The Hockey Stick

In 1999, Mann, Bradley and Hughes published a reconstruction of temperatures for the past thousand years, later expanded to cover the past two thousand, based on proxy data. It was described as a hockey stick diagram because it showed temperature as fairly flat and declining until about the past century, the handle of the hockey stick, followed by a sharp rise, the blade. One controversial feature was that it did not show the medieval warm period and the subsequent little ice age reported by earlier studies. Their results implied that current temperatures were higher than any in the past  two thousand years, including the peak of the Medieval Warm Period, and that the warming of the past century was substantially faster than warming in the past.

Figure 1 (From Figure 3, Mann, Bradley and Hughes 1999)

Proxies, things affected by temperature, are used to estimate temperatures for which records of measured temperature do not exist. Thus, for example, since the rate of growth of trees depends in part on temperature, the separations between tree rings from old trees can be used to estimate the temperature when they were formed. Other natural processes produce similar information. What the precise relationship is can be unclear, in part because a proxy may be affected by things other than temperature; tree rings might be narrow not because temperatures were low but because water was scarce, they might be broad due to CO2 fertilization. It is risky to extrapolate the relationship beyond the temperatures where it has been observed — the relationship is commonly modeled as linear but cannot be at all temperatures, since if it gets hot enough a tree stops growing and dies.¹

Mann’s work was challenged on a number of bases, two of which were, I think, important. One was that the proxies used made heavy use of tree ring data, argued to be an unreliable measure of temperature that happened to show a steep increase in the past century for reasons unrelated to climate.² The other was that Mann and his coauthors had used a statistical approach which could be expected to give misleading results, that the long handle of the hockey stick was a statistical artifact.

The Problem

Anyone trying to reconstruct temperatures in the distant past has to decide which proxies to use and how to weight them. Mann and his coauthors did so by choosing and combining proxies in a way that gave a good fit to the period for which good instrumental data were available and using the same proxies with the same weighting to extrapolate back to the earlier period.

That sounds like a reasonable procedure but there is a problem, pointed out by McIntyre³ and others. Each proxy gives a series representing in part temperature, in part random variation from other causes. Ones for which the random element happens to make a good fit to the instrumental data will be included, ones for which the random element makes a poor fit left out. With enough proxies to choose among it will be possible to select a group whose combined effect makes a close fit to the instrumental data since with enough parameters you can fit anything. But the farther back you go before the period whose data they were fitted to, the less what you get reflects actual temperature, the more uncorrelated random noise — which explains the straight handle of the hockey stick. The reconstruction had some relation to actual temperatures, just less than its authors thought.

A Corrected Reconstruction

In a later paper,⁴ Loehle et. al. avoided those problems by using estimates of temperature produced by other scholars from a variety of proxies, excluding any that depended significantly on tree rings, and calculating the average of their interpolated values with no attempt to fit them to the instrumental data by either selection or weighting. Doing that produced the graph of temperature shown above. Unlike the hockey stick, it shows both the medieval warm period and the little ice age.

Due to data limitations in the available proxies, the authors only ran the graph up to 1935, estimating the temperature then at .41°C below the peak of the medieval warm period. From 1935 to 1999 global temperature rose by another .60°, making the 1999 temperature .18° higher than their best estimate of the MWP maximum but still lower than the upper bound of their 95% range. Global temperature continued to rise and is now above that upper bound.

Their graph shows considerably more natural variation than Mann’s — it no longer looks like a hockey stick — but not enough to explain recent warming. The most rapid warming that they show for any substantial period is about .4°/century, in contrast to about 1.2°/century for warming from 1911 to 2018.

If we accept their estimate as more reliable than Mann’s, as I am inclined to do, the result remains qualitatively the same but less strikingly so. Current temperature is the highest in the past two thousand years and warming over the past century is about three times as rapid as the fastest warming of the past two thousand years. Temperature has, however, varied considerably more in the past than shown by Mann’s hockey stick.

That fact is not evidence against human causation for current warming, although it suggests that natural processes might be responsible for more of it than one would expect from Mann’s graph. It is mild evidence against the claim that warming has serious negative effects, since past warming apparently didn’t — the medieval warm period is generally viewed as having positive effects, the little ice age negative. The only thing it is strong evidence against is the reliability of sources of information that boosted the hockey stick graph and minimized criticism of it — including Mann himself.

The Loehle graph is only weak evidence that warming does not have serious negative effects, since average global temperature is already above its peak and going higher. Better evidence is global temperature over a much longer period. The fact that it was above its current level by more than five degrees for most of the past 250 million years and by more than ten degrees for substantial parts of the past hundred million is evidence against the more extreme versions of climate catastrophism.

1. For a discussion of some of the problems, see Stephen McIntyre, “On the Divergence Problem.”

2. Stephen McIntyre, “Ring Widths and Temperature #1,” summarizes the literature as of 2006.

3. Stephen McIntyre, Ross McKitrick, “Hockey sticks, principal components, and spurious significance,” Geophysical Research Letters, Vol. 32, Issue 3, February 2005.

4. Craig Loehle, Ph.D. and J. Huston McCulloch, “Correction to: A 2000-Year Global Temperature Reconstruction Based on Non-Tree Ring Proxies,” Energy & Environment, Vol. 19 No. 1 2008.