Some thoughts on statistics

Back when both my arms were fully functional (a time that hopefully will return soon) I would spend one of the two posts I wrote on Saturdays looking at what was being said on some of the Climate debate websites. I visit sites on both sides of the debate, being particularly interested in the evidence that is called forth, and the conclusions drawn from it. (The current list is given by the CC sites on the blogroll). These usually lead on to others, and so one can, to a degree, filter out new evidence from that which is being rehashed. However it can require a bit more due diligence, when both sides claim that the rational answer lies only with their side of the argument.

Consider, for example, the little debate this week between Real Climate and Climate Audit on the analysis of the data from the Antarctic that I have mentioned in an earlier couple of posts. The debate relates to how many Principal Components (PCs)* should be considered in deriving the predictive equation from which to generate the model results that decide whether the Antarctic is warming or cooling.

In the original paper Steig et al had used 3 PCs in order to generate the model and thus to conclude:

Here we show that significant warming extends well beyond the Antarctic Peninsula to cover most of West Antarctica, an area of warming much larger than previously reported. West Antarctic warming exceeds 0.1 °C per decade over the past 50 years, and is strongest in winter and spring. Although this is partly offset by autumn cooling in East Antarctica, the continent-wide average near-surface temperature trend is positive.

The paper had a number of flaws in it, based on the source data, but I initially assumed that the statistical analysis was carried out using reasonably widely accepted methods, a conclusion that I am increasingly unsure of.

In an earlier post at Climate Audit the number of PCs used was shown to have a very dramatic effect on the conclusions that could be drawn from the data with Antarctica getting either warmer or cooler depending on how many PCs were chosen (ranging up to 15). And so it seems that it is time to “bite the bullet” and talk a little about what proxies, PC’s and the terms that crop in these discussions mean. (And then to point to the misdirection of a couple of stories where they aren't).


I originally sought wisdom from review of the debate over the use of recognized statistical methods that was performed for the House Energy and Commerce Committee.

The Chairman of the House Committee on Energy and Commerce along with Chairman of the Subcommittee of Oversight and Investigations have been interested in discovering whether or not the criticisms of Mann et al. are valid and if so, what are the implications. To this end, Committee staff asked for advice as to the validity of the complaints of McIntyre and McKitrick [MM] and related implications. Dr. Wegman formed an ad hoc Committee (Drs. Edward J. Wegman – George Mason University, David W. Scott – Rice University, and Yasmin H. Said – The Johns Hopkins University). The Committee was organized with our own initiative as a pro bono committee.

It submitted a report to the Committee on Energy and Commerce.

As part of that report they explained PC analysis thus:

*Principal component analysis is a method often used for reducing multidimensional datasets to lower dimensions for analysis. In this context, dimensions refer to the number of distinct variables. The time series proxy data involved are transformed into their principal components, where the first principal component is intended to explain most of the variation present in the variables. Each subsequent principal component explains less and less of the variation. In the methodology of MBH98/99, the first principal component is used in the temperature reconstruction, and also has the highest explained variance. This method is intended for dimension reduction. In most datasets, the first principal component should be the least smooth (because of the higher variance).

(MBH98/99 refers to the Mann paper that produced the “hockey stick” curve.)

They discuss the effects of temperature change on tree rings, ice cores and coral (of which more anon). but it doesn’t really help those of us who would like this explained in layman’s language. So let me see if I can do that without getting too many folk offended.

When we want to find out the surface temperature of the Earth at some time in the past, and in places where there were neither thermometers, nor folk who kept records, we have to find some other measure that shows what the temperature was. We call these measures “proxies” in part because the behavior of the selected measure approximates the changes in the value we’re interested in. For example, from the list above, the structure, density and width of the ring that a tree grows in a year will vary with the local temperature. And so, by taking a core that recovers the section through a tree that has been around for a long time, we might get an estimate, from the size and structure of the individual tree rings, of the temperature when each ring was formed.

Unfortunately it is not that simple, for example for a Scots pine in Finland.

Earlywood width is controlled by precipitation in June and temperatures in mid winter (December/January) and March. Low mean temperature in April, adequate precipitation in May and a warm July results in wide rings. A long and warm vegetation period results in high latewood density, the strongest correlations occurring with July and August temperature and precipitation.

