A Modest Cloud Cover Study (part 6)

Today I look at trends in seasonality within the CRU TS4.08 and ICOADS v3 cloud cover monthly datasets for the UK & Ireland over the period January 1901 – December 2023

We can pretty much guess that cloud cover over these islands is going to be strongly seasonal. Even those working underground like I did back during my PhD years can safely assume more clouds in winter and less clouds in summer even if they don’t get to see the sky. But what about spring? And where does autumn sit? We might also wonder whether seasonal patterns in cloud cover have been slowly changing over time; and there will be some of us who’ll wonder if the CRU TS4.08 and ICOADS v4 gridded data products are telling the same story.

I’d like to unravel these mysteries and I’d like to do so using a popular spanner that is univariate analysis of variance (ANOVA). These days I seem to spend my time explaining ARIMA outputs to folk but back in the early days of my career ANOVA was my bread and butter, and I recall the thrill of coming across the magic that is the partitioning of the sums of squares. Back then cruel teachers of statistics required us to derive these by hand using nothing more than pen and gridded paper aided by an electronic calculator. That sort of fiendish slavery builds character and I still use my trusty vintage calculators to this day to double-check a few things.

An Adventure

So, then, we are going to go on a little adventure in ANOVA, and the first thing we must do is check the nature of the distribution of the two datasets of interest. As it so happens ANOVA methods, despite being powerful and magical, are subject to stringent requirements and chief of these is for the distribution of values to be Normal-like. When quizzed by us undergrads as to what ‘Normal-like’ actually meant grumpy lecturers settled for a continuous variate with a central tendency and fairly symmetrical distribution. There are, of course, formal tests for Normality such as the Kolmogorov-Smirnov Test, but these are harsh and unforgiving when in reality you can be fairly sloppy providing you realise what you are doing as a responsible analyst.

Let us now eyeball the histograms of both datasets and see how we feel about applying ANOVA techniques: