10. Breakpoint adjustment and its effect on the scaling behaviour of anomalies

In my previous post (see here) I demonstrated that the noise or random temporal fluctuations in the temperature anomaly from weather station data were not consistent with white noise, but were instead characteristic of a one-dimensional time-dependent fractal with a 1/√ω power spectrum (where ω is the frequency of the oscillations in the noise signal). I then showed that these temperature fluctuations exhibit self-similarity with a fractal dimension of 0.25 (approximately). I also showed that one consequence of this is that the expected long term temperature fluctuations (i.e. those with timescales greater than 100 years) would be at least six times greater in magnitude (almost 1.0 °C) than most climate scientists probably realize. This analysis was done on the original raw unadulterated data (or at least what I assume is the original raw unadulterated data). In this post I shall apply the same technique to data that has been processed and adjusted by Berkeley Earth and look at the difference.

One of the most frequent claims made against climate science by sceptics is that the temperature data is manipulated. It is of course a claim that those climate scientists deny, but ever since the Climategate email scandal there has been a bad smell. It was, after all, that bad smell that prompted Richard Muller to set up Berkeley Earth in order to provide some independent verification of the results that the other groups (NOAA, GISS, HADCRUT) were producing.

That said, the claim that some climate scientists manipulate the data has never been completely rejected by climate scientists themselves. In fact they justify much of it on the grounds that the data is unreliable and needs to be “cleaned up”. Their rationale for these statistical interventions is this: some temperatures records are very long and therefore it is inevitable that something will go wrong with the data in that time. People will change, instruments will change (e.g. changes from Stevenson screens to electronic systems), procedures will change (e.g. time of data collection), and locations will change, so error checking needs to be put in place to compensate for any potential errors that may arise. This is particularly important since the primary purpose of most climate research is to determine the temperature change over time. This in turn requires the scientist to measure two temperatures, under identical conditions, at the same location, but a long time apart. It is therefore no good having very accurate measurements now if what you are comparing them against is uncertain.

In addition, data is often missing or incorrectly entered (e.g. in Fahrenheit rather than Celsius). The result of all this is that the climate scientists believe the data needs to be subject to a strict quality control during the analysis process, and two of the “data cleaning” techniques that they rely on to do this are homogenization and breakpoint adjustment.

Homogenization is a primarily used for two outcomes. The first is to use extrapolation or interpolation to fill in missing data points in the record. The second is to compare records from neighbouring stations and construct a regional average that can be used as a more reliable reference dataset.

Breakpoint adjustment is a data manipulation technique that first uses homogenization to construct an idealized reference for the region and then compares the actual station data to the reference. It then looks for points in the dataset of the target station where the difference between the target and the reference changes over a short time interval by an amount that is much larger than is normally seen. At this point a cut or break in placed in the data and data each side of the cut is shifted up or down. An example (taken from Berkeley Earth) is shown in Fig. 10.1 below.

Fig. 10.1: Anomaly data for Waiouru Airstrip.

In the above data for Waiouru Airstrip (Berkeley Earth ID - 172950) a breakpoint was detected by Berkeley Earth between October and November 1986, as shown below in Fig. 10.2. The red lines in Fig. 10.2 indicate the amount by which the data on the right (post October 1986) is deemed to be too low in value relative to the data before November 1986 when compared with a regional average.

Fig. 10.2: Difference in station anomaly and regional anomaly for Waiouru Airstrip.

This regional average appears to be constructed from the surrounding station data weighted by the square of their correlation coefficient with the target station (Waiouru Airstrip). There is only one problem with this, though; there is only one other station within 100 km with data spanning 1986 and that is at Ohakea 87 km away with only 234 months of data (see below). So how reliable is the weighting process? That is a major issue, particularly in the Southern Hemisphere where station density is much lower than in the USA or Europe.

 Fig. 10.3: Anomaly data for Ohakea.

Nevertheless, it can be seen that the breakpoint correction in Fig. 10.2 is an impressive 1.2 °C. However, this adjustment is not applied evenly. First, it equates to a different amount for each month (January - December) as shown in Fig. 10.4 (see below).

 Fig. 10.4: Total breakpoint correction for Waiouru Airstrip.

This effectively means that while the breakpoint is set at the same point for each of the twelve monthly datasets that make up the whole, the adjustment is different for each. Why? I’m still not sure about this and can see no obvious rationale. But surely if the cause is the same same (e.g. a station move), then the impact on all monthly readings should be the same.

Fig. 10.5: Actual breakpoint correction for Waiouru Airstrip.

