Guest Post by Willis Eschenbach
The discussion of the 1998 Mann “Hockeystick” seems like it will never die. (The “Hockeystick” was Dr. Michael Mann’s famous graph showing flatline historical temperatures followed by a huge modern rise.) Claims of the Hockeystick’s veracity continue apace, with people doggedly wanting to believe that the results are “robust”. I thought I’d revisit something I first posted and then expanded on at ClimateAudit a few years ago, which are the proxies in Michael Mann et al.’s 2008 paper, “Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia” (M2008). This was another salvo in Mann’s unending attempt to revive his fatally flawed 1998 “Hockeystick” paper. I used what is called “Cluster Analysis” to look at the proxies. Cluster analysis creates a tree-shaped structure called a “dendrogram” that shows the similarity between the individual datasets involved. Figure 1 shows the dendrogram of the 95 full-length proxies used in the M2008 study:
Figure 1. Cluster Dendrogram of the 95 proxies in the Mann 2008 dataset which extend from the year 1001 to 1980. The closer together two proxies are in the dendrogram, the more similar they are. Absolute similarity is indicated by the left-right position of the fork connecting two datasets. The names give the dataset abbreviation as used by Mann2008, the type (e.g. tree ring, ice core) the location as lat/long, the name of the princiipal investigator, and if tree rings the species abbreviation (e.g. PIBA, PILO).
What can we learn from this dendrogram showing the results of the cluster analysis of the Mann 2008 proxies?
First let me start by describing how the dendrogram is made. The program compares all possible pairs of proxies, and measures their similarity. It selects the most similar pair, and draws a “fork” that connects the two.
Take a look at the “forks” in the dendrogram. The further to the left the fork occurs, the more similar are the pairs. The two most similar proxy datasets in the whole bunch are ones that are furthest to the left. They turn out to be the Tiljander “lightsum” and “thicknessmm” datasets.
Once these two are identified, they are then averaged. The individual proxy datasets are replaced by the average of the two. Then the procedure is repeated. This time it compares all possible remaining pairs, including the average of the first two as a single dataset. Again the most similar pair is selected, marked with a “fork” (slightly to the right of the first fork), and averaged. In the dataset above, the most similar pair is again among the Tiljander proxies. In this case, the pair consists of the “darksum” proxy on the one hand, and the average of the two Tiljander proxies from the first step on the other hand. These two are then removed and replaced with their average.
This procedure is repeated over and over again, until all of the available proxies have been averaged together and added to the dendrogram and it is complete.
In this case, the clustering is clearly not random. In general a cluster is composed of measurements of similar things in a single geographical area (e.g. Argentinian Cypress tree rings). In addition, the proxies tend to cluster by proxy type (e.g. speleothems and sediments vs. tree rings).
Next, the dendrogram can be read from the bottom up to show which groups of proxies are most dissimilar to the others. The more outlying and more unusual group a group is, the nearer it is to the top of the dendrogram.
Next, note that many of the groups of proxies are much more similar to each other than they are to any of the other proxies. In particular the bristlecone “stripbark pines” end up right at the top of the dendrogram, because they are the most atypical group of the lot. Only when there is absolutely no other choice are the bristlecones at the top of the dendrogram added to the dendrogram.
So how does this type of analysis clarify whether the “Hockeystick” is real? The question at issue all along has been, is the “hockeystick” shape something that can be seen in a majority of the proxies, or is it limited to a few proxies? This is usually phrased as whether the results are “robust” to the removal of subsets of the proxies. And as usual in climate science, there are several backstories to this question of “robustness”.
The first backstory on this question is that well prior to this study, the National Research Council (2006) “Surface Temperature Reconstructions for the Last 2,000 Years” recommended that the bristlecone and related “stripbark” pines not be used in paleotemperature reconstructions. This recommendation had also been made previously by other experts in the field. The problem for Mann, of course, is that the hockeystick signal doesn’t show up much when one leaves out the bristlecones. So like a junkie unable to resist going back for one last fix, Dr. Mann and his adherents have found it almost impossible to give up the bristlecones.
The next backstory is that a number of the bristlecone proxy records collected by Graybill have failed replication, as shown by the Ababneh Thesis. Not only that, but one of the authors of M2008 (Malcolm Hughes) had to have known that, because he was on her PhD committee … so the M2008 study used proxies that were not only not recommended for use, but proxies not recommended for use that they knew had failed replication. Bad scientists, no cookies.
