The 2024 calendar year was the 4th hottest year on record in the UK. Last year, I used a Control Chart to conclude “a step change upwards (in UK temperatures) has taken place but the pace of change is not yet clear“. I am now less confident in my conclusion after updating with 2024 data, especially when I look at temperature trends based on the meteorological year of December to November instead.
Learn how to decide if a trend has changed
This is the third article I have written about trends in UK annual temperatures. My goal is to create a useful series for anyone who wants to learn how to use statistical thinking and methods to detect changes in trends for any time series. If this topic is new to you, I recommend you read the series from the beginning before continuing with this article.
- 2022 – I explain what a Control Chart is which is a technique arising out of the field of Statistical Process Control. I calculate the Control Limits for the control chart using the years 1997 to 2021 and I explain why I use just those years based on an 11 year Centred Moving Average (CMA). When I plot 2022 data on the control chart, I decide there is not enough evidence to conclude the trend has changed.
- 2023 – I update my control chart with 2023 data but I do not change the control limits used in the chart which continue to be based on the years 1997 to 2021. I now conclude “a step change upwards has taken place but the pace of change is not yet clear.”
- 2024 (this article) – I update my control with 2024 data which continues to use control limits based on the years 1997 to 2021. I build another control chart using meteorological year (December to November) data instead to see if my conclusions change as a result of changing the definition of a year. I also discuss another method of detecting trend changes known as CUSUM.
Detecting changes in trends is one of the topics I cover in my training course “Identifying Trends & Making Forecasts“. I also run this course on behalf of the Royal Statistical Society and you can book a place on their next course here.
UK Annual Average 24-Hour Temperatures – Calendar Year
In 2024, the average 24-hour temperature across the whole of the United Kingdom from 1st January to 31st December was 9.78 degrees Celsius. This is the 4th highest on record, exceeded by the years 2014 (9.88 degrees), 2023 (9.97 degrees) and 2022 (10.03 degrees).
All temperature data shown in the chart below can be downloaded from the Met Office. I plot the UK annual average temperature for the calendar years going back to 1884 as purple dots. The solid black line is the 11 year Centred Moving Average (CMA) which is intended to represent the underlying trend. The latest CMA is for 2019 covering the years 2014 to 2024 and was 9.58 degrees Celsius, the highest on record.
The 11 year CMA shows the following –
- Warming at the end of the 19th century.
- Static temperatures up to the end of the 1920s.
- A slight warming in the 30s and 40s.
- A cooling back 1920s levels in the 50s & 60s.
- Erratic temperatures in the 70s & early 80s.
- A sustained rapid warming beginning in the mid 80s that carried on through the 90s.
- Essentially flat for the first 15 years of the 21st century.
- An upward trend over the last 10 years, a trend we are trying to verify in this article.
Control Chart for UK Annual Temperatures – Calendar Year
The control chart for the period 1997 to 2024 is shown below. The years 2022 to 2024 are shown as large squares instead of circles to indicate those years were not used to calculate the control limits (the 5 brown lines). From top to bottom, the values of these, based on standard SPC rules which I first described in 2022, are as follows –
- UCL3 = Upper Action Limit = 10.46
- UCL2 = Upper Warning Limit = 10.07
- Target = Long Term Average = 9.27
- LCL2 = Lower Warning Limit = 8.47
- LCL3 = Lower Action Limit = 8.07
Standard SPC rules consider the following outcomes for any year as a significant indicator that something has changed –
- If a year lies outside either the lower (LCL3) or upper (UCL3) action limits. Such changes can be one off Blips as happened in 2010.
- If 2 successive years lie above the upper warning limit (UCL2).
- If 2 successive years lie below the lower warning limit (LCL2). Mirror image of above.
- If 8 successive years lie above the target value (Target).
- If 8 successive years lie below the target value (Target). Mirror image of above.
SPC rules are not cast in stone and there are many variants. However, they do offer a fairly robust method of detecting changes which are widely used in many industries.
Has a new warming trend begun?
Here’s what I stated after 2023.
“… under SPC rule 4 (8 successive years above the target value), I now conclude a step change upwards in UK temperature has taken place. … the spirit of SPC rule 2 (has also been satisfied) and if I combine this with the 11 year centred moving average reaching new highs, I think this reinforces the conclusion of a step change. What is not yet clear is the pace of change and the now is will our climate warm as rapidly as it did in the 80s & 90s or will it be more sedate?”
On reflection, I want to withdraw the part about rule 2 being satisfied in spirit and confine myself to rule 4. 2024 is the 9th year in a row where the calendar year average was above the target value so I continue to be satisfied that a step change upwards has taken place. What step changes don’t tell us is the pace and extent of changes.
UK Annual Average 24-Hour Temperatures – Meteorological Year
The main reason I withdraw the part about rule 2 being satisfied in spirit is because I decided to spend some time looking at the data by the meteorological year as well which runs from December to November. This is achieved by shifting December data into the following year e.g. December 2024 is part of the 2025 meteorological year. By doing what appears to be a minor change, if my interpretation of the control chart is different, it is a sign that what I see is more likely to be a mirage than a true signal of trend change.
