall that you have ever tried to argue about the facts of the matter, any matter.
Instead, you talk about people who you trust; when the scientific method abhors trust, and relies on replication.
well, that is a warning sign. The issue being raised are that multiple aspects of this paper fail to replicate; and that doesn’t raise uncomfortable issues to you. Replication is the sine qua non of science; and this paper fails.
yours
per
Re #68. Sheesshh, another patronising comment. Ask Michael Mann (that’s if you can do it civilly – the evidence on that is inconclusive btw).
Jean, is CO2 a ghg or not? Has it’s concentration increaded by 30% thanks to our activities? What is the likely temperature rise due to that (from basic atmosphere physics)? What has happened to surface temperatures? What do the climate models predict? What negative feedback could negate such positive feedbacks as decreased snow/ice cover, changes to land use vegitation?
Per, you don’t have to believe me, but you might trying something other than joining in in an attempt to disembowl an 8 year old climate paper.
Peter, patronizing? The questions you asked are unrelated to topic of this discussion. Why don’t you just answer my simple questions?
Peter: I rarely respond to you, because you won’t engage in real debate. But, what do you make of these kind of statements?
T.A. and Lins, H.F. 2005. Nature’s style: Naturally trendy. Geophysical Research Letters 32: 10.1029/2005GL024476
#70 Para 2
I believe Willis has calculated this numerous times here So much that it is difficult to search for. I believe the number is ~0.2C or the same as noise, I’m sure Wills can replicate the calculation easily enough. And when extrapolating into the future, please keep in mind that it is logarithmic, therefor in additional 30% more will have less of an effect.
The rest of the questions in the paragraph are all in dispute, and the the underlying basis for the discusions at hand, and are all extremely difficult to answer with any degree of accuracy.
Peter to follow up on your original question, in relation to a comment Ferdinand submited elsewhere here.
What is the likely temperature change due to solar effects (from basic atmosphere physics) in the past 30 years?
well, peter, that is where you and I part company. If MBH’98 is good, replicable science, and its conclusions stand, that is an important thing to know. If it is bad, that is a very important thing to know also.
Your view is that it doesn’t matter if it is 8 years old ?
per
RE:70
The climate models are scenarios, they don’t predict anything Peter.
Peter,
In comment #30 Jean S. linked to what could arguably be called one of the most important papers written in the past century. It was published in 1948 and no one has been able to put even a small dent in it.
The concept of peer review in math seems to be different than climate science, although I don’t speak from first hand experience. For big papers like Weil’s remarkable proof of Fermat’s Last Theorem, mathematicians try to find the flaw in proofs and see if they work. No one gets huffy about it. In Weil’s first go at proving Fermat’s Theorem (which was still a remarkable piece of work), he had a subtle error which he could not fix. He went back to the drawing board and came up with something that was even more remarkable.
There’s a point in reading “out of date” papers by the leading authors. Even if the science has advanced, there’s an energy to the first proofs that’s often lacking in the textbook versions. You don’t “move on” from great papers. You go back to them for ideas and inspiration. You could read Euclid or Archimedes without fear of wasting your time. I browsed Copernicus recently in a bookstore and there were interesting viewpoints from him on how the earth’s obliquity changes over time, a topic important in Milankowitch, but rather unexpected for me in such an old source.
If something’s good, you never just “move on” like nomads in the desert.
Re: 78. Though working with heuristic methods in artificial intelligence most of my life, I think the ‘continual improvement’ factor in all models, be they machine learning or CGCM’s is a big problem for working out exactly what they are doing. You can’t empirically test on all possible cases for one thing. In contrast, well defined statistical methods, like generalized linear models, will always have a place.
The first reference in “Detection, Estimation and Modulation Theory Part 1”, Van Trees, 1967, is “Essay Towards Solving a Problem in the Doctrine of Chances,” Bayes, 1763 (posthumous). That DETM1 is still widely used as the preeminent detection text and was published nearly 40 years ago is also amazing, let alone the fact that the principles behind detecting signals in noise were established 200 years before the concept of a signal was even known. Moving on isn’t always good.
Mark
I knew I could count on Peter to prove my point.
Back to an earlier point, just how well do the CO2 concentration and solar levels used in Figure 7 correlate with one another?
Peter, since it seems that you have decided not to answer my questions, I ask you an even simpler question: do you think, e.g., Tim Lambert [BTW, is he still alive, haven’t been here for a few days now] should purchase better winter clothing? To help you to decide, I plotted the southern hemisphere temperature from Mann&Jones: Global Surface Temperatures over the Past Two Millennia, GRL, August 2003.
Re #84, Jean, not spoken to MM yet then 😉
Right, well firstly I guess I need to know, do you accept the data? Because, as you know (or you should), recons aren’t the done thing around here (well, you might find out what you don’t want to…). I would guess you don’t (though it shows slow cooling so I don’t rule out you might accept it, it being the right kind of data showing the right things and all that).
Beyond that, yes it’s interesting isn’t it? Lots of water in the southern hemisphere, slow response times by and large. It’s probably warming now, probably more warming to come give both the lag I mentioned and the lag of the atmosphere as wall to CO2 forcing & feedback forcing.
Re #76, no, that’s it’s not been shown (OK, except to the pack here) that it is ‘bad science’. In that’s it’s not out of line with a lot of other analysis. In that other people bar Steve, the pack and the usual suspects show the slightest interest in disembowling it. But, of course, you’re ALL Galileo.
Re #77, Oh, OK.
Re #75, not very much – http://www.pmodwrc.ch/pmod.php?topic=tsi/composite/SolarConstant, or http://en.wikipedia.org/wiki/Image:Climate_Change_Attribution.png for eample.