The final backstory is that the Tiljander proxies a) were said by the original authors to be hopelessly compromised in recent times and who advised against their use as temperature proxies, and b) were used upside-down by Mann (what he called warming the proxies actually showed as cooling).
With all of that as prologue, Figure 2 shows the average signals of the clusters of normalized proxies (averaged after each proxy is normalized to an average of zero and a standard deviation of one). See if you can tell where the Hockeystick shaped signal is located …
Figure 2. Left column shows average signals of the clusters of proxies shown in Figure 1, from the year 1001 to 1980. Averages are of the cluster to which each is connected by a short black line.
You can see the problems with the various Tiljander series, which are obviously contaminated … they go off the charts in the latter part of the record. In addition, if the Tiljander data were real it would be saying record cold, not record hot, but the computational method of Mann et al. flipped it over.
The reason for the unending addiction of Mann and his adherents to certain groups of proxies becomes obvious in this analysis. The hockeystick shape is entirely contained in a few clusters—the Greybill bristlecones and related stripbark species, the upside-down Tiljander proxies, and a few Asian tree ring records. The speleothems and lake sediments tell a very different story, one of falling temperatures … and in most of the clusters, there’s not much of a common signal at all. Which is why the attempts to rescue the original 1998 “hockeystick” have re-used and refuse to stop re-using those few proxies, proxies which are known to be unsuitable for use in paleotemperature reconstructions. They refuse to stop recycling them for a simple reason … you can’t make hockeysticks without those few proxies.
To sum up. Is the mining of “hockeystick” shaped climate reconstructions from this dataset a “robust” finding?
Not for me, not one bit. While you can get a hockeystick if you waterboard this data long enough, the result is a chimera, a false result of improper analysis. The hockeystick shaped signal is far too localized, and occurs in far too few of the clusters, to call it “robust” in any sense of the word.
w.
PS – The entire saga of the Ababneh Thesis, along with lots and lots of other interesting information, is available over at ClimateAudit. People who want to improve their knowledge about things like the proxy records and the Climategate FOI requests and the whole climate saga should certainly do their homework at ClimateAudit first … because in the marvelous world of Climate Science, things are rarely what they seem.
[UPDATE] Some commenters asked for the data, my apologies for not providing it. It is located at the NOAA Paleoclimate repository here.
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“you can get a hockeystick if you waterboard this data long enough”
🙂
A skeptical view of the “hockey stick”, written by McShane and Wyner, is now available in hard copy, with discussion and rejoinder, in the Annals of Applied Statistics, Vol 5, Number 1, dated March 2011, pages 5-123. There is an expanded rejoinder along with lots of data and code from the discussants in the supplemental online material through the Annals of Applied Statistics web page at the Institute of Mathematical Statistics web page: http://www.imstat.org.
Most of this was available on the internet before now, but I think it is worthwhile to read the hard copy version.
Discussants included Schmidt, Mann and Rutherford; and McIntyre and McKitrick; in all, there were 13 papers by discussants, plus the original and rejoinder by M&W. Like Willis today, and others here and there, M&W point to the dependence of the hockey stick shape on a selected subset of the data. Schmidt et al defend the selection, as you’d expect.
Willis,
I think that you should write up today’s comment for a professional journal. I think you have presented a nice clear case.
Willis, thanks for the charts and overview of upside down Tiljander. They clearly show that what was going on here certainly wasn’t science.
Willis, I don’t know quite how you manage to keep producing so many easy-to-read, easy-to-understand articles, but many thanks for another one. Your figure 2 is superb: take out the two known dodgy datasets and the hockey stick evaporates. Once again, many thanks.
Alexander Feht – I completely agree with you. We need a popular, public face to stand up for real science, before the vacuous “celebrities” who regularly trumpet AGW nonsense completely pollute the public’s perception of science. Unfortunately, the fact that no-one springs to mind makes me, too, wonder whether the popular perception of “science” has been so contaminated already as to appear “settled” – at least, for long enough for the shower playing for global power to make their putsch. The next few years are going to be “interesting”, if none too pleasant.
first drown it in holy water , then shoot it with a silver bullet, then drive an oak stake thru its heart, then behead it and finally burn the head and body in the fires of Mount Doom … then maybe it stays down … maybe … also, if you find the ring of power, also drop it in the fires of Mt. Doom just to be sure …
“The discussion of the 1998 Mann “Hockeystick” seems like it will never die.”
