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 have decided to create a series of posts which I will publish at the end of each season showing how that season compares to the weather record. The 2017 summer was wet but unremarkable otherwise and actually quite typical of recent summers as I will explain.
Analysis of trends is a key skill that all statisticians and analysts need to have. Indeed I run a training course on Identifying Trends & Making Forecasts as I have learned over my 25 years as a professional statistician that skills in this area are nowhere near where they should be. By publishing this series of posts about trends in weather and other fields, I hope you will learn something you will be able to apply elsewhere.
As my weather tracker series shows, weather cannot be thought of as a univariate data set. We define weather as a combination of temperature, sunshine and rainfall which makes weather a multivariate data set. There are many ways of displaying multivariate data but one of the first questions that has to be asked is how do we compare 3 variables that use 3 different numerical scales i.e. degrees Celsius, hours and millimetres? The answer is to convert the scales of all 3 variables into a new common scale using a procedure known as STANDARDISATION. The resulting standardised variables are often called Z-SCORES.
Standardisation works as follows. For each year within each variable, we first subtract the average for that variable to get the difference from the average. Then we divide by the standard deviation of that variable. For example, if the average summer temperature over the last 50 years is 14.3 degrees Celsius and the standard deviation is 0.8 degrees Celsius, then the STANDARDISED summer temperature for 2017 will be +0.6 since the actual average 24 hour UK summer temperature in 2017 was 14.7 degrees Celsius so (14.7 – 14.3)/0.8 = +0.6.
Before calculating the z-scores for all weather variables, a decision needs to be made over what timeframe should the average and standard deviation be based on. I have decided to go with a rolling 50-year average and standard deviation so since we are in 2017, these values will be calculated on the 1967 to 2016 timeframe. My reason for using this timeframe is that it seems like a good timeframe for the concept of “living memory” i.e. we evaluate the most recent weather in terms of our experience & memory and being a child of the 70’s I can still remember some of the weather of the late 70’s.
Notice that by dividing by the standard deviation, we convert the scale of any variable to a scale which measures the variable as Number of Standard Deviations Above/Below the Mean value. So summer 2017 was almost 0.6 standard deviations above the average. If you are familiar with the properties of the Normal Distribution, you will know that if your variable follows a normal distribution, then 95% of the data points will lie within +/- 2 standard deviations of the mean and 5% of the data points will lie without +/- 2 standard deviations of the mean. So our +0.6 for the STANDARDISED summer temperature for 2017 does suggest that 2017 was typical for a British summer as this is close to 0 which equates to the average.
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. What is interesting about the chart above is that summers over the last 25 years appear to have been warmer than the previous 80 years. Prior to the famous hot summers of 1975 & 1976, the z-scores were mostly negative showing that summers were cooler than the baseline average. By adding an 11-year centred moving average (shown by the black line), we can see that this has indeed been the case.
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 a CONTROL CHART).
I said earlier that if we have multivariate data sets then standardising variables allows us to compare multiple variables of differing scales. The next two charts show the z-scores for summer sunshine and rainfall in the UK.
The z-score for summer sunshine in 2017 was -0.2 so this is pretty much average. The z-score for rainfall was +1.5 and was the 9th wettest summer on record which puts summer 2017 in the top decile. Those who have been following my monthly UK weather tracker will know that June was very hot and stormy and this was responsible for the above average rainfall. When we combine these two values with +0.6 for temperature, I think it is fair to conclude that summer 2017 was wetter than normal but unremarkable otherwise.
Additionally, since I have standardised the 3 weather variables and calculated centred moving averages to measure the underlying trends, I can now put the 3 standardised moving averages onto the same chart.
Such a chart allows us to characterise British summers over the last 100 years. My characterisation would be as follows.
- 1910-1970 – we had cold wet summers with a brief interlude in the late 30s when summers were normal.
- 1971-1992 – we had cool dry summers.
- 1993-2002 – we had warm dry & bright summers.
- 2003-today – we are in a period of warm wet summers.
In general, my characterisation is driven by rainfall and temperature. Sunshine has been much more stable over time. Using my characterisation, we can reinterpret 2017 as a normal summer for the current phase of our summers. How long this will last and what the next phase will look like is hard to tell.