June 1976 vs. June 2023

In this article I go through some basic stats concepts, and we discover that claims of a truly apocalyptic June 2023 are mere hot air according to the Central England Temperature Record

Location, Location & Location

Let us take three weather stations in the far North of the wet and windy UK (Lerwick, Stornoway Airport and Nairn) and calculate their combined average daily temperature for June 1976. Now let us take three weather stations in the far South of the dry and sunny UK (Camborne, Eastbourne and Hurn) and calculate their combined average daily temperature for June 2023. Would we be surprised if the southern station average turned out to be greater than the northern station average?

No.

Would this difference be due to climate change? Not necessarily.

What we’ve gone and done is confound any genuine warming arising from climate change proper with warmth arising from station location. We’ve compared apples with pears. What we should have done if we were being sensible is compare the combined average daily temperature for June 1976 with June 2023 for the three northerly stations alone, or the three southerly stations alone; and ideally compared the combined average for all six stations for June 1976 and June 2023 to get a balanced picture for the UK as a whole.

Whilst this contrived example is obvious what is not obvious is what happens when the Met Office combine data from hundreds of active stations back in June 1976 with thousands of active stations for June just gone. We have no idea whether this mass pooling of data has introduced a serious amount of sample bias, thereby giving rise to an inaccurate claim that June 2023 is the hottest June on record.

Rigour & Ice Cream

If the Met Office were being rigorous about this they’d take a sample of, say, 500 active stations from June 1976 and then look at their data records for June 2023. If they were top-notch professional and somewhat scientific they’d also check to see whether any of these 500 stations had relocated, or whether their Stevenson screens had been changed or moved, or whether their temperature probes had been updated, or whether their instrumentation software and/or sampling frame had been revised, or whether the equipment had been calibrated each month, or whether the surrounding area had changed in terms of population, development and/or land use, or whether somebody had erected a nearby shed with a corrugated iron roof. They’d also check each site to determine whether ice cream vans had decided to take up residence en masse in June 2023, just in case!

I think you get the picture. The thing is UK weather stations were built for observing UK weather. They were not built for accurate, reliable and consistent measurement of land surface temperature that would require an enormous degree of standardisation, maintenance and regular calibration. We’re talking Stevenson screens of identical build and dimension, with identical sensors located in identical settings (1m above a large expanse of mown grass) in remote rural areas away from populated areas and airfields. That is but a pipe dream and so we have to somehow handle data from weather stations plagued by all manner.

A Thing Called Error

This leads to a thing called error. Not error in the sense of getting it wrong but error in the sense of measurement error. A precision thermometer might be calibrated to read within one tenth of a degree but that is only the beginning. What we’ve then got to do is sample that precise reading. Do we do this every hour, every minute, every second or every millisecond? Do we do this by hand or have we installed an automated system? All of these impinge on measurement error and it should not come as a surprise to learn that an hourly manual reading at a station with a wet bulb thermometer will give a different result to an automated reading from a quick response thermocouple set to a sampling frequency of 10msec. These days daily maxima and minima (from which we calculate the arithmetic mean) are nailed within fractions of a second, whereas this was not the case a few decades ago when the mercury column had to nudge what it could over the course of a day. Please bear these technicalities in mind when considering comparison of temperature data gathered back in 1976 with temperature data gathered last month for they represent a source of measurement error that we cannot possibly hope to estimate.

Statistical Thinking

Where we are headed with all this is statistical thinking. We may acknowledge the problems of station bias and measurement error but that’s not the end of the matter. Whenever we calculate an average daily temperature we are only ever producing a point estimate of a range of possible ‘true’ values. That is, we could calculate the mean daily temperature from 100 weather stations only to find it is different from a sample of another 100 weather stations. So which sample of 100 weather stations should we choose? Well, none of them will do anything but keep providing you with point (sample) estimates of the ‘true’ population mean. In plain English, they’ll all give some sort of figure that straddles the truth. The more stations the better idea since you’ll have a better idea of where the mark actually sits. This is what we may call sample error, and every time we calculate a sample mean from a set of values it comes paired with an estimate of that error. That set of values might be one daily temperature measurement from each of 100 stations or it may be 100 daily measurements from just one station, and it may be 100 daily measurements from 100 stations. Unless the recorded temperature was precisely 20.0°C on every day at every station then we’ll always end with variation (variance) that surrounds the mean value (a measure of central tendency).

Thus, the mean daily temperature for the UK back in June 1976, as offered by the Met Office, will have been derived from a sample of 60 daily observations (30 maxima and 30 minima) at a large sample of stations, but which will come paired with an estimate of the variance of that dataset (usually quoted in terms of the standard deviation, and sometimes the standard error). If the Met Office were being rigorous they’d quote the overall UK mean for June ’76 along with something representing the sample error associated with this estimate. An example would be 21.3°C ± 0.1°C, with that plus or minus 0.1°C representing one standard error about the mean. That is to say the ‘true’ mean temperature likely lies somewhere between 21.2°C and 21.4°C. Even better would be for them to provide the mean and 95% confidence interval, which would look something like 21.3°C [95CI: 21.1; 21.5].