… says Willis in the opening sentence. That is a little bit artful & coy, since WUT
and CA are the main agents keeping this discussion alive at the detriment of a
broader, updated perspective on climate reconstruction studies.
Of course I can see the difficulty for sceptics here: the reconstructions generally
reproduce the MWP and LIA periods, which you are fond of, but at the same
the recent warming peak invariably shows up and most often, it already exceeds
the MWP peak. With (a) warm years piling up recently, (b) new proxy studies
being published all the time, your battle against the Hockey Stick is doomed
to fail.
The bristlecone data is erroneous? Exclude it, no major difference.
In fact, exclude all tree ring data? No major difference, now when other proxy
data is increasingly available.
Exclude also the Tillander data? No major difference.
Mikael Pihlström says:
May 31, 2011 at 11:29 am
Check the blogs. I actually said this based on a discussion of M2008 on Judith Curry’s blog, but this question has been (and is being) discussed on a variety of sites. The problem, of course, is that Mann (and folks like you) keep claiming that there were no problems in Mann’s work. If Mann and y’all would simply own up to the egregious errors in his work, the issues would go away … but until then, they will continue to be brought up by folks around the planet. Sorry, but that’s what happens when you claim that errors are correct … it makes them persist.
And a “broader, updated perspective”? What does that have to do with whether M2008 stacked the decks by the choice of proxies? Whenever someone points out problems with Mann’s work, fools always jump up and say “But that doesn’t matter, we’ve moved on to new studies now” or that we have a “broader, updated perspective” now. So what?
Sorry, but Mann’s work is good or bad depending on what he did, not on what new studies might show. And in this case, I can see why you’d like us to look somewhere else, anywhere else … because his work is bad. Really bad. Using proxies upside-down bad. Using Graybill bristlecones bad.
Now, I know you’d much rather we look at something else, but the new “broader, updated perspective” is mostly a repetition of Mann’s work, including the errors. Including the non-recommended proxies like the bristlecones. Heck, even including non-recommended proxies upside-down. And definitely including other bogus proxies like the Polar Urals and Tornetrask. So no, you can’t get out of it by saying that Mann is so yesterday and you’ve moved on.
I also like your dual pronged approach:
• It doesn’t matter that Mann’s work is wrong, because it is no longer relevant as it has been superceded (since 2008?) by newer (although uncited) studies, and,
• Mann’s work is right.
Hmmm … do you see a conflict there? Pick one or the other, Mikael, or you’ll get the splits from riding two horses.
Cite? I love the hand waving and the claims of “new studies”, but without citations that’s just you flapping your lips and hoping people won’t notice the lack of facts. And “warm years piling up recently”? See Phil Jones on how there’s been no statistically significant temperature increase in fifteen years.
Again, I love the handwaving … but some citations would be nice. Michael Mann has made a similar claim, but his graphs show that his claim is just handwaving as well.
And “now when other proxy data is increasingly available”? What does that have to do with the use of bogus proxies in Mann 2008?
Finally, you claim that the “recent warming peak invariably shows up” … to be sure, if you “hide the decline”, you get an incline. You do understand that they needed “Mann’s Nature trick” in order to hide the fact that recent warming didn’t “invariably” show up as you claim?
Or perhaps you don’t understand that. If so, you also may not be aware that Mann’s method finds hockeysticks in random red noise … if you know what that is. See e.g. Principal Components applied to Red Noise. So the Mann himself finding yet another “hockeystick” with a “recent warming peak”, that don’t impress me much, although I can see why uninformed people might think it is important. But since we can get that result from random red noise using Mann’s method, it’s meaningless.
In any case, Mikael, so far in your post you have provided erroneous claims and handwaving … not a good start. There’s further reading for you about the proxies and how Mann can make a hockeystick by proxy selection in M2008 here and here and here and here and here, if you are actually interested in the proxy issues. Yes, you are correct, if you put a bunch of bogus proxies in, you can remove a subset of the bad proxies and still find a hockeystick. You seem to think that means something …
Finally, tree ring width sucks as a proxy for temperature. There’s a good explanation of why (in the process of explaining a much more accurate method for estimating ring width from the variables that control it) here (PDF poster about the Vaganov/Shaskin model of tree ring growth).
