45. Review of the year 2020

I started this blog in May, in part to occupy my time during the Covid-19 lockdown. But I was also motivated by a growing dissatisfaction with the quality of data analysis I was witnessing in climate science, and in particular the lack of any objectivity in the way much of the data was being presented and reported. My concerns were twofold. 

The first was the drip-drip of selective alarmism with an overt confirmation bias that kept appearing in the media with no comparable reporting of events that contradicted that narrative. The worry here is that extreme events that are just part of the natural variation of the climate were being portrayed as the new normal, while events of the opposite extreme were being ignored. It appeared that balance was being sacrificed for publicity.

The second was the over-reliance of much of the climate analysis on complex statistical analysis techniques of doubtful accuracy or veracity. To paraphrase Lord Rutherford: if you need to use complex statistics to see any trends in your data, then you would be better off using better data. Or to put it more simply, if you can't see a trend with simple regression analysis, then the odds are there is no trend to see.

The purpose of this blog has not been to repeat the methods of climate scientists, nor to improve on them. It has merely been to set a benchmark against which their claims can be measured and tested.

My first aim has been to go back to basics, to examine the original temperature data, look for trends in that data, and to apply some basic error analysis to determine how significant those trends really are. Then I have sought to compare what I see in the original data with what climate scientists claim is happening. In most cases I have found that the temperature trends in the real data are significantly less than those reported by climate scientists. In other words, much of the reported temperature rises, particularly in Southern Hemisphere data, result from the data manipulations performed by the climate scientists on the data. This implies that many of the reported temperature rises are an exaggeration.

In addition, I have tried to look at the physics and mathematics underpinning the data in order to test other possible hypotheses that could explain the observed temperature trends that I could detect. Below I have set out a summary of my conclusions so far.

1) The physics and mathematics

There are two alternative theories that I have considered as explanations of the temperature changes. The first is natural variation. The problem here is that in order to conclusively prove this to be the case you need temperature data that extends back in time for dozens of centuries, and we simply do not have that data. Climate scientists have tried to solve this by using proxy data from tree rings and sediments and other biological or geological sources, but in my opinion these are wholly inadequate as they are badly calibrated. The idea that you can measure the average annual temperature of an entire region to an accuracy of better than 0.1 °C simply by measuring the width of a few tree rings, when you have no idea of the degree of linearity of your proxy, or the influence of numerous external variables (e.g. rainfall, soil quality, disease, access to sunlight), is preposterous. But there is another way.

i) Fractals and self-similarity

If you can show that the fluctuations in temperature over different timescales follow a clear pattern, then you can extrapolate back in time. One such pattern is that resulting from fractal behaviour and self-similarity in the temperature record. By self-similarity I mean that every time you average the data you end up with a pattern of fluctuations that looks similar to the one you started with, but with amplitudes and periods that change according to a precise mathematical scaling function.

In Post 9 I applied this analysis to various sets of temperature data from New Zealand. I then repeated it for data from Australia and then again in Post 42 for data from De Bilt in the Netherlands. In virtually all these cases I found a consistent power law for the scaling parameter indicative of a fractal dimension of between 0.20 and 0.30, with most values clustered close to 0.25. The low magnitude of this scaling term suggests that the fluctuations in long term temperatures are much greater in amplitude than conventional statistical analysis would predict. 

For example, in the case of De Bilt it suggests that the standard deviation in the average 100-year temperature is more than 0.2 °C. This means that there is a 16% probability of the mean temperature for any century being more than 0.3°C more (or less) than the mean temperature for the previous century, and therefore a one in six possibility of a 0.6 °C temperature rise in any given century. So a 0.6 °C temperature rise over a century could occur once every 600 years purely because of natural variations in temperature. It also suggests that similar temperature variations that we have seen in temperature data in the last 50 or 100 years might have been repeated frequently in the not so distant past.

ii) Direct anthropogenic surface heating (DASH) and the urban heat island (UHI)

Another possible explanation for any observed rise in temperature is the heating of the environment that occurs due to human industrial activity. All energy use produces waste heat. Not only that, but all energy must end up as heat and entropy in the end. The Second Law of Thermodynamics tells us that. It is therefore inevitable that human activity must heat the local environment. The only question is by how much.

Most discussions in this area focus on what is known as the urban heat island (UHI). This is a phenomenon whereby urban areas either absorb extra solar radiation because of changes made to the surface albedo by urban development (e.g. concrete, tarmac, etc), or tall buildings trap the absorbed heat and reduce the circulation of warm air, thereby concentrating the heat. But there is another contribution that continually gets overlooked - direct anthropogenic surface heating (DASH). 

When humans generate and consume energy they liberate heat or thermal energy. This energy heats up the ground, and the air just above it, in much the same way that radiation from the Sun does. In so doing DASH adds to the heat that is re-emitted from the Earth's surface, and therefore increases the Earth's surface temperature at that location.

In Post 14 I showed that this heating can be significant - up to 1 °C in countries such as Belgium and the Netherlands with high levels of economic output and high population densities. In Post 29 I extended this idea to look at suburban energy usage and found a similar result. 

What this shows is that you don't need to invoke the Greenhouse Effect to find a plausible mechanism via which humans are heating the planet. Simple thermodynamics will suffice. Of course climate scientists dismiss this because they assume that this heat is dissipated uniformly across the Earth's surface - but it isn't. And just as significant is the fact that the majority of weather stations are in places where most people live, and therefore they also tend to be in regions where the direct anthropogenic surface heating (DASH) is most pronounced. So this direct heating effect is magnified in the temperature data.

iii) The data reliability

It is taken as read that the temperature data used to determine the magnitude of the observed global warming is accurate. But is it? Every measurement has an error. In the case of temperature data it appears that these errors are comparable in magnitude to many of the effects climate scientists are trying to measure.

In Post 43 I looked at pairs of stations in the Netherlands that were less than 1.6 km apart. One might expect that most such pairs would exhibit identical datasets for the two stations in the pair, but they don't. In virtually every case the fluctuations in the difference in their monthly average temperatures was about 0.2 °C. While this was consistent with the values one would expect based on error analysis, it does highlight the limits to the accuracy of this data. It also raises questions about how valid techniques such as breakpoint adjustment are, given that these techniques depend on detecting relatively small differences in temperature for data from neighbouring stations.

iv) Temperature correlations between stations

In Post 11 I looked at the product moment correlation coefficients (PMCC) between temperature data from different stations, and compared the correlation coefficients with the station separation. What became apparent was evidence for a strong negative linear relationship between the maximum correlation coefficient for temperature anomalies between pairs of station and their separation. For station separations of less than 500 km positive correlations of better than 0.9 were possible, but this dropped to a maximum correlation of about 0.7 for separations of 1000 km and 0.3 at 2000 km.