The second feature of note is that adjustments are made to data on both sides of the breakpoint, but by different amounts (see Fig. 10.5 above). Those months before November 1985 are adjusted down, while those after are adjusted up. These adjustments are not equal in magnitude, but are scaled in proportion to the number of data points on the opposite side of the breakpoint so that the mean reading remains unchanged but the difference in adjustments equals the total adjustment. For example, the total adjustment for January is 1.21 °C, but there are 12 January data readings before November 1986, and 25 after. So the January readings before November 1986 are reduced by 0.82 °C ( = 1.21x25÷37), with the January readings after November 1986 being increased by 0.39 °C ( = 1.21x12÷37). The mean adjustment is therefore zero but the difference between the two is 0.39 - (-0.82) = 1.21 °C.

 Fig. 10.6: Berkeley Earth adjusted anomaly for Waiouru Airstrip.

The impact of the adjustment on the anomaly data in shown above in Fig. 10.6, the outcome of which is to change the gradient of the best-fit trend line from a negative cooling of -3.24 °C per century (the green line in Fig. 10.1) to a positive warming of +0.82 °C per century (the red line in Fig. 10.6).

Variants on breakpoint adjustment are used by most of the major climate science groups that analyse the global temperature record. In the case of NOAA they are called changepoints and are identified by pair-wise comparisons of neighbouring stations. The effect of these adjustments is to reduce long temperature records to a series of short ones. In the case of NOAA, the records are reduced to a typical length of 15-20 years; for Berkeley Earth it is 13.5 years. You can see this in the New Zealand data I have analysed in the last three posts. Of the ten long records (1200+ months of data) and seventeen medium ones (400+ months of data), all had breakpoints inserted by the Berkeley Earth group, while of the thirty short records only nine did. In the long records alone, there are a total of 46 breakpoints. That is about one breakpoint every 28.6 years and does not include the record gaps and documented station moves that also effectively serve as breakpoints. So the obvious question is, are they justified?

Fig. 10.7: Scaling behaviour of the stemperature anomaly noise for Auckland with and without breakpoint adjustment.

The assumption is that breakpoint adjustments correct the data and return it to its true values and behaviour that would be the case before human error was introduced. Yet if we look at the scaling behaviour I described in the last post, this suggests that the impact may be more negative than positive.

The data in Fig. 10.7 above compares the scaling behaviour of the temperature anomaly for Auckland-Albert Park (Berkeley Earth ID - 157062) before and after the breakpoint adjustments were added. It can clearly be seen that the original data is less scattered than the adjusted data. The gradient for the original data is -0.248 while it is -0.266 for the adjusted. But it is the scatter of the data that is most striking. If we calculate the percentage error (or residual) by comparing the r.m.s. value of the difference between the y-values and the best fit line with the r.m.s. value of the y-values themselves, the results are 4.8% for the original data and 8.1% for the adjusted data.

Fig. 10.8: Scaling behaviour of the temperature anomaly noise for Wellington with and without breakpoint adjustment.

A similar pattern is seen for Wellington-Kelburn (Berkeley Earth ID - 18625) above. The gradient of the best fit line is -0.235 for the original data and -0.239 for the adjusted data. While the gradients are almost identical the residuals are again different, with the adjusted data having a residual (3.3%) that is more than double that of the original data (1.6%).

Fig. 10.9: Scaling behaviour of the temperature anomaly noise for Christchurch with and without breakpoint adjustment.

Finally, if we look at the data above (Fig. 10.9) from the station at Christchurch AP-Harewood (Berkeley Earth ID - 157045), similar differences are seen with the gradient of the best fit to the original data being -0.275 while it is -0.382 for the adjusted data. Here, though, the adjusted data has a residual (20.3%) that is more than seven times that of the original data (2.6%), an astonishing disparity.

Fig. 10.10: Scaling behaviour of the mean temperature anomaly noise for all ten long stations in New Zealand.

It is, though, not just individual stations where this disparity between the scaling behaviour of the original and adjusted data is seen. It is seen in the regional trends as well. So in Fig. 10.10 the trend data from Fig. 7.6 in Post 7 is analysed. This data represents the mean anomaly of all ten long stations in New Zealand. Here the scaling follows a best fit line with a slope of -0.219 and a residual of 1.4%, while the breakpoint adjusted data for all ten long stations (see Fig. 7.8 in Post 7) has a scaling behaviour with a best fit line of slope -0.198 and a residual of 3.2% (see Fig. 10.11 below). So again the residual for the adjusted data is more than double that of the original data.

Fig. 10.11: Scaling behaviour of the mean temperature anomaly noise for all ten long stations in New Zealand after breakpoint adjustment.

What I think this shows is that breakpoints are unsubtle in their impact. The claims that they are surgical in their precision and benign with regard to the general temperature trend are dubious at the very least. At best they may be seen as blunt statistical interventions that correct some of the worst measurement errors, and at worst as being a greater corrupting influence on the data than the errors that they were intended to eliminate.