The 800lb Gorrilla in the Hockey Stick’s Locker Room

Divergence is a serious problem in tree ring climatology reconstructions. Basically divergence means data which years ago vaguely correlated to temperature, diverged from temperature in recent years. So trees which used to be thought of as good thermometers — aren’t. This doesn’t stop scientists from using them however but some creativity in handling this inconvenient data is required. For instance, Mann 08 chopped off the divergent parts and pasted on his own non-divergent data.

In September 2007 Dr. Craig Loehle published a paper on the non-linear nature of tree growth. He holds a PhD in Mathematical Ecology and has published more than 100 papers in applied mathematics and ecology. In short he is the closest thing to an expert we could hope for on tree growth response to temperature. This paper is available on line at the link below.

A mathematical analysis of the divergence problem in dendroclimatology

C. Loehle (B)
National Council for Air and Stream Improvement, Inc. (NCASI),
Climatic Change

Abstract Tree rings provide a primary data source for reconstructing past climates,
particularly over the past 1,000 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

What his abstract is saying is that simply because trees show a positive response to temperature at one point in time doesn’t mean that it will necessarily continue linearly. For instance if temps on average rose 0.4C from 1900-1950 and a certain tree or tree group increased its growth rate in that time frame, that doesn’t mean that another increase in temp will reveal a similar response. Really simply, if trees or plants could grow ever faster we would put corn in a hot house, pump it full of light, heat and nutrients and grow instant vegetables. It doesn’t pass the common sense, there is obviously a limit to plant growth rate and clearly there is a limit to how much an increased temperature would help plant growth. What Dr. Loehle points out in this paper is that the natural growth limit can truncate higher temperatures in the historic signal even if there is a positive response in a certain time frame.

His paper is well referenced and written with proper scientific tone for a publication but this is a blog so we can say whatever we want.

There is substantial evidence to support Dr. Loehle’s paper. Starting with the most obvious, the divergence problem itself. The fact that it has a name at all should give the scientific community pause but Mann 08 isn’t really about science. Dr Loehle was quite thorough, here is a cursory list of reconstructions using tree growth data.

Tree rings have been widely used in recent years for reconstructing past climates,
particularly temperature (e.g. Cook et al. 2004; Crowley 2000; Crowley and Lowery
2000; D’Arrigo et al. 2007; Esper et al. 2002; Jones 1998; Jones et al. 1999; Mann
and Jones 2003; Mann et al. 1995, 1998, 1999; Overpeck et al. 1997)

But the beginning of the doubts has been in place for some time as you can see from this second list of papers addressing the divergence problem.

An analysis of twentieth century tree growth patterns, however, has uncovered what is known
as the divergence problem (Barber et al. 2000; Briffa 2000; Briffa et al. 1998a, b,
2004; Bungten et al. 2006; Carrer and Urbinati 2006; D’Arrigo et al. 2004,
2007; Driscoll et al. 2005; Feeley et al. 2007; Jacoby and D’Arrigo 1995; Jacoby
et al. 2000; Kelly et al. 1994; Lloyd and Fastie 2002; Oberhuber 2004; Pisaric et al.
2007; Vaganov et al. 1999; Wilmking et al. 2004, 2005; Wilson and Luckman 2003;
Wilson et al. 2007). This problem is characterized by trees or assemblages of trees
that showed a positive response to warming in the early part of the century showing
a lessened or even negative response to warming in the period starting in the 1960s
to 1980s.

Check out the size of that list. Wow, climatology is seriously aware of this issue. Mann 08 addressed it fairly uniquely by chopping off the divergent data and fabricating their own data but (without checking everyone) I suspect that is the most bold response and should be rejected by every reasonable scientist just on that basis.

Craig’s paper is quite clearly written, from the papers of his I have read he seems to have a style which presents a minimum of obfuscatory wording which allows people without PhD’s in mathematical ecology (like me) to understand the issue quite clearly. You can actually learn something from it, unlike many other papers I have read.

Let’s look at some graphs. Below is a hypothetical temperature curve and a perfect thermometer tree response.


See its nice and simple, temps go up and down with a sine wave and the AGW guys perfect thermometer tree follows the curve exactly. What happens though when trees can’t grow faster from temp and have reached a limit. Limits are caused by many things but primarily, moisture availability limits growth in high temperature environments. These inverse responses have been noticed and published, yet Mann and many others have ignored the work of the experts. Pretty hypocritical when you hear people in this same circle state that McIntyre or some other scientist is not a climatologist so don’t listen to them. Check out this list of papers revealing an upside down quadratic growth curve– definitely not linear.

An upside down quadratic growth response to temperature (Fritts 1991; Vaganov et al. 1990) has been demonstrated
experimentally (e.g. Fritts 1976; Kramer and Kozlowski 1979; Gates 1980; Lyr et al.
1992; Schoettle 2004). Field studies have also shown that exceptionally warm years
can turn positive responders into negative responders (Case and Peterson 2005,
2007; Oberhuber et al. 2008; Pichler and Oberhuber 2007), which is diagnostic of
an upside down quadratic growth response to temperature.

