52. Texas - temperature trends STABLE

If there is one country in the world where you expect dramatic climate change on account of its own greenhouse gas emissions, then that country would probably be the USA. And if there is one state in the USA that embodies the American passion for fossil fuels, that state would be Texas. So when Texas was hit by extreme weather earlier this month in the shape of winter storms Uri and Viola, which resulted in millions Texans losing their electricity supply, then it was only a matter of time before people started screaming "climate change". Because even extreme cold weather is a symptom of anthropogenic global warming (AGW) and climate change (apparently). Unfortunately there is just one problem: there has been no global warming in Texas. So, given the topical nature of the Texas climate at the moment, I thought I would take a temporary break from Europe and take a closer look at climate change in Texas.

The mean temperature trend for the region is shown in Fig. 52.1 below. This was achieved by averaging the temperature anomalies from the 220 longest weather station temperature records in the region, where the temperature anomalies were measured relative to the monthly reference temperature (MRT) in each case. The MRTs were calculated for the interval 1961-1990. For a more detailed explanation of the MRT calculation process, see Post 47.

 

 Fig. 52.1: The temperature trend for Texas since 1840. The best fit is applied to all the data and has a slight positive gradient of 0.05 ± 0.08 °C per century. The monthly temperature changes are defined relative to the 1961-1990 monthly averages. 

 

For 160 years up to 2013 there was no anthropogenic global warming (AGW) occurring in Texas. In fact the mean temperature for the region rose by less than 0.08 °C. And while there is some evidence of a rise in temperature since the 1960s, this still leaves temperatures lower than in the first half of the 20th century.

 

Fig. 52.2: The number of station records included each month in the mean temperature trend for Texas.

 

The temperature trend shown in Fig. 52.1 is the average of up to 220 of the longest temperature records for the state as illustrated in Fig. 52.2 above. All the temperature records have over 720 months (or 60 years) of data, of which 64 are long stations with more than 1200 months of data. These 220 stations are also distributed fairly evenly over the region as shown in Fig. 52.3 below. This means that a simple average of all the temperature anomalies without additional weighting coefficients should yield a mean temperature trend that is reasonably accurate, even though there does appear to be a slightly higher density of stations in the east of the state than in the west. This conjecture will be tested by comparing results later.

 

Fig. 52.3: The locations of long stations (large squares) and medium stations (small diamonds) in Texas. Those stations with a high warming trend are marked in red.

 

The other point of note about the stations in Fig. 52.3 is the high proportion of stations that appear to exhibit no warming; over 70% of them. Here, a warming station is defined as being one where the temperature gradient is more than twice the uncertainty in the trend and the total temperature rise also exceeds 0.25 °C. 

This high proportion of cool stations is unusual but not unique. It has seen in many other places including New South Wales and Victoria. What it appears to highlight is the strong correlation that exists between the degree of warming seen at a particular location and the size of the local population, degree of economic development and the length of the temperature record itself. 

Short, younger temperature records tend to exhibit greater warming because they only have data from the latter part of the 20th century and post 2000, and increased urbanization in the latter part of the 20th century is clearly warming the local environment. In fact, direct anthropogenic surface heating (DASH) or waste heat equating to about 0.7 W/m² has probably warmed Texas by up to 0.3 °C since 1850. In addition, the short length of modern station records means that they do not include any of the natural variation seen in earlier times such as naturally high temperatures seen in the 19th century. In addition, many rural stations appear to exhibit very little warming, while major cities like Jakarta, Sydney and Melbourne can display very large degrees of warming that do not correspond to the climate of the rest of their regions.

What is interesting is comparing the trend based on the original true temperature data in Fig. 52.1 with the equivalent trend based on an average of the adjusted data used by Berkeley Earth. This adjusted data includes the effects of homogenization and breakpoint adjustments that are supposed to improve the quality and accuracy of the data. The mean of the adjusted Berkeley Earth data for the 220 longest station records in Texas is shown in Fig. 52.4 below.

 

Fig. 52.4: Temperature trend in Texas since 1840 derived by aggregating and averaging the Berkeley Earth adjusted data for the 220 longest data records for Texas. The best fit linear trend line (in red) is for the period 1881-2010 and has a gradient of +0.58 ± 0.04 °C/century.

 

Unlike the original data in Fig. 52.1 which exhibits virtually no warming, the Berkeley Earth adjusted data has a strong positive trend of 0.58 °C per century. In total this equates to a warming of over 0.8 °C from 1880 to 2010, while the 10-year moving average suggests an even greater warming of over 1.2 °C. Again, this may be consistent with IPCC reports, but it is not consistent with the actual real data in Fig. 52.1. It is, however, virtually identical to the published Berkeley Earth version shown in Fig. 52.5 below.

 

 Fig. 52.5: The temperature trend for Texas since 1820 according to Berkeley Earth.

 

The similarity of the data in Fig. 52.4 with the Berkeley Earth published version shown in Fig. 52.5 above in effect validates the simple averaging process I have employed, not only for the data in Fig. 52.4, but also for that in Fig. 52.1 as well. It demonstrates that weighted averages are not needed.

Fig. 52.6: The contribution of Berkeley Earth (BE) adjustments to the anomaly data in Fig. 52.4 after smoothing with a 12-month moving average. The blue curve represents the total BE adjustments including those from homogenization. The linear best fit (red line) to these adjustments for the period 1911-2010 has a gradient of +0.568 ± 0.003 °C per century. The orange curve shows the contribution from breakpoint adjustments only.

 

Overall, the Berkeley Earth adjustments appear to add between 0.6 °C and 1.2 °C to the warming of Texas, depending on how you view it. If we consider the net adjustments made to the data (the blue curve in Fig. 52.6 above) which are the difference between the mean anomalies in Fig. 52.1 and Fig. 52.4, these appear to add about 0.6 °C of warming. On the other hand, the difference in the gradients of the best fit lines in Fig. 52.1 and Fig. 52.4 results in over 0.7 °C of warming being added. Either way, these are significant modifications to the original real data that completely change its properties.

 

Summary

1) The mean temperature of Texas has been stable since 1840 (see Fig. 52.1).

2) In contrast, the Texas temperature trend based on Berkeley Earth adjusted data exhibits a warming of over 0.8 °C before 2010 (see Fig. 52.4).

3) Virtually all the warming seen in the Berkeley Earth adjusted data (as denoted by the trend of 0.58 °C per century in Fig. 52.4) can be accounted for by the adjustments made to the data (as seen in the trend of 0.57 °C per century in Fig. 52.6).

4) Adjustments made to the temperature data by Berkeley Earth via breakpoint adjustments and homogenization (see Fig. 52.6) have profoundly changed the magnitude of the warming of the Texas temperature trend since 1840 (see Fig. 52.4) compared with that observed in the raw original data (see Fig. 52.1).

 

51. The Baltic States - temperature trends STABLE to 1980

The Baltic States are the countries of Lithuania, Latvia and Estonia that used to be part of the USSR and are now part of the EU. For the purpose of geographical convenience I will also include the enclave of Kaliningrad in this analysis, for while it is actually a part of Russia, it is not contiguous with Russia, but is instead bordered by Poland, Lithuania and the Baltic Sea.

