The 2018 autumn was consistent with the step change in the autumnal climate that took place in the 1990s.

Meteorologists define winter in the UK to be the period from December to February so winter is now over and we are officially in spring.

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 winter of 2019, the z-scores for temperature, sunshine and rainfall were respectively +1.2, +1.9 and -0.9. This tells us that temperatures and rainfall were unremarkable but it was a very sunny winter, in fact the 6th sunniest on record.

**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 winter climate over the last 100 years of roughly 1 standard deviation in some cases. 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 1969 to 2018. We can characterise our winters broadly as follows:

- 1930-1990 – we had cold, dull and dryer winters.
- 1995-today – we had warm, bright and wetter winters.

This is more or less the same long term trend seen for our autumns.

**How many dimensions does Winter 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 2019. Scatter plots can be useful to identify unusual years that do not follow the normal relationships. Here we see that 2019 was on the edge of typical historical scatters e.g. it was sunny, warm and dry which is somewhat unusual.

Looking at the 3 scatter plots in turn, we see that sunshine is not correlated with rainfall and temperature but rainfall and temperature have a significant positive correlation. 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 since temperature and rainfall are essentially two aspects of the same component. 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 now, we see that the 1st component accounts for temperature and rainfall, reflecting the correlation we see in the scatter plot above. At the same time, the second component is just sunshine. The 90 degree angle between sunshine and the other two variables is again a reflection of the lack of correlation between this and temperature and rainfall as we saw above. This makes winter one of the cleanest seasons to use PCA and if we wanted to, we could just as easily average the z-scores for temperature and rainfall for the 1st component.

For more information about Principal Components Analysis, please visit my link about training materials for multivariate analysis.

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.