If you torture the data enough, nature will always confess - Ronald Coase.
Facts are stubborn things, but statistics are more pliable. - Anonymous.
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Climatology is the study of average weather over time or in a region. It is very different than Climate Science, which is the study by specialists of individual components of the complex system that is weather. Each part is usually studied independent of the entire system and even how it interacts or influences the larger system. A supposed link between the parts is the use of statistics. Climatology has suffered from a pronounced form of the average versus the discrete problem from the early 1980s when computer modelers began to dominate the science. Climatology was doomed to failure from then on, only accelerated by its hijacking for a political agenda. I witnessed a good example early at a conference in Edmonton on Prairie Climate predictions and the implications for agriculture.

It was dominated by the keynote speaker, a climate modeler, Michael Schlesinger. His presentation compared five major global models and their results. He claimed that because they all showed warming they were valid. Of course they did because they were programmed to that general result. The problem is they varied enormously over vast regions. For example, one showed North America cooling another showed it warming. The audience was looking for information adequate for planning and became agitated, especially in the question period. It peaked when someone asked about the accuracy of his warmer and drier prediction for Alberta. The answer was 50%. The person replied that is useless, my Minister needs 95%. The shouting intensified.

Eventually a man threw his shoe on the stage. When the room went silent he said, "I didn't have a towel". We learned he had a voice box and the shoe was the only way he could get attention. He asked permission to go on stage where he explained his qualifications and put a formula on the blackboard. He asked Schlesinger if this was the formula he used as the basis for his model of the atmosphere. Schlesinger said yes. The man then proceeded to eliminate variables asking Schlesinger if they were omitted in his work. After a few eliminations he said one was probably enough, but you have no formula left and you certainly don't have a model. It has been that way ever since with the computer models.

Climate is an average, and in the early days averages were the only statistic determined. In most weather offices the climatologist's job was to produce monthly and annual averages. The subject of climatology was of no interest or concern. The top people were forecasters who were meteorologists with only learning in physics of the atmosphere. Even now few know the difference between a meteorologist and a climatologist. When I sought my PhD essentially only two centers of climatology existed, Reid Bryson's center in Wisconsin and Hubert Lamb's Climatic Research Unit (CRU) at East Anglia. Lamb set up there because the national weather office wasn't interested in climatology. People ridiculed my PhD being in the Geography Department at the University of London, but university departments weren't doing such work. Geography accommodated it because of its chorologic objectives. (The study of the causal relationships between geographic phenomena in a region.)

Disraeli's admonition of lies, damn lies and statistics was exemplified by the work of the IPCC and its supporters. I realized years ago that the more sophisticated the statistical technique the more likely the data was inadequate. In climate the data was inadequate from the start as Lamb pointed out when he formed the CRU. He wrote in his autobiography "...it was clear that the first and greatest need was to establish the facts of the past record of the natural climate in times before any side effects of human activities could well be important." It is even worse today. Proof of the inadequacy is the increasing use of more bizarre statistical techniques. Now they invent data such as in parameterization. Now they use output of one statistical contrivance or model as real data in another model.

The climate debate cannot be separated from environmental politics. Global warming became the central theme of the claim humans are destroying the planet promoted by the Club of Rome. Their book, Limits to Growth did two major things both removing understanding and creating a false sense of authority and accuracy. First, was the simplistic application of statistics beyond an average in the form of a straight-line trend analysis: Second, predictions were given awesome, but unjustified status, as the output of computer models. They wanted to show we were heading for disaster and selected the statistics and process to that end. This became the method and philosophy of the IPCC. Initially, we had climate averages. Then in the 1970s, with the cooling from 1940, trends became the fashion. Of course, the cooling trend did not last and was replaced in the 1980s by an equally simplistic warming trend. Now they are trying to ignore another cooling trend.

One problem developed with switching from average to trend. People trying to reconstruct historic averages needed a period in the modern record for comparison. The 30-year Normal was created with 30 chosen because it is a statistically significant sample, n, in any population N. The first one was the period 1931-1960, because it was believed to have the best instrumental data sets. They keep changing the 30-year period, which only adds to the confusion. It is also problematic because the number of stations has reduced significantly. How valid are the studies done using earlier "Normal periods"?

Unfortunately, people started using the Normal for the wrong purposes. Now it is used as the average weather overall. It is only the average weather for a 30-year period. Actually it is inappropriate for climate because most changes occur over longer periods.

But there is another simple statistical measure they effectively ignore. People, like farmers, who use climate data in their work know that a most important statistic is variation. Climatology was aware of this decades ago as it became aware of changing variability, especially of mid-latitude weather, with changes in upper level winds. It was what Lamb was working on and Leroux continued.

Now, as the global trend swings from warming to cooling these winds switched from zonal to meridional flow causing dramatic increases in variability of temperature and precipitation. The IPCC, cursed with the tunnel vision of political objectives and limited by their terms of reference did not accommodate natural variability. They can only claim, incorrectly, that the change is proof of their failed projections.

Edward Wegman in his analysis of the "hockey stick" issue for the Barton Congressional committee identified a bigger problem in climate science when he wrote:
We know that there is no evidence that Dr. Mann or any of the authors in paleoclimatology studies have had significant interactions with mainstream statisticians.
This identifies the problem that has long plagued the use of statistics, especially in the Social Sciences, namely the use of statistics without knowledge or understanding.

Many used a book referred to as SPSS, (it is still available) the acronym for Statistical Packages for the Social Sciences. I know of people simply plugging in numbers and getting totally irrelevant results. One misapplication of statistics undermined the career of an English Geomorphologist who completely misapplied a Trend Surfaces analysis.

IPCC projections fail for many inappropriate statistics and statistical methods. Of course, it took a statistician to identify the corrupted use of statistics to show how they fooled the world into disastrous policies, but that only underlines the problem with statistics as the two opening quotes attest.

There is another germane quote by mathematician and philosopher A.N. Whitehead about the use, or misuse, of statistics in climate science.
There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.
Other quotes about statistics reveal a common understanding of their limitations and worse, their application. Here are a few;
He uses statistics as a drunken man uses lampposts - for support rather than for illumination. - Andrew Lang.

One more fagot (bundle) of these adamantine bandages is the new science of statistics. - Ralph Waldo Emerson

Then there is the man who drowned crossing a stream with an average depth of six inches. - W E Gates.

Satan delights equally in statistics and in quoting scripture. - H G Wells

A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions. - M J Moroney.

Statistics are the modern equivalent of the number of angels on the head of a pin - but then they probably have a statistical estimate for that. - Tim Ball