i) Weather station distribution
The location of the 57 long and medium stations are shown in Fig. 21.1 below. Most of the stations are situated towards the south of the state, with only 10 medium stations located above the 32nd parallel (which bisects the state). This means that the stations in South Australia are not evenly distributed across the state, nor are they fully representative of the overall climate of the state.
Fig. 21.1: The locations of long stations (large squares) and medium stations (small diamonds) in South Australia. Those stations with a high warming trend since 1841 are marked in red.
The station locations shown in Fig. 21.1 differentiate between those stations that have warming trends and those where the trend is negative or stable. I have defined a warming trend to be one where the slope of the best fit to the temperature trend is positive and more than twice the error in the gradient (i.e. 95% confidence). Based on the distribution of stations in Fig. 21.1, it appears that most of the warming in South Australia is found in the west of the state. However, it needs to be recognized that most of those stations are shorter length stations with more recent data. As the data in Fig. 20.2 below indicates, the overall trend in South Australia is a warming one in the latter half of the 20th century. That coincides with the time-frame of operation of most of the medium and short stations.
ii) The trend in mean temperature
Fig. 21.2: Temperature trend for long stations in South Australia since 1857. The best fit linear trend line (in red) is for the period 1857-2012 and has a gradient of -0.087 ± 0.055 °C/century.
Adding the temperature anomalies from all stations in South Australia with more than 480 months of data yields the trend shown in Fig. 21.2 above. In this case the monthly reference temperatures (MRTs) for each station were calculated for the period 1961-1990. The MRT was then subtracted from the raw data to generate the temperature anomaly.
The trend in overall temperature since 1870 indicated in Fig. 21.2 is similar to that seen for both New South Wales and Victoria. There is evidence of a decline in temperatures from 1860 to 1940 followed by a slow rise. In this case the overall temperature trend from 1857 to 2012 (as indicated by the red line) is -0.087 ± 0.055 °C per century. In other words, overall South Australia has experienced a very low or moderate cooling since 1860. However, the real picture is of two distinct trends; a large cooling of over 1 °C for the period up to 1940, and a similar warming for the period since. This suggests that far from the climate being stable, it is continuously changing, and the warming we see in much of Australia since 1940 is not exceptional. Cooling phases of similar magnitudes have occurred previously.
iii) The Berkeley Earth (BE) mean temperature trend
Fig. 21.3: Temperature trend for long stations in South Australia since 1840 derived using the Berkeley Earth adjusted data. The best fit linear trend line (in red) is for the period 1941-2010 and has a gradient of +1.66 ± 0.08 °C/century.
If we repeat the temperature averaging process for the Berkeley Earth adjusted data we get the trend shown above in Fig. 21.3. This also shows an initial slight downward trend before 1940, but one that only amounts to about 0.3 °C. After 1940 there is a strong positive trend of +1.62 ± 0.07 °C/century that raises the overall temperature by over 1.1 °C before 2010. The trend in Fig. 21.3 is qualitatively similar to the plot shown on the Berkeley Earth site (see Fig. 21.4 below), and also resembles both the IPCC "hockey stick" and the instrumental temperature record since 1850. Again, this level of agreement between the data in Fig. 21.3 and Fig. 21.4 effectively supports our averaging process as it implicitly refutes the need to introduce station weighting coefficients.
Fig. 21.4: Temperature trend for South Australia since 1840 according to Berkeley Earth.
The data presented in Fig. 21.3 and Fig. 21.4 is the 12-month moving average, but the same general trends in the data are also seen in the monthly averages of the Berkeley adjusted data (see Fig. 21.5 below). The best fit to this data over the period 1841-2010 is a modest 0.429 ± 0.052 °C per century, but this still equates to an overall temperature rise of more than 0.8 °C since 1841. That is indeed similar to the temperature rise seen after 1941 for the raw data in Fig. 21.2, but the overall picture it presents is completely different. The reason for the difference becomes apparent if you look at how and where the differences arise.
