Open Mind

Hockey Sticks

November 9th, 2006 · 2 Comments

The temperature history of the earth as reconstructed by thermometers only goes back a little over a century. We’d like to have global temperature history back many hundreds or even thousands of years. We can’t rely on a single location, we can’t rely on a single century, and we can’t rely on thermometers. We have to use other data which help us estimate temperature, but aren’t direct temperature measurements. Such data are called proxy data.

There are lots of different proxies for temperature. One of the most useful is tree rings; their width and their density both give clues about temperature. Ice cores and sediment cores can be analyzed to help reconstruct temperature. Borehole temperatures give us terrific information about the past several centuries of temperature change. Studying the advance and retreat of glaciers also provides a proxy for temperature. Historical records can be very useful; even without thermometers, people noted the comings and goings of heat waves and cold spells, and the freezing and melting of lakes and rivers.

Multi-Proxy Reconstructions

No single proxy is accurate enough to paint the overall earth temperature history, and no single location can be considered indicative of the earth as a whole. The logical thing to do is to reconstruct temperature not from a single proxy, but to use all the available information in a multi-proxy reconstruction to estimate how earth’s temperature has varied over the globe in the past. The geographic distribution of temperature is averaged to estimate regional, or even global, average temperature anomaly.

This is exactly what has been done, and I’d like to show you a reconstruction of earth’s global average temperature for the last 1800 years. It’s a multi-proxy reconstruction by two researchers named Mann and Jones (Mann, M.E., and Jones, P.D. 2003, Geophysical Research Letters, Vol. 30, No. 15, pg. 1820), covering the years 200 to 1980, in figure 1 (click on the graph for a larger view).


Figure 1. Reconstructed global average temperature, A.D. 200
to 1980.

There are lots of ups and downs. To get a better picture of the long-term changes, I’ll slow down the fluctuations in two ways. First, I’ll compute 20-year averages, not the smoothest way to isolate long-term changes, but one of the simplest and most reliable. I’ll also compute a smooth-fit curve using a wavelet fit on a 20-year timescale. Figure 2 (wavelet fit in green, 20-year averages in blue) shows that both methods give essentially the same result:


Figure 2. 20-year averages and wavelet fit.

Now we can see that the recent part (up to 1980) has shown a faster sustained rise than any comparable period in the last 1800 years. Also, the most recent 20-year average temperature estimate is hotter than any other.

But it’s not a lot hotter than 20-year average temperatures in the past, and the rate hasn’t been sustained for that long or gone that far. And the hottest individual year in the Mann and Jones reconstruction is 671, over 1300 years ago! This graph alone is suggestive, but not impressive; we should be concerned, but not alarmed.

That’s because this graph only goes up to 1980. That leaves out the last 25 years, the most interesting part. The reconstruction by Mann and Jones doesn’t cover the modern period, but thermometers do, so I’ll add the actual measured annual average global temperature anomaly from 1980 to the present. Figure 3 shows the same data, plus the HADCRU thermometer data as little red squares (I had to expand the temperature axis to make the new data fit).


Figure 3. Additional data (thermometers) from 1980 to 2005.

That’s what this global warming fuss is all about.

This is a good illustration of one way to be deceptive about past temperatures: leave out the data that disagrees with your desired conclusion! I recently encountered a lengthy document prepared to dispute the reality of global warming. It contains a graph illustrating a number of different temperature reconstructions:


Figure 4. Temperature reconstructions as displayed by Monckton.

Note that the caption indicates that “In three of the studies (Esper, Briffa, and Moberg) the mediaeval warm period is shown to have been as warm as, or warmer than, the current warm period.” This is because most of the temperature reconstructions only go as far as about 1980. This leaves out the hottest part: 1980 to the present! When we include the last 25 years, it’s evident that according to all reconstructions, the mediaeval warm period is not as hot as it is today (there’s more about this piece here)

Hemispheric Reconstructions

The Mann & Jones estimate isn’t the first multi-proxy reconstruction of past temperature. One of the “breakthrough” papers on this topic was a 600-year reconstruction, for the northern hemisphere only (which is not the whole globe, but is a rather good proxy for it), by Mann, Bradley, and Hughes (Mann, M.E., Bradley, R.S., and Hughes, M.K. 1998, Nature, vol. 392, pg. 779). It features a rather cluttered and hard-to-read graph (figure 5). Even with the clutter, it’s plain that for the last 600 years in the northern hemisphere, temperatures were reasonably stable until today.


