Craig Loehle on the Divergence Problem

Tree rings are widely used for reconstructing climate and past climates are critical for putting the current climate (including global temperatures) into the proper perspective. Is current warming unusual? Only a comparison to the past can tell.

To help gain a better understanding of the past and how global temperatures may have behaved, researchers frequently try to extract climate information that may be stored in the annual growth ring of trees. The standard practice is to calibrate annual tree ring width (and/or wood density) to the temperature under which the trees were growing using a linear model based on recent (e.g., 20th Century) data, and then interpret past rings widths as indicators of temperature. A linear model is one in which a unit change in temperature produces a corresponding unit change in the tree ring attributes—and a linear model assumes that this relationship applies over the entire range of temperatures.

In a recent research paper (Loehle, 2008), I show that if this linear model is mis-specified (i.e., a linear growth response is assumed but in reality the growth response is non-linear), even a model that appears to work well during the “training” (or “calibration”) period—the time during which both temperature and tree rings are available—may fail miserably during the reconstruction period—the time in the past when only tree rings or available, that is, prior to direct temperature measurements.

For example, Figure 1 shows a hypothetical non-linear growth response curve. On the left-hand side of the curve, as temperature increases, tree ring width also increases, but as temperatures continue to rise and the temperature exceeds a certain threshold, the tree-ring width begins to decline. This could be the result of the physiological response of that particular tree species, or to the influence of other environmental variables (for example, moisture could become limiting at higher temperatures).

Figure 1. Hypothetical non-linear growth curve that shows a changing tree-ring width response to temperature changes (from Loehle, 2008).

If a temperature/tree-ring model is built only during a period of time when the observed temperatures rarely exceeded the threshold temperatures, and thus a linear model is assumed and produces a good fit, the model makes a mess of things when reconstructing the temperature during a time when the true temperature exceeded the threshold temperature. Figure 2 demonstrates this. In this example, the true temperature (the solid black line) is poorly reconstructed (dotted line) from a linear model built when observed temperatures were below the threshold. In fact, the entire character of the true temperature change is misrepresented and warm periods actually are reconstructed as cool periods.

Figure 2. Reconstructed temperature (arbitrary scale) (dotted line) vs. actual (solid line) using a linear approximation to the quadratic from Figure 1. Temperatures larger than the threshold become inverted. Time scale can either be forward, showing divergence, or back in time showing failure to detect past warm periods (from Loehle, 2008).

This result indicates why one can not use tree rings for any periods warmer than the calibration period—a situation which is difficult to know a priori. The same issue could affect certain other types of temperature proxies (besides tree rings) as well.

For a much more detailed description of this “divergence” problem in tree-ring reconstructions of past climate, I invite you the read the full version of my paper.

A MATHEMATICAL ANALYSIS OF THE DIVERGENCE PROBLEM IN DENDROCLIMATOLOGY
Climatic Change
DOI 10.1007/s10584-008-9488-8

Craig Loehle, PhD
National Council for Air and Stream Improvement, Inc. (NCASI)

Abstract: Tree rings provide a primary data source for reconstructing past climates, particularly over the past 1000 years. However, divergence has been observed in twentieth century reconstructions. Divergence occurs when trees show a positive response to warming in the calibration period but a lesser or even negative response in recent decades. The mathematical implications of divergence for reconstructing climate are explored in this study. Divergence results either because of some unique environmental factor in recent decades, because trees reach an asymptotic maximum growth rate at some temperature, or because higher temperatures reduce tree growth. If trees show a nonlinear growth response, the result is to potentially truncate any historical temperatures higher than those in the calibration period, as well as to reduce the mean and range of reconstructed values compared to actual. This produces the divergence effect. This creates a cold bias in the reconstructed record and makes it impossible to make any statements about how warm recent decades are compared to historical periods. Some suggestions are made to overcome these problems.

This paper benefited greatly from discussions at Climate Audit and it is currently available at the journal site http://www.springer.com/earth+sciences/meteorology/journal/10584 under the “Online First” button.

If anyone wants a copy, email me at cloehle AT ncasi.org.

1. Steve McIntyre

Craig sent this to me a while ago and I’d undertaken to post this some time ago. We’ve discussed the upside down U response on several occasions here – for example http://www.climateaudit.org/?p=397 has a graphic from Schoettle that looks almost exactly like Craig’s Figure 1- referring to bristlecones no less.

I get the impression that a fairly flat curve at the top of the U for a not inconsiderable interval seems possible – which would render a reconstruction rather indeterminate in this interval and that this is just as big a problem as sorting out the two legs of the pant-leg.

• Craig Loehle

Re: Steve McIntyre (#1), When trees grow in a moist habitat, they may not respond to temperature as it warms beyond some point, giving a flat response. I cover this also in the paper and it creates a problem also, though not quite as bad as the parabolic function.

2. Soronel Haetir

Even worse than the upside down U itself, I could easily envision a plot with multiple maximum/minimum points if moisture were considered. This in addition to the even larger “near top” such a graph would exhibit.

3. Geoff Sherrington

Can anyone please point me to a good primary reference which shows a calibration period where a function of tree rings is graphed against known temperature? I’m not being lazy, there just seems to be a shortage of seminal, foundation graphs in the literature among good and bad references. An expert needs to give a recommended reading.

Short thought Craig, ahead of reading your book, you will be no doubt be expecting an argument that it’s not just ring width but isotopes and wood density etc that have been used in dendrothermometry to supplement ring width.

• andy

See Grudd and Torneträsk, at least couple figures there.

http://www.diva-portal.org/su/theses/abstract.xsql?dbid=1034

• Geoff Sherrington

Re: andy (#5),
Thank you, Andy

Re: Gary (#9),
Agreed, Gary. Sporadic temperature records are all we have for most of the time. They are, unfortunately, not a a good proxy for photosynthetic activity.

Re: Craig Loehle (#10),
Thank you Craig. Your clear exposition has been needed for some time now and I note its abundance of references. If you need an additional thinking point, there is “Air Pollution and Plant Life: Edited by J.N.B. Bell and M. Treshow – 2002 – Science – 465 pages”. Among other observations, note that some sulphur gases have been known to be phytotoxic for many years. Also, some plants deficient in sulphur can receive a significant input from mineral smelters. These are some – and there are more – more reasons why the recent, air polluted period is different to the pre-instrumental, (avoiding volcano discussion) again inviting caution.

Re: Rob Wilson (#13),

It is not easy to argue against the non-linear response that Craig has summarised. I am unaware of any method that can reconstruct if a tree spent its time on the left limb, the right limb or both. If you cannot make this distinction, then maybe it is time to state that current dendrothermometry is severly limited and should not be used. Is it time to make the call?

4. John Finn

Craig Loehle

This is fantastic – and exactly what I’ve been trying to say on pro-AGW sites for a number of years (admittedly in my often clumsy way).

The thing that amazes me, though, is how the use of tree ring data gained such wide acceptance in the first place.

One of the first Statistics exercises I was given was a linear regression problem, the purpose of which was to demonstrate how the assumption of a continuing linear trend is more often than not invalid – even if a strong linear trend is evident in the measured data. Recognising this did not require the statistical expertise of Steve McIntyre or Tamino, it just needed simple logic.

It’s incredible to think that high profile climate studies are effectively relying on the very assumptions our old stats lecturer warned us about.

5. Dishman

The species mix for a given region should be more or less optimal for the average climate of that region over one or more lifespans of the species. It’s not really a stable static equilbrium, but that’s a good first approximation.

Temperature excursions in one direction favor competing species that are more competitive in that direction, while harming those that are more competitive in the opposite direction.

For trees in the climate middle of the region, the reduced competitiveness from excursions in each direction should be approximately equal. For these trees, it should be possible to determine the magnitude of the excursions, but not the direction.

It might be possible to extract the direction data by comparing members of the same species from the warmer and cooler portions of its range. Trees in the cooler portion would be more competitive during warm excursions, while those in the warmer portion would be less so. That could still be confounded by variations in moisture, though.

• Dave Dardinger

Re: Dishman (#6),

It might be possible to extract the direction data by comparing members of the same species from the warmer and cooler portions of its range.

I agree and have made the same point here a couple of times. But I don’t know that it’s been implemented in papers purporting to to compare temperature with tree ring data.

6. DaveM

Thank you for this Dr Loehle. This kind of clear and easily understood presentation is of the kind that needs to be more available for individuals to see for themselves.

snip – policy

7. Gary

A complicating factor is that seasonal growth is a function of the number of degree days and not a measure of average temperature. While these two values may be close, they aren’t precisely the same thing. And when tree rings are calibrated to measured and adjusted temperatures at stations with reliability issues, the correlations become much less certain.