Tree Ring structure Source NOAA

Since the density and width of the ring can vary from more than one cause, the obvious two cited above are temperature and rainfall, we need to know how much each contributes to the change in the ring. This is not that easy, since the above quote shows that you can’t just use an average value for the year, but have to look at seasonal variables within the year, and this imposes additional variations in the result that we are using as our measure. Further there are some things that may change around the tree that we don’t know about. (from the Wegman report)

Each tree ring is composed of large thin walled cells called early wood and smaller more densely packed thick walled cells called late wood. The average width of a tree ring is a function of many variables including the tree species, tree age, stored carbohydrates in the tree, nutrients in the soil, and climatic factors including sunlight, precipitation, temperature, wind speed, humidity, and even carbon dioxide availability in the atmosphere. Obviously there are many confounding factors so the problem is to extract the temperature signal and to distinguish the temperature signal from the noise caused by the many confounding factors.

Given that complexity the first thing that we need to do is to create a model from data that we already have sufficient information so that we can estimate the impact of changing different values. And this is where our Principal Component comes in. (And for the purists again my apologies I am trying to keep this simple). We can take, for example, data from the last 100 years for a site where we know the variations in temperature, rainfall, relative sunlight etc, and plot the variation in our ring values against these various factors to see which ones best explain the changes in the tree value. The ones that correlate best are called the Principal Components. For example we might find that we explain 60% of the change in tree value by change in temperature, and then when we add rainfall that we have an equation that explains 80% of the variation. By adding further factors (say number of sunny days) we can improve our model so that it predicts with increasing accuracy (smaller variance) the actual values that we found from measuring the rings. So we build our predictive model, adding additional PCs (say soil nutrition) in order of their effectiveness in reducing the variation in the model from the measured data. At some point the improvement is too small to be considered significant, and variables that fall below that value (perhaps insect density) can be neglected.

Having got, or “calibrated” the model, we can then go back from the time and values that we know the PC values for, to look at times when we don’t. Knowing the inter-relationship between the factors and the values, it is possible to estimate what the temperatures were back when the tree rings were grown. (The process is also described by NOAA)

At least that is the basis of the procedure. The problem comes in the complexity of some of the proxies that have been used to assess what the temperatures were back then. To make calculations simpler the data that is used does not use the actual values, but rather looks at the variation in the proxy value from the averaged value over the time period. So that the variation in value from that mean is the measured value against which the models are calibrated. (The process is known as centering the model, since it is the variation from the central value of the data that is used in the subsequent analysis). One of the reasons for doing this is to cope with conditions that are below the average. (By using variation from the mean one can more easily note that a drop in temperature below the average can create a negative growth in the ring that year.) It is important that this be carried out correctly since, when it has not been, and the Wegman report notes that the “hockey stick” paper did not do so, then the results obtained can be flawed.

Our committee believes that the assessments that the decade of the 1990s was the hottest decade in a millennium and that 1998 was the hottest year in a millennium cannot be supported by the MBH98/99 analysis. As mentioned earlier in our background section, tree ring proxies are typically calibrated to remove low frequency variations. The cycle of Medieval Warm Period and Little Ice Age that was widely recognized in 1990 has disappeared from the MBH98/99 analyses, thus making possible the hottest decade/hottest year claim. However, the methodology of MBH98/99 suppresses this low frequency information. The paucity of data in the more remote past makes the hottest-in-a-millennium claims essentially unverifiable.

It also comments on something else that I find quite troubling, namely the very small circle that is formed of the “climate scientists” that publish in this area, and their inter-relationships, with most of the major authors in the field being tied to Dr. Mann – but that is an issue for another day. However, this "clique" does not include many with a strong grounding in statistics, and it is this weakness, and the errors generated in the predictions as a result, which make the papers that the groups generate (and which get significant international publicity) very vulnerable to criticism, which may well be justified.