Figure 5. 600-year reconstruction of Mann et al. 1998.

By the time the Intergovernmental Panel on Climate Change (IPCC) published its third assessment report (TAR) in 2001, the same three researchers had extended the northern hemisphere reconstruction back 1,000 years. Figure 6 reproduces the version published in the IPCC TAR (from Mann, M.E., Bradley, R.S. and Hughes, M.K. 1999, Geophysical Research Letters, vol. 26, pp. 759-762). The shape of earth’s temperature history somewhat resembles a hockey stick, with the long slow decline the handle and the recent sharp rise the blade. Therefore this graph has been dubbed the “hockey stick.” This particular chart is probably the most famous graph in all of climate science.


Figure 6. The hockey stick: from IPCC Third Assessment Report.

Most climate reconstructions cover only the northern hemisphere; because there’s far less data for the southern hemisphere than for the northern, hemispheric reconstructions are more reliable than global. In general, the northern hemisphere tends to show more temperature variation than the globe as a whole; because the oceans have so much “thermal inertia,” and the southern hemisphere has far more ocean than the northern, southern hemisphere temperatures respond more slowly to changes than northern.

Let’s take a look at two such reconstructions, which represent the range of results found so far, looking for variation in past temperature. One is by Mann & Jones (Mann, M.E., and Jones, P.D. 2003, Geophysical Research Letters, Vol. 30, No. 15, pg. 1820), covering the years 200 to 1980; the other is from Moberg et al. (Moberg, A., D.M. Sonechkin, K. Holmgren, N.M. Datsenko and W. KarlĂ©n, 2005, Nature, Vol. 433, No. 7026, pp. 613-617) for the years 1 to 1980. In figure 7 I’ve plotted 10-year averages for both reconstructions.


Figure 7. Northern hemisphere temperature reconstructions.

Clearly the reconstruction by Moberg et al. shows much more past variation than that by Mann & Jones. In the Moberg et al. series we can plainly see a warm period around the year 1000 which is called the “medeival warm period.” It’s a matter of dispute whether this period was a global phenomenon, or confined to the northern hemisphere. We can also see that there was a cooler period from about 1400 to about 1800, that is often called the “little ice age.”

Both these reconstructions end in 1980, so figure 8 shows both reconstructions together with thermometer data (for the northern hemisphere) since 1980. Whichever reconstruction turns out to be more correct, the modern period is still hotter, and shows faster temperature increase, than any time during at least the last two thousand years.


Figure 8. Northern hemisphere temperature reconstructions
together with thermometer data since 1980.

The original hockey stick and its successors have incited great effort on the part of global warming denialists, to discredit them. But all the efforts to debunk the proxy reconstructions, have themselves been debunked. And, many other investigators have estimated proxy reconstructions of earth’s temperature history, both hemispherically and globally, on scales of a thousand years or more. The details always differ, but the bottom line is always the same: that sharp rise on the far right-hand side.

In fact, the National Academy of Sciences has issued a report on the state of the science of temperature estimates from proxy reconstruction. They urge caution interpreting results, and estimating the error ranges of past numbers, but their bottom line is that cutting-edge proxy reconstructions are most likely a correct reflection of the fact that temperatures now are higher than they’ve been in a very long time.

Categories: Global Warming

2 responses so far ↓

  • John Finn // Nov 14th 2006 at 3:27 pm

    Just a few comments on the above post.

    1. You are comparing “apples with oranges”. You can’t simply graft the post-1980 thermometer record on to a proxy reconstruction and claim it shows unprecedented global warming. The next point illustrates just one reason why.

    [Response: Oh Puhleez. I’m not comparing apples to oranges, I’m comparing temperature to temperature. That’s the whole point of temperature reconstructions — to compare our best estimate of temperature centuries ago with temperature today. And most historical studies published in the peer-reviewed scientific literature do exactly what you’ve “accused” me of: superimpose modern thermometer records (our best estimate of temperature over the last century) on proxy reconstructions (our best estimate of temperature over the last millenium or two). Look again at the graphs in the post (from Mann, Bradley, and Hughes), note the lines indicating “actual data” and “instrumental data”.]