Another issue is the plasticity of the genome and the responses of individual trees to different climatic conditions. A long-lived tree that endured the LIA and the current warming most likely grows better at one time or the other. If two trees are sampled, one for the LIA and the other for the 20th century, both may be best-adapted to their particular temperature regimes. When spliced in a reconstruction the two-tree series may more accurately reconstruct temperatures than a single tree spanning the whole period. So while it might be argued that a tree that can survive a broad range of temperatures over many years is a valuable proxy merely for it’s age, where’s the evidence that it is equally sensitive to temperatures over that range?

8. Craig Loehle

It is well to remember that the use of tree rings for analyzing climate effects on trees was initially only for the recent time period. It was a way of understanding what influences tree growth. It was gradually extended to periods farther back without ever solving the nonlinearity problem that even Fritts in his 1976 book was aware of.

9. Rob Wilson

Greetings,
As I made comments on Craig’s original paper, and the divergence phenomenon is something that I have been looking at over recent years, I feel some comments might be helpful.

1. I entirely agree that linear modelling of tree-growth relationships is not ideal and the field is certainly ripe for some fancy non-linear modelling to be made. However, please do not forget that within the limitations of the instrumental data we have available, it is standard practices to test the temporal response using a spilt period calibration/verification procedure. Linearity is an assumption forced upon us. The non-linearity nature of tree-growth is relatively easy to model in a forward modelling sense, but it is a huge challenge to invert such models and reconstruct climate back in time. This has been debated for many years in the dendro-community and is certainly not new to ClimateAudit.

2. The divergence phenomenon is simply not noted at all sites around the world and critics of dendroclimatology and dendrochronologists themselves need to be careful about seeing divergence everywhere. If a site chronology correlates with some climate parameter for an earlier period with an r value of ~0.4, then do not be surprised if this weak relationship is not stable through time. We need to focus on those TR chronologies with the strongest signals, which are often easily explained through a simple ecological understanding of the location and site.

3. Non-linearity is simply one of many potential factors that need to be taken into account when addressing the divergence phenomenon. Please see the D’Arrigo et al. (2008) review.

4. Craig’s paper is very much theoretical in basis. Let’s look at Keith Briffa’s NH MXD based temperature reconstruction. This is, in some respects, Steve’s poster child for the divergence phenomenon and the question is, can we use this series to test Craig’s hypothesis.

Figure A below shows the NHD1 reconstruction. This is from Briffa et al. (1998) where the data were NOT processed to capture low frequency information as the focus of the paper was to identify volcanic signatures. The data have been regressed to extra-tropical land April-September temperatures using the 1851-1960. The divergence is quite clear after ~1970.

Between Figures A and B are correlations between NHD1 (and NHD2 – another flavour – different weighting) with the instrumental data for the periods 1851-1960, 1961-1994 and 1851-1994.

Figure B is the same as Figure A, but the time-series have been transformed to 1st differences.

Figure C shows running 51-year correlations between the time-series in Figure A (red) and Figure B (blue).

So what do these figures show:

1. The MXD data are much better than RW derived reconstructions, at these hemispheric scales, in picking up the year-to-year signal – as shown by the correlations using the 1st difference transform.

2. Despite the clear post ~1970s divergence in trend, the year-to-year signal post 1960 is actually stronger than the 1851-1960 period. Surely, if the relationship was quadratic in some way as Craig implies in the paper, the correlations would weaken and at some stage go negative. This is not the case.

3. Despite the limitations of regression (and reduced variance and amplitude etc), the NHD1 series tracks well the warm temperatures in the mid 20th century. However, the NHD1 series does not pick up the similar temperature ‘levels’ from 1970s to mid 1980s. Why would the trees respond to the earlier warm period and not to the later warm period.

So – take home message – blaming non-linearity is all well and good, and it is certainly something that needs to be considered, but the fact is, when one looks at real data, the answer is not that simple.

Rob

• Mark T

Re: Rob Wilson (#13),

1. I entirely agree that linear modelling of tree-growth relationships is not ideal and the field is certainly ripe for some fancy non-linear modelling to be made. However, please do not forget that within the limitations of the instrumental data we have available, it is standard practices to test the temporal response using a spilt period calibration/verification procedure. Linearity is an assumption forced upon us. The non-linearity nature of tree-growth is relatively easy to model in a forward modelling sense, but it is a huge challenge to invert such models and reconstruct climate back in time.

Yes, the data are “forced upon” dendros, but that is not an excuse to continue using linear reconstruction methods when they are clearly inappropriate. It’s a cop-out: “we have nothing better so this suffices.” No, it doesn’t. It’s not sufficient, and “not ideal” is an understatement.

Mark

• Craig Loehle

Re: Rob Wilson (#13), With all due respect, Rob, the fact that some sites do not show divergence in the late 20th Century does NOT mean that the linear assumption holds for even warmer periods, such as perhaps the MWP, in the past. All it means is that during the period in question you have not YET exceeded the linear portion of the growth curve. I also take exception to my work being merely theoretical, as I based my growth model curve shape on studies of tree growth, which I cite.

• Posted Dec 1, 2008 at 10:28 AM | Permalink | Reply

Re: Rob Wilson (#13),

Figure A below shows the NHD1 reconstruction. This is from Briffa et
al. (1998) where the data were NOT processed to capture low
frequency information as the focus of the paper was to identify
volcanic signatures. The data have been regressed to extra-tropical
land April-September temperatures using the 1851-1960. The
divergence is quite clear after ~1970.

Looks like ICE to me ( http://signals.auditblogs.com/2007/07/05/multivariate-calibration/ ) . Where can I find this data ?

• Posted Dec 1, 2008 at 11:00 AM | Permalink | Reply

Re: Rob Wilson (#13),

If a site chronology correlates with some climate parameter for an earlier period with an r value of ~0.4, then do not be surprised if this weak relationship is not stable through time. We need to focus on those TR chronologies with the strongest signals, which are often easily explained through a simple ecological understanding of the location and site.

This is incorrect in that higher signal strength in calibration will not lead to removal of divergent trees. I think Dr. Loehle’s paper pretty well lays this point to rest.

A second problem is that correlation sorting data with noise will distort the otherwise divergent shape of the data. Something I will post on tonight.

• Craig Loehle

Re: Rob Wilson (#13), A second point Rob is that if you only have a model calibrated against a certain period such as 1880 to 1960, there is no way to predict whether the model will show divergence against the instrumental record in a later period such as after 1980. You can have data that goes into the recent period, like Grudd’s Tornetrask, and say “look, no (very little) divergence” but you can’t predict it a priori.

• Kenneth Fritsch

Re: Rob Wilson (#13),

Non-linearity is simply one of many potential factors that need to be taken into account when addressing the divergence phenomenon.

So – take home message – blaming non-linearity is all well and good, and it is certainly something that needs to be considered, but the fact is, when one looks at real data, the answer is not that simple.

The Craig Loehle (2008) paper like that of Douglass et al.(2007) will probably serve climate science best by the replies to the paper’s agruments that are intent on showing some level of disagreement but at the same time show the theoretical and empirical weaknesses of the more widely used and accepted existing theories.

• Dave Dardinger

Re: Rob Wilson (#13),

I think we need to do some active listening (or reading in this case) of what Rob is saying before we run off in the various directions which seems to have happened.

Rob, I think you’re saying that if we want to claim that there’s a problem with tree rings having regions of nonlinear reaction to temperature, we should have seen signs of this when looking at yearly or short-term growth. Since there’s no sign of this in the graphs your present, it is unlikely there is such a problem. In Craig’s first response Re: Craig Loehle (#17), he brings up sites without a divergence, but I believe the site you’re looking at does show a divergence, so I believe he needs to recast his complaint (assuming it’s still valid).

As an afterthought it should be obvious that it’s a shame the reconstructions haven’t been brought up to date. This is clearly one of Steve M’s favorite points as can be seen by looking at the title of the #1 item in the “Favorite Posts ” category in the left column.

• MC

Re: Rob Wilson (#13), Just a quick question: the 1st difference transform is the difference between last year and this year plotted against this year (or last year, its not that much of a difference)? The reason I ask is this appears to show a linear trend with a stronger correlation to NH temps.
Well if this is the case and the 1st difference transform is as you have said then you have implicitly shown a quadratic relationship in real time. Your 1st transform is simply a discrete differential function i.e. large delta x, which if this shows a linear trend means the actual function is quadratic.
For any person in doubt consider that a continuous derivative is defined as:
df/dx = lim (delta x tends to infinity) ( f(x + delta x) – f(x) ) / delta x. A difference function can be related to this definition quite easily.

• MC

Re: MC (#39), Mistake in this, ha ha. Delta x tends to zero it should read.