I want to go back, however, to the comments on coral, since the growth of coral is one of the parameters that are used to assess Climate Change. The Wegman Report noted:

Reef-building corals are strongly affected by temperature and, as temperature drops, the rate of calcification drops with lower temperature potentially presaging the death of the colony. Coral growth rates vary over a year and can be sectioned and x-rayed to reveal high- and low-density bands. High density layers are produced during times of higher sea surface temperatures. Thus not unlike tree rings, data on corals also can be calibrated to estimate (sea) surface temperatures.

I draw attention to that since there is a current interest in coral data, with stories commenting on the “ravages” that will occur to coral with increasing temperature. And yet, even in those stories, dealing with coral damage one finds

Sea level rise, which is projected to occur this century as the world's glaciers melt, would not necessarily kill coral reefs, Tamelander said, since the reefs can grow as waters get higher.

"A healthy reef should be able to keep up," Tamelander said.

. Climate Audit points out the inadequate statistical analysis behind the headline, and then when the statistics are applied the conclusion is wrong.

But then these facts, and the impact of land sinking

"It doesn't matter who's causing global warming. Sea-level rise is something we can measure," said Rob Young, a geosciences professor at Western Carolina University. "You can't argue that sea level isn't rising."

And it has been rising faster in the mid-Atlantic because the land here is sinking. Understanding this phenomenon requires thinking of the Earth as an enormous balloon. Push down in one spot on the ball's surface and surrounding areas are raised up. Glaciers did this to Earth's surface during the last ice age: They pressed down on northern North America and areas to the south tilted up, like the other end of a seesaw. Today, thousands of years after the glaciers retreated, the seesaw is tipping back the other way, and the region from New York to North Carolina is falling about six inches per century.

And this is my gripe for the day – we see anecdotal headlines about how this disaster or that is coming, courtesy of global warming, but these warnings are rarely accompanied by an adequate statistical analysis that shows that the facts discussed are in fact real and correlated to global warming in the manner projected.

One can see this, for example, in the recent comment by Kofi Annan story on the level of death caused by global warming. This is rebutted by the statistics as noted in the Wall Street Journal (Hat tip Irv.) There is no mention of the hundreds of thousands of acres of the sub-Sahara that have been converted to agriculture in the last decade, thereby prolonging, instead of shortening life. Rather those stories are hidden in the headlines of starvation

Oxfam expects cereal production across five countries in the dry Sahel belt south of the Sahara -- Burkina Faso, Mali, Mauritania, Niger and Senegal -- will be a record 18.5 million tonnes this year, but the food on sale will be beyond the budget of many in these, some of the world's poorest countries.

Saturday Pick Points

Normally this is the point every week where I wander around the Climate Change sites, just to see what is stirring them up. And the controversy continues over the statistics of the paper by Steig that I first mentioned back in January. There is a very well done dismemberment of the underlying statistics given at Watt’s Up With That this week. Basically part of the criticsm is based on the relatively obvious point that as you move two weather stations further apart, then the likelihood of them both having the same weather at the same time becomes less, particularly at greater distances. (For example the snow storm that will hit the East Coast Sunday night and Monday hit Missouri Saturday and was somewhat milder – we got 2 inches, Maine will get 12 inches. On the other hand Waynesville and Salem in Missouri both reportedly got the same amount). However when you look at the statistics that were used in the paper the likelihood of the weather being the same stays the same regardless of their distance apart. And it even stays the same when you consider satellite data. Which sadly implies that the results as quoted in Nature and given national prominence are in error and in fact where a more realistic model is used the continent returns to a largely cooling phase and the furor the paper raised is shown to be based on a false premise. (Not of course that this finding will get much mention in the MSM). Though the controversy may well continue, since the new story is that the speed of the glaciers is accelerating. There is very little data from down in the Antarctic and so it will be interesting if this particular study gets picked up.*
*Since this deals with a topic that I actually teach to students, I will have a small technical note at the end.


Speaking of furors the little tempest over the article that George Will wrote on Climate Change in the Washington Post two weeks ago continues to churn. I talked a little about temperature fluctuations last week, explaining the trends as to why it might have seemed that the world was cooling in 1975. The other major issue was:

As global levels of sea ice declined last year, many experts said this was evidence of man-made global warming. Since September, however, the increase in sea ice has been the fastest change, either up or down, since 1979, when satellite record-keeping began. According to the University of Illinois' Arctic Climate Research Center, global sea ice levels now equal those of 1979.