There were also clear differences between the behaviour of the raw anomaly data and the Berkeley Earth adjusted data. The Berkeley Earth adjustments appear to reduce the scatter in the correlations for the 12-month averaged data, but do so at the expense of the quality of the monthly data. This suggests that these adjustments may be making the data less reliable not more so. The improvement in the scatter of the Berkeley Earth 12-month averaged data is also curious. Is it because it is this data that is used to determine the adjustments and not the monthly data, or is this not the case and instead there is some other reason? And what of the scatter in the data? Can we use this to measure the quality and reliability of the original data? This clearly warrants further study.

Fig. 45.1: Correlations (PMCC) for the period 1971-2010 between temperature anomalies for all stations in New Zealand with a minimum overlap of 200 months. Three datasets were studied: a) the monthly anomalies; b) the 12-month average of the monthly anomalies; c) the 5-year average of the monthly anomalies. Also studied were the equivalent for the Berkeley Earth adjusted data.

2) The data

Over the last eight months I have analysed most of the temperature data in the Southern Hemisphere as well as all the data in Europe that predates 1850. The results are summarized below.

i) Antarctica

In Post 4 I showed that the temperature at the South Pole has been stable since the 1950s. There is no instrumental temperature data before 1956 and there are only two stations of note near the South Pole (Amundsen-Scott and Vostok). Both show stable or negative trends.

Then in Post 30 I looked at the temperature data from the periphery of the continent. This I divided into three geographical regions: the Atlantic coast, the Pacific coast and the Peninsula. The first two only have data from about 1950 onwards. In both cases the temperature data is also stable with no statistically significant trend either upwards or downwards. Only the Peninsula exhibited a strong and statistically significant upward trend of about 2 °C since 1945.

ii) New Zealand

Fig. 45.2: Average warming trend of for long and medium stations in New Zealand. The best fit to the data has a gradient of +0.27 ± 0.04 °C per century.

In Posts 6-9 I looked at the temperature data from New Zealand. Although the country only has about 27 long or medium length temperature records, with only ten having data before 1880, there is sufficient data before 1930 to suggest temperatures in this period were almost comparable to those of today. The difference is less than 0.3 °C.

iii) Australia

Fig. 45.3: The temperature trend for Australia since 1853. The best fit is applied to the interval 1871-2010 and has a gradient of 0.24 ± 0.04 °C per century.

The temperature trend for Australia (see Post 26) is very similar to that of New Zealand. Most states and territories exhibited high temperatures in the latter part of the 19th century that then declined before increasing in the latter quarter of the 20th century. The exceptions were Queensland (see Post 24) and Western Australia (see Post 22), but this was largely due to an absence of data before 1900. While there is much less temperature data for Australia before 1900 compared to the latter part of the 20th century, there is sufficient to indicate that, as in New Zealand, temperatures in the late 19th century were similar to those of the present day.

iv) Indonesia

Fig. 45.4: The temperature trend for Indonesia since 1840. The best fit is applied to the interval 1908-2002 and has a negative gradient of -0.03 ± 0.04 °C per century.

The temperature data for Indonesia is complicated by the lack of quality data before 1960 (see Post 31). The temperature trend after 1960 is the average of between 33 and 53 different datasets, but between 1910 and 1960 it generally comprises less than ten. Nevertheless, this is sufficient data to suggest that temperatures in the first half of the 20th century were greater than those in the latter half. This is despite the data from Jakarta Observatorium which exhibits an overall warming trend of nearly 3 °C from 1870 to 2010 (see Fig. 31.1 in Post 31).

It is also worth noting that the temperature data from Papua New Guinea (see Post 32) is similar to that for Indonesia for the period from 1940 onwards. Unfortunately Papua New Guinea only has one significant dataset that predates 1940, so conclusions regarding the temperature trend in this earlier time period are difficult to ascertain.

v) South Pacific

Most of the temperature data from the South Pacific comes from the various islands in the western half of the ocean. This data exhibits little if any warming, but does exhibit large fluctuations in temperature over the course of the 20th century (see Post 33). The eastern half of the South Pacific, on the other hand, exhibits a small but discernible negative temperature trend of between -0.1 and -0.2 °C per century (see Post 34).

vi) South America

Fig. 45.5: The temperature trend for South America since 1832. The best fit is applied to the interval 1900-1999 and has a gradient of +0.54 ± 0.05 °C per century.

In Post 35 I analysed over 300 of the longest temperature records from South America, including over 20 with more than 100 years of data. The overall trend suggests that temperatures fluctuated significantly before 1900 and have risen by about 0.5 °C since. The high temperatures seen before 1850 are exclusively due to the data from Rio de Janeiro and so may not be representative of the region as a whole.

vii) Southern Africa

Fig. 45.6: The temperature trend for South Africa since 1840. The best fit is applied to the interval 1857-1976 and has a gradient of +0.017 ± 0.056 °C per century.

In Posts 37-39 I looked at the temperature trends for South Africa, Botswana and Namibia. Botswana and Namibia were both found to have less than four usable sets of station data before 1960 and only about 10-12 afterwards. South Africa had much more data, but the general trends were the same. Before 1980 the temperature trends were stable or perhaps slightly negative, but after 1980 there was a sudden rise of between 0.5 °C and 2 °C in all three trends, with the largest being found in Botswana. This does not correlate with accepted theories on global warming (the rises in temperature are too large and too sudden, and do not correlate with rises in atmospheric carbon dioxide), and so the exact origin of these rises appears to be unexplained.

 

viii) Europe

Fig. 45.7: The temperature trend for Europe since 1700. The best fit is applied to the interval 1731-1980 and has a positive gradient of +0.10 ± 0.04 °C per century.