10. Posted Dec 1, 2008 at 10:12 AM | Permalink | Reply

Took me a while to remember where I read this, hope you find it relevant:

“…the changes during the entire Holocene have been only 1 [degrees] or 2 [degrees] F–too small to ascertain with the natural climate indicators we have been using until now (such as tree rings and fossil pollen), whose accuracy is no better than 2 [degrees] F.”

http://findarticles.com/p/articles/mi_m1134/is_8_110/ai_79051532?tag=content;col1

• tty

That bit about Holocene climate changes being only 1-2 degrees Fahrenheit is completely wrong. It is true if applied only to the last millenium or two, but the early Holocene optimum was 2 or even 3 degrees centigrade warmer than the present over large parts of Eurasia and the Arctic. Such a change is easily visible in both pollen records and macrofossils.

11. Steve McIntyre

Jeff, take a look at the following by David Stockwell on correlation sorting. Reconstruction of past climate using series with red noise url, which was discussed here a couple of years ago. See also here. I’d previously done some simulations of the Jacoby-d’Arrigo picking procedure where they picked the 10 most “temperature sensitive” of 35 series series (all highly autocorrelated) and then averaged them. I calculated the hockey-stickness arising from this procedure as compared to the hockey-stickness of the Jac-dArr 1989 reconstruction and their recon was about at the median of the red noise examples. Jacoby and d’Arrigo refused to disclose the results of the “other” 25 series citing the “few good men” “argument” in a quite remarkable bit of stonewalling.

12. Sam Urbinto

What things tend to or might show is all good and fine. During period Y, site A shows divergence but site B doesn’t. It says nothing certain about what either did during period Z.

• Posted Dec 1, 2008 at 12:44 PM | Permalink | Reply

It does say for certain that you can’t trust A though.

13. Peter D. Tillman

Here’s the direct links to Craig’s paper:

14. MC

Good paper. Very straight forward. I didn’t know that some people have managed to show an inverted quadratic behaviour in trees, but at least its a start. The basic idea is a common one in science: you must characterise to your best ability a relationship before extrapolating. But its also a very obvious relationship in science that people sometimes step over and forget to do so thoroughly.
Re: Rob Wilson (#13), that first graph of NH temperature kind of looks like there’s a slow linear (maybe periodic on timescales of 200 years) heating since 1900 imposed on a 80 year cycle. I’ve never noticed it before. It looks surprisingly solar in origin i.e. the Suess and Gleisberg cycles. In fact what a laugh the next Suess maximum was 2002! But that’s a subjective statement in that I’m just eyeballing it.

15. tty

Re: Dishman (#6)

“The species mix for a given region should be more or less optimal for the average climate of that region over one or more lifespans of the species. It’s not really a stable static equilbrium, but that’s a good first approximation.”

This is simply not so. Climate change is often faster than the ability of plants (especially forest trees) to migrate, and the flora is often not in equilibrum with climate. An example that has only recently become clear is the Early Holocene (Preboreal-Boreal). This has traditionally been considered a dry, but fairly cool interval in northern Europe, based on the flora (pine, birch, willows). However recent work shows that the treeline was actually higher than today and consequently the climate was much warmer than previously thought. The reason is that temperate trees like oak, elm and ash had simply not had time to immigrate from their glacial refuges in southern Europe.

Very mobile organisms like insects frequently indicate much larger climate swings than traditional palynological analysis. For example during the last (Ipswichian) interglacial palynology indicates summer temperatures 1-2 degrees centigrade warmer than today in southern England while insects indicate about 4 degrees, a figure that is supported by other vagile organisms (mammals (e. g. Hippopotamus) and birds).

16. Rob Wilson

You are all missing the point.
I purposely used the Briffa NHD1 series where NO “correlation sorting” was made. It used ALL TR density data in the Schweingruber network.

Secondly, yes, there is a divergence – but it is in the trend – not in the inter-annual signal. In this example, Craig’s theory simply does not stand up – unless the tree growth response is frequency dependent – which is another debate altogether.

Anyway, I am obviously wasting my breath. I was not saying Craig’s hypothesis is wrong, but I would really like to see his hypothesis tested using some real TR proxy data and I am not sure if that is possible.

anyway – enough with venturing into blog space
R

• Craig Loehle

Re: Rob Wilson (#29), Rob: I did not say my theory explains everything. Why would trees track a warm spell at one time and not another? Perhaps there was more rainfall at the period when they responded. My point in my paper was principally that a good correlation during the calibration period does not guarantee that divergence will not occur later (as has been seen) or at an earlier time such as the MWP. I did NOT say that divergence will always occur, because that depends on the tree’s response and where you are on the growth curve when you do the calibration AND on what precipitation does when the warmer period occurs. Some trees and regions will show divergence and some not. Did you read my final paper?

• Mark T.

My point in my paper was principally that a good correlation during the calibration period does not guarantee that divergence will not occur later (as has been seen) or at an earlier time such as the MWP.

Exactly. It is impossible to make claims about whether or not divergence occurs during times from which no instrumental data are available.

Mark

17. Posted Dec 1, 2008 at 1:23 PM | Permalink | Reply

#30, yes, but the point is that the margin of accuracy of some proxies are no better than 2 degrees, which is, at least to this untrained eye, rather large.

18. Steve McIntyre

#31. Actually, the issue is a little different. Some of the important reconstructions have been brought up to date, as I observed in my August presentation in Erice.

For example, Ababneh updated the Sheep Mt record; Grudd updated Tornetrask; an updated Polar Urals version is used in Esper 2002. Each of these updates has a material change on medieval-modern relationships in series used over and over again.

But these updated version are ignored in the multiproxy reconstructions.

19. Steve McIntyre

#13. Rob, the large-scale Schweingruber series are networks that are well worth considering and I’ll definitely take a look at your observations, which are, I’m sure, thoughtful. If you’ve got a theory about this series, then great. The observation that you make in this post, whatever its validity, has, to my knowledge, not appeared in dendro literature, despite the divergence problem being an outstanding issue for over a decade.

I made no claim to priority in raising this issue, referring in my own threads to dendo literature, including Briffa et al 1998. While you credit dendros with raising this issue, the matter was not raised in IPCC drafts and NO dendo made any review comments noting this. As a reviewer, I objected to the truncation of the post-1960 Briffa data – the justification of this truncation has been scandalous. As an IPCC reviewer, I asked Briffa to include the post-1960 portion and explain it as best they could. While they did not agree to show the truncated data (that would be “inappropriate” , they did agree to include comments on divergence.

If the points in your above comment had pre-existed in the literature, then I think that you would be entitled to reproach Loehle for not considering the points. However, to my knowledge, they don’t and your points are worth considering but there’s no reason to snip at Loehle for not considering them.

20. xtronics

RE:Rob Wilson (#13),

We need to focus on those TR chronologies with the strongest signals, which are often easily explained through a simple ecological understanding of the location and site.

Is this true? What justifies such an approach? Most sites don’t have this situation so it would not represent most sites.

You need to be very careful if you want this to be considered real science – ‘Even a broken clock is right twice a day’.

“The only way to have real success in science … is to describe the evidence very carefully without regard to the way you feel it should be. If you have a theory, you must try to explain what’s good about it and what’s bad about it equally. In science you learn a kind of standard integrity and honesty.”
–Richard Feynman

What is missing from a lot of what is called ‘climate science’ are papers that understand what Feynman is talking about. He talked about a special ‘bending over backwards’ to be honest.

Where is the ‘what’s bad about it’? Are there things that could confound tree rings as a signal to temperature even besides moisture? Off the top of my head I can imagine that volcanic activity – even very remote – can fertilize. Where are the lists of confounding variables and what has been done to mitigate their effects in these papers?

At some point, I worry that Mr. McIntyre’s efforts could be better spent. I think that once these players show that they won’t share the code or data from their papers they are no longer in a world recognizable as science. How much effort should be focused on their work?

21. Sam Urbinto

Jeff Id: It tells us how much we can rely upon any particular metric and may give us insight on ways to try and increase the reliability of data.

Mark T: Exactly. Does divergence occur during times from which no instrumental data are available? Maybe. Maybe not.

Rob Wilson: Perhaps if the point was more clear at first, people wouldn’t have missed it? Something like

The Briffa NHD series with no “correlation sorting” was used specifically because It used all TR density data in the Schweingruber network. There is a divergence, but in the trend, not in the inter-annual signal. Craig’s theory only stands up if the tree growth response is frequency dependent. (Which is another debate altogether.) Craig’s hypothesis should be tested using some real TR proxy data, although that may not be possible.

22. Steve McIntyre

Rob, it’s not just Craig who implies a nonlinear relationship. Here’s a graphic from a dendro specialist.

It’s not unreasonable to consider the effect on inverting ring widths under such conditions.

As to your point that other factors may be involved:

blaming non-linearity is all well and good, and it is certainly something that needs to be considered, but the fact is, when one looks at real data, the answer is not that simple.

fair enough. But that does not remove the obligation for proving the proxies that lies upon multiproxy users of such proxies and the fact that there are problems over and above simple non-linearity hardly offers much reassurance.