If you actually are interested in the proxy issues, come back and tell us how all of those analyses are wrong, with real facts and citations and leaving out the handwaving.
All the best,
w.
Steve C says:
May 31, 2011 at 10:50 am (Edit)
Thanks, Steve. Actually, there’s more than two dodgy datasets in the group. See the links in my post to Mikael immediately above for a non-exhaustive list. Also Steve McIntyre pointed out a few more above.
w.
PaulD says:
May 31, 2011 at 8:09 am
Paul D, thanks for a very clear explanation of the issues. Mikael (above) thinks that it is sites like WUWT and CA that keep this issue alive. What keeps it alive is that Mann and folks like Mikael won’t concede even the most obvious of errors, for example that Mann used Tiljander a) in defiance of the instructions of the original authors not to use the whole dataset for reconstructions, and b) upside-down.
There’s a report of the original finding of upside-down use of Tiljander here, and a good discussion of related issues here.
w.
PS – Relevant citations. Mann’s comment, that the claim that Tiljander was used upside-down is “bizarre”, was in reply to McIntyre and McKitrick’s rebuttal in PNAS. Mann’s reply is here.
Willis:
I did not have the background to figure out use of R readily when I once tried or else I’d look into using this type of analysis also on long running (century old) tide gauge records, of which there are dozens. They are here: http://www.psmsl.org/data/obtaining/. I do believe the resulting analysis would be highly damning to claims of recent surges in sea level since very much like these proxies the vast majority of records show no trend change at all, at least by eye. They are, on average, a characterized by a lack of trend change on the decadal scale, which is not something you find so readily in single site thermometer records, so sea level in my mind becomes a potentially much better counter to one of the two central tenants of AGW: that both T and and sea are suddenly surging.
-=NikFromNYC=-
NikFromNYC says:
May 31, 2011 at 2:01 pm
Thanks, Nik. I don’t think that cluster analysis of tidal gauges would reveal what you think it might. The problem is that tides are a basically non-repeating series, which kinda repeats every eighteen years or so, and pretty much repeats every fifty two years or so, but which contains even longer cycles than that.
These cycles overwhelm everything, so just getting a trend from tidal data is a difficult and very long-term exercise. You kind of have to work it backwards. You use the data to take the best estimate of the “tides of the moon”, that is to say, the size of the effect of each of the fifty or so cyclical earth-moon-sun interactions (apogee, perigee, phase, declination, the list is long) on the local tide.
Then you remove those cyclical influences, and what’s left is your best estimate of the trend … not a pretty way to get a number, but it’s the best we have. The ugly reality is that there is absolutely no theoretical way to determine the tide at a random point. We can only do it as a result of a long, long series of observations.
In addition, the tide at a given location is a function of where it is on the earth (tides near the poles tend to be larger), the nature of the oceanic basin, and any land features (bays, lagoons, etc).
For example, most places have either one high and one low tide per day, or two high and two low tides per day. The Solomon Islands, on the other hand, has one high and low tide for part of the year, and has two highs and lows for part of the year.
So overall I don’t think cluster analysis would be much help there. All you would end up saying is “well, the tides in the Solomons are most like the tides in X”, but that doesn’t help much.
w.
Mikael Pihlström.
All you need to produce a flat shaft is some proxy that has a blade.
1. BCP
2. Tiljander
3. yamal.
So, its easy to drop BCP and get a flat shafted hockey stick
easy to drop Tiljander, easy to drop yamal.
Thats been the trick. drop one keep the others. drop 2 keep one.
pea thimble.
if you understood what the underlying methods did to supress variability in the shafts you’d understand better. read Jeff id. or better run his code
trees are a very poor proxies for temperature. when you look at water content/sun/food/temp the combinations and variables can lead you astray very quickly. especially if you have no records or observations to verify the findings.
makes one wonder what Mann was thinking when he used them. a questionable source and hard to verify… that’s the answer…. hide the data and hard to replicate.. where have i heard that process before?