In Post 44 I used the 109 longest temperature records to determine the temperature trend in Europe since 1700. The resulting data suggests that temperatures were stable from 1700 to 1980 (they rose by less than 0.25 °C), and then rose suddenly by about 0.8 °C after 1986. The reason for this change is unclear, but one possibility is that it has occurred due to a significant improvement in air quality that reduced the amount of particulates in the atmosphere. These particulates, that may have been present in earlier years, could have induced a cooling that compensated for the underlying warming trend. Once removed, the temperature then rebounded. Even if this is true, it suggests a maximum warming of about 1 °C since 1700, much of which could be the result of direct anthropogenic surface heating (DASH) as discussed in Post 14. In countries such as Belgium and the Netherlands the temperature rise is even less than that expected from such surface heating. It is also much less than that expected from an enhanced Greenhouse Effect due to increasing carbon dioxide levels in the atmosphere (i.e. about 1.5 °C in the Northern Hemisphere since 1910). In fact the total temperature rise should exceed 2.5 °C. So here is the BIG question? Where has all that missing temperature rise gone?

42. A study of fractal self-similarity and scaling for the De Bilt temperature data

In Post 9 (Fooled by randomness) I looked at the possibility of fractal behaviour occurring in the temperature records of individual stations and regions. In particular, I was interested to see if those records exhibited any form of self-similarity, and whether that self-similarity could account for the magnitude of fluctuations seen in the long term temperature records.

My initial analysis was performed on data from New Zealand and it seemed to suggest that fractal behaviour may be present. This behaviour is quantified by the fractal dimension which, in the case of temperature data, defines how the amplitude of the temperature fluctuations changes with the time interval those readings represent. Most of the data I look at on this blog consists of monthly average temperatures. For these readings the data typically has a spread of up to ±5 °C, while the standard deviation of the monthly fluctuations is usually between 1 °C and 2 °C. But what would the same temperature records look like if one considered the 12-month averages? Or the 10-year averages? 

Well, as I explained previously in Post 9, if the fluctuations in the temperature data conformed to a white noise spectrum, the power spectrum would be expected to be independent of frequency for all frequencies below the fundamental or cutoff frequency (see Eq. 9.1). The consequence of this is that smoothing the data with a sliding window, or moving average, of width N (where N is the number of months in the new average) should reduce the cutoff frequency by a factor of N, and thus reduce the signal power below the cutoff by a factor of N. That in turn should reduce the amplitude of the random noise fluctuations by a factor of √N. So, smoothing the monthly average data with a 24 month moving average should reduce the amplitude of the fluctuations by a factor of √24, or about a factor of five. Except that this does not happen.

As I have demonstrated in numerous previous posts, the noise amplitude in the monthly temperature data decreases much more slowly than expected as the width of the sliding window in the smoothing algorithm is increased. In fact it appears to decrease as N ^-p. where p tends to be in the range 0.20 < p < 0.35, but is generally concentrated around p = 0.25. This was shown in Post 9 for New Zealand data, in Post 17 for individual sites in Australia, and in Posts 18-21 for various Australian states. In most cases the same behaviour was seen. The only two exceptions I have found so far were for data from the South Pole (Amundsen-Scott), and also for the trend for South Australia (see Post 21) but only if the parabolic long term trend was removed. In both cases the data behaved like classical white noise with p = 0.5.

Why is this behaviour important? Well, for three reasons. Firstly, if there is a definite trend, it would allow us to estimate the amplitude of natural temperature fluctuations over timescales that are much longer than we have data for. Secondly, it could allow us to differentiate between natural and anthropogenic sources of climate change. And finally, it may shed light on possible natural mechanisms that may underpin long term climate change rather than assuming that everything is a consequence of carbon dioxide emissions, or that every current change in climate behaviour has a cause that is local, either spatially or temporally.

So why I am revisiting this now? Well, because in my last post I presented some data from a station at De Bilt (Berkeley Earth ID: 175554) in the Netherlands that is one of the longest continuous sets of temperature data that exists. What also set this data apart, though, was the fact that there was complex structure to the data that was much greater in amplitude than the continuous upward trend expected from global warming. Moreover, the underlying continuous upward trend could also be easily removed so that the remaining data could be studied, just as I removed the parabolic background from the South Australia data in Post 21. The question is, would I see the same result as for South Australia? Namely, that the remaining temperature fluctuations behaved like white noise. Well, the answer is no.

Fig. 42.1: The monthly temperature anomalies for De Bilt since 1706 with the linear trend of +0.29 ± 0.04 °C per century removed (blue curve). The standard deviation is 1.855 °C (for N = 1). The yellow curve is the 12-month moving average of the blue data (N = 12) and has a standard deviation of 0.810 °C.

The data in Fig. 42.1 above shows the same monthly temperature anomaly data that was presented in Fig. 41.1 of the previous post, except with the long-term upward trend of 0.23 °C per century removed. The yellow curve is the 12-month moving average of the blue data which clearly has a much lower noise amplitude, and therefore a lower standard deviation of 0.81 °C compared to 1.85 °C for the monthly data. In both cases the standard deviation was measured for data over the same 275 year period (or 3300 months) from 1731-2005.

Fig. 42.2: The 3-month (N = 3) moving average (blue curve) of the monthly data in Fig. 42.1 above. The standard deviation of this data is 1.326 °C. The yellow curve is the 24-month moving average (N = 24) of the same data in Fig. 42.1 and has a standard deviation of 0.664 °C.

 

The data in Fig. 42.2 above shows the same monthly temperature anomaly data as shown in Fig. 42.1, but after smoothing with a 3-month moving average (blue curve) and alternatively a 24-month moving average (yellow curve). As a result of the smoothing, the standard deviation reduces to 1.326 °C for the 3-month window (N = 3) and 0.644 °C for the 24-month sliding window (N = 24).

Fig. 42.3: The 6-month (N = 6) moving average (blue curve) of the monthly data in Fig. 42.1 above. The standard deviation of this data is 1.046 °C. The yellow curve is the 5-year moving average (N = 60) of the same data in Fig. 42.1 and has a standard deviation of 0.536 °C.

Next, if we smooth the original monthly temperature anomaly data in Fig. 42.1 with 6-month and 5-year moving averages or sliding windows we get the data shown in Fig. 42.3 above. Now, after smoothing with a 6-month moving average (blue curve) the standard deviation has reduced to 1.046 °C (and N = 6), while that for the 5-year moving average (yellow curve) is now 0.536 °C (and N = 60).

Fig. 42.4: The 9-month (N = 9) moving average (blue curve) of the monthly data in Fig. 42.1 above. The standard deviation of this data is 0.894 °C. The yellow curve is the 10-year moving average (N= 120) of the same data in Fig. 42.1 and has a standard deviation of 0.462 °C.

