Arguments
New temperature reconstruction vindicates ...
Posted on 28 September 2010 by Ned
Guest post by Ned
A new temperature reconstruction has been published in the Swedish journal Geografiska Annaler: Series A, Physical Geography. The reconstruction (hereafter Ljungqvist 2010) covers the past 2000 years for the middle and high latitudes of the Northern Hemisphere.
This reconstruction includes a number of new proxies that have not been included in previous hemispherical or global temperature reconstructions, and avoids many of the proxies that have been the subject of contention in the past. The results are shown in Figure 1:
Figure 1. Extratropical (30-90 N) northern hemisphere temperature reconstruction by Ljungqvist (2010). Northern hemisphere instrumental temperature records shown for comparison (CRUTEM land only, and HADCRUT land/ocean).
Ljungqvist notes that this reconstruction shows a Roman Warm Period prior to AD 300, followed by a Dark Ages Cold Period (AD 300 to 800), a Medieval Warm Period (AD 800 to 1300), the Little Ice Age (AD 1300 to 1900), and modern warming in the 20th century. While there has been debate about how "globally consistent" these various warm and cold periods have been, they have long been recognized as prominent features of the extratropical Northern Hemisphere temperature record, so their appearance in Ljungqvist 2010 is not surprising.
Readers may wonder how this new reconstruction compares to previous hemispherical and global temperature reconstructions. In his conclusion, Ljungqvist (2010) reports that:
"Although partly different data and methods have been used in our reconstruction than in Moberg et al. (2005) and Mann et al. (2008), the result is surprisingly similar. The inclusion of additional records would probably not substantially change the overall picture of the temperature variability."
On the other hand, Craig Loehle claims that Ljungqvist's work vindicates his own previous "global" reconstruction (Loehle and McCulloch 2008, previously discussed elsewhere on this site). Writing on the website Watts Up With That, Loehle claims:
"In this post I demonstrate perhaps a little vindication [...] There is excellent agreement over the past 1100 years [...] My peak temperature occurs about 100 years earlier, but I agree with the new reconstruction [....] The MWP looks real."
So who's right? Does Ljungqvist confirm the results of Mann (2008) and Moberg (2005)? Or do his results agree with Loehle and McCulloch (2008)? Figure 2 provides a comparison of them all, starting in AD 500 (the earliest date in Mann 2008's global reconstruction), with the northern hemisphere instrumental record shown for comparison.
Figure 2. Comparison of northern hemisphere and global temperature reconstructions. Northern hemisphere instrumental temperature records shown for comparison (CRUTEM land only, and HADCRUT land/ocean).
It's worth noting that all the reconstructions show the Medieval Warm Period, the Little Ice Age, and 20th-century warming (though Loehle 2008 only runs through 1935).
Loehle's Medieval Warm Period is both warmer and earlier than the rest (and, as noted above, Loehle recognizes that his early peak circa AD 850 is probably incorrect). Loehle also shows a much colder Little Ice Age. All of the reconstructions diverge more in the period before AD 800, with Moberg being the coolest, Loehle the warmest, and Mann and Ljungqvist being in the middle of the pack.
When comparing Ljungqvist 2010 to Loehle 2008, it's important to remember that Ljungqvist's reconstruction is for the mid- and high-latitude Northern Hemisphere only, while Loehle's was supposed to be global. In this light, the presence of relatively extreme temperatures in Loehle's reconstruction during both the Medieval Warm Period and the Little Ice Age ought to be viewed somewhat skeptically. Whether or not these episodes were truly "global", they were certainly strongest in the Northern Hemisphere, particularly in the North Atlantic region. Ljungqvist 2010 suggests that his own reconstruction may have underestimated the magnitude of Northern Hemisphere cooling during the Little Ice Age, but Loehle's still appears to be an outlier if it is considered as a global reconstruction.
Finally, it's worth noting that comparison to the instrumental record suggests that modern temperatures are significantly warmer than those during the height of the Medieval Warm Period. Additional projected 21st Century warming will produce a climate unlike anything experienced in the history of human civilization.
Update (29 Sep 2010)
Several people have expressed interest in seeing how the various reconstructions compare to current temperatures (from the instrumental record). In order to do this, it's important to carefully "center" each reconstruction such that it matches the instrumental record as closely as possible during the period of overlap.