The mean temperature trend for the region is shown in Fig. 51.1 below. This was achieved by averaging the temperature anomalies for all the weather station temperature records in the region, where the temperature anomalies were measured relative to the monthly reference temperature (MRT) in each case. The MRTs were calculated for the interval 1991-2010. This is rather later and shorter (only 20 years rather than 30) than usual due to the need to maximize the available data and avoid the jump in temperature in 1988. For a more detailed explanation of the MRT calculation process, see Post 47.

 

Fig. 51.1: The temperature trend for the Baltic States since 1775. The best fit is applied to the interval 1781-1980 and has a negative gradient of -0.08 ± 0.08 °C per century. The monthly temperature changes are defined relative to the 1991-2010 monthly averages.

 

For 200 years up to 1980 there was no anthropogenic global warming (AGW) occurring in the Baltic States. In fact the mean temperature for the region fell by about 0.15 °C. Then around 1988 it suddenly jumped by about 1.1 C (see Fig. 51.1 above). Even then the temperature is less than it was in the 1820s, although the data for that period needs to be treated with some caution. That is because it is based on less than five station temperature records (see Fig. 51.2 below). 

However, the more significant factor in explaining the caution over the temperature peak around 1824 in Fig. 51.1 is probably the fragmentation of some of the temperature records in that era, particularly for Dorpat, Tallinn and Riga. This, when combined with the low number of stations overall, can lead to discontinuities in the temperature trend. 

Having said that, data from Vilnius, Sovetsk and Mitau all appear to show similar peaks in the temperature trend around 1824, and their data are continuous. So maybe the peak around 1824 is real. In which case temperatures in the 1820s really were higher than today.

Fig. 51.2: The number of station records included each month in the mean temperature trend for the Baltic States when the MRT interval is 1991-2010.

The temperature trend shown in Fig. 51.1 is the average of just 23 medium and long station records with over 480 months of data. Of these, seven are long stations with more than 1200 months of data. In fact four have over 1800 months (or 150 years) of data. The 23 stations are also distributed evenly over the region as shown in Fig. 51.3 below, with each of the four regions (Kaliningrad, Lithuania, Latvia and Estonia) also containing one of the four longest records. The HTML links above link to a list of stations for each region.

Fig. 51.3: The locations of long stations (large squares) and medium stations (small diamonds) in the Baltic States. Those stations with a high warming trend are marked in red.

What is interesting is comparing the trend based on the original true temperature data in Fig. 51.1 with the equivalent trend based on the data used by Berkeley Earth after they have adjusted the data. The Berkeley Earth version is shown in Fig. 51.4 below.

Fig. 51.4: Temperature trend in the Baltic States since 1775 derived by aggregating and averaging the Berkeley Earth adjusted data for all long and medium stations. The best fit linear trend line (in red) is for the period 1841-2010 and has a gradient of +0.45 ± 0.04 °C/century.

Unlike the original data which has a slight negative trend before 1980, the Berkeley Earth adjusted data has a strong positive trend of 0.45 °C per century. In total this equates to a warming of over 0.8 °C before 1980. When the temperature jump after 1980 is included, the total temperature rise since 1800 is over 2 °C. This may be consistent with IPCC briefings, but it is not consistent with the actual real data in Fig. 51.1.

Fig. 51.5: The contribution of Berkeley Earth (BE) adjustments to the anomaly data in Fig. 51.4 after smoothing with a 12-month moving average. The blue curve represents the total BE adjustments including those from homogenization. The linear best fit (red line) to these adjustments for the period 1841-2010 has a gradient of +0.351 ± 0.007 °C per century. The orange curve shows the contribution from breakpoint adjustments.

Overall, the Berkeley Earth adjustments appear to add between 0.6 °C and 1.0 °C to the warming, depending on how you view it. If we consider the net adjustments made to the data (the blue curve in Fig. 51.5 above) which are the difference between the mean anomalies in Fig. 51.1 and Fig. 51.4, these appear to add about 0.6 °C of warming. The difference in the gradients, however, results in over 0.9 °C of warming being added. Either way, these are significant modifications to the real data that completely change its properties.

Summary

1) In the 200 years before 1980 the mean temperature of the region decreased by 0.15 °C (see Fig. 51.1).

2) Once again we see a sudden rise in temperature in 1988 of about 1 °C that is difficult to explain (see Fig. 51.1). Similar rises were seen in Poland (see Post 50), Germany (see Post 49) and Denmark (see Post 48).

3) Even after the 1988 temperature rise, temperatures post-2000 are still below those pre-1830 (see Fig. 51.1).

4) The temperature trend based on Berkeley Earth adjusted data has a warming of over 0.8 °C before 1980 and over 1 °C of additional warming after 1980 (see Fig. 51.4).

5) Adjustments made to the temperature data by Berkeley Earth via breakpoint adjustments and homogenization have profoundly changed both the magnitude of the warming since 1800 and its significance (see Fig. 51.4 and Fig. 51.5).

50. Poland - temperature trends WARMING 0.9°C

There are over 100 temperature records for Poland. The longest is the Warsaw record (Berkeley Earth ID: 157587) which dates back to 1779 (see Fig. 50.1 below) and exhibits a strong warming trend of 0.71 °C per century. However, this warming trend is not continuous but has considerable variability, with temperatures in the 1930s being comparable to those of today.

 

Fig. 50.1: The temperature trend for Warsaw since 1779. The best fit is applied to the interval 1811-2010 and has a positive gradient of +0.71 ± 0.08 °C per century. The monthly temperature changes are defined relative to the 1951-1980 monthly averages. 

 

Of the 100 or more stations in Poland (for a full list see here), 60 have over 480 months of data (these are medium stations) and five have over 1200 months of data (long stations). In fact over 40 of the medium station have over 720 months (or 60 years) of data which is fairly unusual. This is because there was a significant and abrupt increase in the number of weather station records in Poland in 1951. Similar investments in new stations are seen in many other countries as well in the latter part of the 20th century, but these tend to occur around 1960 or 1970-1973.

The locations of these long and medium stations are shown below in Fig. 50.2. The map indicates that the stations are fairly evenly distributed across Poland which means that a simple average of the anomalies from all these stations should approximate very well to the temperature trend for the country as a whole.

Fig. 50.2: The locations of long stations (large squares) and medium stations (small diamonds) in Poland. Those stations with a high warming trend are marked in red. 

 

In order to determine the mean temperature change for Poland, I first calculated the temperature anomalies for each temperature record relative to its monthly means (MRTs) for the period 1951-1980. These anomalies were then averaged to produce the trend shown in Fig. 50.3 below.

The 1951-1980 interval was chosen because it allowed the maximum number of stations to be included in the mean (see Fig. 50.4 below) while also avoiding the sudden jump in temperatures seen around 1988 in many European temperature records (see Post 44 and Post 49) that could destabilize the MRTs. For a moredetailed description of how the monthly reference temperatures (MRTs) are calculated and why, please refer to Post 47.

 

Fig. 50.3: The temperature trend for Poland since 1779. The best fit is applied to the interval 1811-2010 and has a positive gradient of +0.45 ± 0.08 °C per century. The monthly temperature changes are defined relative to the 1951-1980 monthly averages. 

