The longest continuous regional temperature record in the world is Central England Temperature, a.k.a. CET (data available here). It reports the mean temperature over a large region of central England, giving monthly averages since 1659, daily values starting January 1st, 1772, and both daily high and overnight low temperatures since 1878. It is a combination of thermometer records from several stations in the area, but the earliest estimates are based on less data and of less precision, reflecting the infancy of thermometry (in 1659 there wasn’t yet a modern temperature scale; not until 1724 did we get degrees Fahrenheit, degrees Celsius in 1742).

But from 1772 onward we have over 250 years of daily mean temperature in Central England (mean temperature is the average of the daily high and overnight low). Graphing the values doesn’t show much, other than the fact that it varies a lot, from -11.9°C (10.6°F) to +28.1°C (82.6°F):

If we zoom in the time axis to focus on the data since the year 2000, we see the annual up-and-down fluctuation of a seasonal cycle:

This is even clearer when we plot temperature, not by time, but by day of the year:

This motivates us to perform what is often the first important step in analyzing climate data: transforming raw values (in this case, daily mean temperature) to anomaly values, the difference between the value and what it would have been at the same time of year according to the average seasonal cycle. That estimate of the seasonal cycle is called climatology, and is based on a time span chosen to serve as a baseline period (usually at least 30 years long). The data during the baseline defines the average seasonal cycle.

I’ll choose the 128-year time span from 1772 through 1899 as my baseline, so that climatology will represent the average temperature prior to the year 1900. During the baseline period the average anomaly value will be zero, so with this choice of baseline period, anomalies represent how much hotter or colder temperature is than its pre-1900 average for the given time of year — an estimate of how much the region has warmed “since pre-industrial.” Computing anomalies that way, I get this:

Daily anomaly values range from -14.93°C (-26.87°F) to +12.10°C (21.78°F). Although their variation is considerably less than that of temperatures, the graph still looks like a random scatter of anomalies over the last two and a half centuries.

Now we’ll apply what is often the second important step in analyzing climate data: averaging anomalies over periods of time longer than a single day. In many situations, doing so reduces the level of random fluctuation more than it smears out the underlying trend. Averaging over each year results in 254 annual averages (although the current year is not yet complete) and gives this:

Now we see visible signs of a trend over time, with temperature on the rise recently and especially this last (incomplete) year. Of course “visible signs” aren’t statistical proof, but they are indispensable clues, which become even clearer when we push the time scale to 10-year averages, and add “error bars” to show the (95% likely) range of natural variation over each 10-year period:

In Central England, the last few decades have been extra hot.

More than that, it reveals an interesting pattern of how temperature has changed in Central England. From 1772 to the early 1900s, it fluctuated but showed no discernable trend pattern, as indicated by the fact that every decade up to the 1920s includes zero in its confidence interval; the fluctuations are plausibly due to natural variation. But in the rest of the first half of the 20th century, average temperature increased, only slightly but with statistical significance. It leveled off to start the second half of the 20th century, but since the 1980s Central England has warmed dramatically faster than seen before in the historical record. The most recent value (for the as-yet-unfinished decade of the 2020s) can only be described as “alarming.”

Let’s push the idea even farther, averaging over 30-year periods:

This shows the time evolution about as clearly as one could hope. But it is worth noting that in the very first 30-year period, from 1770 to 1800, the data don’t start until 1772 so the 1st average only has 28 years’ data, and the last average is also incomplete with only 17 years’ data. This is because we started our first episode at 1770 (a multiple of 30); a different choice would yield slightly different averages (but the same evolutionary pattern).

We can use all possible starting values; essentially, we take every possible 30-year period and compute its average, then use that average as our estimated trend value as the midpoint of that 30-year time span. The (30-year) averaging interval advances by one time step, until we have an estimate for every possible uninterrupted 30-year time period. Such values are called running means, and with a 30-year time scale they look like this (running mean as a blue line, original yearly averages as gray dots):

Running means gives a statistically simple picture of the underlying trend, but does have some drawbacks. For one thing, it shows quick fluctuations from moment to moment which are probably not representative of genuine trend. For another thing, the values don’t extend all the way from start to finish of the underlying data; we lose half a time span (= half of 30 years) at the beginning and end of the time series.

We can improve things by using a fancy-math estimate of the underlying trend which is tuned to the same time scale as our 30-year running means. I prefer a modified lowess smooth, which gives me this:

I can use the lowess smooth to estimate the uncertainty (i.e. 95% likely range of natural variation) for my smooth signal, and when I plot it along with the 30-year running means it shows just how similar the two analyses are (during the times covered by both):

This enables us to identify the genuine trend in climate change at Central England from 1772 to the present. For the first 130 years or so, temperatures varied only slightly, and only as much as one would expect from natural variation. Hence there isn’t really any evidence of climate change during this period. After about 1910, however, CET rose to levels warmet than can be attributed to natural variation. There is a possible slight decline from about 1945 to 1975, but since then temperature has risen at a truly dramatic pace.

The important message from CET is that the warming we’ve seen in the last several decades is a new phenomenon. Since the early 1900s, greenhouse gases have accumulated to sizeable levels in our atmosphere. Before that time, temperature fluctuated (as it always will) but showed no discernible trend. Since the early 1900s the trend is obvious and lately, it’s extreme.

Something that surprises me (at least a little) is how similar this pattern is to the global temperature trend over the same time period:

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