Finally, if we smooth the original monthly temperature anomaly data in Fig. 42.1 with 9-month and 5-year moving averages or sliding window we get the data shown in Fig. 42.4 above. Now, after smoothing with a 9-month moving average (blue curve) the standard deviation has reduced to 0.894 °C (and N = 9) while that for the 10-year moving average (yellow curve) is now 0.462 °C (and N = 120).

All the standard deviations (σ) for the different sets of smoothed data are summarized in the table below.

Table 42.1

N	σ	ln(N)	ln(σ)
1	1.855	0.000	0.618
3	1.326	1.099	0.282
6	1.046	1.792	0.045
9	0.894	2.197	-0.112
12	0.810	2.485	-0.211
24	0.664	3.178	-0.409
60	0.536	4.094	-0.624
120	0.462	4.787	-0.772

If we now combine these results into a single plot we get the graph shown in Fig. 42.5 below. The gradient of this log-log plot is the exponent of N ^-p in the power law we expect to see for the decrease in the noise amplitude as we increase the smoothing interval N. Once again we see that the value for the exponent p is well below the 0.5 expected for white noise. In fact p = +0.31 ± 0.01, indicating that the fractal dimension is 0.31. In addition, the quality of the fit (as indicated by the R² value) is very high.

Fig. 42.5:  Plot of the standard deviation of the smoothed anomaly data against the smoothing interval N for temperature data from De Bilt. The best fit line is fitted to all the data except that from the 10-year moving average (as indicated by the length of the red line). The gradient of the best fit line is -0.31 ± 0.01 and R² = 0.9943.

Conclusions

1. The quality and linearity of the best fit in Fig. 42.5 indicates that there is a high degree of self-similarity in the data. This in turn also suggests that all the significant features seen in the original data (such as the large broad peaks at 1725 and 1860) are natural and not the result of external or artificial biases. If such artificial biases were present, and were significant in magnitude, they would probably manifest themselves as significant deviations of the data in Fig. 42.5 from a linear trend.
2. From the gradient of the trend line in Fig. 42.5 we can estimate the standard deviation of temperature data for the case N = 1200 as being 0.20 °C. In other words, the fluctuations in the 100-year average will typically be of the order of ±0.2 °C. This in turn suggests that changes in the mean temperature from century to century of more than 0.5 °C are likely to be very common.
   

27. Scaling of temperature anomalies for Australia

In my analysis of temperature data from both New Zealand (Posts 6-10) and Australia (Posts 18-21) I have speculated about the nature of the temperature fluctuations. These fluctuations have not behaved like normal white noise. For a start, when data from multiple stations are averaged, the standard deviation of the fluctuations barely changes. If the fluctuations behaved like white noise then the standard deviation would be expected to decrease by a factor of √N, where N is the number of stations in the average. This does not happen.

Then there is the scaling behaviour. If the data is smoothed with a moving average of length N points, again you would normally expect to see the standard deviation of the smoothed data decrease by a factor of √N compared to the unsmoothed data. Again this does not happen. The standard deviation decreases, but generally only by about a factor of N ^0.25. This is important because it essentially predicts how big the fluctuations will be for longer temperature records where each data points represents a longer time interval, such as yearly or decadal averages, rather than the monthly averages that form the basic station records I have been discussing here.

So what do we see for the mean temperature for Australia that I presented in Fig. 26.1 in the last post? In the following discussion I have restricted the analysis to data over a 140 year period from 1874 to 2013. This is because data earlier than this is derived by averaging over much less than 7 states, and will also be based on a much smaller number of individual stations.

Well, firstly the standard deviation of the data in Fig. 26.1 is only 0.627 °C. This is significantly less than that seen in individual temperature records, and in individual states like New South Wales where the value was 1.07 °C. The reason for this decrease is that the temperature record for Australia involves combining records from across the country, and the country is very big. It is, for example over 3600 km from Perth to Brisbane. Yet in Post 11 I showed that the correlation between monthly temperature records for stations that are spatially separated decreases almost linearly with the distance of separation (see Eq. 11.1). In fact, once you get to separations of more than 3000 km, the data in Fig. 11.2(a) suggest station records become completely uncorrelated. This is what appears to be happening here.

The monthly temperature data from Western Australia and Queensland will be almost totally uncorrelated as most of their respective stations are over 3000 km apart. So averaging the two will reduce the standard deviation by a factor of almost √2. Including the other states in the average could increase the reduction factor to √7, but this will be mitigated by the fact that the distances between those states are much less and so their correlations will be greater. The net result is a compromise with the standard deviation appearing to decrease by about 40% compared to the individual state values.

The second point to note is that the fluctuations in the mean temperature for Australia in Fig. 26.1 appear to conform to a Gaussian noise spectrum. This is confirmed below in Fig. 27.1.

Fig. 27.1: The distribution of anomaly values for the mean temperature record for Australia (blue curve), together with the predicted Gaussian distribution for a standard deviation of 0.627 °C.

However, these fluctuations are not white noise. If we smooth the data with different moving averages of size N months, and then recalculate the standard deviation, we get the data shown in Fig. 27.2 below. This is the scaling behaviour I described in the second paragraph above. For a more detailed explanation of its methodology, see Post 17.

Fig. 27.2: The change in standard deviation of the mean temperature anomaly for Australia (see Fig. 26.1) after smoothing with a moving average of size N. The gradient of the best fit line is -0.256 ± 0.003 and R² = 0.9993

The two significant features of the data in Fig. 27.2 are the gradient of the linear regression best fit line and the magnitude of the residual for the data relative to that line. The gradient is -0.256 ± 0.003 while the rms (root mean square) residual is 2.7% of the standard deviation of the y-values, the residuals being the vertical distance from the data point to the best fit line. This gives a value for R² of 0.9993, indicating a very good fit to the data.

The rms residual of 2.7% is incredibly low compared to previously determined values for individual states, while the gradient is incredibly close to -1/4. These two results may not be coincidental, and hint at the existence of a fundamental truth within the data, that these temperature records are fractal in nature, with the patterns of fluctuations over different timescales exhibiting strong self-similarity. If so, then this implies even 100-year mean temperatures would exhibit fluctuations with a standard deviation of over 0.1 °C and a range of over 0.4 °C. It would also suggest that changes of more than 0.5 °C in the average temperature of different centuries would be commonplace over the course of millenia. It should be noted that the data in Fig. 26.1 in the last post indicates that the average temperature in Australia over the whole of the 20th century was actually 0.063 °C less than that for the last 50 years of the 19th century.