I've taken the three Northern Hemisphere reconstructions (Mann, Moberg, and Ljungqvist) plus Loehle's "global" reconstruction, and carefully matched each one to the same instrumental temperature record (CRUTEM Northern Hemisphere land temperatures). The results are in Fig. 3:
Figure 3. Comparison of temperature reconstructions, re-centered to match CRUTEM NH land record (based on each reconstruction's period of overlap).
Bit of a mess, eh? To focus on just the Medieval Warm Period and the Little Ice Age, I've pulled out the three warmest decades and three coolest decades in each reconstruction (during the period from AD 500 to 1900).
Figure 4. Warmest decades of the Medieval Warm Period, and coolest decades of the Little Ice Age, after re-centering each reconstruction to match the instrumental temperature record during the period of overlap.
Moberg is a bit on the cool side overall -- which might just mean it was anomalously warm during the calibration period used for centering. Mann and Ljungqvist agree very closely on the Medieval Warm Period, though Mann's Little Ice Age is not as cold.
Loehle manages to be both too warm and too early on the Medieval Warm Period and on the cool side during the Little Ice Age. This difference would not be all that noteworthy, except for the fact that Loehle 2008 is supposed to be a global reconstruction ... and the magnitude of the MWP-LIA difference should almost certainly be smaller for a global reconstruction than for a Northern Hemisphere one.
The other obvious point is that when we compare these to the current instrumental temperature record, the Medieval Warm Period seems to be about 0.7 degrees C cooler than the 2000-2010 mean temperature.
So currently NH land-surface temperatures (as per CRU) are about 1 C warmer than they were during the much touted MWP. That is impressive
Fantastic post Ned! Thanks.
That's an useful analysis pulled together in a very short time, Ned.
The temperature since AD 1990 is, however, possibly higher than during any previous time in the past two millennia if we look at the CRUTEM3+HadSST2 90–30°N instrumental temperature data (Brohan et al. 2006; Rayner et al. 2006) spliced to the proxy reconstruction. The proxy reconstruction itself does not show such an unprecedented warming but we must consider that only a few records used in the reconstruction extend into the 1990s. Nevertheless, a very cautious interpretation of the level of warmth since AD 1990 compared to that of the peak warming during the Roman Warm Period and the Medieval Warm Period is strongly suggested.
Thank you, Doug. I hope this will not turn out to be a case of "post in haste, repent at leisure" ...
Have you thought about including M&M2005 and/or M&W2010 for comparison?
Much to my surprise, I have not been able to find a figure for M&M's temperature reconstruction. Did they even produce one which could be compared with the above?
M&W seems a variation of "post in haste, repent at leisure." There is some discussion here at Skeptical Science, on the Is the hockey stick broken thread.
Basically, Loehle's reconstruction tells us what we already know - that temperatures were warmer 1000 years ago than 400 years ago. But he provides no real possibility to compare past temperatures to current values, although he seems happy to make speculative conclusions about the matter. Also RealClimate has a good discussion about many of the problems in Loehle's 2007 analysis.
Ljungqvist's reconstructed temperatures are relative to the same base period as the HadCRU instrumental temps. For what it's worth, Figure 1 by Ned is easy to recreate and clearly shows that Ljungqvist's reconstruction is in agreement with the conclusion that recent temperatures are anomalously high compared the last thousand years (I was actually working on this before I read this post – Tamino got me interested):
-Alden
Rather than vindicating Loehle, it shows his reconstruction to be an outlier. This incident is (or should be) leaving Loehle and Watts with egg over their faces, again.
Could someone in the know here please confirm whether or not M&M have actually put together or published a temperature reconstruction that could be compared with the above reconstructions? Thanks.
Albatross... (If I can allowed to mix my metaphors a bit.) Yes, I think they've got egg on their face but if you go over to the comments section there you find it's more than that. They're having a massive egg party! Egg is all over the place!
By Loehle making this rather bizarre statement he is placing the CA team in a rather awkward position.
If CA audit Ljungqvist 2010 and find substantial errors which call into question the validity of Ljungqvist's analysis, then Loehle, by his own words, has not been vindicated.
If the CA team audit Ljungqvist and find that the results stand, then others here and elsewhere have shown that Ljungqvist 2010 vindicates Mann and Moberg, not Loehle. In fact they show Loehle to be an outlier.
