<\/p>\n
Latest Z-Scores<\/strong><\/span><\/h4>\nThe Z-Scores for Temperature, Sunshine and Rainfall are shown in the 3 charts below.\u00a0 Each chart also contains an 11-year centred moving average which gives an idea of the underlying trend.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2023\/03\/UKweatherTracker2023WIN1.png\")
<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2023\/03\/UKweatherTracker2023WIN2.png\")
<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2023\/03\/UKweatherTracker2023WIN3.png\")
<\/p>\n
Standardised variables aid interpretation of data in many ways.\u00a0 If the standardised value is positive, it means that the value is above your average or expected value.\u00a0 If it is negative, then the value is below your expected value. \u00a0If 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.\u00a0 Z-Scores in the range -1<\/strong><\/span> to +1<\/strong> are considered typical values and completely unremarkable.\u00a0 Z-scores in the ranges -2<\/strong><\/span> to -1<\/strong><\/span> and +1<\/strong> to +2<\/strong> are considered to be uncommon values but still entirely plausible and such values should not cause us concern.\u00a0 When Z-Scores get into the ranges -3<\/strong><\/span> to -2<\/strong><\/span> and +2<\/strong> to +3<\/strong>, 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<\/span> <\/strong>or greater than +3<\/strong>, that is normally regarded as a clear call to action.\u00a0\u00a0There are in fact many ways of interpreting Z-Scores and\u00a0what I have said so far\u00a0merely a gives an overview of the most basic interpretations.\u00a0 A whole field of study known as Statistical Process Control (SPC) <\/a>is dedicated to building and interpreting such charts (known as Control Charts).<\/p>\nFor the winter of 2023, the z-scores for temperature, sunshine and rainfall were respectively +0.4<\/strong><\/span>, +1.7<\/strong> <\/span>and -0.7<\/strong><\/span>.\u00a0 This tells us that the season was notably sunnier than the baseline whilst temperature was slightly above and rainfall slightly below the baseline.<\/span><\/p>\n <\/p>\n
Long Term Climate Trends<\/strong><\/span><\/h4>\nSince the 3 moving averages in the above 3 charts all use the same units, they can be plotted onto the same chart as below.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2023\/03\/UKweatherTracker2023WIN4.png\")
<\/p>\n
This clearly shows a shift in our winter climate over the last 100 years of 1.5 standard deviations for all 3 variables.\u00a0 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 1972 to 2021. \u00a0 We can characterise our winters broadly as follows:<\/p>\n
\n- 1930-1990 – we had cold, dull and dryer winters.<\/li>\n
- 1995-today – we had warm, bright and wetter winters.<\/li>\n<\/ul>\n
This is more or less the same long term trend seen for our autumns<\/a>.\u00a0 Clearly the 2023 winter is entirely consistent with the recent climate period.<\/p>\nHowever I am wondering I should reclassify the era 1995-2015 as bright but with normal temperature and rainfall.\u00a0 The last couple of years now seem to be pointing to a new era of warm, wet & bright winters.<\/p>\n
It’s also worth noting that the step change in our climate that we’ve seen over the last 30 years has been most pronounced in the winter.\u00a0 All seasons are now about 1 standard deviation warmer but winter has the largest standard deviation of all seasons and has seen increases closer to 1.5 standard deviations.<\/p>\n
<\/p>\n
How many dimensions does Winter have?<\/strong><\/span><\/h4>\nThe long term trends chart above suggests that the z-scores for temperature, sunshine and rainfall all appear to be correlated.\u00a0 In fact this can be illusory as the above chart uses moving averages.\u00a0 If we look at the actual z-scores, we can see what the actual correlations are in the 3 scatter plots below.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2023\/03\/UKweatherTracker2023WIN5.png\")
<\/p>\n
The brown square in each chart is 2023.\u00a0 Scatter plots can be useful to identify unusual years that do not follow the normal relationships.\u00a0 Here we see 2023 was consistent with the correlations seen over history.<\/p>\n
Looking at the 3 scatter plots in turn, we see sunshine is not correlated with rainfall and temperature but rainfall and temperature have a significant positive correlation.\u00a0 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.\u00a0 By using the method of PCA (Principal Components Analysis)<\/a> 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 below the 1st component accounts for 1.5 dimensions whilst the 2nd component accounts for 1 dimension.<\/p>\n![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2021\/06\/PCA_Screes-1024x200.png\")
<\/p>\n
** In the bi-plots below, rainfall has been replaced with dryness (= -1 x rainfall z-score) in spring, summer & autumn whilst winter retains rainfall.\u00a0 This is to aid visualisation of the biplots in terms of how the correlations change over the year.\u00a0 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.<\/em><\/span><\/p>\n![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2021\/06\/PCA_BiPLots3.png\")
<\/p>\n
Looking at the correlation bi-plot now, we see the 1st component accounts for temperature and rainfall, reflecting the correlation we see in the scatter plot above.\u00a0 At the same time, the second component is just sunshine.\u00a0 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.\u00a0 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.<\/p>\n
