Tuesday 5 January 2016

UK Rainfall: Loading the Dice

Using UK annual precipitation, the probability of a very wet year has increased, from 1/6 before 1990 to 3/6 after 1990.

In simple terms:

Before 1990 a very wet year had the same probability as that for rolling one dice for the number you picked, after 1990 three sides have the number you pick.

UK precipitation data has now been updated for 2015 through to December. December 2015 is the wettest of any of the 1272 months from January 1910 to December 2015, at 230mm this is about 15mm above the previous such record set in November 2009. The current El Nino probably plays a role, but such short term issues do not concern me.

The longer term context is revealed by the anomalies. Anomalies are the difference from the long term mean, in this case I have calculated the mean for 1951 to 1980 and graphed the difference from that mean. Click to enlarge.

This pattern does not appear in the monthly timeseries of UK precipitation, nor does it appear in the England/Wales/Scotland regional data. However focussing on regions or months and ignoring this strong pattern in the wider data is a classic case of failing to see the wood for the trees (wood as in forest). It only rains when conditions are right, sometimes it rains little, some regions like the South East of England have been undergoing dryer, not wetter weather. All of these factors are averaged out by stepping back and taking the wide view of annual precipitation over the whole of the UK.

There seems to be a shift in the above data in 1998, I am not convinced about that. I think it is feasible that higher rainfall may have onset earlier given slightly different conditions, indeed, note that since the 1970s anomalies have been generally positive. This is similar to the early part of the series which plays a strong role in setting monthly precipitation records, for example the August record was set in 1912, the September record was set in 1918. However what has happened in recent years is truly unprecedented.

To get a numerical grasp on the data in the first graph I have set out two time periods, before and after 1990. This is a conservative choice that understates the change since 1998 but happened to produce numbers amenable to an analogy of dice, also sticking to decades means the uncertainty around the 1998 shift, so I stuck with it.

So I have graphed the probability distributions of the actual data from 1910 to 1989 and 1990 to 2015.

Summing all the probabilities above 1200mm as being the probability of a very wet year gives a probability of 16% for the period before 1990 and 50% for the period after. This approximately corresponds with one side and three sides of a dice respectively.

Note: Strictly dice is the plural of 'die', however the usage in common English now seems to favour dice as the noun for both plural and singular, so I have chosen that common vernacular.


dreesen said...

Hey Chris,
I wanted to know what your thought was on the Arctic sea ice extent being at or near the lowest for this time of year. Do you think this trend is going to continue for the rest of the year, or is this just a temporary blip due to that huge storm over the North pole?

Chris Reynolds said...

Hi Dreesen,

It's been low all winter so I don't think that Storm Frank had a role. Will it continue? I don't know, however the first five days of this year are the lowest on record since 1979 for NSIDC Extent. And the linear trend fit has an R2 of 0.87 (0 is no fit, 1 is a perfect fit), with a loss of 44,000 kmsq per year.

The relationship between overall extent now and that in March follows the long term trends of loss in both periods, but is not strong enough to narrow down the odds any more than common sense expectations: A record low at minimum (March) is possible, but not guaranteed.