While the trend in Fig. 50.3 above is the result of averaging over 60 separate records, no more than 58 are included in any single monthly average, and before 1950 this is typically less than ten (see Fig. 50.4 below). Overall, the temperature trend exhibits a significant warming of about 0.9 °C since 1800, but this is much less than that seen in the trend for Warsaw as shown in Fig. 50.1 above. The difference is almost certainly due to anthropogenic effects such as the urban heat island (UHI) effect or waste heat emissions from human and industrial activity. Overall such direct anthropogenic surface heating (DASH) would be expected to increase the temperature of the whole of Poland by about 0.2 °C.

The other detail that is noticeable about the data in Fig. 50.3 is that the temperatures in the 1930s were similar to those of today. This is despite temperatures appearing to have jumped suddenly by about 0.84 °C in 1988. A similar and larger jump of 0.97 °C was seen in the temperature data across Germany at the same time (see Post 49).

Fig. 50.4: The number of station records included each month in the mean temperature trend for Poland when the MRT interval is 1951-1980.

What is clear is that the warming seen in Poland, while significant, is much less than that expected based on IPCC and Berkeley Earth reports. These have suggested that the warming is over 1.5 °C and fairly monotonic. In reality there is a large amount of what looks like natural variation in the data that persists even for very long time-averaged data such as the 5-year moving average.

Fig. 50.5: Temperature trend in the Poland since 1779 derived by aggregating and averaging the Berkeley Earth adjusted data for all long and medium stations. The best fit linear trend line (in red) is for the period 1801-1980 and has a gradient of +0.32 ± 0.03 °C/century.

For comparison, the temperature trend that results from averaging the temperature data after it has been adjusted by Berkeley Earth is shown in Fig. 50.5 above. This trend shows a modest warming of 0.32 °C per century before 1980, or about 0.6 °C in total, followed by a major temperature increase of over 1 °C after 1980. This trend is also virtually identical to the one published by Berkeley Earth (see here) as shown in Fig. 50.6 below.

Fig. 50.6: The temperature trend for Poland since 1750 according to Berkeley Earth.

If we look at the difference between the mean trend in Fig. 50.3 (based on the original true data) and the trend in Fig. 50.5 that is the result of using the Berkeley Earth adjusted data we see that the adjustments made by Berkeley Earth are again not neutral. In fact the Berkeley Earth adjustments add nearly 0.6 °C of warming since 1840 (see Fig. 50.7 below).

Fig. 50.7: The contribution of Berkeley Earth (BE) adjustments to the anomaly data in Fig. 50.5 after smoothing with a 12-month moving average. The blue curve represents the total BE adjustments including those from homogenization. The linear best fit (red line) to these adjustments for the period 1841-2010 has a gradient of +0.335 ± 0.007 °C per century. The orange curve shows the contribution from breakpoint adjustments.

Conclusions

It is clear from the results shown here that temperatures in Poland have increased over the last 250 years, but by how much and for what reason remains unclear. There has certainly not been the catastrophic warming due to carbon dioxide emissions (i.e. more than 1.5 °C) that has been claimed by climate scientists, although there might have been some warming from this source. However, such warming cannot realistically be greater than 0.7 °C (i.e. the 0.9 °C seen in Fig. 50.3 minus the 0.2 °C we would expect from DASH or UHI effects). The problem is that any remaining warming that may be due to CO₂ emissions does not correlate well with CO₂ levels in the atmosphere over time. And then there is the uncertainty over the amount that natural variation in the temperature record may be contributing to the relatively short-term trends (less than 250 years) that we are observing.

We can probably claim with a fair degree of confidence that the data after 1950 in Fig. 50.3 is likely to be highly reliable as it is based on over 50 station records that are evenly spaced geographically (see Fig. 50.2). But this raises the question of what is causing the sudden jump in temperatures seen in 1988 which is also seen in other countries such as Germany (see Post 49).

For data before 1950, this is based on between about four and ten station records, at least back to 1830. The overall trend for 1831-1980 suggests a total temperature rise of only about 0.35 ± 0.15 °C, which is less than the standard deviation of the temperature fluctuations in the 5-year moving average for that period. This suggests that these temperature changes could be explained by natural variability.

Finally, it is apparent that once again there is a large discrepancy (0.6 °C) between any temperature rises seen in the raw data (see Fig. 50.3) and the rises claimed by climate scientists (see Fig. 50.5). This difference is largely due to adjustments made to the raw data by climate scientists (see Fig. 50.7).

49. Germany - temperature trends PARABOLIC

If any country in Europe were to exhibit the effects of anthropogenic global warming (AGW) and climate change, then you might expect that country to be Germany. Except that it doesn't.

There are over 135 sets of weather data for Germany that contain over 480 months of data (see here). Of these 34 are long stations with over 1200 months of data while the remainder I denote as medium stations. In fact ten temperature records have over 2000 months of data. This makes the temperature data for Germany some of the best available.

The geographical locations of these weather stations are indicated on the map below (see Fig. 49.1). This shows that both the long and medium stations are distributed fairly evenly, although there appear to be slightly fewer medium stations in the former East Germany. The stations are also differentiated according to the strength of their warming trend. Those with a large warming trend are marked in red, where a large trend is defined to be one that is both greater than 0.25 °C in total and also more than twice the uncertainty. 

The threshold of 0.25 °C is set equal to the temperature rise that one would expect in the EU as a whole due to waste heat or direct anthropogenic surface heating (DASH) due to human and industrial activity. In fact for Germany, based on its population, area and energy consuption, we would expect the temperature rise since 1700 due to DASH to be at least 0.6 °C (see Post 14), even without the effects of an enhanced greenhouse effect.

 

Fig. 49.1: The locations of long stations (large squares) and medium stations (small diamonds) in Germany. Those stations with a high warming trend are marked in red.

 

The longest data set is for Berlin-Tempelhof (Berkeley Earth ID: 155194) which has data that extends back to 1701. This data is shown in Fig. 49.2 below as the temperature anomaly after subtracting the monthly reference temperatures (MRTs) based on the 1971-2000 averages. The method for calculating the anomalies and MRTs from the raw temperature data is described in Post 47. However, there are two caveats that need to be applied to the data in Fig. 49.2. Firstly, there are significant gaps in the data before 1756, and secondly any data before 1714 needs to be treated with caution simply because thermometers did not exist then, at least not in their current form. 

Fig. 49.2: The temperature trend for Berlin-Tempelhof since 1700. The best fit is applied to the interval 1821-1980 and has a positive gradient of +0.13 ± 0.10 °C per century. The monthly temperature changes are defined relative to the 1971-2000 monthly averages.

In order to determine the temperature trend for Germany I have averaged the temperature anomalies from all 135 long and medium stations. The result is shown in Fig. 49.3 below. All stations with data less than 480 months are excluded as they add no real value to the result, particularly if the data is very recent (i.e. after 1980). This is because the temperature change over time is small, typically 1 °C per century, so you really need at least 40 years of data to detect a measurable trend above the noise.

Fig. 49.3: The temperature trend for Germany since 1700. The best fit is applied to the interval 1756-2005 and has a negative gradient of -0.02 ± 0.05 °C per century. The monthly temperature changes are defined relative to the 1971-2000 monthly averages.

What is immediately apparent is that the trend in Fig. 49.3 differs significantly from the widely publicized IPCC version. Firstly, temperatures before 1850 appear to be higher than they are now, not lower. Secondly, temperatures were stable or declining for over 150 years prior to 1980, not rising. And finally, the mean temperature appears to jump suddenly in 1988 just as the IPCC was being established. Some of these traits are also seen in the mean temperature trend I constructed for the whole of Europe that was published in Post 44. The 19th century cooling is also seen in the temperature data of New Zealand (see Post 8) and Australia (see Post 26).