What a pickle people sometimes get themselves into when they try and spin things. I can only imagine what a mess the thread is over at WUWT. One can only hope that some saner voices are trying to politely point out the huge problems with Loehle's assertion.
Although it looks like we used different approaches for centering the series. Zeke's lineup is more similar to Tamino's. This doesn't affect the amplitude of the reconstructions (e.g., the difference between the MPW peak and LIA trough) but it does make a difference in terms of comparison to current (instrumental) temperatures.
Argh, you're right of course. And while I could edit the text of the post, the "global" label is burned into the graphic of Figure 2. Well, I'll have to fix that...
Anyway, thanks for pointing it out.
Good post! Way better than my comment on "Is the Hockey Stick Broken" but I do have some quibbles.
You say:
"It's worth noting that all the reconstructions show the Medieval Warm Period, the Little Ice Age, and 20th-century warming (though Loehle 2008 only runs through 1935)."
This is clearly not the case as Mann's original Hockey Stick denied both the MWP and the LIA.
[edit]
I keep getting this sense that Loehle is just pissed that Mann's original hockey stick graph was straight and he thinks it should have bends in it. He seems to go out of his way to try to make his own hockey stick (with hidden blade) as exaggeratedly bent as possible.
But still, I keep coming back to the fact that what makes the hockey stick a hockey stick is the blade. Current warming. (We sure ain't playing Lacrosse here.) Loehle can tie the handle up in knots for all I care, it just seems to me that what is important is that current warming is unprecedented no matter how many crooks the handle has.
Am I missing something?
[edit]
Moreover, as can be seem for all to see here, Figure 2 above shows the Mann08 reconstruction, which has a very distinct MWP and LIA.
Yet you insist on harping on about a 12-year old paper. Why? In case you have not noticed it is 2010 GC, the science has advanced and moved on, might I suggest that you do too...
"Am I missing something?"
As far as I can tell, they (Loehle et al.) want to try and show that the current warming is not unprecedented. Their argument goes something like this "it has been as warm before and it is mostly natural cycles driving changes in global SATs".
So, it seems, that they wish to try and detract people from the big elephant in the room, the blade. Their argument also ignores the fact that the blade is only going to get longer as the radiative forcing from increasing GHG concentrations increases.
Also, the MWP and LIA are both indications that climate sensitivity is not as low as the "skeptics" would like think, b/c fairly large temperature departures in the past were invoked with very little forcing.
Never mind that the inconvenient fact that temperatures are already much warmer than (reliable reconstructions indicate) for the MWP.
Another way to compare the two is to essentially recalibrate the reconstructed temperatures against the instrumental values. I adjusted Loehle, Ljungqvist, and HadCRU instrumental values to the base period 1850-1899. I then plotted the reconstructions with the land / land&sea instrumental values (using the same level of smoothing as the reconstructions), using global or hemispheric datasets where appropriate. Again, I’m not sure how Loehle feels vindicated:
Moreover I wish the folks at WUWT would stop confusing the conclusion that there was a Medieval Warm Period (which there very likely was) with the separate conclusion that the recent temperature trend is rather unusual. That comes out in Loehle’s reconstruction as well. And more importantly, these graphs say nothing about whether it’s all a “natural cycle”. We have a pretty good understanding of why temperatures were warmer in the Middle Ages and why they were cooler in the Little Ice Age. We also have a really good understanding of why recent temperatures are increasing and that they will continue to do so. Let’s see what Loehle has to say in another 20 years...
-Alden
Just a little reprisal from months ago when I wrote Kung-fu Climate... Even using numbers that Loehle provided for me, with his own acknowledgement that they were an apple-to-apple comparison, we see that current warming IS unprecedented.
And this doesn't even account for the fact that:
1) Loehle's figures are mostly NH
2) The Hadley figures still stop over a decade ago
3) Loehle's figures are the most exaggerated of any of the reconstructions
So, even with all those handicaps current warming is still more rapid and higher than any time in the past 2000 years.
And, as you say Albatross, if Loehle is anything close to right that suggests a climate sensitivity that... well, we don't wanna go there, that's for sure.
