4. Data analysis at the South Pole

If there is one place on Earth that is synonymous with global warming, it is Antarctica. The conventional narrative is that because of climate change, the polar ice caps are melting, all the polar bears and penguins are being rendered homeless and are likely to drown, and the rest of the planet will succumb to a flood of biblical proportions that will turn most of the Pacific islands into the Lost City of Atlantis, and generally lead to global apocalypse. Needless to say, most of this is a gross exaggeration.

I have already explained that melting sea ice at the North Pole cannot raise sea levels because of Archimedes’ principle. The same is true of ice shelves around Antarctica. The only ice that can melt and raise sea levels is that which is on land. In Antarctica (and Greenland) this is virtually all at altitude (above 1000 m) where the mean temperature is below -20 °C, and the mean monthly temperature NEVER gets above zero, even in summer. Consequently, the likelihood of any of this ice melting is negligible.

The problem with analysing climate change in Antarctica is that there is very little data. If you exclude the coastal regions and only look at the interior, there are only twenty sets of temperature data with more than 120 months of data, and only four extend back beyond 1985. Of those four, one has 140 data points and only runs between 1972 and 1986 and so is nigh on useless for our purposes. The other three I shall consider here in detail.

The record that is the longest (in terms of data points), most complete and most reliable is the one that is actually at the South Pole. It is at the Amundsen-Scott Base that is run by the US government and has been permanently manned since 1957. The graph below (Fig. 4.1) illustrates the mean monthly temperatures since 1957.

Fig. 4.1: The measured monthly temperatures at Amundsen-Scott Base.

The thing that strikes you first about the data is the large range of temperatures, an almost 40 degree swing from the warmest months to the coldest. This is mainly due to the seasonal variation between summer and winter. Unfortunately, this seasonal variation makes it virtually impossible to detect a discernible trend in the underlying data. This is a problem that is true for most temperature records, but is acutely so here. However, there is a solution. If we calculate the mean temperature for each of the twelve months individually, and then subtract these monthly means from all the respective monthly temperatures in the original record, what will be left will be a signal representing time dependent changes in the local climate.

Fig. 4.2: The monthly reference temperatures (MRTs) for Amundsen-Scott Base.

The graph above (Fig. 4.2) illustrates the monthly means for the data in Fig. 4.1. We get this repeating data set by adding together all the January data in Fig. 4.1 and dividing it by the number of January readings (i.e. 57). Then we repeat the method for the remaining 11 months. Then we plot the twelve values for each year to give a repeating trend as illustrated in Fig. 4.2. If we then subtract this data from the data in Fig. 4.1 we get the data shown below (Fig. 4.3). This is the temperature anomaly for each month, namely the amount by which the average temperature for that month has deviated from the expected long-term value shown in Fig. 4.2. This is the temperature data that climate scientists are interested in and try to analyse. The monthly means in Fig. 4.2 therefore represent a series of monthly reference temperatures (MRTs) that are subtracted to the raw data in order to generate the temperature anomaly data. The temperature anomalies are therefore the amount by which the actual temperature each month changes relative to the reference or average for that month.

Fig. 4.3: The monthly temperature anomalies for Amundsen-Scott Base.

Also shown in Fig. 4.3 is the line of best fit to the temperature anomaly (red line). This is almost perfectly flat, although its slope is slightly negative (-0.003 °C/century). Even though the error in the gradient is ±0.6 °C per century, we can still venture, based on this data that there is no global warming at the South Pole.

The reasons for the error in the best fit gradient being so large (it is comparable to the global trend claimed by the IPCC and climate scientists) are the large temperature anomaly (standard deviation = ±2.4 °C) and the relatively short time baseline of 57 years (1957-2013). This is why long time series are essential, but unfortunately these are also very rare.

Then there is another problem: outliers. Occasionally the data is bad or untrustworthy. This is often manifested as a data-point that is not only not following the trend of the other data, it is not even in the same ballpark. This can be seen in the data below (Fig. 4.4) for the Vostok station that is located over 1280 km from the South Pole.

Fig. 4.4: The measured monthly temperatures at Vostok.