23. Craig Loehle

What concerns me is Rob’s statement that a certain data set is a “good” one. How can he be sure of this BEFORE testing it for divergence? What is different about good data? I think Steve M has been asking this for a long time.

24. Craig Loehle

To put it another way, if you can only pick the winning horse after the race is run, then you are perhaps not so good at picking horses. I hope you can see, Rob, that the decisions made about which proxies are “good” rather look like that.

25. Steve McIntyre

#42. I agree. This whole thing of deciding after the fact drives me crazy. I wish you could do it for stocks.

Howeer, as Rob points out, the Schweingruber chronologies used in Briffa et al was picked before the fact. I’m pleased that Rob used this as an example, as this is a valid population. It took me about three years and FOI actions to get them to identify which sites were used, but this information is now available.

However, in most Briffa articles (tho perhaps not NDD!, I’ll have to check), there is a selection from this network depending on correlation to gridcell temperature – so not all instances of this network are clean.

And not all chronologies in the network are available (most are, but not all) – despite Jones’ untrue claims on this matter to the 17 Santer coauthors,

26. Posted Dec 1, 2008 at 5:05 PM | Permalink | Reply

Rob does make a good point about the high frequency aspects still having a positive correlation.

I’m no expert on tree responses but it does seem likely to me that simply the earliness or lateness of frosts (length of growing season) would continue the positive high frequency temperature correlation while the net growth enhancement could be inverse quadratic. How would you sort those variables out?

Maybe I’m remembering incorrectly but I recall reading something about gridded Schweingruber MXD data being processed in such a way as to “possibly” create an artificial temperature component in it during the recent years. This could explain it as well.

It seems to me Any way it’s cut, divergence or the possibility of divergence should invalidate the use of tree rings, MXD or any proxy until they are demonstrably shown to be non-divergent in the present and in history. Then the group can be used together as Rob did – not sorted by correlation. The fact that there is a nearly trend-less high frequency correlation in the average doesn’t change anything for me. The data clearly isn’t temp in recent years so we know it can diverge from temp at any time. This is not being a “denier” but rather placing the burden of proof where it belongs, on the authors and users of the data.

Re: Sam Urbinto (#38),
I was just trying to say, IMO divergence at any time invalidates group A. No disagreement from me.

27. Steve McIntyre

#44. Quite so. This is elementary statistical procedure. Amazing that it’s so controversial.

28. Hans Erren

check these!

Summer maximum temperature in northern France over the past century: instrumental data versus multiple proxies (tree-ring isotopes, grape harvest dates and forest fires)
N. Etien, V. Daux, V. Masson-Delmotte, O. Mestre, M. Stievenard, M. T. Guillemin, T. Boettger, N. Breda, M. Haupt and P. P. Perraud

The IPCC on a heterogeneous Medieval Warm Period
Jan Esper and David Frank

6 Conclusions
The debate on MWP heterogeneity started over a decade ago, when Hughes and Diaz (1994) compared several long-term climate reconstructions available that time.
This early analysis, however, suffered from comparing tree-ring records where the low-frequency climate variability was preserved (i.e., RCS detrended) with non-RCS chronologies, and overlooking sample replication issues. These factors helped in reaching the conclusion that the MWP was heterogeneous. Since then, several large-scale studies have been published demonstrating that data sparseness and low replication before about 1200 introduce random variations in the single records and increase uncertainty in any subsequent hemispheric scale average (Cook et al. 2004; D’Arrigo et al. 2006; Frank et al. 2007b). This evidence should not be confused with spatially heterogeneous temperatures during MWP. Given the wide acceptance of the AR4 and the notion of a more chaotic climate towards the Dark Ages, it thus seems relevant to recall that we currently do not have sufficient widespread, high-resolution proxy data to soundly conclude on the spatial extent of warmth during MWP.

(emphasis mine)

29. Pat Frank

Rob Wilson (#13), wrote, “We need to focus on those TR chronologies with the strongest signals, which are often easily explained through a simple ecological understanding of the location and site.” (emphasis added)

And which ecological understandings are judgmentally qualitative. Data resting on qualitative judgments permit the extraction of no quantitative metrics. Absent a quantitative physical theory, statistical correlations have no obvious physical meaning. TR paleo-temperature reconstructions are a crock, and are especially ludicrous when plotted to 0.1 C.

30. Kenneth Fritsch

I think the refusal to see the dangers of using in-sample data versus out-of-sample in arriving at conclusions has something to do with the observer not being capable of seeing how well data snooping can build a correlation. I think the observer does not recogonize how easily these high, but spurious, correlations are to come by in the selection process.

31. Steve McIntyre

Let me try to re-state the point that Rob made above in what I think is a clearer way than Rob did, while preserving the point. Below is a graphic comparing the Briffa NHD1 series – which is a relatively non cherrypicked series and as Rob observes, the typecase for ‘divergence’. Below is a simple scatter plot showing the relationship of the MXD index to temperature, stratified by period 1880-1960 and 1960-1994. This is the sort of baby food analysis that should be the first statistical report upon observing the phenomenon, though I am unaware of this simple plot in the dendro literature.

As you see, in both periods, notwithstanding the “divergence” problem, there is a linear relationship between CRU99 temperature and the Briffa NHD1 index in both the the truncated and non-truncated period (t-values of 8 and 3 for the two periods.)

Based on this plot, I agree with Rob’s point that, whatever the cause of NHD1 divergence, it is not, in this case, due to upside-down quadratic nonlinearity or else we would see the development of a negative relationship between temperature and MD in the latter period.

As Rob observes, this is a topic that he has reflected on. Indeed, as I discussed last year, Rob was a co-convener of an excellent AGU session on the divergence, where I characterized the “young dendros” as being discontented with the platitudes espoused in the literature papering over the problem.

a) In one of Rob’s articles, he wondered about the instrumental record in Yukon. In that article, he eventually decided that the GHCN adjustments to the temperature record were problematic and has elsewhere encouraged the ongoing examination here of adjustments to the instrumental record. Speculating a little on this, if, by any remote chance, there were inhomogeneities in the Russian temperature records (which are a large portion of the relevant records), perhaps arising out of incidental events like the Russian Revolution, World War I, Stalin’s gulags or World War II, this could explain the apparent drift in the relationship. The required drift would imply warmer temperatures in the 1880-1960 than presently thought.

b) In another one of his articles, he wondered about what I’ll call “plasticity” in temperature distribution about the same mean i.e. one could contemplate altered distributions of temperature maxima and minima so that the active ingredient affecting MXD varied without a commensurate variation in average temperature. Thus, one could contemplate a situation where there was a substantial increase in Siberian winter temperatures, without a commensurate increase in summer temperatures. Rob investigated details like this in respect to B.C. series.

c) In my opinion, the issues with Graybill bristlecone chronologies are far more likely to arise out of mechanical deformations arising out of the strip bark process itself than from CO2 fertilization. However, believers in CO2 fertilization can hardly cavil at the idea that CO2 fertilization (or ozone or whatever) could cause some change in MXD versus temperature. My beef here is not that such a relationship is conceptually impossible – only that it’s not enough for engineering quality analysis (or even scientific analysis) to simply throw the possibility into the ring and then pretend that that’s a proof. I’m not saying that Rob does this, but the handling of the divergence problem in institutional literature (e.g. NRC, IPCC) is very unsatisfactory and, to my knowledge, Rob and his practical colleagues have not spoken out against this.

In respect to the matter at hand – inversion of MXD data, if the problem arises out of a) or b) type problems, it seems to me that one gets the same sort of problem as in the situation discussed by Craig Loehle.

PS. This only refers to MXD data. I’ve never seen any corresponding information on the Schweingruber RW data. Briffa et al 1998 alluded to a similar problem with RW data and illustrated it in a graphic that I’ve used on many occasions but they did not provide a digital version of the RW composite and never discussed it in subsequent articles. Maybe Rob could comment on whether there is a corresponding situation with the Schweingruber RW network.