Anyways, another way to compare to the instrumental data is to actually do a regression-based proxy reconstruction. So I calibrated the mean data vs. the CRUTEMP3v data using simple linear regression, and used those parameter estimates to project them back.
as far as I know, M&M only ever did a reconstruction from 1400AD. Dunno if it's useful to you, but it's on page 765 [p. 17 in Acrobat] in their 2003 paper.
http://www.uoguelph.ca/~rmckitri/research/MM03.pdf
No other reconstruction puts 15th century temps at higher than modern.
Judge: "Ladies and gentlemen of the jury, have you reached a verdict?"
"We have, your honor".
"And what say you?"
"In the matter of Scientific Method v. Loehle and Mann, we find:
"On the charge of having incorrectly depicted the significance and magnitude of 20th century warming, we find Dr. Loehle 'Guilty' and Dr. Mann 'Not Guilty'.
On the charge of having incorrectly depicted the significance and magnitude of the Medieval Warm Period, we find Dr. Loehle 'Guilty', and Dr. Mann, 'Guilty'. (A stunned murmur ripples through the courtroom.)
On the charge of having incorrectly represented the impact of anthropogenic forcing on climate change, the jury finds Dr. Loehle 'Guilty', and Dr. Mann 'Not Guilty'.
On the charge that these inaccuracies were premeditated and intentional, the jury was unable to reach a verdict."
Judge: "In consideration of the jury's decision, I sentence Dr. Mann to serve 20 years of community service, in addition to the 15 years he has already served.
And I sentence, Dr. Loehle to life without parole publishing his findings in Energy and Environment. Bailiff, you may release the defendants on their own recognizance."
Members of the jury, the Court thanks you for your service. You are dismissed."
Ned did not mention those old papers; I was just trying to make sure that everyone here remembers how wrong they were.
It is great to see the LIA and MWP emerging, albeit somewhat attenuated compared to Hubert Lamb's work but let's not forget that sites like Climate Audit played a part. It is no longer possible to get away with reconstructions that ignore history.
What I like about Ljungqvist 2010 and most recent papers is that the data is easily accessible to the general public. This represents a sea change compared to the stonewalling and resistance to FOI requsts that were common in this field.
It seems that you are arguing that we should not be using the modern instrumental record at all? Or should we just refuse to countenance comparing it to the proxy record? Or is there some other subtlety I'm missing about your argument? Because my two interpretations seem to suggest that your position is pretty absurd.
Nice to get that sorted out. Time to move the conversation.
Thanks!
You say: "It's worth noting that all the reconstructions show the Medieval Warm Period, the Little Ice Age, and 20th-century warming (though Loehle 2008 only runs through 1935)." This is clearly not the case as Mann's original Hockey Stick denied both the MWP and the LIA.
"All the reconstructions" refers to all the reconstructions shown in Fig. 2 and discussed in the post.
Rob Honeycutt writes: it just seems to me that what is important is that current warming is unprecedented no matter how many crooks the handle has.
Yes, exactly. A lot of "skeptics" seem to have some kind of gut-level impression that if they can just keep pointing to evidence for a MWP the case for AGW will magically evaporate. But our confidence that CO2 and other greenhouse gases are responsible for modern warming doesn't rest on the question of how much warmer it is today than during the MWP.
The reasoning here isn't "Gosh, it's much warmer now, must be due to all that CO2!" Wally Broecker made the case that AGW was a threat way back in 1975, at a time when temperatures had been more or less flat for a couple of decades.
The idea that the existence of previous "natural" climate change would somehow disprove the existence of AGW is very poor reasoning. Does the fact that some fires are caused by lightning mean that some other fire couldn't have been caused by arson?
Plus, of course, there's the fact that Ljungqvist 2010 is a mid- to high-latitude Northern Hemisphere reconstruction. We know perfectly well the MWP and LIA were prominent in the extratropical Northern Hemisphere.
Albatross writes: Also, the MWP and LIA are both indications that climate sensitivity is not as low as the "skeptics" would like think, b/c fairly large temperature departures in the past were invoked with very little forcing.
Yes, that's a very good point. If the MWP turned out to be a large amplitude and globally synchronous event, it would be cause for serious concern. The logical implication would be that climate sensitivity is higher than we think, and therefore the projections for warming in the 21st century should be increased.
Alden Griffith writes: I adjusted Loehle, Ljungqvist, and HadCRU instrumental values to the base period 1850-1899. I then plotted the reconstructions with the land / land&sea instrumental values (using the same level of smoothing as the reconstructions), using global or hemispheric datasets where appropriate.
