The claim that “the precipitation anomaly of the past few decades in Law Dome is the largest in 750 years, and lies outside the range of variability for the record as a whole”, is a ‘Hockeystick-like’ claim. Such claims have a considerable literature, and the analysis I have been doing is reminiscent of Rybski et.al. on the temperature record.

Koutsoyiannis has a career of work grappling with non-normal statistics in hydrological data, using models with long-term-persistence, and the difficulty of prediction. These more advanced analysis attempt to account for the fact that precipitation has a long-term correlation structure, extreme events happen more frequently than expected, etc, and are well worth the study. That is, there is no need to reinvent the wheel here.

Below is the Law Dome snowfall data illustrating aggregation at the scales of 10, 20, 30 and 40 years where previous posts suggested the divergence of recent snowfall is significant.

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The data order is reversed to ensure the correct aggregation of the most recent years, as the final years could be missed when the scale of aggregation is not an even multiple of the whole record.

The recent increased snowfall can be seen at the left of the record, but it is not particularly unusual, and certainly doesn’t rise to the level of ‘unprecedented’ as there is a similar period of high snowfall early in the record.

Prima face I treat the claim in van Ommen’s paper that this is a 1:38000 year event with some skepticism. Anytime I see these high significance levels in natural data I get skeptical — it’s just not possible from a 750 year record of precipitation.

The previous posts indicate a significance around 3 sigma, that is 99% confidence. However these values also depend on the actual distribution, which is not easy to determine. Precipitation records have been variously described by the normal, lognormal, and gamma distributions. Wiki has good write-ups on these and why they might be applicable, based on the generating process. They are shown with the LD snow data below.

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None of these distributions are ‘fat-tail’ distributions — that is they decline almost exponentially in the tails, so that extreme events happen increasingly infrequently as the size of the events increases.

The green line in the plot above is an example of a ‘fat-tail’ distribution, using the R package ‘fBasics’ and the skew fat-tail functions related to ‘stable’. There is a slightly higher frequency of extreme events in the tails, as can be seen by the green line lying above the other lines on the right hand side.

Nassim Taleb explains it well. He says we believe we live in a world called “Mediocristan”, and consequently underestimate the probability of large infrequent events. However, we actually live in the world of “Extremistan” where the frequency of extreme events don’t follow a normal distribution.

This apparently small difference in probability makes a big difference to the significance tests of extreme events. Below is the plot of the significance of the final snow ‘event’ as shown in other posts in the series, using the estimates of the ‘stable’ function.

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This reduces the significance of the final event even further. A scholarly approach to quantifying the significance of extreme events such as the snowfall at Law Dome does not rely on analysis that is virtually guaranteed (by virtue of the use of the normal distribution with exponential tails) to underestimate the probability of extreme events, but considers the considerable literature on alternative distributions that have been used to more accurately represent the true expectations of the likelihood of extreme climatic events.

This doesn’t disprove the claim that the snowfall in Antarctica has been significant, although I think a 99%CL is more realistic that the stated limits. Tas van Ommen also goes on to say that the correlation between SW Western Australian rainfall and Antarctic rainfall (which was confirmed at a range of scales in a previous post) implies that the drought in SWWA is similarly significant. He said in the ABC interview that the ‘natural’ explanation for the drought is human influence.

I’d like to propose an alternative ‘natural’ explanation, described in Structural break models of climatic regime-shifts: claims and forecasts, that of the Great Pacific Climate Shift, a far-reaching regime-shift in oceanographic currents in 1976. Below is the rainfall Tas used for SWWA, with the step shift in 1976 indicated in red.

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While the GPCS does not necessarily exclude an AGW explanation, it does argue that better understanding of the causes of both the excess of precipitation in Law Dome and the deficit in SWWA may require better understanding of the GPCS. One take-away message from Tas and Vin’s study may be evidence of the influence of the GPCS reaching as from where it was initially recorded in the Pacific NE, to the Southern Ocean and Antarctica.

UPDATE: These images accompany the comment by Demetris below.

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