It is important to note (though it is rarely mentioned in the row) that satellite records have only been available since 1979, and that is why that particular date was chosen.

Well there were the usual diatribes, with ad hominem attributes – “Is George Will the Most Ignorant National Columnist” is a good example, and the controversy ran for a week, so that George Will’s column a week later also dealt with the subject. It pointed out that, within a reasonable scale of accuracy, what he had said was correct. Which, of course, led to a second set of diatribes . After another week of comments the Post Ombudman wrote a column this weekend. Basically it said that the facts that George Will used were accurate, but that since there had been a big change in the relative volumes of ice (the Arctic had lost a lot which growth of ice in the Antarctic had almost offset) this should have been brought out in the article. And just to emphasize this, Real Climate, in writing "the article that Will should have written", notes

The source of the original quote was a Daily Tech blog post published in early January. While that post itself was heavily criticized as being misleading, it did use data from a reliable scientific source which was technically accurate at the time. My error was in assuming that scientific 'facts' don't change over a month or two and thus it was not necessary to revisit the source of the original data before writing my column. What was true in January would still be true in February, right? Wrong.

Of course that does not mention that the sensor doing the measurement went wonky. Now it turns out that the folks gathering the data have given a very rational explanation at WUWT about all this, and why they are now catching on to to demands of the internet, but still.

Well that has not quieted the complaints, though it is interesting to note from the ombudsman’s column

Although I didn't render a judgment, my response was understandably seen as an institutional defense and prompted an orchestrated e-mail campaign in which thousands demanded that The Post correct Will's "falsehoods." Like they say when the pro football rookie gets clobbered: "Welcome to the NFL."

The messages, often identical in wording, were soon countered by waves of e-mails defending Will and attacking what many labeled "global warming alarmists" trying to muzzle him.

It is the “often identical in wording” which shows the footprints of the thought police. Sadly it is almost impossible to have a reasoned debate on this issue, since any attempt to bring up the topic either gets this treatment (as I noted earlier) or is ignored, as the testimony by Professer Happer before the Senate Environment and Public Works Committee Senator Barbara Boxer, Chair has largely been.

Similarly John Tierney wrote about Climate Change in the New York Times noting that scientists are tending more to Apocalyptic statements, and urging instead that they behave as honest brokers. Since the scientists who get quoted most often are those who are promising that the conditions are getting worse rather than better and this does help to sell newspapers and air time, he has a point. Needless to say he is not popular with those that advocate AGW. showing their desire to keep the debate at a sophisticated level they have opening statements such as

Tierney is easily the worst science writer at any major media outlet in the country. Pretty much every energy or climate piece he writes is riddled with errors and far-right ideology, including this one.

. And then you get the latest, after Tierney’s recent column

The backlash from George Will's disinformation rightly grows each day that the Washington Post stands behind his lies (see here). Media Matters has samples of widespread outrage in the country here, and a new report [PDF] from CAPAF challenges the WP to issue a correction.

Now it is time for outrage over John Tierney, who not only makes stuff up just like Will, but is actually on the New York Times staff as their 'science' columnist. When we last saw Tierney, he was spreading lies and disinformation about science adviser nominee John Holdren (see here).

Today, the NYT not only let him print more egregiously made up stuff to smear Holdren (and Energy Secretary Steven Chu). But they actually published an article "Politics in the Guise of Pure Science" (see here) under the heading "FINDINGS" about Chu, Holdren, climate science, and climate solutions with precisely one source -- Roger Pielke, Jr. That would be like publishing an article critical of Obama's handling of the financial crisis and only citing Bernie Madoff.

Sigh! At the risk of being repetitive, the Senate Committee took testimony this past week, from Chris Field (pdf) and (among others) Professor Happer as cited. They hold strongly different views, yet are the two positions debated in the press, or in Congress as they should be, or are we still being subjected to the “ad hominem “ types of attack that seems to be the fall-back position of what, sadly I am beginning to truly think are those setting out to be thought police for this nation. The Bernie Madoff case illustrates the need for open debate and making this whole debate more open, and more based on science. What Joseph Romm and his ilk seem bent on doing is to have us instead behave as Bernie Madoff sycophants and not ask questions.

