Over in the Melting thread, Siffy posts some graphs made by Wipneus of sea ice extent in various arctic seas. The graphs display standard deviation bands assuming the distribution of data points for sea ice extent on a date are normally distributed. However, the data is fairly clearly not normally distributed.

In hopes of getting at least a short detailed mathematical discussion out of this, I've created this new thread.

Siffy, your question has been mostly answered by others. The grey bands show the average cover with error bands of 1 and 2 standard deviations.

That is ignoring a geographical maximum cover in some region, but also the very skewed behavior of ice cover deviations: negative swings are much larger than positive ones even with no physical maximum's.

Note that just cutting the grey's off is not a sound solution. The possibilities that have been cutoff will have to appear somewhere else, that is in other regions. Before you know it you get into modelling so complicated that it cannot possibly be useful anymore.

For the sake of simplicity and because such issues are commonly ignored in the field I did choose not to do anything about it. I am open to suggestions though.

The data distribution looks like a response time latency distribution. An overly quick google search suggests that modeling this as an "Ex-Gaussian" distribution might work. That still looks a bit complicated to implement. It's not immediately obvious to me where you would draw the equivalent of the standard deviation bands.

The other approach is to simply draw in the bands given the data and avoid modeling a distribution for it. (Well, we will still be modeling some sort of distribution, but...) E.g. Sort the data points. Find the median. Find the points that are 1/3rd above and below the median (or choose whatever gradiant seems interesting to draw). Find the points that are 3% from the top and 3% from the bottom or so.

Perhaps there are too few points (we have, what, 20 or 30?) for this exercise to be sufficiently meaningful, but it should be at least as meaningful as trying to force a normal distribution to the data.

[Edit: seaicesailor gives the same suggestion using simpler language some 8 hours before me, if I would bother to read ahead before responding...]