In 2024, the average 24-hour temperature across the whole of the United Kingdom from 1st December 2023 to 3oth November 2024 was 9.73 degrees Celsius. This is the 3rd highest on record, exceeded by the years 2014 (9.97 degrees) and 2022 (10.20 degrees).
The overall history in this chart is no different from what is shown in the same chart for the calendar year. The 11 year CMA as of 2019 is 9.58 degrees Celsius, the highest on record.
Control Chart for UK Annual Temperatures – Meteorological Year
The control chart for the period 1997 to 2024 is shown below with these control limits. The numbers in brackets show the difference from the control limits based on calendar years.
- UCL3 = Upper Action Limit = 10.38 (-0.08)
- UCL2 = Upper Warning Limit = 10.00 (-0.07)
- Target = Long Term Average = 9.23 (-0.04)
- LCL2 = Lower Warning Limit = 8.46 (-0.01)
- LCL3 = Lower Action Limit = 8.08 (+0.01)
Using meteorological years, rule 2 is nowhere close to being satisfied in spirit. In fact, rule 4 is not satisfied either because 2021 is just below the target value.
Overall we are left with an 11 year CMA at new highs and apparently on an upward trend. We have evidence of a step change under rule 8 for calendar years but not quite for meteorological years. Taken together it feels like I can conclude the UK is in a warmer phase but are there other methods of trend change detection that could help confirm or refute this feeling of mine?
Does CUSUM confirm a trend change?
The CUSUM approach is not one I use much in my professional life but I want to demonstrate it here because it is considered part of the SPC toolbox.
The CUSUM chart below (based on meteorological year data) plots two separate Cumulative Sums, Sh to detect upward trends and Sl to detect downward trends. If Sh exceeds +4, that is usually taken as a signal that the trend has turned upwards, if Sl is below -4, that is usually taken as a signal that a downward trend has begun. Some people prefer to use thresholds of +5 and -5 but I will use +4/-4 for now.
As of 2024, Sl is 0 and Sh is +3.7. On this basis, there is again insufficient evidence to confirm an upward trend! If I use calendar year’s data instead, Sh would be +3.5 and I would come to the same conclusion.
How are Sh and Sl calculated?
CUSUM uses Z-Scores. If you follow my seasonal trends blogs (link to these at the bottom of this article), you will be familiar with z-scores. A Z-Score is a recalculation of a year’s value by subtracting an average and dividing by a standard deviation. For meteorological year data, the mean is 9.27 degrees and the standard deviation is 0.40 degrees.
Both Sh and Sl are cumulative z-scores over the years but with a couple of twists. The first twist is the cumulative z-score is never below zero for Sh and never above zero for Sl. That is why in the chart above, Sl appears as brown bars below zero and Sh as purple bars above zero. The second twist is how the z-score for each year is added to the cumulative z-score from the previous year –
- For Sh, the CUSUM increases by the z-score of the current year minus a predefined positive number K (sometimes called a “tuning” constant). For example if K is +0.5 and the latest Z-score +0.7, then Sh goes up by only 0.2 (= 0.7 – 0.5) whereas if the latest z-score is -0.7 then Sh goes up by –1.2 since -1.2 = -0.7 – 0.5. Bear in mind though Sh can never be less than zero so if in fact Sh in the previous year was +1 then if this scenario unfolds, Sh falls by 1 instead of 1.2.
- For Sl, the CUSUM decreases by the z-score of the current year plus a predefined positive number K (sometimes called a “tuning” constant). For example if K is +0.5 and the latest Z-score -0.7, then Sl goes down by 0.2 (= –0.7 + 0.5) whereas if the latest z-score is +0.7 then Sl goes down by –1.2 since +0.7 + 0.5 = +1.2. Bear in mind though Sl can never be greater than zero so if in fact Sl in the previous year was -1 then if this scenario unfolds, Sl increases by 1 instead of 1.2.
In the chart I showed above, I did indeed “tune” this with K set to 0.5. This was an arbitrary choice on my part but I consider it a reasonable starting point.
What will it take for CUSUM to signal a trend change?
Sh in 2024 is +3.7 for meteorological years and +3.5 for calendar years. For both to exceed 4 in 2025, it is possible to work backwards to calculate what the 2025 annual average would need to be for this to happen. It turns out that if the calendar year average is greater than 9.48 degrees Celsius and the meteorological year average is greater than 9.33 degrees Celsius then Sh will be greater than 4 and signal an upwards trend change.
If you want to read my other Weather Trends posts, please click on the link or the Weather Trends hashtag below this post. Otherwise, please click the relevant season from the list below.
- 2024 – Winter, Spring, Summer, Autumn
- 2023 – Winter, Spring, Summer, Autumn, Annual
- 2022 – Winter, Spring, Summer, Autumn, Annual
- 2021 – Winter, Spring, Summer, Autumn
- 2020 – Winter, Spring, Summer, Autumn
- 2019 – Winter, Spring, Summer, Autumn
- 2018 – Winter, Spring, Summer, Autumn
- 2017 – Winter, Spring, Summer, Autumn