Here is code for the above analysis:

url=”ftp://ftp.ncdc.noaa.gov/pub/data/paleo/treering/reconstructions/n_hem_temp/nhemtemp_data.txt”
names(nhd)=c(“year”,”nhd1″,”nhlmt”,”nhd2″)
nhd=ts(nhd,start=1400)
#this goes to 1400- 1994

url< -"ftp://ftp.ncdc.noaa.gov/pub/data/paleo/treering/reconstructions/n_hem_temp/briffa2001jgr3.txt&quot;
temp<-(Briffa< -900); Briffa[temp]<-NA
dimnames(Briffa)[[2]]=1880) &(Data\$year<1960);
temp2=(Data\$year>=1960)
layout(1);par(mar=c(4,4,2,1))
plot(Data\$cru[temp1|temp2],Data\$mxd[temp1|temp2],xlab=”NH Temperature”,ylab=”MXD Index”,type=”n”)
points(Data\$cru[temp1],Data\$mxd[temp1])
points(Data\$cru[temp2],Data\$mxd[temp2],col=2,pch=”+”)
fm1=lm(mxd~cru,data=Data[temp1,])
lines(Data\$cru[temp1],predict(fm1,newdata=Data[temp1,]))
fm2=lm(mxd~cru,data=Data[temp2,])
lines(Data\$cru[temp2],predict(fm2,newdata=Data[temp2,]),col=2)
legend(“topleft”,fill=1:2,legend=c(“1880-1959″,”1960-1994″),cex=.8)
title(“Briffa NHD1 vs CRU99 Temperature”)

• Posted Dec 2, 2008 at 5:13 AM | Permalink | Reply

looking at the temperature data, it is clear that recent data is not ‘like’ the calibration period data. In such case, Brown’s book, page 23. says

then one is restricted to inference from the conditional distribution of Y for given x

that is, CCE in my terms, Y=proxy, x = temperature. So, if one uses incorrect calibration method, it is not a surprise that one finds divergence.

• Kenneth Fritsch

Re: UC (#53),

looking at the temperature data, it is clear that recent data is not ‘like’ the calibration period data

Steve M, how about providing us with the regression statistics for the two time periods plotted? Can we say that they are statistically different?

• Dave Dardinger

As you see, in both periods, notwithstanding the “divergence” problem, there is a linear relationship between CRU99 temperature and the Briffa NHD1 index

Isn’t it actually the case that you can find a linear relationship in any such cloud of data? Just eyeballing it it’s clear you could draw a non-linear curve through the data which would fit better.

• Kenneth Fritsch

Actually, by eyeballing , the more recent data plot does look decidedly nonlinear or at least much less than the earlier data. At what point does an a priori allow one to look further than a linear relationship. I do not think it would be proper to just drop this analysis where it stands.

For the casual observer, a separate plot of both time periods or a more differentiated plot color would show the difference better.

• Kusigrosz
Posted Dec 2, 2008 at 11:52 AM | Permalink

Re: Kenneth Fritsch (#58), I wonder if the Akaike Information Criterion (probably the AIC-c version) might be of use here; it can give a clue how many parameters are justified when fitting the data. There are however other criteria of such kind (Bayesian Information Criterion, etc), and AFAIK there is no universal agreement which one should be used in any given case.

• Craig Loehle

Re: Steve McIntyre (#51), Thank you Steve, that is quite clear. I frankly did not follow Rob’s description of the data. I don’t think this case is helpful for any argument that a linear model can be extrapolated beyond the calibration period, however.

• Craig Loehle

Re: Steve McIntyre (#51), It looks to me like if we did not know this data was supposed to be separated into two time periods and we just evaluated the entire data set, the regression would be very very weak (very low R^2). That is, it looks like virtually NO relationship with temperature (I’m not an R programmer so hard for me to test this).

• RomanM

The simple regression gives an R-square of .19.

For Steve’s combined two-line regressions, if you program it as a single regression, the R-square rises to .47, a considerable improvement. The difference in slopes is not significant (p = .323), but the “shift” in the lines definitely is with a t = -7.573 and a really small p-value.

Looking at the residual vs. fit plots does not always tell the whole story. It is often informative to look at the residuals from the regression, plotted against other variables which have not been used in the regression. In this case when you look at the residuals vs. year, you get:

The difference between the two plots is mainly the shift at 1960 since the difference between the two slopes in the two-line fit is not that big. It seems there might be some time autocorrelation in the residuals and it is pretty clear from the simple regression plot that something is happening in the post 1960 time period that is affecting the mxd variable even after the effect of annual temperature has been linearly removed.

The R script continuation for the two-line regression and the plots is

#Steve’s two line regression

post60 = c(rep(0,80),rep(1,38))
post60cru = post60*Data[temp3,]\$cru
fm3=lm(mxd~post60+cru+post60cru, data = Data[temp3,])

#simple regression :
temp3=(Data\$year>=1880)
fm4=lm(mxd~cru,data=Data[temp3,])

par(mfrow = c(2,1))
plot(1880:1994,fm3\$res, type=”l”,main =”Residuals from Two Line Fit”,ylab =”Residual”, xlab=”Year” )
plot(1880:1994,fm4\$res, type = “l”, main = “Residuals from Simple Regression”, ylab =”Residual”, xlab=”Year”)

• Kenneth Fritsch
Posted Dec 2, 2008 at 7:03 PM | Permalink

Re: RomanM (#76),

Roman, the “simple regression” as I surmise it from your code was using all the data from Steve M’s plots from 1880-1994 and that yields an R^2 = 0.19. You then describe a two line regression that from the residual plot versus year extends over the period 1880-1994. That R^2 = 0.47, which is a major improvement.

The two line separates the post 1960 data but covers the period from 1880-1994 (as noted from the residual analysis). I think I know what the two line represents but I am not sure.

Also could the residuals of the simple regression be indicative of a nonlinear relationship. The higher temperatures, where one would expect the nonlinear effects to show, are, of course, not reached until the divergence period, post 1960.

• RomanM
Posted Dec 3, 2008 at 7:00 AM | Permalink

Sorry if I wasn’t clear enough in my description. Yes, you surmise correctly. The simple regression involves the linear relationship MXD = a + b Cru across the same period used by Steve 1880 – 1994. The “two-line” regression does in a single procedure what Re: Steve (#51) did in his earlier post by splitting the data into pre and post 1960 and then fitting two lines independently to the data. By doing both of these in a single equation, it enables the ability to calculate a single R-square for the combined line fits as well as formally testing whether parameters such as the slopes of the two lines are different.

The standard diagnostic graph for evaluating a regression is to look at the residuals vs. fits plot which visually displays possible relationships between the “errors” made by using the regression and the value predicted by the line. It can indicate that the assumption that the variability of points from the line does not depend on the values of the predictors is not tenable and, in the simple case of a single predictor, can indicate the presence of non-linear relationships between the variables (although a similar effect is obtained by viewing the line graphed on the same plot as the points themselves). If there are more predictors or if there are other variables not used in the prediction process (such as year in this situation), graphing the residuals against those variables can indicate whether something else is going on. My intent in providing such graphs was to show that there appeared to be a time-varying “pattern” in the mxd variable after the CRU temperatures were used in a linear fashion to account for temperature effects.

What causes that relationship? The higher temperature nonlinearity could possibly be such a factor because the temperatures are related to time in this case. However, Steve raised a variety of other issues which conceivably could also produce such an effect. I don’t think this question can be answered meaningfully solely on this data and that more examination of the issues with the proxies is the route to go.

• Kenneth Fritsch
Posted Dec 3, 2008 at 8:11 AM | Permalink

Re: RomanM (#91),

Thanks, Roman for the explanations. I thought what you did was a segmental regression and for the reasons that you list. Is it completely proper to use such a regression if the curve is rounded and does not display a sharp break between two straight lines?

• RomanM
Posted Dec 3, 2008 at 8:55 AM | Permalink

It depends on what you are trying to do with it. In practice, it is probably a rare occasion that something is exactly linear so we often approximate situations with a linear regression function. If the function is severely nonlinear with unknown mathematical form, we can use segmented and spline regression techniques.

However, in the case at hand, I would not really use the term “segmented” since the variable dividing the data set into two parts (year) is not the independent variable in the regression (cru). The “trick” using indicator variables to turn it into a single procedure just makes it look like a segmented regression. In fact, I would tend to call it an analysis of covariance if I had to give it a classification.

• MC

Re: Steve McIntyre (#51), I agree with Dave Re: Dave Dardinger (#55), Thank you Steve for this graph. Finally the crux of the matter. I know that statisticians fit linear trends as the simplest relationship but just look at the uncertainty in that fit. Get rid of this linear trend assumption and accept we just have nowhere near the accuracy in the data to say anything. This is the plain truth. But finally its good to see a graph like this to say so.
If you showed that graph to any reasonable engineer or physicist and said what kind of relationship do you see they would just say ‘I couldn’t begin to tell you’. For fits in engineering/physics we are talking r^2 of 0.950 and way better before we believe the fit might be meaningful. Which is also why a lot of physicists and engineers don’t use statistics to any great detail. They don’t have to rely on it. They just try and improve the experiment/process.
Also I think Re: UC (#63), has just demonstrated the absurdity of it all.

• Posted Dec 2, 2008 at 2:57 PM | Permalink | Reply

Re: MC (#71),

For fits in engineering/physics we are talking r^2 of 0.950 and way
better before we believe the fit might be meaningful.

The two estimators I’m talking about are related by

ICE=r^2*CCE ,

so with high correlations the question which one to use is not that
important. But in the case we have here, there is a big difference,
as #63 shows.