Willis: “There’s a report of the original finding of upside-down use of Tiljander here, and a good discussion of related issues here. ”
Okay, I think I get it. Basically, Mann’s software picked the sign. Since upside down Tijander data would coorelate to other data for the last 100 years, Mann’s software simply decided for itself how the data should be interpreted – ignoring the real world interpretation. The odd thing about this is that the software would have to decide that it didn’t care that the coorelation for the MWP and LIA was destroyed by doing such a sign inversion. Mann probably used the results without checking since it gave him what he wanted. Then, after his error was exposed, Mann had to make a decision, lie or acknowledge that he had done something really stupid.
As always, Mann choose to lie. If I’m interpreting this correctly, what he said was, “using the data with the sign as I have used it causes the data to coorelate with other data around the world, so – my sign is correct.” Basically, he called Tiljander a fool who didn’t understand the physical interpretation of his own data. He ignored the inverted correlation that his interpretation caused for the MWP and LIA, and he ignored the fact that his misinterpreted hockey blade actually had the shape that it had due to man made construction projects screwing up the data for the last 80 years. And he purposely ignored these things even though they were pointed out to him just so that he could make the claim involved in his lie.
Going one step futher, Gavin is not so stupid that he did not realize that Mann was lying. And yet he helped to prop up Mann’s lie. I don’t know how else to say this, but how is it possible for Realclimate to be considered anything but a propaganda organization for a warmist mafia.
Come on Leif, get off the fence – say something. This issue looks to be 100% clear cut to me. Can you think of any defense for Mann’s actions?
The AGW crowd keeps telling us that Mann’s results are supported by “independent” studies. OK, when will someone list and review those “independent” studies? I’m available to assist in any reviews of these “independent” studies.
steven mosher says:
May 31, 2011 at 8:15 pm
Exactly. Since most of the other proxies basically average each other out, adding a few hockeystick shaped proxies dominates the entire thing. So they pull out some and not others and say see, our hockeystick signal is robust.
My analysis, however, shows how few proxies from how few places actually have a hockeystick shape. The asian tree ring series, the bristlecone and stripbark pines, and Tiljander.
This is not to say that there are not problems, in some cases large problems, with other individual proxies. But those few groups are the source of the hockeystick.
The key is in the picking of the proxies. Mann is always trying out new techniques for extracting the data, but the techniques are not the point, that’s all misdirection. You could use plain averaging and get a hockeystick, as long as you have some hockeystick records in the data. Doesn’t take too many, particularly if your algorithm weights them heavily compared to the others …
w.
Willis Eschenbach says:
May 31, 2011 at 11:24 pm
steven mosher says:
May 31, 2011 at 8:15 pm
“So, its easy to drop BCP and get a flat shafted hockey stick
easy to drop Tiljander, easy to drop yamal.
Thats been the trick. drop one keep the others. drop 2 keep one.”
OK. It is principally correct to watch out for such easy tricks. But, on the other
hand, it is also very easy to post-facto identify anything resembling a HS shape and dismiss those datasets with something less than impartiality. And that is my main point: with the increasing basic evidence available the sceptic tenet that all
HS-resembling datasets are corrupt/misinterpreted/falsified is faring badly.
Willis, you are in error when you say the computational method of Mann et al flipped over Tiljander. The software does not do any flipping of Tiljander proxies. The error was that Mann should have manually flipped Tiljander before using it, to make warm point upwards. Then after this flip, the software would have dropped it for being uncorrelated.
Mikael Pihlström says
“And that is my main point: with the increasing basic evidence available the sceptic tenet that all
HS-resembling datasets are corrupt/misinterpreted/falsified is faring badly.”
As someone who is actually interested in understanding this issue and getting to the bottom of it, I would appreciate a link or a citation that would support this point. I would actually like to investigate whether it is true. When I have evaluated similar claims from other websites I have found such claims to be unsupported.
My own reading leads to me to a different conclusion: There are a few basic proxy series that are responsible for the blade of the hockey stick in all of the supposedly “independent” reconstruction. When those proxies are examined, there are sound physical reasons to conclude that they are not good temperature proxies. (e.g. the Tiljander series, the strip bark series).
Nothing that I have read would cause me to reach the conclusion that, “the sceptic tenet that all HS-resembling datasets are corrupt/misinterpreted/falsified is faring badly” I am willing to be persuaded otherwise, but you will need to point me to some evidence.
Mikael Pihlström: “But, on the other hand, it is also very easy to post-facto identify anything resembling a HS shape and dismiss those datasets with something less than impartiality.”