The abuse that I have seen showered on articles that raise technical and scientific questions is clearly an attempt to shout them down. It has been my experience and that of others. With the numbers of identically worded letters going to the WP Ombudsman it is clear that these are orchestrated campaigns.

To end with a slight technical comment, that I will expand into a Tech Note one of these days. For my sins I am one of the few people I believe that has videotaped a landslide from in front and beneath it, and got away with it. I have used that video in a class I teach on the movement of geotechnical material and the forces that drive that movement. As part of the class the first homework assignment begins "Take a can of your favorite beverage, drink it. Now fill it full of water and place it on a flat surface. Slowly tilt the surface and note the angle at which the can slides. Now poke a small hole in the bottom of the can and repeat." The class has been doing this and reporting the results for decades, they vary quite considerably, depending on the nature of the surface, its roughness and a number of other factors (and in the course of those decades the favorite beverage has undergone a number of changes). The assignment is not original, but it has shown that there are a number of factors that govern block movement - about which more anon.

Saturday Pick Points

There were only a couple of entries over in Real Climate this week, and they seem to be becoming more remarkable for their defensive nature. But it has been that sort of a week. It really began over at Climate Audit following up on the paper that I mentioned a couple of weeks ago, in which Eric Steig et al wrote about a change in the calculations on Antarctic temperatures, resulting in a greater warming than had been projected in earlier evaluations.

So Steve McIntyre has a look at the data that was used for that re-evaluation, and focused in on data from one of the Automated Weather Stations (AWS) called Harry, which had shown the greatest trend in data. And he found that some of the data that had been originally reported for Harry, instead belonged to a station called Gill.

Writing this up at his site he noticed that the data at the British Antarctic Survey (BAS) was in the process of being corrected. It turns out that it was being corrected because Gavin Schmidt, who writes for Real Climate, had contacted them about the error, though that did not become clear until February 4th. On which day Gavin wrote the somewhat defensive post at Real Climate, sensibly saying that by correlating manned station data with that from satellites and the AWS it had been possible to extend the estimates of actual temperatures, and that within the context of the process that was used, the erroneous data from Harry, and a third station known as Racer Rock, really didn’t make any difference to the results. (Incidentally Gavin’s actions drew a rebuke at Science Policy ).

In the process he admitted that the data from the AWS could be flawed, since the stations were, on occasion buried in the snow. (see photos at the Harry website above). Which was a timely comment, given that Anthony Watts was just posting photos that showed some of the problems in acquiring temperature data in the Antarctic. And Climate Audit being the site that it is, on the 6th the new data was reviewed to see what it changed. The results (bear in mind that there are only a few stations in the area) show that it may not have been as inconsequential as stated.

And so we leave CA for another week, just as another controversy is starting , Steve draws attention to a letter by Michael Mann which is, sadly, another demonstration of how easily the AGW group slip into ad hominem attacks rather than debate the science.. The issue this time is an article by Lawrence Solomon, and it is another take on the Antarctic discussion. It points out that when the data shows that one thing is happening (Antarctic cooling) and you would prefer that it not, you can use statistics to show that the opposite (Antarctic warming) is occurring. He also takes a dig at the “hockey stick” and that is the cause of Dr. Mann’s ire. The controversy is likely to go on into next week, and the latest response is from Mr. Solomon.

That whole relationship between Climate Audit and Real Climate looks to continue to be adversarial, since the new paper that is discussed at RC today has met with a rejoinder at CA suggesting that the data in the paper gives a different conclusion to that drawn.

Well, other than that WUWT points to a post where the new Secretary of Energy is predicting the end of agriculture in California, and has more pictures of inappropriate siting of weather stations, while promising a comment on fossil fuels in the near future.

Gristmill points to a new site on coal that will be interesting to follow. There is also a move to get to 25% renewable energy by 2025, as well as a lead to an initiative in Georgia to restrict coal use. And EPA is starting to work on the new sets of rules that will apply to coal-fired power stations.

Well these stories have kept me fascinated all day (the Antarctic ones) so I am going to stop before I get too far into the backstory . . and off to get back to Peak Oil for the week.