Actual field studies have actually noted inverse (trees grow slower with higher temp) responses and even upside down quadratic responses to temperatures. What does upside down quadratic growth curve mean?


The horizontal and vertical axes are just example values, if you imagine this graph’s left side extended, it is symmetric about the 0 temp axis. This graph means the tree grows equally fast at a temp of -2 as it does at +2. That means at a certain tree ring width, we don’t know what temperature it is -2 or +2 This result is absolutely critical and quite devastating to tree ring papers in general. In addition, it matches what has been found from actual field data. It also “conveniently” results in a guaranteed reduction of historic temperatures in comparison to recent times using averaging methods — how can I say that? you ask.

In the second graph above, tree growth response is linear no matter how high the temperature goes. We know from the divergence problem that temperature growth enhancement is nearly at its limit in many samples. When calibration is done, recent temperature is compared to tree growth using “correlation”, if it passes a weak correlation to temperature it is considered a thermometer tree. Since each tree is temperature related growth limited at some point, some of the trees in a group must be near their limit (or divergence wouldn’t exist). This means that any historic temp higher than today would necessarily limit some of the trees reducing the historic peaks of the average. — My words not Dr. Loehles.

What happens to the tree response to temperature with a non – linear upside down quadratic response. Check out this graph.


The dotted line is the tree ring widths using the quadratic response curve above. This shows clearly that extreme temps do not result in extreme tree ring widths so they cannot be detected in tree ring data. Another very important point is that in the period Dr. Loehle labels the calibration period above, the temperature matches quite well to growth, in theory sorting by correlation would naturally separate out trees in this range of the quadratic curve. Of course the reality is that trees react to everything in their environment so this is a drastic oversimplification of their biological processes. Things like extra moisture will cause trees to sporadically pass and fail correlation to temperature signals in some cases but these effects are ignored with a bit of hand waiving in temp reconstructions.

In dendroclimatology studies, the raw data consist of tree ring series for many trees.
Of these, some trees show a positive response to temperature, and these (or sites
showing generally more response) are the ones generally used for reconstruction.
However, many trees also show a negative response or are “nonresponders.” These
latter trees appear to be further to the right on the quadratic or ramp function growth
curve. That is, under the growing conditions for that tree either temperature is not
a limiting factor or further temperature increases cause drought (or other) stress.
The fact that divergence has been so widely observed across tree species and regions
indicates that choosing positive responders (or responsive sites) does not guarantee
linearity of response.

This quote from the first paragraph of the discussion is quite interesting to me. There is so much divergence that this effect must not be ignored simply because of passing calibration.

The nonlinear response of trees to temperature, which can produce divergence,
makes it difficult to detect past climate episodes warmer than those occurring during
the calibration period. If all trees grow at temperatures far below the inflection point
of the growth curve (Fig. 3) during the calibration period, then it may be possible to
detect warmer past temperatures, but this will not be known a priori from the data or
the fit statistics. That is, one can not tell if a given tree or composite proxy is able to
detect past temperatures warmer than those present in the calibration data, though
it might. Thus it is fundamentally impossible using tree ring data to say that recent
decades are warmer than any time in the past n years because temperatures warmer
than those of the first half of the twentieth century are likely to be suppressed by
the method used for reconstruction.

There it is, right from the experts, right from the simplest and most obvious evidence. What can we say in conclusion?

— Trees make lousy thermometers.

— Divergence is well known and documented indicating the truth of this paper.

— Correlation analysis doesn’t fix the problem but falsely hides it

— Historic temperatures are suppressed by non-linear response

— Temperature reconstruction by tree ring width is not useful for historic climate prediction and must not be trusted.

Here’s my own take on it. This is too simple to miss. Recent papers and possibly historic ones know tree rings will suppress historic signals, I believe they know exactly what they are doing and it is being done with intent. If my strong suspicion is correct, they know damn well how non linear response flattens historic signals yet they do it anyway and their buddies pass them right through peer review. What’s more the peer’s accepting tree ring papers represents the same kind of corruption the greens are so eager to heap on oil companies.

Make no mistake there is serious money powering this issue. The IPCC needs hockey sticks to make the case that we are warmer than ever. If we’re not warmer than ever why would governments need to spend so much money?

Unfortunately, you can’t make a temperature hockey stick without wood.

My next post will look at what happens when non-linear response is run through Mannian CPS correlation methods. We’ll put the known signal in and go look for it using Mann 08 math to see how the “divergence” problem is addressed by correlation.

3 thoughts on “The 800lb Gorrilla in the Hockey Stick’s Locker Room

  1. So what we can say about tree rings, is (a) you can tell how old the tree is (b) even if you don’t know when it died you can use correlation against other local species to work that out (c) you can tell how well a particular radial sample was growing in a given year (d) trees are largely made of wood. Did I miss anything?


  2. Well, Ian, if you tattoo the number of rings onto your forehead, the next day you will meet the love of your life. And you won’t get together because you’ve got a number tattoo’d on your forehead.

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