So, are all the instrumental temperature records and their averages fractals? Do they exhibit self-similarity with a fractal dimension of 0.25 as I have suggested previously? Or is the data just white noise on an oscillating background as the data from South Australia might suggest? The answer is, it is too early to tell. We need more data and longer datasets. What we can say is that the temperature trend for Australia since 1853 in Fig. 26.1 is not a simple hockey stick.

21. South Australia - temperature trends PARABOLIC

South Australia has a population density of 1.7 people per square kilometre. Only Western Australia and Northern Territory have lower densities. Yet South Australia still has 57 weather stations with more than 480 months of data. Of these 7 are long stations with more than 1200 months of data, and an additional 11 have between 900 and 1200 months of data. Its data is, therefore, comparable in terms of length and quality with that found in Victoria, but is still not as good as that for New South Wales.


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).

19. Victoria (Australia) - temperature trends PARABOLIC

The state of Victoria in Australia has 65 sets of weather station data that are longer than 480 months (the equivalent of 40 years), of which 15 are long stations with over 1200 months of data. While this is not as extensive a set of station data as is seen for New South Wales (NSW) and was discussed in the previous post, it is still more than was seen for New Zealand. In this post I will essentially repeat the analysis that was performed on the NSW data last time but with data from Victoria. The aim is to see if the trends seen in NSW and Victoria are just local, or whether they are indicative of a common trend across the whole of Australia.


i) Weather station distribution

The long stations in Victoria are fairly evenly distributed across the state, as illustrated in Fig. 19.1 below. So, in their totality, they are fully representative of the overall climate of the state.

Fig. 19.1: The locations of long stations (large squares) and medium stations (small diamonds) in Victoria. Those stations with a high warming trend since 1871 are marked in red.

The station locations shown in Fig. 19.1 also 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. 19.1, it appears that most of the warming in Victoria is found in and around Melbourne. A similar trait was seen in New South Wales around Sydney, suggesting that urban heating is a significant issue.

 Fig. 19.2: The amount of warming for long and medium stations in Victoria. The stations with definite warming trends are shown as red squares.

It can be seen in Fig. 19.2 that only 4 of the 15 long stations have a warming trend. For stations with more than 600 months of data only 15 of the 42 stations have a warming trend. For shorter length stations the warming is more pronounced, but these stations add little to the overall trend for the region because of their limited length.


ii) The trend in mean temperature

Fig. 19.3: Temperature trend for long and medium stations in Victoria since 1850. The best fit to the data has a gradient of -0.05 ± 0.08 °C per century.

Adding the temperature anomalies from all stations with more than 480 months of data yields the trend shown in Fig. 19.3 above. In this case the monthly reference temperatures (MRTs) were calculated for the period 1981-2010. This period is longer than1981-2000 period used for the New Zealand data so the MRT values are likely to be more stable. The period is also 20 years later than the 1961-1990 period favoured by most climate scientists. The 1981-2010 period was chosen because it allows most of the medium station data to be used. However, overall these changes make little difference to the final result.

The trend in Fig. 19.3 very similar to that for New South Wales shown in Fig. 18.3 previously. In this case the overall temperature trend from 1890 to 2007 (as indicated by the red line) is -0.05 ± 0.08 °C per century. In other words, there is no warming taking place.


iii) The Berkeley Earth (BE) mean temperature trend 

Fig. 19.4: Temperature trend for long and medium stations in Victoria since 1850 derived using the Berkeley Earth adjusted data. The best fit to the data has a gradient of +1.64 ± 0.08 °C per century.

However, if we repeat the averaging process for the temperature data, but use Berkeley Earth adjusted data, we get the trend shown above in Fig. 19.4. This also initially shows a slight downward trend, but only before 1940, after which there is a strong positive trend of +1.64 ± 0.08 °C/century that raises the overall temperature by over 1.1 °C before 2010. The trend in Fig. 19.4 is almost identical to the plot shown on the Berkeley Earth site (see Fig. 19.5 below), and also resembles both the IPCC "hockey stick" and the instrumental temperature record since 1850, at least qualitatively.

Fig. 19.5: Temperature trend for Victoria since 1840 according to Berkeley Earth.

The difference between the data in Fig. 18.5 (or Fig. 18.4) and that in Fig. 18.3 is almost entirely due to the adjustments made to the data by Berkeley Earth. These are shown in Fig. 18.6 below.

Fig. 19.6: The Berkeley Earth breakpoint adjustment for Victoria 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 difference data is +0.60 ± 0.02 °C per century. The yellow curve is the contribution to the difference from breakpoint adjustments

The adjustments made to the data by Berkeley Earth appear to be of two main types. The most significant are 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. 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 just averaging the data from within that dataset as I have done. The homogenization process probably uses data from adjacent local stations to help refine the MRT. Whatever the source, it is clear from Fig. 19.6 that these adjustments are not neutral and they significantly alter the temperature trend.

What we can see in Fig. 19.6 is that the total effect of all the adjustments is to introduce a positive warming of +0.60 ± 0.02 °C/century for the period 1881-2010, of which +0.39 ± 0.02 °C/century is due to the breakpoint adjustments. This equates to a temperature rise of at least 0.78 °C being added to the original data between 1881 and 2010 by the Berkeley Earth data processing.


iv) Noise and scaling behaviour

Fig. 19.7: The change in standard deviation of the Victoria mean temperature anomaly after smoothing with a moving average of size N. The gradient of the best fit line is -0.257 ± 0.015 and R² = 0.9842.

Finally, if we look at the effect of data smoothing on the noise level, we again see strong evidence of scaling behaviour (see Fig. 19.7 above). This time the noise (as defined by the standard deviation) again scales as N ^-a with the exponent a = 0.257 ± 0.015. Once again, this is very similar to the scaling seen for New South Wales previously where a = 0.272 ± 0.005, and implies a noise level (i.e. standard deviation) on 100-year averaged temperature data of at least 0.16 °C. This is similar to the value predicted for individual stations such as Newcastle Nobbys Signal Station (Berkeley Earth ID - 152044) that was studied in Post 17. That study indicated that fluctuations in the 100-year temperature average of over 0.5 °C could be commonplace over 2000 year time periods (see Fig. 17.8).


v) Conclusions

1) Based on the original station data, there is no evidence of any rise in overall temperatures in Victoria since 1881 (see Fig. 19.3).

2) The overall temperature trend for Victoria since 1850 is very similar to that seen for New South Wales.