Hey, very nicely done. I was hoping that by starting this thread I would provoke other people into doing their own comparisons. (At the time I started writing this, neither Tamino nor Zeke had yet posted anything, so there wasn't really anything out there yet aside from Loehle's own spin over at WUWT).
apeescape writes: It's interesting how Loehle (corrected paper) does the "reconstruction." It's just a simple average across years [...] maybe I'm reading it incorrectly, but it seems like a very weak and inconsistent way of reconstructing temperatures [...]
Yes, exactly. I didn't want to get into the methodologies involved, but suffice it to say there's a reason why Loehle 2007/2008 was published in E&E. The methods used are absolutely atrocious. Frankly, the wonder is that the results of the reconstruction look as reasonable as they do.
There are a lot of different ways you could do a hemispherical/global reconstruction. You could use regression (like in the figure in apeescape's comment) or you could spatially weight the proxy temperature records so they're representative of the region, etc. Lots of different possibilities.
But just picking a bunch of time series (virtually none of which are in the Southern Hemisphere), averaging them, and calling it a "global temperature reconstruction"? As I said, there's a good reason it was published in E&E.
Shirley_Rocks writes: the record I found shows this as a 2009 release FWIW. I didn't find a 2010 record at all
You might be looking at a previous paper:
Ljungqvist, FC. 2009. Temperature proxy records covering the last two millennia: a tabular and visual overview. Geografiska Annaler: Series A, Physical Geography, 91(1): 11-29.
That was basically an article describing the proxy records that would then be used to create the reconstruction in this year's paper.
The new paper, with the reconstruction, is by the same author and in the same journal:
Ljungqvist, FC. 2010. A new reconstruction of temperature variability in the extra-tropical northern hemisphere during the last two millennia. Geografiska Annaler: Series A, Physical Geography, 92(3): 339-351.
It's new, so perhaps the database you were searching hadn't listed it yet?
CoalGeologist writes: The court is now convened. [....]
Heh. Very clever! I like the respective sentences...
Baz writes: Ah, I get it now! I forgot about different baselines. Thanks.
No problem. Dealing with differing baselines for temperature anomalies trips everybody up sooner or later.
fdijkstra writes: The red curves in the reconstruction graphs should be omitted, because the instrumental data are not comparable to the proxy records. Using non homogeneous data is an unsound scientific practice.
I don't agree. We know (from instruments, and other lines of evidence) that it is much warmer now than it was during the final years of Loehle's reconstruction (1900-1930). Ignoring that fact would be misleading.
When these red curves are omitted, Loehle is right, that Ljunggqvist confirms his results.
No, actually. The amplitude of the MWP-LIA difference in Loehle is anomalously large, particularly for what is allegedly a "global" reconstruction. The presence of a smaller MWP-LIA amplitude in Ljungqvist's extratropical Northern Hemisphere reconstruction does not "vindicate" Loehle's reconstruction.
There's also the issue that, whatever you may think of his results, Loehle's methods were exceptionally poor.
----------------
Whew! Did I miss anyone?
Loehle did his best to exaggerate the MWP, LIA and -for added effect- cut off the last 70 years or so, effectively "hiding the rise".
To be a denier is a good way of getting attention.
Seconded. That was an extremely nice analysis; the comparison between proxies and instruments 1850- was especially intriguing.
I used to get all excited about these temperature reconstructions too, until I started to understand the forcing imbalance components and the significance of the total energy gain or loss of the earth system over time in explaining warming or cooling of a massive body of land, ice, atmosphere and ocean.
Oh, and all the temp charts in this thread seem to stop at year 2000 - missing the last 10 years of flattening at a time when claimed AGW forcing is 'the highest decade in history'.
And; can anybody out there tell me what is the 'equilibrium TSI' and 'equilibrium surface and cloud refection' of the pre-industrial Earth?
Without those numbers - an accurate calculation of Solar forcing cannot be made and the relative proportions of CO2GHG and Solar forcing determined over time.
The data in Ljungqvist 2010 run through the 1990s (they are decadal means). The instrumental data shown in Figure 1 and Figure 2 run through 2010, though it's not particularly relevant at this scale.
And; can anybody out there tell me what is the 'equilibrium TSI' and 'equilibrium surface and cloud refection' of the pre-industrial Earth? Without those numbers - an accurate calculation of Solar forcing cannot be made and the relative proportions of CO2GHG and Solar forcing determined over time.
