Antarctic Snowfall Wrap-up

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.

fig11

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.

fig9

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.

fig8

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.

fig12

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.

TasmanianGraphs_Page_1

TasmanianGraphs_Page_2

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0 thoughts on “Antarctic Snowfall Wrap-up

  1. Extreme events can be extreme both because they last a long time and because the height of the peak is greater, or both. Do you have stats ways that account for both frequency and amplitude to your satisfaction? How do you get on when an eztreme event is sigmoidal in amplitude, with the complete signal being a positive and a negative following each other, one or the other first, like an El Nino is followed by a La Nina or vice versa.

  2. David,Thanks for the reference to my work. Your article is very interesting and I tried to locate on the internet the data you analyze–but without success. From your rainfall plot, I can guess (from visual inspection) that Tasmania rainfall should be consistent with Hurst-Kolmogorov dynamics. In looking for Tasmania rainfall data, I stumbled upon the rainfall time series of Maatsuyker Island Lighthouse (Australia, coordinates: -43.65N, 146.27E, 147m, WMO station code: 94962; http://climexp.knmi.nl/data/pa94962.dat). This should be just south of Tasmania. There are 113 years of data, from 1892 to 2004. There are only three missing monthly values, which I filled in by local averages. Well, this rainfall time series is the most impressive I have ever seen. It is absolutely consistent with Hurst-Kolmogorov behaviour with a Hurst coefficient as high as H = 0.99! I have never seen such a high H in rainfall series (but I have seen in temperature series). Of course, such high H entails high uncertainty and we cannot be sure about this value. I am sending you by email my plots, in case you wish to publish them along with my comment. The method I used to estimate the standard deviations for different time scales is explained in equation (13) of my 2009 paper “A random walk on water” (http://www.itia.ntua.gr/en/docinfo/923/)–but even a typical estimation of standard deviation after constructing non-overlapping series of averages of 1, 2, 3, … years would not give any substantial difference. I examined the annual series, but the monthly are very interesting too (July in particular).This result is so impressive that I am afraid that there may be some problem with the data. If any one has any information about the reliability of the data set, I will appreciate letting me know.Demetris

  3. Extreme events can be extreme both because they last a long time and because the height of the peak is greater, or both. Do you have stats ways that account for both frequency and amplitude to your satisfaction? How do you get on when an eztreme event is sigmoidal in amplitude, with the complete signal being a positive and a negative following each other, one or the other first, like an El Nino is followed by a La Nina or vice versa.

  4. David,

    Thanks for the reference to my work. Your article is very interesting and I tried to locate on the internet the data you analyze–but without success. From your rainfall plot, I can guess (from visual inspection) that Tasmania rainfall should be consistent with Hurst-Kolmogorov dynamics. In looking for Tasmania rainfall data, I stumbled upon the rainfall time series of Maatsuyker Island Lighthouse (Australia, coordinates: -43.65N, 146.27E, 147m, WMO station code: 94962; http://climexp.knmi.nl/data/pa94962.dat). This should be just south of Tasmania. There are 113 years of data, from 1892 to 2004. There are only three missing monthly values, which I filled in by local averages.

    Well, this rainfall time series is the most impressive I have ever seen. It is absolutely consistent with Hurst-Kolmogorov behaviour with a Hurst coefficient as high as H = 0.99! I have never seen such a high H in rainfall series (but I have seen in temperature series). Of course, such high H entails high uncertainty and we cannot be sure about this value. I am sending you by email my plots, in case you wish to publish them along with my comment. The method I used to estimate the standard deviations for different time scales is explained in equation (13) of my 2009 paper “A random walk on water” (http://www.itia.ntua.gr/en/docinfo/923/ ) –but even a typical estimation of standard deviation after constructing non-overlapping series of averages of 1, 2, 3, … years would not give any substantial difference. I examined the annual series, but the monthly are very interesting too (July in particular).

    This result is so impressive that we should be very careful about the reliability of the data. If any one has any information about the reliability of the data set, I will appreciate letting me know.

    Demetris

  5. Apparently, in my above comment I misplaced the area (SWWA) where this post refers too, thinking that it is close to Tasmania, which is south but east… I hope the readers can forgive an inhabitant of SouthEastern Europe for this terrible error. However, with this mistake I was very lucky that I found this very interesting rainfall record.