    2. The Briffa and Esper reconstructions both extend into the 1990s, i.e. they do not finish in 1980. Both reconstructions significantly under-estimate (by around 0.3 deg C) the late 20th century thermometer readings. Both papers comment on these massive discrepancies, but blame “unknown 20th century factors” This leads us on to point 3.

    3. Why does anyone assume that there is a simple linear relationship between tree rings and temperature. There isn’t. If there were we could presumably expect a tree growing in the Malaysian rain forest (annual average temperature ~26 deg C) to produce the same growth if it were in the Western Sahara (annual average temperature also ~26 deg C). At best you might be able to plot the temperature contribution to tree growth. But this alone will produce a ‘flatter’ variability than is the actual case. That’s not all, though. If the climate becomes too hot (or too cold), one species of tree will die out to be replaced another. So not only is the tree ring/temperature relationship not linear - it may not always be positive.

    4. The Hockey stick is wrong. The period immediately following the start of the 20th century should tell you that. What was it that caused the sudden sharp upwards inflexion just after 1900? It can’t have been carbon dioxide (CO2), because atmospheric CO2 levels in 1900 were pretty much what they were in pre-industrial times. So this spectacular increase (relative to the previous 900 years) must have been entirely ‘natural’. But it’s so ‘out of character’ with the previous 900 years - you sense some sort of sales pitch at work. Fortunately, Steve McIntyre (with Ross McKitrick), after months and years of research, got to the bottom of what turned out to be just one of a number of errors in the hockey stick reconstruction. The following is a very brief summary of the main argument against the h-s .

    [Response: Atmospheric CO2 levels in the first half of the 20th century were not “pretty much what they were in pre-industrial times.” CO2 concentration crossed the 300ppmv level in 1910, for the first time in 23 million years. By the end of the first episode of temperature increase in the 20th century (about 1945), levels had risen to about 310 ppmv, an 11% increase over average pre-industrial levels.

    Contrary to oft-made claims, climate scientists do not attribute all climate change to CO2 increase. The first-half-of-the-20th-century warming is believed to be due to a combination of factors, including anthropogenic (increased greenhouse gases) and natural ones (a slight increase in solar output and an unusual low in volcanic activity).

    As for the lengthy dissertation of the flaws in the hockey stick (based on McIntyre & McKitrick), that has been dealt with at length many times, quite adeptly here. I’ll just mention two points: 1. The Mann et al. reconstruction is only one of many, so even if McIntyre & McKitrick’s critique were correct (which it isn’t) there are plenty of other “hockey sticks” to go around; 2. The most reliable assessment of hockey sticks in general is the National Academy of Sciences report. Fascinating reading.]

    When data is collected from a number of different sources there are sometimes problems because the data has been measured using different units (e.g. inches, cm etc). One way round this is to ‘normalise’ the data. This involves subtracting the mean of the data from the entire data set and then dividing it by the Standard Error (a measure of the data’s variability). This results in a normalised data set with Mean=0 and SE=1. Tree ring data does not require normalisation since it is usually archived in it’s normalised form. It should be noted, though , that using the standard normalisation technique for a second time would leave the data unchanged (since the data would be subtracted by zero mean and divided by 1). Mann et al did decide to ‘re-normalise’ the tree ring data in their study but, bizarrely, instead of using the mean of the entire data set they chose to use the 1902-1980 mean. The effect of this was to inflate the variance of any data which exhibited 20th century ring growth. I don’t want to get bogged down in detail about PCA (Principal Component Analysis), i.e. the statistical method used to produce the hockey stick, but it’s important to understand that the greater the variance of a particular series the greater it’s influence in explaining the variance of a particular group of data. As is normal in PCA, Mann, produced an algorithm which selected the data series with greatest variance and then gave it a weighting to reflect it’s importance in the analysis.
    But the upshot of this is that

    Mann used a methodology which identified data series with 20th century growth and then ensured that these data would be most influential in the eventual reconstruction. This is known as ‘data mining’. The result is the ludicrous spike just after 1900.

    One particularly influential series was the Bristlecone Pine series. Bristlecone Pines displayed anomalous 20th century growth but a number of studies have shown it is not related to temperature. Nevertheless the BP data makes a significant contribution to the H-S shape.

    Whatever other debate there is regarding AGW, the Hockey-Stick episode is over.

  • Bender Rodriguez // Nov 17th 2006 at 10:53 pm

    How about showing climate data - 2000 years is barely weather.

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