No seperate thread needed, I don't think there's a great deal more to say...

Nick,

2012, or any other year, would just be a shift in the distribution. In practice the curves change slightly because even with 1,000,000 iterations the results haven't converged totally between runs. With 100,000 runs the standard deviation of the average for each run is around 0.001, 1,000,000 should be good enough.

I have attached a plot of 2012 and 2015 start extent for the 18 July.

You are right about the probability for 2012, see my comment below to OSMM. The probability for the 2015 start extent is 0.012%, for the 2012 start extent it is 0.082%.

OSMM,

For each day there are 8 possible losses from years 2007 to 2014, increment day through 18 July to 15 Sept and randomly select one loss from the 8 losses for that day.

I can't add anything more to what Nick has said about autocorrelation. I think the major issue here however is not autocorrelation but dependence on initial conditions. 2012 appears to be a very unlikely event with this monte carlo approach. In reality it was not. Initial (April) volume (or thickness) provided conditions conducive to high loss due to extensive thin ice and a low export from the central arctic of MYI. This manifested as very low compactness by July, which in a different approach could be used to add priming information to a prediction. However this information, which suggested strong August losses was not available in the monte carlo approach, as I have implmented it. So it gives an unrealistically low probability of the 2012 minimum.

Note that in the approach used now I have deliberately chosen Arctic Ocean (which includes CAA, Barents & Greenland Seas), this is because of my reading of ice state in the peripheral seas (Beaufort round to Latpev) which suggests to me that overall extent is giving an inaccurate impression of ice state. Like 2012 I expect above average losses in August due to state in the peripheral seas. However the choice of Arctic Ocean rather than whole Arctic does itself reflect my bias (or prior).

Jai,

The standard deviation of the 1,000,000 'predictions' is 0.308M km^2, which can be applied to the peak value of 4.5. However due to the autocorrelation as mentioned by OSMM using the probabilities normally associated with the standard deviations is not really sound.