3) The long-term temperature trend for Victoria exhibits fluctuations of more than ±2 °C over timescales of more than 100 years (see Fig. 19.3). Even the 5-year moving average has fluctuations of at least ±0.5 °C, and maybe as much as ±1 °C. This adds to previous evidence that suggests that what we are probably seeing in these temperature trends is primarily low frequency noise or random fluctuations.

4) Breakpoint adjustments and other adjustments (possibly from homogenization) can completely change the form and shape of the long-term temperature trend (see Fig. 19.4). They are not neutral.

5) Breakpoint adjustments added at least 0.5 °C to the long-term temperature trend for Victoria (see Fig. 19.6). Other adjustments increased this to nearly 0.8 °C.

6) The noise in the regional temperature average for Victoria scales in a similar way to that seen for New South Wales except that the power law is N ^-0.26, where N is the size of the sliding window in the moving average (see Fig. 19.7).

7) As the standard deviation for the 60-month smoothed temperature anomalies is 0.36 °C, this means that there is still a 50% probability of a temperature rise of more than 0.65 °C occurring over the course of a century in Victoria purely by random chance, as I explained here.

8) The statistical results presented here, and for New South Wales, imply that chaotic effects in the temperature record are important, and probably dominant in many cases, even over long (i.e. more than 100 years) timescales. 

vi) Addendum

One noticeable feature of the temperature trend in Fig. 19.3 is the large dip in temperature values before 1875. It may tempt some to think that this is evidence of an upward warming trend. It is not. It is because there are only two temperature records in Victoria with data before 1877, Melbourne Regional Office (Berkeley Earth ID: 151813) and Cape Otway Lighthouse (Berkeley Earth ID: 151786). 

The Cape Otway data exhibits no warming. So the mean temperature before 1880 is similar to that after 2000. However, the Melbourne data exhibits a strong warming trend of more than 1.5 °C from 1860 to 2010. This warming trend is cancelled after 1875 by the data from other stations that are generally stable or cooling. However, without these other stations, as is the case before 1875, the Melbourne data is able to dominate. The net result is that the overall trend suddenly jumps by almost 1 °C after 1875. For this reason the data before 1876 cannot be regarded as representative of the temperature of the entire state because it is dominated by one station: Melbourne Regional Office.

It should also be noted that changing the period for the MRT calculation can also affect the data slightly, either by changing the number of stations that qualify for the final averaging process, or by altering the offsets of the different datasets relative to each other. These effects are usually small but noticeable.

 

Fig. 19.8: Temperature trend for long and medium stations in Victoria since 1876. The best fit (red line) to the temperature data for 1880-2007 is -0.02 ± 0.07 °C per century.

For example, the trend in Fig. 19.8 above was derived by calculating the MRT for the period 1966-1995. This increases the number of stations incorporated into the trend by one to 66. The peak in the 5-year moving average at 1880 is now slightly higher than the one at 1890 so the overall trend (red line) becomes less negative, -0.02 ± 0.07 °C compared with -0.05 ± 0.08 for the data in Fig. 19.3 above. Note also that the data in Fig. 19.8 is truncated at year 1876. It is therefore much more representative of the overall trend in Victoria than the data shown in Fig. 19.3.

18. New South Wales - temperature trends PARABOLIC

In Post 7 and Post 8 I looked at the temperature trend in New Zealand since 1850. As I pointed out there, New Zealand has one of the longest and best temperature records in the Southern Hemisphere. However, in both respects the country is surpassed by Australia.

Overall, Australia has the best temperature records of any country in the Southern Hemisphere. Only Rio de Janeiro has a longer record than any of those found in Australia or New Zealand. And of the eight states that comprise Australia, the one with the most comprehensive records is New South Wales (NSW). Where New Zealand has 10 long station records with more than 1200 months of data, NSW has 33. It also has another 71 stations with more than 600 months of data, and another 31 with between 480 and 600 months of data. So, as the state with the best records, it is the obvious place to start when studying climate change in Australia.

Fig. 18.1: Location of NSW long stations (large squares) and medium stations (small diamonds). Those stations with a high warming trend since 1871 are marked in red.

i) The long station records

As already stated, these long stations have over 1200 months (or the equivalent of 100 years) of data. They are also fairly evenly distributed across NSW as shown in the map illustrated in Fig. 18.1 above. The stations in Fig. 18.1 are also differentiated according to the size of their warming trend. A high warming trend is defined as one where the trend is greater than twice the error or uncertainty in the trend (i.e. 95% confidence). Typically, the uncertainty for long stations is about ±0.1 °C per century, so the stations with a high warming trend will generally have a warming trend of over 0.2 °C per century. Only 11 of the 33 long stations fall into this category, while 14 have a negative trend (see Fig 18.2 below).

Fig. 18.2: Temperature trends of NSW weather stations for the period 1871-2010 plotted against the length of the temperature record in months.

The data in Fig. 18.2 shows that the stations with the largest warming trend are more likely to be those with the least data. This is mainly because they are also the stations that are least likely to have data that extends back before 1960. The long-term temperature trend in New South Wales is shown in Fig. 18.3 below and shows how the local climate has cooled for most of the 20th century before warming after 1960. As the shorter station records are concentrated in the post-1960 period, they tend to have warming trends, whereas the longer records that extend back to 1900 and beyond will be cooler because they also encompass the cooling period. The long station records will also be more important in determining the long-term trend of the region overall, again because they are the longest records and encompass the entire record, not just a small part of it.

Fig. 18.3: Temperature trend for NSW long stations since 1850. The best fit to the data has a gradient of +0.07 ± 0.08 °C per century.

The temperature trend in Fig. 18.3 was determined by calculating the mean of the anomalies of all 33 long stations. These stations are listed on Berkeley Earth here. The procedure for determining the temperature trend in Fig. 18.3 was as follows.

For each station record the monthly reference temperature (MRT) for each month was calculated by finding the mean temperature for that month for the period 1961-1990 (as explained here). These mean values were then subtracted from the raw temperature data to yield the anomaly for each month.  The mean deviation was then calculated for the anomaly and any data that was found to lie outside 6 deviations from the mean was labelled an outlier and excluded.

The factor of 6 was chosen because it relates to 6-sigma accuracy (99.9999998%), which is the standard tolerance level used in manufacturing and physics. As there could be up to 3000 data points per record potentially, an accuracy of less than 99.97% (3-sigma) would be highly likely to exclude a valid data point, even if it wasn't a genuine outlier. It would then require at least 4-sigma accuracy to differentiate an outlier and even then there would still be a 20% chance that the point was good.

