The 2023 calendar year was the 2nd hottest year on record in the UK just behind the hottest year ever in 2022. Last year, I showed how a technique known as a **Control Chart **could be used to decide if the UK is now in a new warming trend and after adding 2023, my answer is now “*a step change upwards has taken place but the pace of change is not yet clear*“.

**UK Annual Average 24-Hour Temperatures**

In 2022, the annual average 24-hour temperatures across the whole of the UK exceeded **10** degrees Celsius for the first time ever and 2023 was fractionally under **10** degrees Celsius.

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 (not the meteorological year of December to November) 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 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 in the 21st century but with signs of renewed warming.

In particular I note the 11 year CMA hit a trough in 1982 at **8.18** degrees and a peak in 2002 at **9.35** degrees. The 2002 peak has now been exceeded with the latest CMA (covering 2013 to 2023) now at **9.49 **degrees. This does not definitively mean a new upward trend like that seen in the 80s/90s has begun because we can see similar false alarms in previous years (e.g. early 70s). So is there a way to decide with more certainty as to when a new trend has begun?

**Detecting New Trends**

Before we can decide if a new trends has begun, we need to identify the current trends. When I look at the chart above, I would characterise the late 80s/90s period as a **Step Change** between two time periods that were relatively flat before and after the step change. Given the 1982 CMA covers the years 1977-1987 and the 2002 CMA covers the years 1997-2007, I regard the step change period to be the 9 years from 1988 to 1996. I will ignore these years going forward and compare the following two time periods.

**Era B**= Before =**1913 to 1987**: Sample size**n1**=**75**, Mean =**m1**=**8.32**, Std Deviation =**s1**=**0.43****Era A**= After =**1997 to 2021**: Sample size**n2**=**25**, Mean =**m2**=**9.27,**Std Deviation =**s2**=**0.40**

The choice of the number of years in era B is an arbitrary 3 times the number of years in era A. Notice I’ve left out 2022 & 2023 from the After era because I am trying to see if they are exceptional relative to the first 25 years of this era. Before I do that, I will note that a simple 2-sample t-test of the difference between the means **m2** & **m1** of eras A & B results in a t-statistic of **9.36** (p-value 0.000) which is overwhelming evidence of a significant step change taking place between the two eras.

The method I will use to evaluate 2022 & 2023 comes from a field of statistics known as **SPC** (**Statistical Process Control**) and is known as the **Control Chart**. A control chart can be used if the following conditions are satisfied –

- The data used to build the control chart has no discernable trend
- The data used follows a symmetrical single peak (preferably normal) distribution
- Each year is IID (Identically Independently Distributed) i.e. the value of next year does not depend on the previous year.

These conditions are satisfied for the 25 years of the After era A. If you would like to know more about why I can I say this, then please book a place on my training course “** Identifying Trends & Making Forecasts**” which will cover all of the points raised in this article in more depth.

**A Control Chart for UK Annual Temperatures**

The control chart for the After era is shown below. The purple dots are the actual years with 2022 & 2023 shown as large squares to indicate those years were not used to calculate the control limits (the 5 brown lines). The 5 control lines (from top to bottom) are calculated as follows using standard SPC rules –

**UCL3**= Upper Action Limit =**10.46**=**m2**+ 3***s2****UCL2**= Upper Warning Limit =**10.07**=**m2**+ 2***s2****Target**= Long Term Average =**9.27**=**m2****LCL2**= Lower Warning Limit =**8.47**=**m2**– 2***s2****LCL3**= Lower Action Limit =**8.07**=**m2**– 3***s3**

The average temperatures in 2022 & 2023 were **10.03 **and **9.97** degrees Celsius respectively which are just below the Upper Warning Limit (UCL2) of **10.07**. Standard SPC rules (but there are many variants) would consider the following outcomes for 2022 and any future 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**). Including 2022, we have had**7**years in a row above the target so if 2023 is also above target that would indicate at least a step change upwards. - 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?**

Last year, I stated in advance when I would answer this question in the affirmative –

- “
*Whilst 2022 did not quite reach UCL2, if 2023 is a repeat of 2022, I would take that as an indication of change.*“ - “
*…if the annual average ends up greater than the target value of***9.27**, I would take that as an indication that a step change up has taken place.”

The second condition has been satisfied and so under SPC rule 4, I now conclude a step change upwards in UK temperature has taken place. The first condition has been satisfied in the spirit of SPC rule 2 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?

**Compare my article with the BBC’s!**

The BBC has published an article on the exact same topic here. This is an opportunity for you to compare my article with the BBC and to let me know which one you think is better. I would be grateful if you could spare the time to give me feedback on which one you think is the better article and why.

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.