Re #78 – good, must be solid stuff then.
So let me get this straight.
Increasing temperatures in a reconstruction (or via instrumental record) are evidence of global warming.
Decreasing temperatures in a reconstruction (or via instrumental record) are evidence that global warming is just getting started.
So, is there anything which ISN’T evidence consistent with global warming? Just curious… I assume the answer is no, whatever evidence there is, you can find a way to justify it as being consistent with your beliefs.
RE# 79
Astronomy & cosmology theorists (just for two examples) want their theories & models out there and empirically tested. One recent cosmology paper I read said the authors could hardly wait for observations to try to reject their theory. These sciences are quickly progressing.
Doesn’t quite sound like the current attitude in AGW “science”.
Re: # 86
Nicholas, you won’t get anywhere with Peter. Why?….
Yossarian looked at him soberly and tried another approach. “Is Orr crazy?”
“He sure is,” Doc Daneeka said.
“Can you ground him?”
“I sure can but first he has to ask me to. That’s part of the rule.”
“Then why doesn’t he ask you to?”
“Because he’s crazy,” Doc Daneeka said. “He has to be crazy to keep flying combat missions after all the close calls he’s had. Sure I can ground Orr. But first he has to ask me to.”
“That’s all he has to do to be grounded?”
“That’s all. Let him ask me.”
“And then you can ground him?” Yossarian asked.
“No, then I can’t ground him.”
“You mean there’s a catch?”
“Sure there is a catch,” Doc Daneeka replied. “Catch-22. Anyone who wants to get out of combat duty isn’t really crazy.”
Peter believes the climate models are “broadly right”.
If you point out flaws in a particular climate model, that doesn’t matter, because despite the particular flaws, he believes they are broadly right.
If you pick the flesh off a particular climate model so that the bones fall apart in front of your eyes, that doesn’t matter, because there are heaps of other climate models out there.
If you point out that other climate models have the same failings, that doesn’t matter, because Peter believes that they are broadly right.
….Catch 22.
On atribution studies I would be interested in views on the paper by Kaufman, Kauppi and Stock available here:
Click to access Emiss-concent-temp.pdf
Stock is a well known econometrician. The paper has nothing to say about reconstructions before the instrumental period, but does suggest that post 1870 its the net effect of CO2 and sulphur that is responsible for the warming of the earth. The paper deals carefully with issues of spurious regression and looks in a different league from the Mann papers, though admittedly about a different question.
I am much more inclined to believe their results which yield:
instead of the 1.5 to 6 or 11 degrees or whatever that is bandied around by climate alarmists.
re: 89. I didn’t study the paper carefully, but on first blush, it looks to me that they might be falling into the “correlation means cause/effect” trap. It is certainly possible for a natural warming cycle (probably the sun) to occur concurrently with increases in SO2 and CO2.
For those downplaying the effect of MBH98 in IPCC TAR, here is a nice quote (The Scientific Basis, p. 709) related to the topic (my emphasis):
IPCC, let’s face it, you were punk’d!
#85
Peter. I didn’t ask you to regurgitate stuff about how the solar output “hasn’t changed signfigantly” In response to you request calculate current warming based on CO2 increases, I asked for you to calculate how mauch warming we should have seen based upon the change in solar output, however minor that change is.
It’s the single most important driving factor, as such it needs to be quantified preciselsy before you can move onto anything else.
RE: #58. He appears to be a classic watermelon – green on the outside and red on the inside. “The ends justify the means.”
RE: #61 – Totalitarians, demogogues, and other similar archetypes operationally defined by Hoffer’s “The True Believer” all share this in common. Stalin “banned” certain science because its conclusions threatened his utopian project. Hitler banned “Jew science” based on a similar psychotic outlook. Frighteningly, those esconced in the post WW2 / 1960s upwelling of radicalism, alternative culture and rebellion tend to want to embrace a similar viewpoint. There is a rising confluence of Gaia worship, secular Apocolyptic beliefs, Western self hatred and self loathing, hatred of cultural Judeo-Christianity, and a desparate clinging to utopian, globalist, universal leveling notions hatched during the period bracketed by the Hobbes/Rousseau phase of the Enlightenment and 9/11/2001. Those caught up in it are in grave danger of repeating the well documented excesses of the last bloody century in a manner which would vastly eclipse that ugly century’s worst villains.
And on a lighter note, is this for real ?
Re #95: “There is a rising confluence of Gaia worship, secular Apocolyptic beliefs, Western self hatred and self loathing, hatred of cultural Judeo-Christianity, and a desparate clinging to utopian, globalist, universal leveling notions hatched during the period bracketed by the Hobbes/Rousseau phase of the Enlightenment and 9/11/2001.”
Well said! You left out the misanthropic nature of many members of the AGW crowd.
I call it neo-paganism. We must make sacrifices to Gaia for we are a cancer on her perfect body.
RE: #96. Well I must give fair credit for their sense of public relations. Go for the emotional, it works every time! LOL!
Jean S, I’d love to have you comment on the latest Mann/Jones math.
They have taken April temperature average and standard deviation for Svalbard for the period 1961-1990.
They have used those numbers to derive the odds of the April 2006 temperature.
I say you can’t do this, it’s meaningless, you don’t get accurate results.
Comments? Their procedure is described at http://www.realclimate.org/index.php/archives/2006/05/more-on-the-arctic/
Many thanks,
w.
Re 95& 97
snip
Steve: Sorry, but you had a few religious references. Yeah, I know I let Carl Christensen’s stuff through butI figured he was just embarrassing himself.
re #99: Willis, I posted yesterday some comments under ‘Lamb on the Northeast Atlantic’ which I felt was more appropriate place for the post.
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