 

Fig. 49.4: The amount of temperature data from Germany included in the temperature trend each month for three different choices of MRT interval.

As I pointed out in Post 47, the choice of interval for determining the MRTs can influence the number of station records that are included in the final average for the temperature trend, and thus can also influence the nature of the trend itself. In order to test how robust the trend in Fig. 49.3 is regarding changes to the MRT interval, I repeated the calculation for three different MRT intervals. The curves in Fig. 49.4 above show how the number of stations in the final trend changes for each of the different MRT intervals. 

It is clear that there is very little difference between choosing MRT intervals of 1956-1985 and 1971-2000, although the latter does result in a slightly larger number of stations being included in the trend calculation after 1960. The advantage of using the former interval is that it corresponds to a part of the temperature record where the mean temperature is fairly stable whereas the latter interval spans the abrupt increase in temperature seen around 1988. Despite this, in both cases the final trends are very similar, with the best fit in each case being -0.015 °C/century for the 1971-2000 MRT and -0.032 °C/century for the 1956-1985 MRT. In both cases the fitting range was 1756-2005.

The 1901-1930 interval enables more data from before 1930 to be included in the trend (from stations that were closed down before 1930), but significantly less after 1950 when many new stations were set up. Nevertheless, the final trend is almost identical to the those for other two MRT intervals with the best fit being only slightly higher at +0.0004 °C/century. In all three cases temperatures before 1850 were about as high as those after 2000, and in all three cases the mean temperature trend exhibited a large jump in temperature in 1988 as is shown clearly in the 5-year moving average in Fig. 49.3.

Fig. 49.5: The temperature trend for Germany since 1750 according to Berkeley Earth.

Irrespective of which interval is used to determine the MRTs, the resulting temperature trend I have constructed and published in Fig. 49.3 differs significantly from that published by Berkeley Earth which is shown in Fig. 49.5 above. The difference, as I have noted before, is due to homogenization and breakpoint adjustments used by Berkeley Earth to create their adjusted anomalies for each station. Averaging their adjusted anomalies yields the trend shown below in Fig. 49.6, which is virtually identical to the one shown above in Fig. 49.5. This demonstrates that it is not a difference in averaging method that is responsible for the difference between my results in Fig. 49.3 and the Berkeley Earth result. So it must be a difference in the anomaly data itself that is responsible. This can only be due to the adjustments made by Berkeley Earth.

Fig. 49.6: Temperature trend in Germany since 1750 derived by aggregating and averaging the Berkeley Earth adjusted data for all long and medium stations. The best fit linear trend line (in red) is for the period 1801-1980 and has a gradient of +0.29 ± 0.03 °C/century.

The actual temperature difference between the data in Fig. 49.6 and that in Fig. 49.3 is shown below in Fig. 49.7 (blue curve) as the the total adjustment made to the data by Berkeley Earth. The data in Fig. 49.7 highlights two points of note. Firstly, the Berkeley Earth adjustments are not neutral: they add about 0.3 °C to the warming after 1840. Secondly, the adjustments flatten the curve before 1840 and so remove the warm period that mirrors the one seen after 1988. In so doing these adjustments radically change the nature of the temperature trend from an oscillatory one in Fig. 49.3 to the infamous hockey stick shape in Fig. 49.6 that is now synonymous with anthropogenic global warming (AGW).

Fig. 49.7: The contribution of Berkeley Earth (BE) adjustments to the anomaly data in Fig. 49.6 after smoothing with a 12-month moving average. The blue curve represents the total BE adjustments including those from homogenization. The linear best fit (red line) to these adjustments for the period 1841-2010 has a gradient of +0.173 ± 0.003 °C per century. The orange curve shows the contribution from breakpoint adjustments.

Conclusions

The results I have presented here clearly show that the real temperature trend for Germany over the last 300 years differs significantly from the conventional view of global warming. These differences can be summarized as follows.

1) Temperatures before 1840 were comparable to those of today (see Fig. 49.3).

2) The overall temperature trend since 1800 is broadly flat (see the best fit line in Fig. 49.3). 

3) At least 0.6 °C of any temperature rise since 1700 should be due to direct anthropogenic surface heating (DASH) or waste heat from human activity, and not from greenhouse gas emissions.

4) There is a large and seemingly unnatural temperature rise of 0.97 °C in 1988 that occurs at the very moment the IPCC is being formed (see the 5-year mean in Fig. 49.3).

5) Berkeley Earth adjustments have added 0.3 °C of warming to the temperature trend since 1840 and erased most of the warm temperatures before 1840 (see Fig. 49.7).

6) Of the 1.5 °C of warming since 1750 claimed by Berkeley Earth (see Fig. 49.6), 0.6 °C could be due to DASH (see point 3 above) and 0.3 °C is due to adjustments made to the temperature data by Berkeley Earth (see point 5 above).

40. Belgium and Luxembourg - temperature trends 1°C WARMING

In the next few posts I am going to take a look at the temperature trends in a few countries in western Europe, starting with Belgium. The unique feature of these countries is that they have some of the longest instrumental temperature records in the world.

Fig. 40.1: The temperature trend for Brussels since 1794. The best fit is applied to all the data and has a positive gradient of +0.67 ± 0.05 °C per century. The monthly temperature changes are defined relative to the 1976-2005 monthly averages.

 

The longest temperature record in Belgium comes, not surprisingly, from Brussels, and extends back to 1794 (see Fig. 40.1 above). That is the good news. The bad news is that there are no other temperature records with significant temperature data before 1973. Four records do have a couple of years of data in the early 1940s. But this data is probably not very reliable as there is then a thirty year gap to the rest of the data, and the early data was clearly collected under conditions of wartime occupation. The only other significant dataset comes from Luxembourg to the south of Belgium (see Fig. 40.2 below) which extends back to 1878.

The blue data in Fig. 40.1 above is the monthly temperature anomaly for Brussels, i.e. the amount by which each month's mean reading deviated from a reference value for that month for that station. Those monthly reference temperatures (MRT) were calculated by averaging all equivalent months (i.e. January or February etc.) in that dataset over the period 1976-2005. This is a later period than that used for most previous blog posts (most use 1961-1990) and is solely because of the lack of data before 1973. The monthly reference temperatures (MRT) are then subtracted from the raw monthly data to generate the monthly anomaly data. For a longer explanation of this process see Post 38 and Post 4.

It can be seen from the anomaly data in Fig. 40.1 that the range of anomaly values can be up to 12 °C, with the extreme negative values being more extreme than the extreme positive ones. These extreme negative values almost always correspond to severe winters; the winter of 1942 was particularly bad with two consecutive months (January and February) recording monthly means that were over 6 °C below normal. In the middle of a Nazi occupation I suspect that was really grim. Overall, though, this suggests that extreme winter cold spells are much deeper and longer lasting than prolonged summer heatwaves.