There is clearly an extreme value for the January 1984 reading. There are also others, including at March 1985 and March 1997, but these are obscured by the large spread of the data. They only become apparent when the anomaly is calculated, but we can remove these data points in order to make the data more robust. To do this the following process was performed.

First, find the monthly reference temperaturs (MRTs) and the anomalies as before. Then, calculate the mean anomaly. Next, calculate either the standard deviation of the anomalies, or the mean deviation (either will do). Then I set a limit for the maximum number of multiples of the deviation that an anomaly data point can lie above or below the mean value for it to be considered a good data point (I generally choose a factor of 5). Any data-points that fall outside this limit are then excluded. Then, with this modified dataset, I recalculated the MRTs and the anomalies once more. The result of this process for Vostok is shown below together with the best fit line (red line) to the resulting anomaly data (Fig. 4.5).

Fig. 4.5: The monthly temperature anomalies for Vostok.

Notice how the best fit line is now sloping up slightly, indicating a warming trend. The gradient, although looking very shallow, is still an impressive +1.00 ± 0.63 °C/century, which is more than that claimed globally by the IPCC for the entire planet. This shows how difficult these measurements are, and how statistically unreliable. Also, look at the uncertainty or error of ±0.63 °C/century. This is almost as much as the measured value. Why? Well, partly because of the short time baseline and high noise level as discussed previously, and partly because of the underlying oscillations in the data which appear to have a periodicity of about 15 years. The impact of these oscillations becomes apparent when we reduce or change the length of the base timeline.

Fig. 4.6: The monthly temperature anomalies for Vostok with reduced fitting range.

In Fig. 4.6 the same data is presented, but the best fit line has only been performed to data between 1960 and 2000. The result is that the best fit trend line (red line) changes sign and now demonstrates long-term cooling of -0.53 ± 1.00 °C/century. Not only has the trend changed sign, but the uncertainty has increased.

What this shows is the difficulty of doing a least squares best fit to an oscillatory dataset. Many people assume that the best fit line for a sine wave lies along the x-axis because there are equal numbers of points above and below the best fit line. But this is not so, as the graph below illustrates.

 Fig. 4.7: The best fit to a sine wave.

The best fit line to a single sine wave oscillation of width 2π and amplitude A is 3A/π² (see Fig. 4.7). This reduces by a factor n for n complete oscillations but it never goes to zero. Only a best fit to a cosine wave will have zero gradient because it is symmetric. Yet the problem with temperature data is that most station records contain an oscillatory component that distorts the overall trend in the manner described above. This is certainly a problem for many of the fits to shorter data sets (less than 20 years). But a far bigger problem is that most temperature records are fragmented and incomplete, as the next example will illustrate.

Fig. 4.8: The measured monthly temperatures at Byrd Station.

Byrd Station is located 1110 km from the South Pole. Its local climate is slightly warmer than those at Amundsen-Scott and Vostok but the variation in seasonal temperature is just as extreme (see Fig. 4.8 above). Unfortunately, its data is far from complete. This means that its best fit line is severely compromised.

Fig. 4.9: The monthly temperature anomalies for Byrd Station.

The best fit to the Byrd Station data has a warming trend of +3.96 ± 0.83 °C/century (see the red line in Fig. 4.9 above). However, things are not quite that simple, particularly given the missing data between 1970 and 1980 which may well consist of a data peak, as well as the sparse data between 2000 and 2010 which appears to coincide with a trough. It therefore seems likely that the gradient would be very different, and much lower, if all data were present. How much lower we will never know. Nor can we know for certain why so much data is missing. Is this because the site of the weather station changed? In which case, can we really consider all the data to being part of a single record, or should we be analysing the fragments separately? This is a major and very controversial topic in climate science. As I will show later, it leads to the development of controversial numerical methods such as breakpoint alignment and homogenization.

What this post has illustrated I hope, is the difficulty of discerning an unambiguous warming (or cooling) trend in a temperature record. This is compounded by factors such as inadequate record length, high noise levels in signals, missing and fragmented data, and underlying nonlinear trends of unknown origin. However, if we can combine records, could that improve the situation? And if we do, would it yield something similar to the legendary hockey stick graph that is so iconic and controversial in climate science? Next I will use the temperature data from New Zealand to try and do just that.