Here is the distribution of annual snowfall in Law Dome Antarctica over the last 750 years (blue), compared to a normal (dashed red) and a lognormal (solid red) distribution.
Remember that in the finest Popperian tradition we are trying to disprove that the snowfall in the last few decades at Law Dome has been unusual. To do this, I have used a robust approach of aggregation (splitting the series into equal sized section), estimating the parameters of the lognormal distribution, then plotting the actual mean snowfall in the final aggregate against the calculated confidence limits.
The previous plots using the van Ommen approach, and an assumed normal distribution, have shown the recent snowfall at LD is significantly high at aggregation from about 25 years on.
While a qualitatively similar result is found when tested with a lognormal distribution, the ‘unnaturalness’ is further reduced. Here the snowfall could be regarded as quite unusual when aggregated between 25 and 40 years, capturing the length of the snowfall period since 1970, but beyond that the snowfall is marginally significant.
However, we don’t really know that this data has a lognormal distribution. There might be arguments for a related distribution with a ‘fatter tail’ that would suggest that extreme events are more probable than the lobnormal distribution would suggest.
Remember the ABC transcript regarding Antarctic snowfall that started this was:
Well, it is a real smoking gun I guess. It could be that we have just happened to find something that is really one in actual fact, thousands flukey event to get such a large snowfall. The more natural interpretation is that there is something been going on in the last 30 to 40 years and we know what that something is. It is the human impact on the atmosphere.
In my view there is some evidence that the event is unusual, and certainly I haven’t falsified the claim here with robust statistics, I don’t think it rises to a 1:38,000 year event as claimed. I suspect that ‘data peeking’ was going on. That is, seeing a large snowfall event, a novel methodology was sought that profiled that event with the highest possible significance.