• MC
Posted Dec 3, 2008 at 3:08 AM | Permalink

Re: UC (#75), I see what you mean, though I only used the r^2 reference in passing. To tell you the truth I don’t use it. I’ll say that again: I don’t use it, nor any other correlation type analysis. What I do is define my measurement errors and apply appropriate error bars, then fit the simplest relationship with minimum assumptions. If the error bars are large I don’t do a fit and I can’t say anything but “we need to be more accurate”; if they are really tight then I would try a fit, but on the understanding that it is only valid of the range of the data set (unless I can derive some type of first principle relationship). Then I repeat the measurements and see if the relationship is still there.
The big problem I see is that the repeatability of climate data sets is very low and this makes trend fitting etc very dubious. The other problem is that people aren’t being realistic about trend fitting hence all the low correlation trends still be used and bandied about.

32. lgl

“Many scientists previously thought the reduction in sunlight lowered the Earth’s temperature and slowed plant and soil respiration, a process where plants and soil emit CO2. But this new research shows that when faced with diffuse sunlight, plants actually become more efficient, drawing more carbon dioxide out of the air.”
http://www.gsfc.nasa.gov/topstory/20011210co2absorb.html

33. Posted Dec 2, 2008 at 5:26 AM | Permalink | Reply

The moral of this story is that tree growth is as complicated a thing to predict as climate and is subject to many exernal influences other than climate.

We’re trying to guess box office receipts for a particular movie by counting the number of people coming out of a multiplex. Or, more accurate, counting the number of people leaving a shopping mall that has a multiplex in it.

34. Steve McIntyre

#57.Kenneth, I gave the scripts. Just go summary(fm1) and summary(fm2) and you have the regression info.

• Kenneth Fritsch

#57.Kenneth, I gave the scripts. Just go summary(fm1) and summary(fm2) and you have the regression info.

As a retired guy, I can and will, but in the meantime reporting only the p values (or the t equivalents) of the regression without the R^2 and any autocorrelation measures could be misleading.

Further, if one had reason for suspecting a nonlinear relationship over the recent time period, I do not see how reporting the probability of the trend being greater than zero informs as to the question before us. Certainly a true nonlinear relationship could yield a probability (t) that high or higher when assuming a linear relationship.

35. Andrew

There’s a seminar by a PhD student in the stats department at Lancaster University this week:

Climate Reconstruction from Tree Rings

http://www.maths.lancs.ac.uk/department/events/statisticsForum/talk.2008-10-01.5604129588

They’re proposing a Bayesian hierarchical model. I guess how sensible the results will be will depend on the model assumptions and the priors. In particular:

In the environmental sciences, a large knowledge base is typically available on an investigated system or at least on similar systems. This makes the application of Bayesian inference techniques in climatic reconstruction very promising.

seems to be suggesting they’ll use informative priors.

• John Baltutis

Re: Andrew (#60),

Bayesian hierarchical model implies BS output.

36. Steve McIntyre

#61. Craig, the payback time for learning R is almost instantaneous so I’d urge you to take the plunge. The scripts here are a good way of learning with data sets of practical interest.

37. Posted Dec 2, 2008 at 10:22 AM | Permalink | Reply

So, just for fun, let me try regressing proxies on temperature,

and take a closer look on the problematic period:

38. Posted Dec 2, 2008 at 10:45 AM | Permalink | Reply

The NHD1 seems to be variance-adjusted, another advantage unique to dendroclimatology. Any change to find the non-adjusted version ?

39. Steve McIntyre

#64. Nope. Briffa refused for years to even identify the sites used in this reconstruction, so the chance of getting unadjusted NHD1 as less than zero. We eventually got the sites identified through British FOI, but that took a long time. From time to time, I’ve done work on replicating their methods. I need to re-visit this now that FOI has produced a better foothold. They still haven’t produced all the data though much is available. I’m reluctant to spend a lot of time on this until I can get a complete data set in case the discrepancies matter. This is now nearing 4 years of obstruction by Briffa to me directly and over 10 years of data withholding overall.

40. Patrick M.

Possibly off topic, if so, go ahead and snip:

When dendros use tree rings in proxys do they just use the ring width or do they use chemical analysis of the matter that makes up the rings also?

• Posted Dec 2, 2008 at 12:36 PM | Permalink | Reply

Re: Patrick M. (#67),

Others are better qualified to answer so someone correct me if I mess up but there are multiple types of data. The MXD type is a latewood density analysis, some of which has undisclosed processing steps hidden in the data before it is presented as raw that’s why Briffa data cannot be trusted. Even if the Briffa work is the best in the world they have to disclose their methods and original data to be trusted. Most of the tree proxies (ITRDB) that I have seen is ring width but there is also some work on isotope measurement. I had asked Dr. Loehle in the past about other biological chemical traces in the cells but at the time he didn’t know of anything in particular off-hand.

• Craig Loehle

Re: Jeff Id (#69), Jeff: I came across this paper using δ13C variations in tree rings of Japanese cedar
Kitagawa, H. and Matsumoto, E. 1995. Climatic implication of δ13C variations in a Japanese cedar (Cryptomeria japonica) during the last two millennia. Geophysical Research Letters 22, 2155-2158.

• Kenneth Fritsch

Re: Patrick M. (#67),

When dendros use tree rings in proxys do they just use the ring width or do they use chemical analysis of the matter that makes up the rings also?

Your post gives me the lead in to note something that disturbs me about what I see as a recent development in obtaining a good correlation in regressing tree growth to temperature. I must be careful here as I have not read extensively on this matter but have seen such methods used in some papers that I have read.

I have seen a combination of TW (tree ring widths) and MXD (density measure) used in further combination with selected (contiguous) months and in further combination with maximum temperatures. If all these criteria were clearly spelled out a priori and then put to the test, I would not have as big a problem as at the other extreme where the criteria selection process becomes one of simple data snooping and over fitting.

• Craig Loehle

Re: Kenneth Fritsch (#72), Kenneth: you are not wrong. When these types of analyses were used in an exploratory mode as “what governs tree growth at this site?” which leads into further studies, no problem. But when you allow various combinations of months and even last year’s weather (which can have biological meaning for some species which set buds the previous year) the potential for snooping is enormous.

41. GTFrank

All of this hand wringing over divergence.

1. There has been divergence in the recent past between TR proxies and global temperature.
2. I have read that the divergence may be related to CO2 fertilization.
3. We have records of global CO2 in the recent past.
4. We have records of global rainfall in the recent past.
5. We have records of global temperature in the recent past.
6. We have records of global solar activity in the recent past.
7. We have records of global volcanic activity in the recent past.
8. We have TR records in the recent past.
9. We probably have records of other applicable global data that I am not aware of.

The “true” model for TR width is obviously not a simple temperature to width linear relationship. (witness divergence) It might be a somewhat linear relationship, but with other nonlinear factors in the equation, which may have more of a contribution in the recent past. It could obviously be nonlinear in the same fashion.

Why doesn’t someone (not this EE) use the known factors to create a model that is truly “rigorously consistent” with the temperature record in the recent past. Understanding that model well could put historic TR data in perspective.

Heck, make a bunch of models so we can check them all 10, 20, and 30 years down the road and see how they track.

Just tell me it’s not that simple, and I’ll go back to lurking.

• Kenneth Fritsch

Re: GTFrank (#74),

Why doesn’t someone (not this EE) use the known factors to create a model that is truly “rigorously consistent” with the temperature record in the recent past. Understanding that model well could put historic TR data in perspective.

Heck, make a bunch of models so we can check them all 10, 20, and 30 years down the road and see how they track.

Just tell me it’s not that simple, and I’ll go back to lurking.

It is not that simple, but that would be no excuse for going back to lurking.

GTFrank, you will get little response here because it is unclear what you are proposing. If you make a model inputting all your conjectured variables using in-sample data you will be able to come up with an excellent correlation. It will be a prime example of over fitting and data snooping. If you come up with sufficient numbers of models, one of them will likely look valid with out-of-sample data by pure chance.

I think that you have missed the entire point of what was being said here about the dangers of data snooping and modelling with in-sample data that is used without a priori reasoning. If I am wrong about this, please reply and set me straight. I am forever fascinated by very intelligent people failing to appreciate the dangers of data snooping.

42. Steve McIntyre

#76. Roman, an important nuance here: as I mentioned above, it is possible that a) inhomogeneity in the temperature record or b) changes in the relation of “active” temperature (which for the trees is summer temperature) and annual average temperature, could also cause this sort of drift. There are also inhomogeneities in how tree ring data is collected – these biases have been discussed form time to time and one potential bias noted in the dendro literature is that the typical sampling restriction to trees with a minimum diameter creates an inhomogeneity relative to historical records.

Another defect in tree ring records is that altitudes of trees can migrate up and down their range and dendros do not record the sample altitudes in their archived records.