Climate forcings can be defined relative to any base period. I don't know why you have this obsession with trying to pin down "equilibrium" conditions, but you shouldn't assume that others here will share that obsession.
First, thanks for your valuable contributions here.
There is some squirming going on at AirVent, where Loehle has said this:
"but I eventually have remembered that my own reconstruction is set to a zero baseline for the entire 2000 yrs, so it is only possible to compare to other series that are centered likewise."
How might doing this affect the comparisons?
To compare it to anything else, you have to pick a period of time and assume that both Loehle and whatever-it-is should have the same mean during that period of time, then recenter Loehle's reconstruction to match that mean.
Loehle chooses to assume that his reconstruction and Ljungqvist's have the same mean over the entire 2000-year period (I basically did the same in Fig. 2). Alden Griffith's very nice graphic here is based on the assumption that Loehle should have the same mean as the instrumental data during their period of overlap. Both of these are probably defensible choices but it's important to understand the differences.
If you're most interested in comparison to the instrumental record, it's probably best to recenter Loehle's reconstruction to match that. Unfortunately, the period of overlap is only 80 years, since Loehle ends so early (1930s).
Thanks. That is what I understand reading this (I was trying not to "lead" you). But Loehle seems to be invoking the above quote as evidence that when done his way, his reconstruction is vindicated. Worse still, some are now using that quote above to suggest that people who are trying to realistically compare Loehle's reconstruction with Ljungqvist's are not being honest.
But what the heck does one do when Loehle's poor methodology has made it almost impossible to properly compare his reconstruction with those from other paleo groups? IMO, people are nevertheless sincerely trying (despite all the hurdles). Besides why should we take Loehle's word for it? That is how scientists test/validate their colleagues work/hypotheses. Scientists "A" (Loehele) makes an assertion, and others then test said assertion.
Well, going by the evidence submitted here and elsewhere Loehle's assertion/hypothesis fails horribly.
Figure 4. Warmest decades of the Medieval Warm Period, and coolest decades of the Little Ice Age, after re-centering each reconstruction to match the instrumental temperature record during the period of overlap.
Moberg is a bit on the cool side overall -- which might just mean it was anomalously warm during the calibration period used for centering. Mann and Ljungqvist agree very closely on the Medieval Warm Period, though Mann's Little Ice Age is not as cold.
Loehle manages to be both too warm and too early on the Medieval Warm Period and on the cool side during the Little Ice Age. This difference would not be all that noteworthy, except for the fact that Loehle 2008 is supposed to be a global reconstruction ... and the magnitude of the MWP-LIA difference should almost certainly be smaller for a global reconstruction than for a Northern Hemisphere one.
The other obvious point is that when we compare these to the current instrumental temperature record, the Medieval Warm Period seems to be about 0.7 degrees C cooler than the 2000-2010 mean temperature.
I agree the amplitude of anomalies the Loehle reconstruction are clearly too high for the excellent reason that you provided.
If anything, going by that Figure @ 50, Ljungvist agrees best with Mann08, not Loehle08. WUWT should have a post saying that Mann08 has (yet again) been vindicated...not going to happen of course.
Anyhow, IMHO, the important observation here is that current warm temperatures in the N. hemisphere are very likely to be unprecedented over the last 1500 years. Exactly how much is difficult to say, but I do not think that one can simply say "we can't be sure today's N. Hemisphere temperatures are warmer than those in the MWP". Zeke has demonstrated that current N. Hemi. temperatures are almost certainly warmer than those observed during the MWP, so has Tamino, apeescape, Ned and Alden......a nice coherent picture. The only incoherence that I can see is in the scrambling and weaseling going on by the "skeptics" and "lukewarmers".
The quote that Albatross cites a few comments back is rather illuminating. Loehle writes:
my own reconstruction is set to a zero baseline for the entire 2000 yrs, so it is only possible to compare to other series that are centered likewise
To be technically precise, it would only be possible to directly compare Loehle to other series that are centered on the 2000-year mean of Loehle's own reconstruction. That, of course, is probably the null set.
If you want to see whether Loehle's MWP is warmer or cooler than the present, you need to re-center Loehle to match some other series that includes present-day temperatures. This is what we do in the update to the post (above).