The other main feature of the data in Fig. 40.1 is the overall upward trend. Apart from a significant dip around 1890, this is almost continuous, and is illustrated more clearly by the 5-year moving average (yellow curve). Overall the mean temperature in Brussels rises by over 1 °C, as indicated by the red best fit line, from 1794 to 2013. However, as I pointed out in Post 14, the growth in energy usage in Belgium over the same period would be expected to raise temperatures by around 0.98 °C anyway. This would appear to indicate, that while the temperature rise is probably man-made, it is in all likelihood not entirely due to the emission of carbon dioxide and the Greenhouse Effect. 

It may be tempting to also discount this temperature record for Brussels as being an aberration or anomaly from the norm. However, if we compare it to the data for Luxembourg shown in Fig. 40.2 below, we see similar trends and features. There is a similar temperature rise after 1985, similar peaks in the 5-year moving average around 1947 and 1960, and a similar trough around 1890. The gradients of the best fit lines are similar in both cases as well, although the uncertainty for the Luxembourg best fit is much greater at almost ±0.16 °C. This, though, is partly due to the shorter time span of the Luxembourg data. 

Fig. 40.2: The temperature trend for Luxembourg since 1878. The best fit is applied to the interval 1895-2004 and has a positive gradient of +0.49 ± 0.16 °C per century. The monthly temperature changes are defined relative to the 1976-2005 monthly averages.

If we now look at the remaining data for Belgium and Luxembourg we see that there are an additional fourteen medium stations with temperature records that contain at least 480 months of data (see here for a list). Most of this data is for the period 1973-2013. The locations of the two long stations (Brussels and Luxembourg) and the fourteen medium stations are shown on the map in Fig. 40.3 below.

 

Fig. 40.3: The locations of long stations (large squares) and medium stations (small diamonds) in Belgium and Luxembourg. Those stations with a high warming trend are marked in red.

The map in Fig. 40.3 indicates that the two long stations with over 1200 months of data and the fourteen medium stations with over 480 months of data are distributed fairly evenly across Belgium and Luxembourg. This is important because it means that we probably don't need to resort to complex weighted averages when finding the overall temperature trend. A simple mean will suffice. In which case, combining the anomalies for the sixteen stations indicated in Fig. 40.3 gives the overall trend shown in Fig. 40.4 below.

Fig. 40.4: The temperature trend for Belgium and Luxembourg since 1794. The best fit is applied to the interval 1895-2004 and has a positive gradient of +0.52 ± 0.15 °C per century. The monthly temperature changes are defined relative to the 1976-2005 monthly averages.

 

As can be clearly seen, the overall trend for the whole of Belgium is not that different from that illustrated for Brussels in Fig. 40.1, but then why would it be? Over 80% of the trend in Fig. 40.4 is entirely due to the data from two stations: Brussels and Luxembourg. This is shown graphically in Fig. 40.5 below.

 

Fig. 40.5: The number of sets of station data included each month in the temperature trend for Belgium and Luxembourg.

 

Finally, if we compare these results using the raw data with those produced by Berkeley Earth which used adjusted data, we see broad similarities but some notable differences.

 

Fig. 40.6: Temperature trends for all long and medium stations in Belgium and Luxembourg since 1794 derived by aggregating and averaging the Berkeley Earth adjusted data. The best fit linear trend line (in red) is for the period 1801-1980 and has a gradient of +0.28 ± 0.03 °C/century.
 

Combining the Berkeley Earth adjusted anomaly data for the same sixteen station records as in Fig. 40.4 and taking the mean value yields the two trends shown in Fig. 40.6 above: one trend for the 12-month average (in black) and a second for the 10-year average (in orange). For temperature data after 1860 the two trends are very similar to those published by Berkeley Earth and shown in Fig. 40.7 below, with the curves exhibiting similar patterns of peaks and troughs in the two figures. This does appear to validate our initial assumption that weighted averages are unnecessary when combining these temperature records due to their even geographical spacing. However, the Berkeley Earth data before 1860 looks slightly different, and quite frankly is unlikely to be very reliable, given that it is based on only one temperature record, or for the curve before 1794, on no local data at all. 

Fig. 40.7: The temperature trend for Belgium since 1760 according to Berkeley Earth.

Finally, if we look at the difference between the raw data shown in Fig. 40.4 and the Berkeley Earth adjusted data presented in Fig. 40.6 we see that while the overall net adjustments Berkeley Earth made to the data in this instance are small and result in a slightly negative contribution to the trend, there were still large corrections made to segments of the data before 1930 that in effect attempt to "flatten the curve". These do not appear to have a significant impact on the overall trend though.

Fig. 40.8: The contribution of Berkeley Earth (BE) adjustments to the anomaly data after smoothing with a 12-month moving average. The linear best fit to the data is for the period 1831-2010 (red line) and the gradient is -0.048 ± 0.009 °C per century. The orange curve represents the contribution made to the BE adjustment curve by breakpoint adjustments only.

Conclusions

It is clear from Fig. 40.4 that there has been a large degree of warming in Belgium and Luxembourg over the last 200 years. It is likely, given the agreement between the data from the two longest temperature records and their significant spatial separation, that this warming is a feature of the entire region, and is not localized to just one area (or maybe two) of the country, although given the lack of data before 1973, that is not a certainty. The magnitude of this warming is probably in excess of 1 °C. However, this temperature rise is only what one would expect from the growth of industrial energy use over this period (for Belgium it should be about 0.98 °C) as explained in Post 14. It is also less than the 1.5 °C we are told to expect for anthropogenic global warming (AGW) in the Northern Hemisphere as claimed by the IPCC and the HadCRUT4 data. Consequently, it does not really add support to the theory that carbon dioxide is the primary driver of warming, otherwise the warming should be much larger.

36. Lateral thought #2 - does human respiration cause carbon dioxide levels in the atmosphere to increase?

Does breathing contribute to a build-up of carbon dioxide in the atmosphere? This was the subject of an article on the Skeptical Science website that I came across recently that claimed to be debunking a climate myth. That supposed myth was that breathing contributes to a build-up of CO₂ in the atmosphere.

The article is not new: it was first published ten years ago. The central point of the article was to refute claims supposedly made by climate sceptics that breathing by humans adds carbon dioxide to the atmosphere, and so contributes to global warming. But after reading the article and many of the comments I realized that not only was the entire article wrong, so too were most of the comments. 

The motivation for the article appears to be a throw-away comment by Australian academic Professor Ian Plimer, Professor of Mining Geology (University of Adelaide) and Emeritus Professor of Earth Sciences (University of Melbourne), in an ABC radio interview regarding his latest book. The comment was a response to claims made in a green paper by Australian Climate Minister and Senator Penny Wong regarding the threat of climate change where she claimed carbon was a pollutant. In reply Professor Plimer said:

"If Senator Wong was really serious about her science she would stop breathing because you inhale air that's got 385 parts per million carbon dioxide in it and you exhale air with about ten times as much, and that extra carbon comes from what you eat."

I'm still not sure why that statement riled the people at Skeptical Science so much, other than it came from a climate sceptic attacking a supporter of global warming. To me it just seems like a statement of fact and a reference to the carbon cycle. It is therefore doubly puzzling that those same people at Skeptical Science then chose to use the carbon cycle to refute a claim that was not explicitly made, namely that breathing contributes to a build-up of CO₂ in the atmosphere. The argument outlined in the rebuttal by Skeptical Science basically came down to saying:

"Therefore, when we breathe out, all the carbon dioxide we exhale has already been accounted for. We are simply returning to the air the same carbon that was there to begin with."