43. John F. Pittman

RomanM don’t know if this is appropriate.

Interesting part….
The distribution of known adjustments is not symmetric — adjustments are more likely to be negative than positive. The most common reason for a station needing adjustment is a site move in the 1940-60 period. The earlier site tends to have been warmer than the later one — as the move is often to an out of town airport. So the adjustments are mainly negative, because the earlier record (in the town/city) needs to be reduced [Jones et al., 1985, Jones et al., 1986]. Although a real effect, this asymmetry is small compared with the typical adjustment, and is difficult to quantify; so the homogenisation adjustment uncertainties are treated as being symmetric about zero.

44. Old Chemist

I know most of you are number jocks, but there is a fundamental issue which appears to be missing here — if you apply statistal analysis to some problem there should be some basis in reality for obtaining an answer. Tree ring growth is not only regulated by a host of environmental factors but also by genetics. Feed-back mechanisms regulate the deposition of polysaccharides, lignans and other molecules which make up the heartwood of the tree. Not only is tree growth developmentally regulated it is limited and controlled by the genotype of that tree. The idea of coaxing out a temperature from a tree ring analysis does not appear to me to be valid — I note most of the tree ring reconstuctions are flat lines which to me makes the argument for a tightly genetically regulated process rather than a constant temperature regime.

• Craig Loehle

Re: Old Chemist (#81), Even after cherry picking which season combination to use, most tree ring regressions do not exactly rise to the level of “highly significant”, as you might guess.

45. Geoff Sherrington

For those who choose to cherry-pick CO2 as a fertilizer able to influence tree rings in recent decades, please take a couple of hours to come up to steam with both the complexity of systems and the complexity of their analysis, as regards plant growth.

After a quick Internet search, I found a series of papers that deal mainly with ornamental plants and so are not optimum for this post, but which have scope to display this complexity. See http://www.sna.org/pdf/2002/section01.pdf

Those who rush to attribute CO2 fertilization to the divergence problem have about the same level of comprehension of growth complexity as a linguist who gets no further than “You Jane, me Tarzan, grunt”.

Steve: To my knowledge, no one has attributed the divergence problem to CO2 fertilization – Briffa attributed it to ozone stunting growth, but this was just arm-waving and he’s not followed up with any evidence. Briffa just assumes that it’s due to something anthropogenic and assumes the problem doesn’t exist. Google “cargo cult” at CA and yu”l find some discussion.

• Geoff Sherrington

Steve, but I bet (with no evidence other than the odd passing remark) that a few people are trying. That’s why I phrased it to include the future. So, congratulations to those who resisted the knee-jerk.

46. Posted Dec 2, 2008 at 11:36 PM | Permalink | Reply

3. Despite the limitations of regression (and reduced variance and amplitude etc), the NHD1 series tracks well the warm temperatures in the mid 20th century. However, the NHD1 series does not pick up the similar temperature ‘levels’ from 1970s to mid 1980s. Why would the trees respond to the earlier warm period and not to the later warm period.

Dr. Wilson

Is is possible that the trees are right and the instrumental record is wrong? This goes to the problems with the instrumental data that has been shown in the auditing of the climate stations from http://www.surfacestations.org? I have looked quite a bit at the UAH rural data and those data sets look to be closer to your trees than the standard composite instrumental record.

47. Posted Dec 3, 2008 at 6:21 AM | Permalink | Reply

I’ll waste your time a bit more,

my CCE data, along with Briffa’s data is here,

http://signals.auditblogs.com/files/2008/12/briffa98cce.txt

This time I used 1881-1994 instrumental for calibration, as Briffa98 seems to use that. Result is centered to 1881-1960.

This verifies ICE=r2*CCE :

brifm=D(:,6)-mean(D(482:end,6)); % Briffa recon, center 1881-1994
ccm=D(:,3)-mean(D(482:end,3)); % cce, center 1881-1994
C=corrcoef(D(482:end,end),D(482:end,5)); %r2 of NHD1 vs. temperature, calibration period 1881-1994
r2=C(2,1)^2 %

%r2 =
%
% 0.19501

[std((ccm*r2-brifm)) max(abs(ccm*r2-brifm)) mean(ccm*r2-brifm)]‘

%ans =
%
% 0.00372397717628816
% 0.0234624642423634
% 0.000494578436263923

Let’s compare Briffa’s CIs with CCE CIs,

close all
Xcce=[D(:,4); flipud(D(:,2))];
Y=[D(:,1); flipud(D(:,1))];
Hcce=patch(Y,Xcce,’y’);
set(Hcce,’EdgeColor’,’none’)

Xice=[D(:,6)+0.3; flipud(D(:,6))-0.3]; % Briffa estimates +- 0.3 C
hold on
Hice=patch(Y,Xice,’r’);
set(Hice,’EdgeColor’,’none’)

plot(D(482:end,1),D(482:end,end),’g’)
legend(’95 % CI CCE’,’95 % CI ICE’,’Instr.’)
set(gca,’FontSize’,13)
xlabel(‘Year’)
ylabel(‘Temperature’)
title(‘1881-1994 calibration’)

quite a difference!

48. Kenneth Fritsch

Warning this post could be detrimental to your statistical health.

Craig Loehle, if you are in the process of using R to make the download of MXD and temperature data, you should continue, otherwise here is a simple way of doing it without R.

Go to Steve M posted R script in the his Post #51 linked below and go to the first appearing ftp to find a text file that can be readily downloaded to Excel. The second column to the right (NHD1) is the MXD data used by Steve M and RomanM. The fourth column to the right (NHD2) is also MXD data that might be compared with NHD1. Go to the second appearing ftp link in the script and download the temperature data which is in the 7th column to the right and is from Jones et al.

From the following statement in the file, I assume that the observed temperatures are for all land regions north of 20N for the months April-September:

The following reconstructions have been taken from the source “references listed below, and then RECALIBRATED to obtain estimates” of April-September mean temperatures from all land regions north of 20N. All series are temperature anomalies in degrees C with respect to the 1961-1990 mean.

We are not exactly looking at local temperatures here for correlating to the MXDs. From my layperson’s view I can see where it might be difficult to use these data to say anything definitive about the quadratic growth aspects of trees. It is interesting that the post 1960 data looks different than that for the entire period or that prior to 1960, but I would conjecture that one must look at all the data to see any hints of a nonlinear fit anticipated from quadratic growth. I would like to put my observations up for discussion when I have had time to analyze the data in more detail. In the meantime I’ll take my lead from RomanM, UC and Steve M.

49. Geoff Sherrington

Craig, Geoff Sherrington (#84), was about ornamental plants, but there is a nice case from life of the inverted curve response. It is too tiny a figure to show here, but try page 46 of
http://www.sna.org/pdf/2002/section01.pdf

The caption is in part:

B. Effect of light intensity and fertilizer concentration on water use efficiency of wax begonias at the end of the experiment. The lines indicate a significant quadratic effects

Another exercise – throw a handful of urea on the lawn in one spot. After a few weeks you get a little “fairy ring’, dead in the middle, surrounded by a tall and lush ring, then back to normal lawn, like a bump function.

There are a million stories in the big city – these are but two of them.

One might almost regard the cusp curve as the norm. Maybe we seldom force data to the far limbs to see it strongly, but even if we do not, the low slope between presents its own problems as you noted.

If you accept this ubiquity, then a difference between the historic era and the instrument era has been the growth in air pollution and its gas and light effects on photosynthesis. It would be complicated to tease this out, but maybe it could help explain divergence.

50. Posted Dec 4, 2008 at 7:55 AM | Permalink | Reply

I have a post up on this at niche modeling and have posted a bonus chapter 9 from my book that can be downloaded.

The most interesting issue for me is that because over the course of one climate cycle, the tree passes through two optimal growth periods, the tree is, in electrical terms, a frequency doubler. This would create enormous difficulties in trying to detect major features such as Medieval Warm Periods and Little Ice Ages from such a responder.

But the problems do not end there. According to the latitudinal (or attitudinal) location of the tree, relative to its optimal growth zone, the location of the doubled peaks is shifted temporally. This shifting of the peaks is illustrated in the post, as taken from my chapter. The picture is even more murky when two drivers such as temperature and rainfall are involved.

As Steve mentioned, previous discussions of the topic at ClimateAudit are acknowledged.

• Craig Loehle

Re: David Stockwell (#95), I highly recommend David’s book chapter, of which I was not aware previously. He adds some things I did not have space to cover in my paper. I have urged him to mail copies of this chapter to key people in the dendro world.

51. Steve McIntyre

#95. I urge readers to look at David’s post. David observes that we discussed this issue a couple of years ago. He refrained from mentioning that he had sent me a draft of a paper for joint submission building on these ideas, which was very similar in concept to Craig’s paper (something that I didn’t mention before), but I didn’t follow up properly on the topic. My apologies to David.