Once the outliers have been excluded, the MRTs and the anomalies are recalculated. Finally, the mean of the anomalies of all 33 long stations is determined by adding the records and dividing the sum of the anomalies for each month by the number of temperature records for that month. This average trend is shown in Fig. 18.3.

The striking feature of the data in Fig. 18.3 is that there is no overall upward trend. The mean temperature in 2010 is no higher than it was in 1880, as indicated by the 5-year moving average. In between those dates the temperature trend declines by about 0.6 °C until the mid-1950s, and then rises again. The other main feature is the dip in the mean temperature before 1870. How long into the past this downward trend persists is impossible to determine though. The key question though is, what is the overall trend of the data? Are we seeing a rise or fall in temperature?

It may seem that the obvious way to answer this question is to perform a linear regression on all the available data. It is what Berkeley Earth do to their data, but this would be a mistake. The reason is that we do not have data that is randomly distributed around a straight line. There are oscillations in the data that we need to consider as well. The positions where these oscillations or peaks occur will affect the gradient of the best bit. That means our choice of time-frame for the fitting will affect our result as well.

As I pointed out in Post 4 (Fig. 4.7), the best fit to a sine wave is not a horizontal line of zero gradient, even if an integer number of periods are included in the fitting, and despite there always being equal amounts of data equally distributed above and below the x-axis. The key point is that the oscillatory component has to be symmetric about the centre of the fitting range, otherwise the asymmetry of the oscillations will bias the best fit line. For the data in Fig. 18.3 that means the fitting range needs to be from the first peak to the last peak, i.e. from 1884 to 2007. If we do this then we get a best fit trend of 0.07 ± 0.08 °C per century. In other words, there is a 19% probability that the trend is less than zero, and only a 5% probability it is more than +0.2 °C per century. Of course, if the data before 1884 is included, then the trend would be different. In fact it would be 0.23 ± 0.06 °C per century, but the data before 1884 is not a complete cycle.

Fig. 18.4: Temperature trend for NSW since 1840 according to Berkeley Earth.

Either way, the data in Fig. 18.3 bears no relation to that calculated by Berkeley Earth which is shown in Fig. 18.4 and is different is two major respects. Firstly, the Berkeley Earth trend is virtually zero from 1870 until 1960, and secondly it then exhibits a huge rise in temperature of more than 1 °C after 1960. The reason for this discrepancy will become apparent later in this post, but it is mainly to do with our dear old friend, the breakpoint adjustment.

One final point to note is the "noise level" of this averaged regional data. The anomaly data in Fig. 18.3 has a standard deviation of 1.03 °C even though it is an average of data from 33 different datasets, each of which also has a standard deviation of about 1 °C for its anomalies, as was illustrated in the last post. If those datasets were independent we would expect the "noise" or fluctuations in data values about the mean to reduce to about 0.17 °C, yet it doesn't. This shows that averaging data from different stations does not reduce the noise level significantly. This is because, as I pointed out in Post 11, the temperature data between stations is strongly correlated over distances up to at least 500 km, and therefore it is not independent in a statistical sense. It also means that even regional temperature data for entire countries or continents is still very noisy, and is likely to be subject to the same fractal behaviour I have described here and here. I will demonstrate this again in part (iii) below.


ii) The long and medium station records

The data in Fig. 18.3 only includes data from stations with more than 100 years of data. If we also include stations with over 40 years or 480 months of data (which I denote as medium length stations) the results do not change significantly from that illustrated in Fig. 18.3. In this case the MRTs were calculated for the period 1981-2000.

Fig. 18.5: Temperature trend for NSW long and medium stations since 1850. The best fit to the data has a gradient of +0.02 ± 0.08 °C per century.

The mean anomaly for all long and medium stations in New South Wales (and Australian Capital Territory) is shown in Fig. 18.5 above. The trend of the best fit line is +0.02 ± 0.08 °C per century for the data between 1884 and 2006. Nevertheless, the data is still very different from that shown in Fig. 18.6 from Berkeley Earth. In fact, if we use the Berkeley Earth adjusted data to construct an equivalent trend we get a very different result.

Fig. 18.6: Temperature anomaly and 5-year moving average for Berkeley Earth adjusted data from NSW since 1840. The anomaly data was constructed by averaging the adjusted anomalies for each Berkeley Earth dataset. The best fit line (in red) is for the period 1861-1960 and has a gradient of -0.09 ± 0.11 °C per century.

The data shown in Fig 18.6 above was constructed in exactly the same manner as that described above for the construction of the regional trends in Fig. 18.3 and Fig. 18.5. It was formed simply by averaging the data from all the relevant station datasets. In this case, however, the data was not the raw temperature anomalies from all long and medium stations, but the Berkeley Earth adjusted anomalies from all long and medium stations.

What we find is that simply by adding the Berkeley Earth adjusted anomalies with no additional weighting, we obtain curves that are almost identical to those published by Berkeley Earth and shown in Fig. 18.4. Moreover, the Berkeley Earth adjusted data in virtually horizontal from 1861 until 1960, and then it exhibits a huge rise in temperature of more than 1 °C up to about 2010. The gradient of the trend before 1960 is -0.09 ± 0.11 °C per century (red line in Fig. 18.6), while after 1960 it is +2.2 ± 0.2 °C per century (red line in Fig. 18.7 below).

Fig. 18.7: Smoothed temperature trends (12-month and 10-year) for NSW since 1840 based on Berkeley Earth adjusted data. The best fit line (in red) is for the period 1961-2010 and has a gradient of +2.2 ± 0.2 °C per century.

The data in Fig. 18.7 is just the regional monthly anomaly data in Fig. 18.6 that has been smoothed, either with a 12-month moving average, or a 10-year moving average. This data demonstrates two things. Firstly, because it is virtually identical to the data in Fig. 18.4, it shows that the data in Fig. 18.4 is also effectively just the sum of the adjusted anomalies. This then also demonstrates that the effect of any weighting that Berkeley Earth may have applied to those different stations, to account for differences in the density of stations across the region, is negligible in terms of the overall result, and can therefore be ignored. More importantly, it demonstrates that the differences between the averaged anomaly I have presented in Fig. 18.5 and the Berkeley Earth adjusted data in Fig. 18.6 cannot be due to a lack of appropriate weighting of the individual stations in Fig. 18.5. Therefore, the only place that the difference in the two datasets can come from is in the breakpoint adjustments (and other minor adjustments) which were introduced by Berkeley Earth. The sum total of these adjustments is shown below in Fig. 18.8 together with the best fit for the range 1881-2010.

