There’s rather a strange post over on Bishop Hill called Met Office admits claims of significant temperature rise untenable. The post discusses the Met Office’s response to a parliamentary question by Lord Donahue in which he asked
…Her Majesty’s Government … whether they consider a rise in global temperature of 0.8 degrees Celsius since 1880 to be significant.
The response from the Met Office was that the “the temperature rise since about 1880 is statistically significant”.
The basic argument in the post seems to be that the response requires an explanation of the statistical model that they’ve used and hence allows for the possibility that another statistical model would be equally valid. So, is there any merit in this claim? Well the technique that is being used by the Met Office to make the claim that the rise in global surface temperatures is “statistically significant” is known as linear regression. Basically, it is a technique that determines the best-fit straight line through a dataset (in this case the temperature anomaly data). It also allows you to determine the error on the best-fit line. In the case of temperature anomaly data, the data points are correlated (the anomaly values depend on previous values) and so determining the error is somewhat more complicated than for basic linear regression (you can download a basic linear regression routine from the internet). You also need to decide on the significance of the error. Typically, for temperature anomaly data the significance is taken to be 2σ, which means that there is a 95% chance that the trend is between trend + error and trend – error.
So, what do you get if you use linear regression to analyse the Met Office’s temperature anomaly data. The data from 1880 to 2013 has a best-fit linear trend of 0.062oC per decade with a 2σ error of 0.008oC per decade. Therefore there is a 95% chance that the trend is between 0.053 and 0.071oC per decade. So, when the Met Office responded that it was “statistically significant” what they meant is that there is virtually no chance that there has been no underlying linear warming trend in the temperature anomaly data since 1880.
So, is there any merit to the suggestion that some alternative statistical technique could have been used to analyse this data and that the actual long-term trend is different to what the Met Office obtained using linear regression? In a sense, yes. By simply applying linear regression to the temperature anomaly data, we have no idea why the data has behaved in the way that it has since 1880. The Bishop Hill blog also goes on to quote a Met Office statistician (Doug McNeall) as saying that the trending autoregressive model is “simply inadequate”. What the Bishop Hill post fails to clarify is that he actually says inadequate to capture all of the timescales that are apparent in the Earth system. Indeed, I agree. Linear regression simply determines the underlying linear trend. It tells you nothing about other variations that may be present in the data. This is precisely the point. You need to do more than simply fit a line or a curve to a dataset to understand the underlying physical processes.
So, what do you do to try and explain the underlying linear trend in the Met Office temperature anomaly data? Well, you may notice that there has been a significant rise in atmospheric CO2 levels since the mid-1800s. This is a greenhouse gas and so increasing its concentration in the atmosphere could lead to a rise in global surface temperatures. You could also notice that the ocean heat content has risen by about 2.5 x 1023 J since 1960 (about 5 x 1021J per year). You eventually get satellite data that tells you that – for at least the last 10 to 20 years – the Earth has been receiving 0.5 – 1 W m-2 more energy from the Sun than it loses into space. This indicates that the Earth has been receiving between 2 – 4 x 1021 J of excess energy every year (very similar to the increase in ocean heat content). You could then conclude that there is evidence to suggest that the underlying rising linear trend in the global surface temperature anomaly is part of a process of global warming driven by the increase in atmospheric CO2 resulting from our use of fossil fuels. There are other processes producing variations in the global temperature anomalies, but the underlying warming trend seems as though it is being driven by enhanced global warming due to increasing atmospheric CO2 concentrations.
Now, one could apply a different statistical technique to analyse the global surface temperature anomalies. Maybe see if one can fit some kind of sinusoidal variation in which the data from 1880 to 2013 is on the rising part of the sinusoid. I’m sure that this is possible. What you have to do next, however, is determine what physical process explains this long-term sinusoidal variation. I can’t think of one, but maybe the author of the Bishop Hill post is cleverer than me.
The Bishop Hill post finishes by saying that the basis for the claim that the warming is statistically significant
has now been effectively acknowledged to be untenable. Possibly there is some other basis for the claim, but that seems extremely implausible: the claim does not seem to have any valid basis.
Plainly, then, the Met Office should now publicly withdraw the claim. That is, the Met Office should admit that the warming shown by the global-temperature record since 1880 (or indeed 1850) might be reasonably attributed to natural random variation. Additionally, the Met Office needs to reassess other claims that it has made about statistically significant climatic changes.
Really? I don’t think that the Met Office made any claim about statistically significant climatic changes. All they claimed is that the underlying linear trend in their temperature anomaly data is statistically significant at the 2σ level. Any claims about the significance of global warming (and consequently climate change) is based on extensive research aimed at understanding why there is a an underlying warming trend in the temperature anomaly data. If the author of the Bishop Hill post wants to claim that it is simply natural random variations, they need to do the research that attempts to understands what this random natural variation is. Even a random natural variation has to obey the basic laws of physics and if you can’t find some physical process that produces such a random natural variation then the chance that it is driving the observed warming seems rather small.
This post has become quite long, but the basic point is that our understanding of global warming and associated climate change is based not only on linear regression analysis of the global temperature anomalies, but on a host of other measurements, analyses and modelling. If someone is to claim that they can use a different statistical method to analyse the global temperature anomaly data, that’s fine. That – in itself – isn’t enough to disprove the basic tenets of anthropogenic global warming. They need to make all the other measurements, analyses and modelling that provides evidence for their alternative. Until they’ve done that, their alternative has no intrinsic value.