  6. Apparently, in my above comment I misplaced the area (SWWA) where this post refers too, thinking that it is close to Tasmania, which is south but east… I hope the readers can forgive an inhabitant of SouthEastern Europe for this terrible error. However, with this mistake I was very lucky that I found this very interesting rainfall record.

    • Demetris

      This rainfall record looks correct to me. I lived in NW Tasmania 1975 – 1978. Anecdotal evidence from many farmers and the elderly people (ages 70 – 98) suggested the period since about 1970 were the wettest (highest rainfall) in living memory i.e. going back to at least the early 1900s. They even made a joke to describe the weather as follows:

      One farmer says to another ‘Summer came very late this year.’
      The other farmer says ‘Yes, came on a Saturday instead of a Wednesday.’

      The Maatsuyker Island Lighthouse record (continuously manned for over 100 years) bears this out. It is well know that Tasmania has enjoyed a much milder climate over the last 15 years.

  7. David,I think you're right to query any reliance on normal assumptions to make inferences about rare events. And people should test for normality more often.I don't think there's much use in looking for some other distribution. The basic problem is, as you say, you can't make 1 in 38000 statements on 750 years of data. The testing for normality is of some interest to me, because it also arises in arguments about temperature trends. The residuals there are also not normally distributed, and look fat-tailed. So it's very hard to get a true significance result. Doesn't mean it's not warming, BTW.

  8. Nick, Always appreciate your comments. I have used a 'stable'function (billed as a generalization of Gaussian with a Pareto tailand skew parameter -fBasics package in R) and am very happy with it.The anomaly is still significant but only 1:100. Have you used'stable' functions?

  9. I have a friend whose an enthusiast for stable (Cauchy) distributions in the context of options pricing. But I don't share his enthusiasm for basically the same reasons. I think that the hope of identifying tail probabilities by fussing over the fitting of the central behaviour of the distribution won't work. There are no real laws about distributions except the central limit theorem. Otherwise WYSIWYG; they are just mathematically convenient descriptors of the data. You can't use the mathematical form to tell you stuff that the data can't. If you want to know about the tail, you have to observe it.

  10. Yes though I suspect there must be some intrinsic value in usingstable distributions in nature, due to the closure property. Thisissue is similar to the DECR issue in that the handling of the extremevalue statistics seem, well, kind of basic. There's an opportunitythere for a center for extreme event studies to promote bettertreatment of these problems.

  11. David,
    I think you’re right to query any reliance on normal assumptions to make inferences about rare events. And people should test for normality more often.

    I don’t think there’s much use in looking for some other distribution. The basic problem is, as you say, you can’t make 1 in 38000 statements on 750 years of data.

    The testing for normality is of some interest to me, because it also arises in arguments about temperature trends. The residuals there are also not normally distributed, and look fat-tailed. So it’s very hard to get a true significance result.

    Doesn’t mean it’s not warming, BTW.

    • Nick, Always appreciate your comments. I have used a ‘stable’
      function (billed as a generalization of Gaussian with a Pareto tail
      and skew parameter -fBasics package in R) and am very happy with it.
      The anomaly is still significant but only 1:100. Have you used
      ‘stable’ functions?

      • I have a friend whose an enthusiast for stable (Cauchy) distributions in the context of options pricing. But I don’t share his enthusiasm for basically the same reasons. I think that the hope of identifying tail probabilities by fussing over the fitting of the central behaviour of the distribution won’t work.

        There are no real laws about distributions except the central limit theorem. Otherwise WYSIWYG; they are just mathematically convenient descriptors of the data. You can’t use the mathematical form to tell you stuff that the data can’t. If you want to know about the tail, you have to observe it.

      • Yes though I suspect there must be some intrinsic value in using
        stable distributions in nature, due to the closure property. This
        issue is similar to the DECR issue in that the handling of the extreme
        value statistics seem, well, kind of basic. There’s an opportunity
        there for a center for extreme event studies to promote better
        treatment of these problems.

      • Hi David

        OT I know (and would require a new thread), but speaking of stable distributions in nature, I’d be very interested in your take on this intriguing paper based on the levels of multivariate climate correlations which has just appeared in Nature (pun not intended):

        http://economics.huji.ac.il/facultye/beenstock/Nature_Paper091209.pdf

        Here we have, for probably the first time I can recall, mathematically sophisticated (?) economists (!?! 😉 weighing into the AGW debate – and on the sceptical side too. What is it about these pesky Israelis?

        As a ‘niche modeler’ I though you’d be intrigued by their argument of the supposed transient nature of CO2 and CO2-related forcings.

