### How the ipcc invented a new calculus

A new form of calculus has been invented by the authors of the the IPCC's Fourth Assessment Report (AR4), in order to create the false impression that global warming is accelerating.

### How the new IPCC calculus works

Here's how it works. Look at the following graph:

Now consider the following question:

Is the slope of the graph greatest at the left hand end of the graph, or the right hand end?

By just looking at the graph, or by using old-fashioned calculus developed by Newton and Leibnitz, you might think that the slope of the graph is similar at both ends. But you would be wrong. In fact, the slope is much greater towards the right hand end of the graph. To prove this, we need to apply the new calculus developed by the IPCC. To do this, we draw a sequence of straight-line best fits backwards from the right-hand end-point:

This clearly shows how the slope of the graph is in fact increasing.

### How IPCC calculus is used in the IPCC report

Here is one of the key graphs from the AR4 report:

The graph is Figure 1 from FAQ 3.1, to be found on page 253 of the WG1 report. The slope over the last 25 years is significantly greater than that of the last 50 years, which in turn is greater than the slope over 100 years. This 'proves' that global warming is accelerating. This grossly misleading calculation does not just appear in chapter 3 of WG1. It also appears in the Summary for Policymakers (SPM): "The linear warming trend over the last 50 years is nearly twice that for the last 100 years". Thus, policymakers who just look at the numbers and don't stop to think about the different timescales, will be misled into thinking that global warming is accelerating. Of course, we could equally well start near the left hand end of the graph and obtain the opposite conclusion! (Just in case this is not obvious, see here, here, here or here for examples). A similar grossly misleading comparison appears at the very beginning of chapter 3, page 237: "The rate of warming over the last 50 years is almost double that over the last 100 years (0.13°C ± 0.03°C vs. 0.07°C ± 0.02°C per decade)." The trick appears again on page 249, "A HadCRUT3 linear trend over the 1906 to 2005 period yields a warming of 0.74°C ± 0.18°C, but this rate almost doubles for the last 50 years."

### ## How did this get through the IPCC's review process?

The IPCC reports are subjected to careful review by scientists. So how did this blatant distortion of the temperature trends get through this rigorous review process? The answer to this question can now be found, because the previous drafts of AR4, and the reviewer comments, can now be seen on-line. (The IPCC was reluctant to release these comments, but was forced to do so after a number of freedom of information requests). The answer is quite astonishing.  The misleading graph was not in either the first or the second draft of the report that were subject to review. It was inserted into the final draft, after all the reviewer comments. It is not clear who did this, but responsibility must lie with the lead authors of chapter 3, Kevin Trenberth and Phil Jones. Here is the version of the graph that the reviewers saw in the second draft:

Note that in this version there is only one trend line drawn.

So why was this graph replaced by the grossly misleading one? Did any of the reviewers suggest that a new version should be drawn with a sequence of straight lines over different time intervals? No. One reviewer made the following remark: 'This whole diagram is spurious. There is no justification to draw a "linear trend" through such an irregular record',... but his comment was rejected.

It is the same story with the misleading comment in the SPM mentioned above ("The linear warming trend over the last 50 years is nearly twice that for the last 100 years"). This statement was not in the original version reviewed by the scientists. It was inserted into the final draft that was only commented on by Governments.  The Chinese Government suggested deleting this, pointing out that 'These two linear rates should not compare with each other because the time scales are not the same'. Well done to the Chinese Government for spotting that. Too bad their valid comment was ignored by the IPCC.

Update after climategate 2

In the climategate 2 emails there is an interesting discussion between Jones, Trenberth and Brian Hoskins that sheds light on the origins of this graph, see email 2432.txt.  Hoskins says: "However I certainly defend the use of the 25, 50,100, 150 year trend lines on the temperature curve as in the TS and Chapter 3 as being better than the alternatives. A linear fit may not be a good one but when one is trying to make the smallest number of assumptions it is more defensible than for example putting in seemingly arbitrary break-points... The monotonically increasing slopes as one moves from the longer to the shorter time-scales is a strong indication of acceleration."