Once you have calculated your components, you can then plot these over time.\u00a0 I find these components over time to be more meaningful of the long term trends in our weather.\u00a0 In the chart below, I have flagged the years where the z-score exceeded +1.5 or -1.5.\u00a0 Ten years are highlighted and these are our notable winters.\u00a0 It is quite striking that the 1st 4 notable winters are all cold & dry winters and the last 6 are all warm and wet winters starting in 1990.\u00a0 This reinforces the long term trend observations I made about our winters earlier.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2023\/03\/UKweatherTracker2023WIN6.png\")
<\/p>\n
For more information about Principal Components Analysis, please visit my link about training materials for multivariate analysis<\/a>. and read the information in section A.<\/p>\n
\nIf you want to read my other Weather Trends posts<\/a>, please click on the link or the Weather Trends<\/a> hashtag below this post.\u00a0 Otherwise, please click the relevant season from the list below.<\/p>\n\n- 2023 – Winter, Spring, Summer, Autumn<\/em><\/li>\n
- 2022 – Winter<\/a>, Spring<\/a>, Summer<\/a>, Autumn<\/a><\/li>\n
- 2021 – Winter<\/a>, Spring<\/a>, Summer<\/a>, Autumn<\/a><\/li>\n
- 2020 – Winter<\/a>, Spring<\/a>, <\/em>Summer<\/a>, <\/em>Autumn<\/a><\/li>\n
- 2019 – Winter<\/a>, <\/em>Spring<\/a>, <\/em>Summer<\/a>, <\/em>Autumn<\/a><\/li>\n
- 2018 – Winter<\/a>, Spring<\/a>, <\/em>Summer<\/a>, <\/em>Autumn<\/a><\/li>\n
- 2017 – Winter<\/em>, Spring<\/a>, Summer<\/a>, Autumn<\/a><\/li>\n<\/ul>\n
<\/p>\n<\/p>\n<\/p>\nFor the winter of 2023, the z-scores for temperature, sunshine and rainfall were respectively +0.4<\/strong><\/span>, +1.7<\/strong> <\/span>and -0.7<\/strong><\/span>.\u00a0 This tells us that the season was notably sunnier than the baseline whilst temperature was slightly above and rainfall slightly below the baseline.<\/span><\/p>\n <\/p>\n 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.<\/p>\n This clearly shows a shift in our winter climate over the last 100 years of 1.5 standard deviations for all 3 variables.\u00a0 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 1972 to 2021. \u00a0 We can characterise our winters broadly as follows:<\/p>\n This is more or less the same long term trend seen for our autumns<\/a>.\u00a0 Clearly the 2023 winter is entirely consistent with the recent climate period.<\/p>\n However I am wondering I should reclassify the era 1995-2015 as bright but with normal temperature and rainfall.\u00a0 The last couple of years now seem to be pointing to a new era of warm, wet & bright winters.<\/p>\n It’s also worth noting that the step change in our climate that we’ve seen over the last 30 years has been most pronounced in the winter.\u00a0 All seasons are now about 1 standard deviation warmer but winter has the largest standard deviation of all seasons and has seen increases closer to 1.5 standard deviations.<\/p>\n <\/p>\n The long term trends chart above suggests that the z-scores for temperature, sunshine and rainfall all appear to be correlated.\u00a0 In fact this can be illusory as the above chart uses moving averages.\u00a0 If we look at the actual z-scores, we can see what the actual correlations are in the 3 scatter plots below.<\/p>\n The brown square in each chart is 2023.\u00a0 Scatter plots can be useful to identify unusual years that do not follow the normal relationships.\u00a0 Here we see 2023 was consistent with the correlations seen over history.<\/p>\n Looking at the 3 scatter plots in turn, we see sunshine is not correlated with rainfall and temperature but rainfall and temperature have a significant positive correlation.\u00a0 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.\u00a0 By using the method of PCA (Principal Components Analysis)<\/a> 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 below the 1st component accounts for 1.5 dimensions whilst the 2nd component accounts for 1 dimension.<\/p>\n ** In the bi-plots below, rainfall has been replaced with dryness (= -1 x rainfall z-score) in spring, summer & autumn whilst winter retains rainfall.\u00a0 This is to aid visualisation of the biplots in terms of how the correlations change over the year.\u00a0 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.<\/em><\/span><\/p>\n Looking at the correlation bi-plot now, we see the 1st component accounts for temperature and rainfall, reflecting the correlation we see in the scatter plot above.\u00a0 At the same time, the second component is just sunshine.\u00a0 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.\u00a0 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.<\/p>\n Once you have calculated your components, you can then plot these over time.\u00a0 I find these components over time to be more meaningful of the long term trends in our weather.\u00a0 In the chart below, I have flagged the years where the z-score exceeded +1.5 or -1.5.\u00a0 Ten years are highlighted and these are our notable winters.\u00a0 It is quite striking that the 1st 4 notable winters are all cold & dry winters and the last 6 are all warm and wet winters starting in 1990.\u00a0 This reinforces the long term trend observations I made about our winters earlier.<\/p>\n For more information about Principal Components Analysis, please visit my link about training materials for multivariate analysis<\/a>. and read the information in section A.<\/p>\n If you want to read my other Weather Trends posts<\/a>, please click on the link or the Weather Trends<\/a> hashtag below this post.\u00a0 Otherwise, please click the relevant season from the list below.<\/p>\nLong Term Climate Trends<\/strong><\/span><\/h4>\n
<\/p>\n\n
How many dimensions does Winter have?<\/strong><\/span><\/h4>\n
<\/p>\n<\/p>\n<\/p>\n<\/p>\n
\n\n