The problem is this is not quite true. Actually, it is not true at all. In fact I will now explain why breathing by humans may have actually contributed to a build-up of CO₂ in the atmosphere over the last 100 years.

 Fig. 36.1 The carbon cycle.

The first problem with invoking the carbon cycle is that there is no such thing. There is no single carbon cycle. Instead there are multiple interlocking cycles as illustrated in Fig. 36.1 above. I've listed three possibilities below.

Atmosphere  ==>  plants  ==>  soil (bacteria)  ==>  atmosphere.

Atmosphere  ==>  plants  ==>  animals  ==>  atmosphere.

Atmosphere  ==>  ocean plants (algae)  ==>  oceans (bacteria)  ==>  atmosphere.

So the CO₂ doesn't just go round in a circle, as is claimed: it goes around multiple circles. 

The second problem is that the carbon cycle only describes the steady state. So you can’t use it to prove that human respiration isn’t increasing CO₂ levels in the atmosphere because the human population has grown exponentially over the last 100 years. It has almost quadrupled since 1920. That is not a system operating in the steady state or at long-term equilibrium.

In essence, the carbon cycle describes five competing carbon reservoirs or sinks (vegetation, animals, soil, the ocean and the atmosphere) all of which also act as carbon pumps. Moreover, these five reservoirs are all interconnected, and the pumping capacity of each depends on their size. Generally, the bigger they are, the more carbon they will pump. That interconnection means that changing the size of one will change the size of all the others in order to a) balance the pumping rates, and b) to ensure that the law of conservation of mass, as applied to the amount of carbon in the system, is never violated. These changes will happen as the system seeks to find a new equilibrium position or steady state. 

So in principle, any change to either the pumping rate or the size of a reservoir will have knock-on effects throughout the rest of the carbon cycle. That means that any increase in the human population will affect everything else. We can, however, estimate what some of these changes might be based on what we know about the change in human population over the last 100 years.

As the average 70 kg person generates about 1 kg of CO₂ per day, that means they transfer 100 kg of carbon to the atmosphere every year. This carbon comes from the food they eat. With nearly 8 billion people on the planet that equates to about 0.8 GtC per annum (GtC = gigatonne of carbon) being transferred into the atmosphere.

But that is not all. The average person probably eats their own bodyweight in meat every year. So the growth in the human population since 1920 must be reflected in a similar percentage growth in the number of farm livestock. If we assume there is about 2 kg of livestock per 1 kg of human (i.e. a 2 year supply of meat in production), then the overall CO₂ production from both will be about 2.4 GtC per annum. This is about a quarter of our fossil fuel CO₂ output so it is not insignificant. But is this directly increasing atmospheric CO₂ levels as some climate change deniers might claim (although I'm not entirely sure which)?

Some people have suggested that the increases in human and livestock CO₂ emissions are offset by increased crop production. Their argument is that, as all the carbon we breathe out comes from crops, any increase in the CO₂ produced by the human population will be offset by a commensurate increase in crop production required to feed the extra humans and their livestock. That in essence is the core of the original rebuttal from Skeptical Science outlined above. The problem is that this is not true either.

Increased crop production comes at the expense of other types of vegetation (e.g. forests). The total area under human cultivation may increase, but the total amount of land and vegetation won’t. All available fertile land is already fully occupied with vegetation, so any increase in farmland will be at the expense of wild countryside. Changing usage from one to the other does not increase CO₂ uptake because both types of land are already doing this. For example, deforestation in the Amazon region driven by the desire to grow crops and farm cattle does not increase the rate of CO₂ capture in the region. If anything, it decreases it. Forests, so we are told, are the best carbon dioxide scrubbers.

Also, increasing the number of animals does not increase the amount of vegetation or its growth rate. Instead it decreases the amount of carbon going into the soil. Animals eat plants before those plant can die and before they can decay in the soil. This means that animals replace the CO₂ producing capacity of the soil. That is where the substitution occurs. And if the pumping efficiencies of both animals and the soil were the same then nothing much would change as the animal population increases. But they aren’t the same. 

The carbon pumping efficiency of the soil is only 4%. As Fig. 36.1 indicates, the soil contains 1580 GtC globally but emits 60 GtC per annum. Humans store only 0.1 GtC but emit 0.8 GtC per annum. That is an efficiency of 800%. If we include livestock, the efficiency will be broadly the same (800%) but the size of the carbon reservoir and CO₂ emissions will both be about three times greater, for the reasons outlined above. This also means that the increase in CO₂ production from humans and livestock is the same as that produced by about 4% of the Earth’s soil. The consequence of this is that the volume of the soil must reduce by 4% over time as its pumping capacity is replaced by human and their animals, and the amount of carbon entering it from dead plants declines. 

So 63.2 GtC will be lost from the soil while only 0.3 GtC will be transferred to storage in humans and animals, and none to plants. There is only one other place that most of the 62.9 GtC can go: the atmosphere. This 62.9 GtC will increase the atmospheric CO₂ concentration by about 25-30 ppm. So the human population increase could have increased atmospheric CO₂ levels by up to 30 ppm over time, and about 20 ppm since 1920.

Fig. 36.2: A schematic illustration of the carbon cycle on land.

 

To understand this more fully consider the schematic diagram in Fig. 36.2 above. This represents the part of the carbon cycle involving exchange of carbon between the air and land in the case where initially there are no animals in existence. The terms T₁-T₄ are the flow rates of carbon between the three reservoirs, with the size of each reservoir indicated in parentheses. The four flow rates represent carbon capture in plants by photosynthesis (T₁), respiration from plants and animals (T₂), the transfer of dead plant and animal matter to the soil (T₃), and the decay of organic matter in the soil to release CO₂ back into the atmosphere (T₄).

In equilibrium the flow rates into and out of each reservoir must balance. So 

T₁ = T₂ + T₄

(36.1)

 

T₁ = T₂ + T₃

(36.2)

and

T₃ = T₄

(36.3)

Only two of these equations are independent. In addition, the total amount of carbon in the system must remain constant at 2940 GtC (=1580+610+750).

Now suppose the ecosystem outlined in Fig. 36.2 initially contains only plants and bacteria in the soil. Then we introduce some animals. The effect of animals is to eat some of the plants and emit CO₂. This means respiration (T₂) must increase by an amount x and the amount of plant matter entering the soil (T₃) must decrease by the same amount in order for Eq. 36.2 to balance. For the case of the addition of humans and livestock we have already estimated that x = 2.4 GtC per annum. 

The problem is that both Eq. 36.1 and Eq. 36.3 now no longer balance. Only Eq. 36.2 remains balanced. So the soil will lose 2.4 GtC per annum and the atmosphere will gain 2.4 GtC per annum. There is a mass transfer of carbon from the soil to the atmosphere. This will only stop when the emission of CO₂ from the soil (T₄) decreases, as it will do gradually due to the slow and gradual reduction in its volume. When that happens both Eq. 36.1 and Eq. 36.3 will once more balance and the mass transfer will stop. That will happen when T₄ has also decreased by x. As T₄ was initially about 60 GtC per annum, this requires a 4% reduction in T₄, and therefore a 4% reduction in the volume of the soil, i.e. 63 GtC (the rate of decay of the soil and its rate of emission of CO₂ must be proportional to the soil volume). That amounts to a total mass transfer of approximately 63 GtC to the atmosphere, the same as in our preliminary calculation above.

