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Mathematica Tests the St. Swithun’s Day Proverb

Like most in the United Kingdom, I have been trapped in my house by snow for most of the last week.

Waking up again like Bill Murray in Groundhog Day, to another snowy view, I have been dreaming of summer days to come. It was against this background that I thought I would get around to testing whether an old British weather proverb was true:

St. Swithun’s day if thou dost rain
For forty days it will remain
St. Swithun’s day if thou be fair
For forty days ’twill rain no more

I read about this in the Times last summer. The article claimed that there was some truth in it based on stable jet streams, and supported that claim with some very general statement about particular years, but with no actual raw data. Like many analysis tasks, it turns out to be quite easy to do more precise analysis yourself, when you have Mathematica. But like many ill-defined problems, the results turned out to be a bit more interesting than I expected.

First let’s define the date range that we need. St. Swithun’s day is July 15, and we want to look at the following 40 days too.

Let’s look at my local rainfall for the 40 days following the last St. Swithun’s day. Mathematica has a built-in ability to query weather stations for the actual data (in this case located at Oxford’s airport).

Or more visually…

For convenience I will pack that into a function that takes any location and year and returns just the precipitation amounts and discards the dates. I will do a bit of extra work to record the occasional missing data point, when the weather stations have been broken, to make some of the later steps easier.

and test it on the same range…

The proverb doesn’t say anything about amount of rain, only that the rain will remain. So we want to reduce this data into True (it rained) and False (it didn’t). But in a generally damp country like the UK, does a little drizzle count as rain? Let’s duck that question for now by allowing a threshold parameter for what constitutes a rainy day.

And test again on the same year, using 0 as the threshold—any rain is rain.

We can now apply that function to the available data from 1900-2008.

Now we just have to pull out the rows that started with True (rainy St. Swithun’s day) and count the rainy days that follow. If the proverb is accurate, we should get a list of 40 days.

Not exactly compelling. Let’s compare to the days of rain in years when it didn’t rain on St. Swithun’s day, which should be a list of zeros.

It doesn’t look substantially different. So let’s package those preceding steps into a single function and find the averages of each list, and make a pretty table…

So not only does the proverb not, on average, apply to Oxford over the last 100 years, but it is actually a counter-indicator to rain. A wet St. Swithun’s day means you are, on average, going to get a dryer period to follow.

What happens if we use a less absolute definition of rain? Perhaps it must be at least 2 mm accumulation.

That makes a wet St. Swithun’s day even more of a counter-indicator of rain to come. A properly wet St. Swithun’s day leads to, on average, about 2 fewer wet days out of the next 40.

So it seems like an open-and-shut case. The proverb doesn’t work. But we mustn’t forget that St. Swithun was Bishop of Winchester Cathedral in the 9th century, so perhaps it only applies to Winchester. The nearest weather station to Winchester, according to Wolfram|Alpha, is Eastleigh.

In Winchester then, it has at least been a positive indicator, and the part about fair weather has come close to being true. It is still far from the 40 days of rain promised after a rainy St. Swithun’s day.

Two data points isn’t enough, so lets look at each of the 68 largest towns and cities in the UK.

So if we are selective about our point of observation, then we can get pretty good support for the theory. For example, we could rewrite the proverb like this:

St. Swithun’s day if thou dost rain (in St. Helens)
For (the majority of) the next forty days it will remain (in St. Helens)
St. Swithun’s day if thou be fair (in St. Helens)
For forty days ’twill rain (not much) more (in St. Helens)
(on average)

Looking over the table, it does seem that there are lots of places where the theory is a positive indicator, plenty where it makes no difference, and very few where it is a counter-indicator. So averaging over the whole country will make it a positive indicator, but far short of the promise.

But perhaps we need to consider this as a collective experience of the country rather than personal experience in a particular location. What if we define “Dry” as being rain in less than half of the top 68 towns and cities, and “Rain” as being rain in at least half? I need to rewrite the code for that…

Now let’s try this, with any rain counting as a rainy day, and more then half the top 68 cities needing rain to count the country as having a rainy day. I am running this over a shorter period, of 1980 to 2009, only to reduce the number of times I have to query the weather stations.

So we do get a little positive bias, but barely very much. I suspect selecting out any period that starts with rain will give a positive bias towards rain, compared to selecting periods that start with sun. But I will leave that as an exercise for the reader.

So, if there is anything in the St. Swithun’s day legend, it has been greatly overstated.