I've used Met Office rainfall figures for the United Kingdom, from here. The stated summer average (JJA) has been ordered in descending order of total rainfall to give the following top ten wettest years. The total series is from 1910 to 2013, so is 104 years long.
In order to preserve the statistical distribution of rainfall in the data I have opted for a monte-carlo based assessment of probability, rather than an algebraic one.
I have loaded the data into an array and with each iteration of the subsequent calculation have re-seeded from that unchanged source data array. The source data is copied into a parallel array, and the data in that array is then shuffled by swapping randomly selected pairs of rainfall amount 500 times. Thus I have a randomised set of the original time series, and the occurrence of years from 2007 to 2013 is then identified from the top ten rainfall amounts in the shuffled data.
In short I am answering the question: How likely is it that four of the top ten rainfall years are found to be between 2007 and 2012?
I have iterated the process, taking four runs of each batch of iterations, to establish stability. 10,000 iterations produced significant standard deviations of results (four runs of 10,000 were done) when compared to the smaller uncertainties. Iterating 100,000 times produced lower but significant standard deviations between the four runs of those iteration sets. So I settled on 1,000,000 iterations as producing relatively stable results. At 1,000,000 iterations the probability of finding four years (from 2007 to 2013) in the top ten rainfall series is over 7 times the standard deviation of the four sample runs. Having taken four runs I have averaged the four runs for the 1,000,000 iterations to produce the estimated probability distribution tabled below.
The probabilities of finding N years that lie between 2007 and 2013 in the top ten highest rainfall amounts over the UK are listed below.
So in plain English:
The likelihood of finding that four of the top ten wettest years in the UK lie between 2007 and 2013 by random chance is 0.14%. Therefore it is a virtual certainty (99.8% probability) that the occurrence of 2007, 2008, 2009 and 2012 in the top ten wettest years in the UK is not by chance, but is due to a shift in the processes at play in delivering rainfall to the UK.No atmospheric pattern over the UK holds sway in every year, in 2013 the new summer circulation pattern didn't appear (I suspect due to slow ice melt in May), but it did in 2011 and was present in 2010 apart from June, as is shown by correlations with the summer pattern.
However this pattern increases the chance of extreme wet summers (in the top ten), and so far in the years the pattern has manifested we have seen 4/6 occurrences of heavy rain, with 2/6 years had severe flooding events. Those are not good odds, and if they persist will see a massive increase in flood event statistics in the UK.
This shift occurred in 2007, simultaneous with a new pattern of atmospheric circulation, and the start of a new regime in Arctic sea ice, featuring unusually aggressive sea ice loss, is not an accident. There is a link between exceptional summer UK rainfall, severe UK summer flooding events, and the loss of Arctic sea ice. As I have argued recently, the rate of sea ice loss indicates that the process is more the ice driving the changes, not the atmosphere driving the ice, as 2013 indicates.
Therefore the UK is experiencing cooler wetter summers, likely as a result of sea ice loss. And this has lead to damaging flooding events in 2007, and 2012. This is not happening by chance, it is climate change, ongoing and causing damaging consequences to lives, property and agriculture.