Is this an upper estimate? Yes, probably. It assumes that the growth in the human population and farming livestock is a net gain in terms of animal numbers and that they do not merely substitute for the loss of other species. But we know this is not true. Humans and their livestock do displace other creatures to some extent. This analysis also omits any additional loss of CO₂ to the oceans and changes to vegetation volumes through loss of soil (down 4%) and increasing growth rates due to increased CO₂ levels in the atmosphere (up by 8%). But what it does demonstrate is that when the human population changes, everything else changes. 

 

Conclusion

What we have shown here is that changes to the ecological balance between plants and animals changes the concentration of CO2 in the atmosphere. So respiration by humans and other animals can contribute to a build-up of carbon dioxide in the atmosphere.

28. No AGW in Australia? A summary of trends.

 

Fig. 28: 10-year average temperature trends for Australia based on actual raw data (blue curve) and Berkeley Earth adjusted data (orange curve). The gradient of the best fit to the actual raw data (red line) is +0.18 ± 0.02 °C per century. The temperature change is relative to the 1961-1990 average.

 

 

 

My previous ten posts have examined the temperature records of Australia, state by state, and then also examined the combined result. The final results, based on my analytical methods, are summarized as follows.

1) The mean temperatures in Australia since 2000 are at most 0.2 °C higher, and probably less than 0.1 °C higher than those seen in the latter part of the 19th century (see Fig. 26.1).

2) The average temperature in Australia over the course of the entire 20th century was 0.063 °C lower than the equivalent value for the last 50 years of the 19th century.

3) The average temperature in Australia from 1950-1999 was only 0.1 °C higher than the average for the last 50 years of the 19th century.

4) The fluctuations in the temperature of Australia show a scaling behaviour with a fractal dimension of 0.26 (see Fig. 27.2). This suggests that most of the features in the smoothed data, or data averaged over long timescales, are just low frequency noise. Similar effects are seen in the data for most states, and also in the data for New Zealand (see Post 9).

5) The scaling behaviour of the anomalies implies that the 100-year average temperature for Australia would still have fluctuations with a standard deviation of more than 0.10 °C. This is more than the temperature difference observed between the values for the mean temperature of the latter half of the 19th century and that of the latter half of the 20th century. Thus, the temperature rise seen in the latter half of the 20th century is within the range that would be expected based on random chaotic fluctuations.

6) Only Western Australia and Queensland appear to have had noticeably higher temperatures after the year 2000 compared to the late 19th century. This is partly explained by the fact that both states have little or poor data before 1890.

7) The various adjustments made to the individual temperature records by climate groups like Berkeley Earth appear to have had a significant impact on the overall warming trend for Australia when compared with my more simplified (but in my view more justifiable) statistical methodology. This means that the statistical methods used to analyse the data, and their rationale, are of critical importance and need to be thoroughly tested, evaluated, and justified. The first step in doing this should always be to compare the results based on the adjustments with those obtained without the adjustments. That has always been the primary raison d'être of this blog.

8) The overall effect of adjustments made to the individual temperature records of Australia by Berkeley Earth, when compared to my results, has been to partially flatten the curve in Fig. 26.1 before 1900 and to increase the warming trend by up to 0.3 °C after 1900 (see Fig. 26.5). These adjustments are not neutral and completely change the shape of the curve.

9) The overall temperature trend for Australia looks more like a parabola or low frequency oscillation when the raw data is averaged according to my statistical procedure. The effect of the adjustments made to the data by Berkeley Earth is to make the temperature trend look more like a hockey stick (see Fig. 26.4).

Given the shape of the overall instrumental temperature record illustrated in Fig. 26.1, it is difficult to see how this could constitute unambiguous evidence for anthropogenic global warming (AGW). The best (or worst) that can be said about the data is that it is ambiguous. However, it also represents an alternative self-consistent narrative that raises profound questions about the current climate warming zeitgeist.

If my averaging methods for the anomaly data were simplistic to the point of being erroneous, the result would be a mean temperature trend in Fig. 26.1 that was totally uncorrelated with the majority of the individual records from which it was formed. Yet there is no evidence that this is the case. In fact the majority of long temperature records for Australia look very similar to the mean trend shown in Fig. 26.1.

But it is the scaling behaviour that is the killer application. If this phenomenon is real and ubiquitous, then it implies that (almost) everything that is seen in the temperature record is just chaotic noise. The only exception might be the urban heating I described here, and which is clearly important in those parts of the world that have high levels of industry and high population densities. But that is unlikely to be important in most of the Southern Hemisphere.

9. Fooled by randomness

Is global warming real? That is probably a justifiable question given what I revealed in the last post about breakpoint alignment. But what I am going to demonstrate here and over the next two or three posts should also make you question everything you think you know about climate change. The first topic I am going to explore is a concept that most physicists and mathematicians are all too familiar with, but which appears to be totally off the radar of climate scientists: chaos theory and fractal geometry.

Fig. 9.1:  Record 1.

First a test. Look at the dataset above (Fig. 9.1) and the one below (Fig. 9.2). Can you tell which one is a real set of temperature data and which one is fake?

Fig. 9.2:  Record 2.

Okay, so actually it was a trick question because they are both real sets of data. In fact they are both from the same set of station data, and they are partially from the same time period as well, but there is clearly a difference. The difference is that the data in Fig. 9.1 above is only a small part of the actual temperature record but the data from Fig. 9.2 is from the entire record. The data in Fig. 9.1 is taken from the Christchurch station (Berkeley Earth ID - 157045) and is monthly data for the period 1974 - 1987. The data in Fig. 9.2 is from the same record but for the time interval 1864 - 2013: it has also been smoothed with a 12 month moving average. Yet they look the very similar in terms of the frequency and height of their fluctuations - why? Well, what you are seeing here is an example of self-similarity or fractal behaviour. The temperature record for Christchurch is a one-dimensional fractal, and so for that matter is every other temperature record.

Self-similarity is common in nature. You see it everywhere from fern leaves and cauliflowers to clouds and snowflakes. It is observed when you magnify some objects and look at them in greater detail, only to find, to your surprise, that the detail looks just like a smaller version of the original object. This is known as self-similarity: the object looks like itself but in microcosm. It is also an example of scaling behaviour. There is usually a fixed size ratio between the original and the smaller copies from which it is made.

In order to make the smoothed data in Fig. 9.2 look similar to the original data in Fig. 9.1 two scaling adjustments were made. First the time scale on the horizontal axis in Fig. 9.2 was shrunk by a factor of twelve. This is to compensate for the smoothing process which effectively combines twelve points into one. The second was to scale up the temperature axis in Fig. 9.2 by a factor 12 ^0.275. The reason for the power of 0.275 will become apparent shortly, but it is important as it has profound implications for the noise level we see in temperature records over long time periods (i.e. centuries).

To demonstrate the scaling behaviour of the temperature record we shall do the following. First we smooth the data with a moving average of length say two points and then calculate the standard deviation of the smoothed data. Then we repeat this for the original data, but with a different number of data points in the moving average and again calculate the standard deviation of the new smoothed data. After doing this for six or seven different moving averages we plot a graph of the logarithm of the standard deviation versus log(N) where N is the number of points used each time for the moving average. The result is shown below in Fig. 9.3.

