Fun with numbers

One theme of this site over the last month or so has been the misleading use of numbers. This is very much related to the ongoing discussion of whether warming has stopped or not. One side, the Anti-AGW, says it has stopped and therefore global warming is not happening and never will, conveniently forgetting that a lot of it has already occurred. The other side, the Pro-AGW, says warming still happening and introduces new metrics to demonstrate this. 

In an age when every ‘scandal’ unearthed by budding ‘Woodward and Bernsteins’ is given a ‘gate’ suffix it is easy to forget that President Nixon was impeached not for the original crime of breaking into offices of the Democratic Party but for the cover up. I wonder if something similar is happening with the Climate Science Community at the moment. I have, in earlier blogs, identified examples of presentations and sites trying to prove that the models’ predictions were accurate which have left off data from the recent years (though internal evidence shows that they could have included it.) Yes, it would be inconvenient to admit that the current climate stasis was not predicted but playing with numbers to try and disguise it opens the Climate Science Community to charges of intellectual dishonesty.

Below I ‘prove’ that there has been no increase in temperatures since 1998. I did this by assuming that temperatures from 1998 onwards have been flat and calculating the temperature perturbation from the flat line. I then regressed this perturbation, after adjusting for residual seasonality, against sunspots, aerosols and a multivariate ENSO index and got the following graph.

Wow – there’s no warming! Eat your heart out you pro-AGW crowd. But, how did I prove it? I cheated. Firstly the coefficients I derived suggested that higher solar irradiance is associated with cooling and higher aerosols are associated with warming; only the El Nino index behaved sensibly. Then I adjusted the format of the equation so the coefficient was shown to only two places of decimals. As the data are monthly this means I could have had warming of 0.049 degrees/month (0.6 degrees a year) and still shown ‘zero’ warming. What is more, if I’d played around a bit more with lag times, different indices, and different amounts of smoothing  I could have produced an even more convincing, but even more dishonest, proof.

I’ve been completely upfront about what I have done but as long as the Climate Science Community tries to avoid the reality of climate stasis they will face a barrage of similar ‘proofs’ but with any underlying falsification being undisclosed.

When is a trend not a trend?

There has recently been discussion on the blogosphere as to whether or not global temperatures are continuing to rise, have levelled off, or are falling.  For example the ‘Met Office in the Media’ site had a rebuttal of an article in the (United Kingdom) Daily Mail which, inter alia, claimed there had been no warming for 15 years. ( http://metofficenews.wordpress.com/2012/01/29/met-office-in-the-media-29-january-2012/)  In their rebuttal the Met Office pointed out that most of the highest temperatures on record have occurred in the last 15 years. They also present a chart of temperature in 10 years blocks which showed that the first decade of the 21^st century was the warmest on record.

In the IPCC Technical Assessment Report of 2007 many of the temperature graphs are smoothed using 13 point binomial moving average (for example figure 3.8). Elsewhere they talk of decadal smoothing. One of the contributors to the blog in support of the Met Office’s position refers to the ‘Skeptical Science’ web site (http://www.skepticalscience.com/global-warming-stopped-in-1998-intermediate.htm). Here they show temperature using an unweighted 11-year moving average but do not include data after 2007. The data they do show has a positive trend. (This is strange as that page of the web site has been updated to include a 2011 paper by Foster and Rahmstorf, which we have discussed elsewhere (http://www.climatedata.info/Discussions/Discussions/opinions.php?id=3871334005763196947), which purports to compensate for the effect of solar irradiance, volcanoes and El Nino.) 

In the graph below we show the HADCRU3V data set (normalised to 1979 to 2008 for compatibility with satellite temperature data series). We have include three smoothed series: 13 point binomial using the weights in the IPCC report, and 11 point unweighted moving average and a 15 year unweighted moving average.

As can be seen, only the 15 year moving average suggests that temperatures are continuing to rise. At the time of the IPCC report in 2007, the authors were happy with a 13 point smoothing or decadal smoothing. Now that these statistics no longer show a rising trend they are finding new ways of presenting the data to claim that the trend continues. I genuinely believe that rather than moving the goal posts the Met Office would better maintain its credibility by admitting that, at the very least, the rate of temperature rise has slowed. The basic truth of course is that extrapolating from the past climate says little about the future (year on year temperatures are correlated so the temperature in one year does have a bearing on following years).
[The following material was added on 3 February 2012.]

This post was, in part, prompted by the exchange on the Met Office site mentioned above. As part of the moderator's reply he referenced a Met Office document of 2010:
http://www.metoffice.gov.uk/media/pdf/m/6/evidence.pdf

This did accept that the rate of temperature rise in the past decade was slower than in the immediately preceding decades and postulated some tentative ideas as to why this might have happened. However it also contained some other metrics which were presented in such a way as to minimise the impact of this fact. Some of them I have commented on in the blog itself. One of them was a plot of decadal temperatures which showed that, despite the slowdown in the rate of temperature increase, the decade from 2000 to 2009 was the warmest on record. Below we give a plot of the decadal rate of change of temperature in C per year both the for observed temperatures  (HadCRU3V annual average values) and the average of 7 climate models combining the 203cm and a1b scenarios to cover the period 1870 to 2010.







This shows two things: that while the rate of rise in the 1990s was the highest on record there were other decades in the past with rises of the same order of magnitude, the models (which get the overall rise fairly accurately) do not represent the rate of rise at a decadal time scale at all well. My purpose in this posting is not to 'rubbish' the models; it is to suggest the selecting data to agree with the science is the wrong approach; it should rather be to admit shortcomings in the science and work on improving it.