Fig. 21.5: Temperature trend for all long and medium stations in South Australia since 1857 based on Berkeley Earth adjusted monthly data. The best fit linear trend line (in red) is for the period 1857-2012 and has a gradient of +0.429 ± 0.052 °C/century.
iv) Comparison of unadjusted and BE adjusted temperature data
The difference between the data in Fig. 21.5 and that in Fig. 21.2 is almost entirely due to the adjustments made to the data by Berkeley Earth (BE). These adjustments are shown in Fig. 21.6 below.
The adjustments made to the data by Berkeley Earth appear to be of two main types. Generally, the most significant tend to be the breakpoint adjustments that I have discussed previously. These are supposed to compensate for measurement errors in the original data. However, there appears to be a second adjustment that is introduced when the MRTs are calculated. As I wrote previously, the source of this is unclear, but I suspect it arises from a homogenization process being used to determine the MRT for each dataset, rather than the MRT being determined purely by averaging the data from within that dataset as I have done for Fig. 21.2.
Fig. 21.6: The Berkeley Earth breakpoint adjustment (in yellow) for Tasmania since 1840 together with the difference between the Berkeley Earth adjusted anomaly and the raw anomaly (in blue). The best fit (red line) to the total adjustment (blue curve) is +0.30 ± 0.03 °C per century.
In the case of the South Australia data, the MRT adjustments, although large in amplitude, do not seem to have as great an impact on the trend as the breakpoint adjustments. The sum total of the two adjustments is illustrated by the blue curve in Fig. 21.6 above. Together they add 0.30 ± 0.03 °C per century to the trend between 1911 and 2010 (see the red best fit line in Fig. 21.6). Of this, the breakpoint adjustments contribute 0.19 °C per century (see the yellow curve in Fig. 21.6). The net result is to lift the slope of the trend curve by 0.3 °C per century between 1911 and 2010. That amounts to a rise in the final temperature after 2010 of 0.3 °C as well. This, though, is only half the story.
What we can also see in Fig. 21.6 is that the total effect of all the adjustments is to introduce a negative cooling for the period 1857-1900 of up to 1 °C. The justification for this is presumably that the high temperatures before 1900 are inconsistent will the global trend. The problem is that they are all too consistent with the trends seen in the rest of Australia and in New Zealand.
As I pointed out in the last post, you do not need to eradicate the peaks and troughs in the temperature trend before 1900 (and nor should you) because these peaks and troughs are real, not erroneous artefacts that need to be expunged. And even if these peaks and troughs are not real, the appropriate way to deal with them is to use more data and see if they average out. In the case of Tasmania this was not possible because there was only one significant but imperfect temperature record for the period 1840-1900. In South Australia, however, we have at least four. And like the Tasmania data, it is consistent with data in NSW and Victoria over the same time-frame.
As I have outlined above, these adjustments that Berkeley Earth apply are not neutral. They significantly alter the temperature trend, and they do this because they do not just add to the positive trend post-1940 (thus enhancing the blade of the so-called hockey stick), they also help to erase the peaks in the anomaly data before 1990 (thereby smoothing the handle of the hockey stick). It is the combination and interaction of these two effects that so dramatically changes the temperature trend from the one I have calculated in Fig. 21.2 to the Berkeley Earth version in Fig. 21.5.
v) Noise and its scaling behaviour
Fig. 21.7: The standard deviation of the South Australia mean anomaly after smoothing with a moving average of size N. The gradient of the best fit line is -0.290 ± 0.015 and R2 = 0.9869.
Finally, if we look at the effect of data smoothing on the noise level, we again appear to see strong evidence of scaling behaviour (see Fig. 21.7 above). Once again the noise (as defined by the standard deviation) scales as N -a with the exponent a = 0.290 ± 0.015. This is similar to the scaling seen previously for NSW (a = 0.272 ± 0.005) and Victoria (a = 0.257 ± 0.015). However, here things are not quite so straight-forward.
The data in Fig. 21.7 shows evidence of a distinct curvature away from the linear regression best fit line. This suggests that the scaling may only be valid for low values of N and the log-log plot may not be truly linear. This appears to be confirmed by the plot in Fig. 21.8 below.