Utterly Wonderful

The reason this would be utterly wonderful for the general public is that we’d then be able to compare estimates for the range of the ‘true’ UK mean for June 1976 with estimates of the range for the ‘true’ UK mean for June 2023. If these ranges overlapped then any difference we see between means would mean nothing. The upshot of such an overlap would be that science journalists and the Met Office couldn’t then go round claiming that June 2023 was hotter than June 1976. I guess you can figure why means and only means are quoted in the media and not means with an associated estimate of the variance. Well that’s the theory, but we can go one better and pull down some real data to see this working in practice….

Central England Temperature Record

This is the dataset I am going to use. Although not perfect it does iron some of the aforementioned winkles out by focusing on a common set of weather stations that are calibrated from time to time and is highly regarded as a reliable temperature record, being the longest temperature record in the world. It also usefully provides daily means so we can compare and contrast all 30 June days and do tasty things like count super hot days as well as calculate the monthly mean and its standard deviation. I suspect now is a good time to get the kettle on, for we are about to determine whether June 2023 was indeed ‘hotter’ than June 1976!

We shall start with a table of the raw data that you can use to derive your own figures:

Before we get stuck into the head-banging statistics again I just want to point out a couple of things:

1. June 1976 saw seven days exceeding a mean daily temperature of 20.0°C whereas June 2023 only saw five.

2. The June 1976 heatwave got going on the 23^rd when the mean daily temperature broke 20.0°C for the first time, whereas the June 2023 heatwave broke 20.0°C for the first time on the 11^th. In terms of heatwave events we are thus not comparing like with like for the 2023 heatwave had fizzled out by the end of June, whereas the 1976 heatwave was just getting in its stride. Comparison on a monthly basis, though ‘legal’, is thus somewhat misleading.

A Weeny Mean Difference

So let us have a look at the mean difference between the two years. To three decimal places we have +0.070°C with a win for June 2023. That’s not a lot, and less than what you’ll see being quoted by the Met Office and others. This is because they’re maximising the sample size with a huge pool of stations and ignoring statistical rigour; in sum they are content on comparing apples with pears. The HadCET mean difference is weeny when we do the sums right!

Below the means you’ll see my generous offer of both the standard deviation and the standard error so you can choose your favourite measure of sample variance. These are sizeable in comparison with the sample mean and mean difference so I can tell you now that the difference we see is well within the bounds of sample error.

I stated that 95% confidence intervals would be a wonderful thing for the Met Office to produce so here they are for the HadCET dataset rounded to a lavish three places of decimal:

• June 1976 mean daily temperature = 16.893°C [95CI: 15.602; 18.185]

• June 2023 mean daily temperature = 16.963°C [95CI: 15.890; 18.037]

Do these confidence intervals overlap? Yes they do – by a long margin of chalk. What does this mean? Any differences fall well within the bounds of error and thus the +0.070°C difference in means has no real world meaning.

I can also whip out my stats package and run a paired samples t-test. Herewith the output for the geek readers:

Right in the bottom corner you’ll see a p-value of p=0.931 which tells us that the weeny difference is insignificant.

How Big Is Small?

We’ve arrived at the conclusion that June 1976 was just as hot as June 2023 based on a sample of 60 mean daily temperature readings taken from the HadCET dataset. What would happen if we’d had access to 60,000 mean daily temperature readings? Well, the standard deviation would grow a little but the standard error would shrink to something seriously small, so small in fact that a difference of +0.070°C might be declared statistically significant. Ouch!

With really big samples we could declare differences of +0.0007°C to be statistically significant even though they have no real world meaning. Thus, if the Met Office do decide to run a really big sample analysis they’ll be able to declare teeny weeny standard errors, microscopic confidence intervals and huge statistical significance that means absolutely nothing. There’s a nice paper on this entitled Too Big To Fail: Large Samples and the p-Value Problem that you can obtain from here.

So what does this mean for normal people? I would suggest we start by asking the Met Office and science journalists whether any temperature difference they’ll push under our noses has any real world meaning. If the average UK temperature for June 2023 was even two degrees hotter than June 1976 then would this matter in any way shape or form? I couldn’t go barefoot on tarmac in June 2023 but then again I couldn’t go barefoot on tarmac in 1976. From what I can recall I sweltered just as much back in 1976 and my ice lollies melted just as quickly. The grass was just as brown (in fact browner in 1976) and friends suffered sunstroke just the same.

Now if that extra two degrees was indicative of a global warming trend that had unequivocally set in then we might sit up and take notice. Except such a trend has not unequivocally set in, as one may gather from browsing through my many articles and listening to the words of a fair few censored scientists. In our household this morning there is talk of putting the heating back on – in July! So let’s keep this real and look out of the window for once. June 2023 was hot, and we enjoyed it. June 1976 was hot and we enjoyed it. Back then the same bunch were trying to frighten us into thinking an ice age was coming. Now that is a genuinely frightening prospect given the same bunch are pushing net zero and minimal agriculture. Let us hope for a warmer and less psychotic future.

Kettle On!