Since the way in which you make your living is dependent upon Mann and the other warmists being right, I don’t think you have much room to talk about impartiality.
Mikael Pihlström: “And that is my main point: with the increasing basic evidence available the sceptic tenet that all HS-resembling datasets are corrupt/misinterpreted/falsified is faring badly.”
No, that is untrue. First of all, there has never been a serious debate about temperature increase in the last century. The debate has been all about that temperature increase being “unprecedented” within the last 2000 years. In other words, it has been about the flat shaft of the hockey stick. And with regard to that the “increasing basic evidence” is that there was a substantial MWP and LIA. And that evidence says that the proxy MWP was as warm as the proxy data for today. So it is the assertion that today’s climate is unprecedented that is fairing badly, because the hockey stick is, is fact, wrong.
Mann’s flipping of the Tiljander data also turned the MWP and LIA upside down and thereby contributed to making the shaft flatter.
What is interesting Mikael, is that you talk about impartiality, but you don’t seem to care how corrupt Mann is in the way that he does his science. All that you seem to care about is being able to declare victory for your agenda at the end.
Here’s something interesting, and slightly off-topic-
I was going to try to locate one of the Graybill Bristlecones during an upcoming fishing trip to the Eastern Sierras. CA531 (Graybill-Onion Valley) seems to be an ideal candidate. Long/Lat and elevation can be found here:
http://www.ncdc.noaa.gov/paleo/metadata/noaa-tree-3393.html
North: 36.77 * South: 36.77
West: -118.35 * East: -118.35
Altitude: 2865 m
When I checked the correlation stats I came up with entirely different coordinates:
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/treering/measurements/correlation-stats/ca531.txt
Latitude : 3546 N
Longitude : 11821 W
Elevation : 2865 M (actual elevation is less than 2000 meters)
This location is in the Sequoia Nat. Forest, near Bright Star Canyon; 100 miles south of Onion Valley and approx. 800 meters lower in elevation. Checked the entire Graybill database for a Bristlecone located at 35.46N/118.21W. Nothing.
How can the same tree be located 100 miles south of Onion Valley?
I always knew Mann-made global warming was real! This further confirms it!
Mikael Pihlström says:
June 1, 2011 at 4:00 am
No, Mikael, that’s not your main point. That’s the point that remains after your other points have been demolished. You had a bunch of other main points before, points that were as lacking of substance and substantiation as this latest one.
Because once again you’re just flapping your lips. CITATIONS, bro’. Citations are your friend.
For example, you say:
“Increasing basic evidence”???
That’s meaningless, Mikael, without some kind of citations. But I’ll bite.
What “increasing basic evidence” is showing that the bristlecones (or the asian tree rings or the Tiljander data) are suddenly somehow correct?
What “HS-resembling datasets” are you claiming are NOT corrupt under the rubric of “increasing basic evidence”? Names, Mikael, locations, specifics, that’s what is necessary. Not your unsubstantiated vague fantasies about some unspecified new “basic evidence”.
Now, please don’t just come back and give us more bafflegab. Your lack of citations has been commented on before. And because of your unwillingness to back your claims up with facts despite repeated requests, at this point your word means nothing. You’ve destroyed your credibility entirely through your extravagant unscientific claims and your obstinate refusal to provide even the merest scrap of evidence for a single one of your claims.
If you come back again for a third time in the same manner, with nothing but your extravagant un-cited claims in one hand and your Johnson in your other hand, I’m not going to answer. I’ll just point and laugh.
w.
Duke C. says:
June 1, 2011 at 9:11 am
Duke, perhaps you should ask that question of Steve McIntyre over at ClimateAudit. He’s done some field investigation of Graybill trees to try to verify the “Starbucks Hypothesis“, and knows more about the subject (and perhaps how you might document the tree) than anyone I know.
w.
>>
Ric Werme says:
May 30, 2011 at 6:34 pm
If it’s any consolation, RGGI’s cost to consumers is totally unclear. Here in New Hampshire, on[e] power producer has come up with estimates of $0.065 cents per month and also $0.36 per month.
<<
Maybe it’s because they’re using the frequency version of Wien’s displacement law for one estimate and the wavelength version of Wien’s displacement law for the other estimate.
/sarc
Jim