Fig. 9.3:  Plot of the standard deviation of the smoothed  anomaly data against the smoothing interval N for temperature data from Christchurch (1864-2013).

The important feature of the graph in Fig. 9.3 is that the data lies on an almost perfect straight line of slope -0.275 (remember that number)? I have to confess that even I was shocked by how good the fitting was when I first saw it, particularly given how imperfect temperature data is supposed to be. What this graph is illustrating is that as we smooth the data by a factor N, the noise level is reducing by a factor N^-0.275. But is this reproducible for other data? Well the answer appears to be, yes.

Fig. 9.4:  Plot of the standard deviation of the smoothed  anomaly data against the smoothing interval N for temperature data from Auckland (1853-2013).

The graph above (Fig. 9.4) shows the same scaling behaviour for the station at Auckland (Berkeley Earth ID = 157062) while the one below (Fig. 9.5) illustrates it for the station at Wellington (Berkeley Earth ID = 18625). The gradients of the best fit lines (i.e. the power law index in each case) are -0.248 and -0.235 respectively. This suggests that the real value is probably about -0.25.

Fig. 9.5:  Plot of the standard deviation of the smoothed  anomaly data against the smoothing interval N for temperature data from Wellington (1863-2005).

But it is the implications of this that are profound. Because the data is such a perfect fit in all three cases, we can extrapolate to longer smoothing operations such as one hundred years. That corresponds to a scaling term of 1200 (because it is equal to 1200 months and thus is 1200 greater in period than the original data) and a noise reduction of 1200 ^0.25 = 5.89. In other words, the noise level on the underlying one hundred year moving average is expected to be about six times less than for the monthly data. This sounds like a lot but the monthly data for Christchurch has a noise range of up to 5 °C (see Fig. 9.6 below), so this implies that the noise range on a 100 year trend will still be almost 1 °C. Now if that doesn’t grab your attention, I have to wonder what will? Because it implies that the anthropogenic global warming (AGW) that climate scientists think they are measuring is probably all just low frequency noise resulting from the random fluctuations of a chaotic non-linear system.

Fig. 9.6:  The temperature anomaly data from Christchurch (1864-2013) plus a 5-year smoothing average.

What we are seeing here is a manifestation of the butterfly effect which, put simply, says that there is no immediate causal link between some current phenomena such as the temperature fluctuations we see today and current global events. This is because the fluctuations are actually the result of dynamic effects that played out long ago but which are only now becoming visible.

Fig. 9.7:  Typical mean station temperatures for each decade over time.

To illustrate the potential of this scaling behaviour further we can use it to make other predictions. Because the temperature record exhibits self-similarity on all timescales, it must do so for long timescales as well, such as centuries. So we can predict what the average temperature over hundreds of years might look like (qualitatively but not precisely) just by taking the monthly data in Fig. 9.6, expanding the time axis by a factor of 120 and shrinking the amplitude of the fluctuations by a factor of 120 ^0.25 = 3.310. The result is shown in Fig. 9.7 above. Because of the scaling by a factor of 120, each monthly data point in Fig. 9.6 becomes a decade in Fig. 9.7. The data in Fig. 9.7 thus indicates that the average temperature for each decade can typically fluctuate by about ±0.5 °C or more over the course of time.

Fig. 9.8:  Typical mean station temperatures over 100 years over time.

Then, if we smooth the data in Fig. 9.7, we can determine the typical fluctuations over even longer timescales. So, smoothing with a ten point moving average will yield the changes in mean temperature for 100 year intervals as shown in the graph above (Fig. 9.8). This again shows large fluctuations (up to 0.5 °C) over large time intervals. But what we are really interested in from a practical viewpoint is the range of possible fluctuations over 100 years as this corresponds to the timeframe most quoted by climate scientists.

To examine this we can subtract from the value at current time t the equivalent value from one hundred years previous, i.e. ∆T = T(t) - T(t-100).

Fig. 9.9:  Typical change in the 100-year mean temperature for a time difference of 100 years.

So, as an example we may wish to look at the change in mean temperature from different epochs, say from one century to the next. Well the data in Fig. 9.9 shows just that. Each data point represents difference between the mean temperature over a hundred years at that point in time with the same value for a hundred years previous. Despite the large averaging periods we still see significant temperature changes of ± 0.25 °C or more. However, if we compare decades in different centuries it is even more dramatic.

For example, Fig. 9.10 below predicts the range of changes in the average decadal temperatures from one century to the next, in other words, the difference between the 10-year mean temperature at a given time t and the equivalent decadal mean for a time one hundred years previous. What Fig. 9.10 indicates is that there is a high probability that the mean temperature in the 1990s could be 0.5 °C higher or lower that the mean temperature in the 1890s, and this is just as a consequence of low frequency noise.

Fig. 9.10:  Typical change in mean decadal temperature for a time difference of 100 years.

So why have climate scientists not realized all this? Maybe it's because their cadre comprise more geography graduates and marine biologists than people with PhDs in quantum physics. But perhaps it is also due to the unique behaviour of the noise power spectrum.

If the noise in the temperature record behaved like white noise it would have a power spectrum that is independent of frequency, ω. If we define P(ω) to be the total power in the noise below a frequency, ω, then the power spectrum is the differential of P(ω). For white noise this is expected to be constant across all frequencies up to a cutoff frequency ω_o.

(9.1)

This in turn means that P(ω) has the following linear form up to the cutoff frequency ω_o.

P(ω) = aω

(9.2)

where a is a constant. The cutoff frequency is the maximum frequency in the Fourier spectrum of the data and is set by the inverse of the temporal spacing of the data points. If the data points are closer together then the cutoff frequency will be higher. Graphically P(ω) looks like the plot shown below in Fig. 9.11, a continuous horizontal line up to the cutoff frequency ω_o.

Fig. 9.11: The frequency dependent power function P(ω) for white noise.

The effect of smoothing with a moving average of N points is to effectively reduce the cutoff frequency by a factor of N because you are merging N points into one. And because the noise power is proportional to the noise intensity, which is proportional to the square of the noise amplitude, this means that the noise amplitude (as well as the standard deviation of the noise) will reduce by a factor equal to √N when you smooth by a factor of N.

For a 100-year smoothing the scaling factor compared to a monthly average is 1200, and so the noise will therefore reduce by a factor of 1200 ^0.5 = 34.64 . That means the temperature fluctuations will be typically less than 0.1 °C. This is probably why climate scientists believe that the long term noise will always be smoothed or averaged out, and therefore why any features that remain in the temperature trend must be "real". The problem is, this does not appear to be true.

Instead the standard deviation varies as N ^-0.25. So the intensity of the noise varies as N ^-0.5 and P(ω) will increase as √N. It therefore follows that the power spectrum is not independent of frequency as is the case for white noise, but instead varies with frequency as

(9.3)

and P(ω) will look like the curve shown in Fig. 9.12 below.

Fig. 9.12:  The frequency dependent power function P(ω) for temperature data.

The net result is that the random fluctuations in temperature seen over timescales of 100 years or more are up to six times greater in magnitude than most climate scientists probably think they will be. So the clear conclusions is this: most of what you see in the smoothed and averaged temperature data is noise not systemic change (i.e. warming). Except, unfortunately, most people tend to see what they want to see.