Meteorologists define autumn in the UK to be the period from September to November so autumn is now over and we are officially in winter. The 2018 autumn was consistent with the step change in the autumnal climate that took place in the 1990s.

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 autumn of 2018, the z-scores for temperature, sunshine and rainfall were respectively +0.4, +1.5 and +0.1. This tells us that temperatures and rainfall were unremarkable whilst it was a sunny autumn, in fact the 5th 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 autumnal 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 1968 to 2017. We can characterise our autumns broadly as follows:

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

**How many dimensions does Autumn 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 2018. Scatter plots can be useful to identify unusual years that do not follow the normal relationships. Here we see that 2018 was completely consistent with historical scatters.

Looking at the 3 scatter plots in turn, we see that the 3 weather variables show little correlation with each other. For spring & summer, I have said that a statistician would look at the equivalent charts for those seasons 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 or 1-dimensional. If the variables were correlated with each other, it would be possible to create Components using a weighted average of these 3 z-scores, 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. These 3 components would also have the property that the first component would account for the greatest possible share of the total 3-dimensional variance and thereby reducing the effective dimensionality of the data to 2 or even 1 dimension.

When I carried out PCA for summer data, I was able to obtain a 1st principal component which accounted for 76% of the total 3-dimensional variance. In other words, our summer weather is effectively 1-dimensional. This is not the case for our autumns as shown by the scree plot here. If the 3 weather variables were completely uncorrelated with each other, then each variable should account for 1/3 of the total 3-dimensional variance or 1 dimension. Our scree plot shows that autumnal weather is not far off that outcome. PC1 accounts for 44% of the total variance, PC2 accounts for 33% and PC3 accounts for the balance of 23%. Given the lack of correlation seen in the scatter plots this is not a surprise.

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.