The UK summer in 2021 was warmer and dryer than normal but when looked at using principal components, the summer cannot be defined as a good one. I am not expecting 2022 to be a good one either!

Meteorologists define summer in the UK to be the period from June to August so summer is now over and we are officially in autumn.

I analyse the long term trends in the UK weather using a statistical tool known as **Standardisation**. This means that the 3 key variables of Temperature, Sunshine and Rainfall are recalculated so that they all have the same units, which is number of standard deviations above or below the mean. Such variables are known as **Z-Scores** which by definition will have a mean value of 0 and a standard deviation of 1. For more information on how I have done this, please read my post on trends in the UK summer of 2017.

**Latest Z-Scores**

The Z-Scores for Temperature, Sunshine and Rainfall are shown in the 3 charts below. Each chart also contains an 11-year centred moving average which gives an idea of the underlying trend.

Standardised variables aid interpretation of data in many ways. If the standardised value is positive, it means that the value is above your average or expected value. If it is negative, then the value is below your expected value. If the original variable is approximately normal in its distribution then the vertical scale gives us an idea of how typical or atypical each year is. Z-Scores in the range -1 to +1 are considered typical values and completely unremarkable. Z-scores in the ranges -2 to -1 and +1 to +2 are considered to be uncommon values but still entirely plausible and such values should not cause us concern. When Z-Scores get into the ranges -3 to -2 and +2 to +3, we should start paying closer attention and asking ourselves if something has changed especially if we get a sequence of successive points in these ranges. Finally, if the Z-scores are less than -3 or greater than +3, that is normally regarded as a clear call to action. There are in fact many ways of interpreting Z-Scores and what I have said so far merely a gives an overview of the most basic interpretations. A whole field of study known as Statistical Process Control (SPC) is dedicated to building and interpreting such charts (known as Control Charts).

For the summer of 2021, the z-scores for temperature, sunshine and rainfall were respectively +1.2, 0 and -1.0. This tells us that whilst the season was above average on temperature and below average on rainfall, it was not unusual.

**Long Term Climate Trends**

Since the 3 moving averages in the above 3 charts all use the same units, they can be plotted onto the same chart as below.

This clearly shows a shift in our summer climate over the last 100 years of roughly 1 standard deviation. Recall that the baseline for the z-score calculation is based on the idea of “living memory” which I have defined to be the last 50 years of 1970 to 2019. We can characterise our summers broadly as follows:

- 1915-1970 – we had cold and damp summers.
- 1970-1995 – we had dryer and almost normal temperature summers.
- 1995-today – a clear shift in our climate occurred to warm and wet summers.

2021 is consistent with the recent climate period in terms of sunshine and temperature but the dryness was somewhat unusual.

**How many dimensions does summer have?**

The long term trends chart above suggests that the z-scores for temperature, sunshine and rainfall all appear to be correlated. In fact this can be illusory as the above chart uses moving averages. If we look at the actual z-scores, we can see what the correlations are in the 3 scatter plots below.

The brown square in each chart is 2021. Scatter plots can be useful to identify unusual years that do not follow the normal relationships. Here we see that 2021 was on the edge of typical historical scatter in the temperature v sunshine plot and broadly in line with the normal scatter in the other 2 plots. In other words, relative to the amount of rain & sun we had, it was warmer than usual.

When we examine the 3 scatter plots, we see that all 3 variables are correlated with each other. A statistician would look at these charts and observe that what appears to be 3-dimensional data (temperature, sunshine and rainfall being the 3 dimensions) is in fact closer to be being 1 dimensional. By using the method of PCA (Principal Components Analysis) which takes our 3-dimensional data set and calculates 3 new components that are statistically uncorrelated with each other, we see from the scree plot that the 1st component accounts for 2.25 dimensions whilst the 2nd component accounts for 0.5 dimension.

*** In the bi-plots below, rainfall has been replaced with dryness (= -1 x rainfall z-score) in spring, summer & autumn whilst winter retains rainfall. This is to aid visualisation of the biplots in terms of how the correlations change over the year. Had I used rainfall in all plots, then in the 3 seasons mentioned, the rainfall label would be on the opposite side of the circles shown.*

For more information about Principal Components Analysis, please visit my link about training materials for multivariate analysis. and read the information in section A.

Summer is the only season where the weather is effectively one dimensional and the 1st principal component, which is basically an average of the 3 z-scores, can be thought of as a measure of how “nice” our summer was. It is worth plotting the 1st principal component over time and in 2018, I showed that good summers in the UK appear to repeat every 6 to 8 years. Since 2018 was the good summer, I found it easy to predict that 2021 would not be a good summer. It was an above average summer but I define a good summer to be one were the 1st component has a score greater than 2 whereas 2021 was +1.4. I am therefore not expecting 2022 to be good either.

I remarked earlier that it was dryer than might be expected given the temperatures we had this summer. That shows up more strongly in the chart of the 2nd principal component below. Bear in mind that the scree plot shows this component is much less important than the 1st component but the consistently negative values we’ve had since 1995 reflects the changing climate of our summers. The bi-plot shows that this component is effectively the difference between the dryness & temperature and when it’s strongly negative it’s because the summer has been both warmer and wetter than normal. However, in 2021 the score returned to zero which differs from recent trends.

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.