Spring 2021 was colder and sunnier than usual in the UK but otherwise unremarkable. However the 3 months of spring were anything but unremarkable.

Meteorologists define spring in the UK to be the period from March to May so spring is now over and we are officially in summer.

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 (CMA) 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 spring 2021, the z-scores for temperature, sunshine and rainfall were respectively -0.8, +1.3 and 0. This tells us that the season was sunnier & colder than usual but not unusually so. Of course that doesn’t mean each month was the same and in fact there was considerable variation between the months with an unremarkable March, an extraordinarily sunny & frosty April & a wet May.

**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 spring climate over the last 130 years of at least 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 1971 to 2020. We can characterise our springs broadly as follows:

- 1900-1925 – we had cool and normal rainfall springs
- 1925-1940 – we had cool, dry and dark springs.
- 1940-1960 – we had sunny, dry and normal temperature springs.
- 1960-1990 – we had cool, dark and normal rainfall springs.
- 1990-today – a clear shift in our climate occurred to warm, sunny and normal rainfall springs.

So spring 2021 was sunny with normal rainfall as per recent trends but it was colder than usual instead of warmer.

**How many dimensions does Spring 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 in line with the correlations seen over history.

Looking at the 3 scatter plots in turn, we see that temperature and rainfall is not correlated but sunshine is positively correlated with temperature and negatively correlated with rainfall. 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 2 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 1.5 dimensions whilst the 2nd component accounts for 1 dimension.

Looking at the correlation bi-plot for spring, we see that the 1st component accounts for temperature and some of sunshine, reflecting the positive correlation we see in the scatter plot above whilst the 2nd component accounts for dryness (**) and some of sunshine again reflecting the negative correlation we see in the scatter plot above. The 90 degree angle between temperature and rainfall reflects the lack of correlation between these two z-scores as we saw above.

*** 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.

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.

- 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

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