 Fig. 18.8: The Berkeley Earth breakpoint adjustment for NSW since 1840 together with the difference between the Berkeley Earth adjusted anomaly and the raw anomaly. The best fit to the breakpoint adjustment is +0.35 ± 0.02 °C per century.

The effect of the breakpoint adjustments in Fig. 18.8 is two-fold. On the one hand they flatten the data before 1920. On the other, they increase the warming trend after 1940. The net result is that a climate record with large temperature fluctuations but no overall warming trend becomes a "hockey-stick" with a catastrophic warming of over 1 °C since 1960.


iii) Noise and scaling

In the last post I analysed the scaling of the noise for a single temperature record in New South Wales - Newcastle Nobbys Signal Station (Berkeley Earth ID - 152044). This station showed a scaling behaviour with a power law of -0.266. If we repeat that analysis, but for the averaged New South Wales monthly anomaly data in Fig. 18.5, we get the data shown in Fig. 18.9 below.

Fig. 18.9: Scaling of the noise for the New South Wales mean anomaly. The gradient of the best fit line is -0.272 ± 0.005 and R² = 0.9985.

Here the standard deviation of the averaged data for NSW obeys a power law of the form N ^-a relative to the size of the smoothing average, N, where a = 0.272 ± 0.005. This is very similar to the values seen for individual temperature records, such as those of New Zealand that were discussed in Post 9 and Post 10, which implies that the averaging of multiple station records does not noticeably affect the overall scaling behaviour.In this case at least 33 station records are averaged. Normally we would expect such averaging to reduce the amplitude of the noise by at least a factor of 6. Yet here there is virtually no reduction in the noise level. This implies that the noise of each temperature record is not independent.

The consistency of this scaling behaviour also allows us to extrapolate in order to predict the value of the standard deviation of temperature records with much longer timeframes or moving averages. For example, from Fig. 18.9 we can infer that a 100-year moving average of the NSW temperature record would still have a standard deviation of 0.15 °C. That means that even over very long timescales there will be fluctuations of up to 0.6 °C in the mean temperature in NSW (to a 95% confidence level).


iv) Final thoughts

I pointed out earlier in this post that the trend I constructed in Fig. 18.5 would be largely dictated by data from the 33 long stations. It is worth noting that for most of these 33 records the temperature trend is very similar to the average shown in Fig. 18.5. Only one record closely resembles the Berkeley Earth trend featured in Fig. 18.4. That station is Sydney - Observatory Hill (Berkeley Earth ID - 151986), which just happens to be bang in the middle of the biggest city in the entire country.


v) Conclusions

1) The average temperatures in New South Wales (NSW) today are no greater than they were in the 1880s, 1920s and 1940s (see Fig. 18.5). This suggests that global warming trends were negligible during the 20th century, at least in NSW.

2) The NSW long-term temperature trend exhibits fluctuations of more than 0.5 °C over timescales of more than 100 years (see Fig. 18.5). So what climate scientists think is anthropogenic is, in reality, possibly (or probably?) just noise.

3) Breakpoint adjustments can completely change the form and shape of the long-term temperature trend (see Fig. 18.7). They are not neutral and they are probably not necessary, particularly if the data from multiple stations is going to be averaged anyway.

4) Breakpoint adjustments can add at least 0.35 °C per century to the long-term temperature trend for NSW (see Fig. 18.8). When combined with the changes to the shape of the trend, their effective contribution can be even greater.

5) The noise present in the NSW regional average data is no less than that seen in data from individual station records (i.e. both have a standard deviation of at least 1 °C) despite the regional average data being the result an averaging process of more than 33 records. This also suggests that the unadjusted monthly temperature fluctuations of most stations are highly correlated, otherwise the averaging process would reduce the noise level.

6) The noise in the NSW regional temperature average scales in a similar way to that seen in data for individual temperature records except that the power law is N ^-0.27, where N is the size of the sliding window in the moving average (see Fig. 18.9). The index of this power law is similar to the values seen in individual station records which appear to be centred around N ^-0.25.

7) As the standard deviation for the 60-month smoothed data is 0.35 °C, this means that there is a 50% probability of a temperature rise of more than 0.65 °C occurring over the course of a century in New South Wales purely by random chance, as I explained here. It also implies that chaotic effects are dominant, even over long (i.e. more than 100 years) timescales.

 

Addendum (21/03/2021)

The trend in Fig. 18.5 above was calculated by averaging the monthly anomalies from all stations in NSW with over 480 months of data. The anomalies were calculated relative to the MRT interval of 1981-2000, and for each station to qualify for inclusion in the average it needed to have at least 12 years of data in the 1981-2000 interval for each of the 12 months of the year.

Fig. 18.10: The number of station records included each month in the mean temperature trend for NSW in Fig. 18.5 when the MRT interval is 1981-2000.

The result is that almost 100 station records are included in the trend between 1970 and 1990 (see Fig. 18.10 above). Even between 1907 and 1957 there are over 50 station records included in the mean trend, and about 20 are included between 1880 and 1907. 

Fig. 18.11: Temperature trend for NSW since 1910 according to the Australian Government Bureau of Meteorology (BoM) in 2014.

In Fig. 18.4 I showed the temperature trend for NSW as reported by Berkeley Earth in 2014. It turns out this is very similar to the trend for NSW reported by the Australian Government's Bureau of Meteorology (BoM). The BoM version for 2014 is shown in Fig.18.11 above. It clearly shows that there is a temperature rise (in the 11-year moving average) of about 1.2 °C from 1950 to 2008, and a rise of about 0.7 °C from 1918 to 2008. Yet curiously the picture seven years later is a bit different, as is shown in Fig. 18.12 below.

Fig. 18.12: Temperature trend for NSW since 1910 according to the Australian Government Bureau of Meteorology (BoM) in 2021.

Note how many of the temperatures before 1970 have decreased compared to the equivalent data in Fig. 18.11, some by up to 0.2 °C, while many of those from 1980-2013 have increased, even though the reference period of 1961-1990 remains the same. This is clearly shown in the 11-year moving average where the net result is that the temperature rise from 1950 to 2008 has increased to about 1.35 °C, while the rise from 1918 to 2008 has increased to 0.9 °C. And yet the raw data for these periods haven't changed: only the interpretation and data analysis have.