        I am slowly accumulating the papers from where they get their correlations. That this has sailed past Nature peer reviewers at this particular point in time raises some interesting questions as well.

        The homeostasis argument raises its head once again. I expect the MEP people (Kleidon etc)to reply to this paper as well.

      • Steve, My first impression is that it deserves careful study, and is
        very well written. I thought the word ‘refute’ too strong for
        something based on observatinos, but I have to read it in toto first.

      • If you mean the last sentence before the Conclusion which reads:

        “However, they also reject the hypothesis that global temperature varies
        directly with the change in greenhouse gas forcings, and indeed, that solar irradiance is
        a driver of climate change.”

        then I agree it is a concern.

        I’ve ordered the Mills (2009) paper (ref viii). This seems to be at the heart of this.

        If CRU and GISS hadn’t fooled with the raw global surface temperatures and numbers of stations so badly over the last 30 – 40 years, not to mention ‘losing’ original raw data sets then, ironically, maybe we wouldn’t be in such a confused position right now.

        Lately I’ve been trying to review some borehole temperature databases.

  12. Hi DavidOT I know (and would require a new thread), but speaking of stable distributions in nature, I'd be very interested in your take on this intriguing paper based on the levels of multivariate climate correlations which has just appeared in Nature (pun not intended):http://economics.huji.ac.il/facultye/beenstock/…Here we have, for probably the first time I can recall, mathematically sophisticated (?) economists (!?! 😉 weighing into the AGW debate – and on the sceptical side too. What is it about these pesky Israelis?As a 'niche modeler' I though you'd be intrigued by their argument of the supposed transient nature of CO2 and CO2-related forcings.I am slowly accumulating the papers from where they get their correlations. That this has sailed past Nature peer reviewers at this particular point in time raises some interesting questions as well. The homeostasis argument raises its head once again. I expect the MEP people (Kleidon etc)to reply to this paper as well.

  13. Steve, My first impression is that it deserves careful study, and isvery well written. I thought the word 'refute' too strong forsomething based on observatinos, but I have to read it in toto first.

  14. If you mean the last sentence before the Conclusion which reads:”However, they also reject the hypothesis that global temperature variesdirectly with the change in greenhouse gas forcings, and indeed, that solar irradiance isa driver of climate change.”then I agree it is a concern.I've ordered the Mills (2009) paper (ref viii). This seems to be at the heart of this.If CRU and GISS hadn't fooled with the raw global surface temperatures and numbers of stations so badly over the last 30 – 40 years, not to mention 'losing' original raw data sets then, ironically, maybe we wouldn't be in such a confused position right now.Lately I've been trying to review some borehole temperature databases.

  15. DemetrisThis rainfall record looks correct to me. I lived in NW Tasmania 1975 – 1978. Anecdotal evidence from many farmers and the elderly people (ages 70 – 98) suggested the period since about 1970 were the wettest (highest rainfall) in living memory i.e. going back to at least the early 1900s. They even made a joke to describe the weather as follows:One farmer says to another 'Summer came very late this year.'The other farmer says 'Yes, came on a Saturday instead of a Wednesday.'The Maatsuyker Island Lighthouse record (continuously manned for over 100 years) bears this out. It is well know that Tasmania has enjoyed a much milder climate over the last 15 years.

  16. Thanks very much Steve. This is important information and makes this record an ideal example for demonstrating long-term changes (fluctuations) of rainfall–which are consistent with a Hurst-Kolmogorov behaviour, rather than with global warming speculations etc.

  17. You are welcome Demetris.For comparison, here is a site with monthly rainfall data for the little fishing village of Stanley on the NW coast of Tasmania. I think you would find this site shows similar long term Hurst-Kolmogorov rainfall behaviour to the Maatsuyker Island Lighthouse (which lies at the southern tip of Tasmania) record. FYI, the Stanley rainfall data record runs from 1868 – 1999:http://www.bom.gov.au/climate/averages/tables/c

  18. You are welcome Demetris.For comparison, here is a site with monthly rainfall data for the little fishing village of Stanley on the NW coast of Tasmania. I think you would find this site shows similar long term Hurst-Kolmogorov rainfall behaviour to the Maatsuyker Island Lighthouse (which lies at the southern tip of Tasmania) record. FYI, the Stanley rainfall data record runs from 1868 – 1999:http://www.bom.gov.au/climate/averages/tables/c

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