Fig. 21.8: The standard deviation of the South Australia mean anomaly after smoothing with a moving average of size N , but with a negative offset of 0.2 applied each time. The gradient of the best fit line is -0.465 ± 0.007 and R2 = 0.9988.
In Fig. 21.8 the standard deviation for each set of smoothed data is offset by a fixed amount (in this case 0.2). The reasoning here is that some of the standard deviation may not be from noise, but from an underlying linear trend for the data such as that seen in the upward slope of the Berkeley Earth data in Fig. 21.3 after 1940. Such a slope would itself have a standard deviation of ∆y/4√3 where ∆y is the change in vertical height up the slope.
The data in Fig. 21.2 effectively has two such slopes, a negative one before 1940 and a positive one after. Each slope will have the same standard deviation of 0.2 °C as ∆y = 1.4 °C (approximately) in each case. Thus if we subtract 0.2 from each standard deviation in Fig. 21.7 we get an approximate value for the standard deviation of the noise and not the slope. This data is plotted in Fig. 21.8 above.
What we find is that we still get a power law of the type N -a, but the index changes to a = 0.465 ± 0.007. More significantly, the residual between the data and the best fit reduces significantly from 11.4% of the standard deviation of y-values to 3.5%, thereby indicating how much the linear regression best fit has improved.
Fig. 21.9: The standard deviation of the South Australia mean anomaly, minus the parabolic best fit, after smoothing with a moving average of size N. The gradient of the best fit line is -0.465 ± 0.007 and R2 = 0.9988.
Alteratively, we could remove the underlying trend in Fig. 21.2 altogether. This trend is clearly parabolic to first order and can be approximated by the equation y = a(x-b)2 - c, where a = 0.00016, b = 1940, and c = 0.2. Subtracting this function from the mean anomaly data in Fig. 21.2 yields a dataset which has no underlying warming trend for the the entire timescale 1857-2013, but has the same monthly fluctuations as the data in Fig. 21.2. If the same scaling analysis is performed on this modified data as was undertaken in Fig. 21.7, the result is a different power law as shown in Fig. 21.9. This time we find that a = 0.456 ± 0.007. This is very close to the value of 0.5 we would expect for white noise. In addition the residual reduces even further to 3.4%.
So do we have white noise on a smoothly varying background (as demonstrated by Fig. 21.9) or do we have a quasi-fractal with a much lower power law? So far it is too early to tell. We do not have enough data. What is clear is that it is not only the South Australia data that exhibits this behaviour. It can also be seen (but was missed on first analysis) in Victoria (see Fig. 19.7) and Tasmania (see Fig. 20.8). In these two cases, however, the underlying trend was not parabolic or linear, particularly before 1900, so the modifications made in Fig. 21.8 and Fig. 21.9 above would not be applicable. In order to investigate this further, we probably need longer datasets. These will only be found in the Northern Hemisphere.
vi) Conclusions
1) The overall temperature trend for South Australia since 1857 shows no evidence of anthropogenic climate change.
2) Temperatures in the 1850s were probably greater than they are now.
3) Temperatures were much lower in the 1940s than they are now.
4) The overall temperature trend for South Australia since 1860 is broadly similar to that seen for both New South Wales and Victoria.
5) Berkeley Earth breakpoint adjustments and other adjustments (possibly from homogenization) have once again significantly changed the form and shape of the long-term temperature trend (see Fig. 21.3 and Fig. 21.5 and Fig. 21.6).
6) The noise level in the regional average of monthly anomalies (see Fig. 21.3) is similar to the noise level in the individual records. The averaging process has little effect on the noise level.
7) The noise in the regional temperature average for South Australia may scale in a similar way to that seen for New South Wales except that the power law is N - 0.29, where N is the size of the sliding window in the moving average (see Fig. 21.7). Or it could be white noise on a parabolic (or sinusoidal) background signal (see Fig. 21.9).
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