Another topic that David and I spent some time on a couple of years ago – with David making many excellent posts on the topic when he started his blog – is how pick-and-average yields hockey sticks. It’s something that has been discussed here more primarily as asides, but David has some thorough analyses and published one short article in an Australian non-climate publication. (I’ll post some links).

This has been an issue in the small-subset collections, but the topic is squarely back in the news as it’s seems increasingly clear that Mann 2008 CPS uses this problematic method and, as is Mann’s wont, has taken it to an extreme. Lubos has published a nice post on the topic. [link]

The point is maddeningly simple, but it seems to confound a lot of people and I guess that it needs to be put into the literature.

• Posted Mar 12, 2013 at 3:55 PM | Permalink | Reply

re: Stockwell 2006, for anyone coming now to this thread:

Conclusions
“The resulting reconstruction is very similar to published reconstructions (e.g. see [1]), exhibiting a gradual decline in temperatures from an apparent Medieval Warm Period (MWP)), and an anomalous 20th Century warming popularly known as the ’hockey-stick’ [4] Clearly the ’hockey-stick’ pattern is easily produced by selecting those random series that correlate over the period of the calibration temperatures (producing the blade) and revert to randomness elsewhere (producing the handle). The apparent height of the MWP is an function of the arbitrary zero calibration point. Thus all the salient aspects of past climate usually associated with millennial reconstructions are essentially already encoded into the methodology, so that a ’hockey-stick’ shape is inevitable on any data resembling natural LTP series.”

52. Posted Dec 4, 2008 at 1:19 PM | Permalink | Reply

Thanks Steve and Craig.

I would also add that the book is not peer-reviewed. As Steve mentioned, I had intentions of publishing in a journal, but after some experiences trying to get similar papers published that point out the lack of rigor in related fields, I simply didn’t have the stamina. I came to the conclusion that unless your paper included a result that supported the status quo, in this case that dendros were a reliable and useful method, you were banging you head against a brick wall.

I greatly admire Craig’s perseverance and scholarship to enable him to publish papers that contribute to rigor of methods in climate science.

• PhilH

Re: David Stockwell (#98), Thanks, David. And that’s a nice looking Jack Russell you have. I have three. Greatest dog in the world.

• Posted Mar 12, 2013 at 3:46 PM | Permalink | Reply

Jim Bouldin continues to develop his series on methodological issues with using tree rings as temperature proxies. He has praised some of Loehle’s work, especially Loehle (2009), highly:

In the mean time, I would like direct answers from some dendroclimatologists to the following absolutely critical questions to the legitimacy of the science, on issues which are almost entirely unrelated to the issues I’ve raised in my paper:

1) Is Loehle* (2009) fundamentally correct in his description of the potentially very serious problems caused by unimodal responses of ring size to temperature. If not, why not?
2) On what mathematical basis, if any, can a modeled, linear (straight line) relationship between climate driver and ring response be used to accurately predict a strongly non-linear relationship?
3) On what basis does one assert that the climatic states experienced during the calibration period are fully representative of the set of states experienced during the pre-calibration (“reconstruction”) period, and that the tree sizes/ages sampled during the calibration period are also representative of the ages/sizes of the pre-calibration period.

53. Posted Dec 4, 2008 at 3:46 PM | Permalink | Reply

Fancy that.

Here’s a quote from David’s post that I am very concerned about.

I would argue that fancy non-linear modeling would probably lead more surely to self deception, and a better path is robust validation.

At least I can figure out the CPS correlation sorting pretty easily, if this get’s into the fancy non-linear modeling as suggested in #13 things would just get murkier.

I really don’t want to pick on Ron but his quote above (while correct) made me cringe.

#13 I entirely agree that linear modelling of tree-growth relationships is not ideal and the field is certainly ripe for some fancy non-linear modelling to be made.

It can do nothing but make the situation worse, the apparently accepted math is already illogically loose. Validation is the only real course, how the answer can be anything else is beyond me. Validation of the methods and data.

David,

I have read some of your work on pick- and -average, have you ever imparted a known signal in the data and gone looking for it in a similar fashion I did on my blog? Did you find the same rescaling of historic signal from CPS style rescaling?

I am just curious because the effect causing demagnification of the historic signal is so simple I wonder if it has already been done elsewhere.

54. Posted Dec 4, 2008 at 4:11 PM | Permalink | Reply

IF, you have a response in just the right part of the response curve, and

IF your can correctly choose which side of the leg you are on, and

IF one variable was the only driver throughout the range, you can conceivably recover the signal.

That a lot of IF’s. I am not surprised by Rob’s response, and would expect all the mainstream reviewers responses to be similar – that more fancy modelling is the cure.

• KevinUK

“I am not surprised by Rob’s response, and would expect all the mainstream reviewers responses to be similar – that more fancy modelling is the cure.

Neither am I. After all how many studies have you ever read that come out of academia that don’t ‘recommend more research’. Oh and who will be getting the funding to do that further research – the authors of the study that recommend the that further research needs to be done of course.

God forbid anyone in academia ever actually solves a problem – they might actually see their grants dry up. If you were in academia what better form of science would you choice to be involved with in order to keep your ‘job for life’ than climate science? Climate science has no chance of ever solving a problem and so will always ‘recommend that more research be carried out’ whether it be yet more regurgitating of the same old proxy data or yet another GCM study that can never be falsified.

KevinUK

55. Mark T.

Why do we have to keep having these discussions? Even MBH98 acknowledges there must be a) linearity (or at least rough linearity) and b) stationarity (again, at least rough stationarity). Linearity problems result in a non-unique solution (for any time), and stationarity problems result in a time-varying solution.

Btw, I’d posit that your last IF (David), should be “primary driver” not “only driver.” There could be 1000 drivers that contribute 1% (or larger, but certainly less than the majority) of the total variance throughout the range and there would be a valid argument that the one contributing 99% is “the signal.” Of course, you’d still have to provide some valid justification other than post-hoc correlation as to what “the signal” represents.

Mark

• Craig Loehle

Re: Mark T. (#101), It is not enough to acknowledge assumptions of linearity and stationarity (if Mann or other dendros do that…) because what they do next is their entire analysis based on those assumptions and no test of the validity of the assumptions. As I showed (and David Stockwell also) is that you can have 99% correlation (or R^2) of tree rings and calibration period temperature and still get gross distortion of the historical record.

56. Posted Dec 5, 2008 at 2:30 PM | Permalink | Reply

Mark. Its not enough to acknowledge linearity assumptions when the expectation is non-linear. If there was a proxy you expected to be linear it would be different. But in the case of trees, linear is the exceptional situation, not the rule.

57. Mark T.

Oh, I know that. I was actually poking at The Team (not you) since they began the discussion with 3 assumptions (in MBH98) and have since completely ignored them all, most prominently the first one, which was that linearity must hold. In other words, in real science discussions folks like you, Steve, Craig, UC, Jean S, RomanM, etc., (me too!) would immediately win the falsification argument simply by saying “you can’t prove linearity.” Bam, contest over. Instead, we have to keep re-treading the same argument over and over and over. It is a tragic shame.

I recall one day a year or two ago when my advisor said something as innocuous as “is that assumption valid?” That cost me a month of work to find another way to prove a point that I just knew to be true. In fact, it wasn’t really true, but my efforts resulted in a derivation that worked out to my advantage, justifying continuation of the algorithm, but from a different angle.

Mark

58. Mark T.

Btw, “you can’t prove linearity” is actually weak counter since all evidence points to non-linearity (as well as non-stationarity).

Mark

• Craig Loehle

Re: Mark T. (#106), I recently got a friendly review on a paper and the guy said: how do you know X? I went back and revisited that part of the analysis and it had to be redone. That is how we should respond to critical comments. If it is wrong, it is wrong. End of story. If the assumption is untested or untestable you are supposed to do a sensitivity analysis at the end (what if it is NOT linear? or NOT stationary?).

59. Posted Dec 5, 2008 at 4:16 PM | Permalink | Reply

Mark. OK, yes I read it the other way. The charitable explanation is that the discourse is about rallying around global warming, and bad news is ignored because it might dilute the story. I actually work in construction now, and judgment and rigor is appreciated. They don’t like it when I give them bad news, but they listen because they know it could be a multi-million dollar problem in time if ignored. And quantifying the risk of assumptions is a huge component of contract preparation, contingency allowances, and ultimately profit.

60. Mark T.

I figured as much. It is hard to convey frustration through the keyboard though if you had heard me say that post you would have gotten it immediately.

My advisor’s innocuous comment, btw, was related to calculating kurtosis for a complex (circularly symmetric) random variable for use in an ICA application. Had I not re-worked it, I would not have graduated (well, that and the algorithm would not have worked). :)

Mark

61. tensorized lurker