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On record-breaking events

Filed under: — rasmus @ 1 August 2005

NASA’s Earth Observatory reports that there was a record low Arctic sea ice concentration in June 2005. There was a record-number of typhoons over Japan in 2004. In June, there were reports of a number of record-breaking events in the US. And on July 28, the British News paper The Independent reported on record-breaking rainfall (~1 m) in India, claiming hundreds of lives. These are just a few examples of recent observations. So, what is happening?

Whenever there is a new record-breaking weather event, such as record-high temperatures, it is natural to ask whether the occurrence of such an event is due to a climate change. Before we proceed, it may be useful to define the term ‘statistically stationary’, the meaning here being that statistical aspects of the weather (means, standard deviation etc.) aren’t changing. In statistics, there is a large volume of literature on record-breaking behaviour, and statistically stationary systems will produce new record-breaking events from time to time. On the other hand, one would expect to see more new record-breaking events in a changing climate: when the mean temperature level rises new temperatures will surpass past record-highs. This is illustrated in Fig. 1.

Fig. 1. An example showing two different cases, one which is statistically stable (upper) and one that is undergoing a change with a high occurrence of new record-events. Green symbols mark a new record-event. (courtesy William M Connolley)
Fig. 1. An example showing two different cases, one which is statistically stable (upper) and one that is undergoing a change with a high occurrence of new record-events. Green symbols mark a new record-event. (courtesy William M Connolley)

Record-events and extremes are closely related. Record-high and low values define the limits (bound or the range) between which observed values lie, and extremes are defined as those values in the vicinities of these limits. The third assessment report (TAR) of the IPCC reported some studies that have found regional trends in temperature extremes (particularly low temperatures). There have also been some reports on trends of more extreme precipitation, although The International Ad Hoc Detection and Attribution Group (IDAG, 2005) did not manage to attribute trends in precipitation to anthropogenic greenhouse gases (G) – a quote from their review article is: “For diurnal temperature range (DTR) and precipitation, detection is not achieved”, here ‘detection’ implying the signal of G. A high occurrence of new record-events is an indication of a change in the ‘tails’ of the frequency distribution and thus that values that in the past were considered extreme are becoming more common.

But how does one distinguish between the behaviour of a stable system to one that is undergoing a change in terms of record-events? This kind of question has traditionally not been discussed much in the climate research literature (e.g. record-events are not discussed in DIAG, 2005 or the IPCC TAR), perhaps because it has been perceived that analysis on record-breaking events is difficult if not impossible. There are many different types of record-events related to climatic and weather phenomena. One hurdle is that the number of record-/extreme-events is very low and there is not enough data for the analysis. Another problem is the data quality: does the sensor give a good reading near the ranges of their calibrated scales?

Yet, there is a volume of statistical literature on the subject of record-statistics, and the underlying theory for the likelihood of a record-breaking event taking place in a stable system is remarkably simple (Benestad, 2003, 2004). In fact, the simplicity and the nature of the theory for the null-hypothesis (for an stable behaviour/stationary statistics for a set of unrelated observations, referred to as independent and identically distributed data, or ‘iid’, in statistics) makes it possible to test whether the occurrence of record-events is consistent with the null-hypothesis (iid). I will henceforth refer to this as the ‘iid-test’ (unlike many other tests, this analysis does not require that the data is normally distributed as long as there are no ties for the record-event). The results for such a test on monthly absolute minimum/maximum temperatures in the Nordic countries and monthly mean temperatures worldwide are inconsistent with what we would see under a stable climate. Further analysis showed that the absolute monthly maximum/minimum temperature was poorly correlated with that of the previous month, ruling out depeendency in time (this is also true for monthly mean temperature – hence, ‘seasonal forecasting’ is very difficult in this region). Additional tests (Monte Carlo simulations) were used to check whether a spatial dependency could explain the deviation from the iid-rule, but the conclusion was that it could not explain the observed number of records. A similar conclusion was drawn from a similar analysis applied to a (spatially sparse) global network of monthly mean temperatures, where the effect of spatial dependencies for inter-annual and inter-decadal variations could be ruled out (Benestad, 2004). Thus, the frequent occurrence of record-high temperatures is consistent with a global warming.

It is not possible to apply the iid-test to one single event, but the test can detect patterns in a series of events. The test requires a number of independent observations of the same variable over a (sufficiently long) period of time. Since climate encompasses a large number of different parameters (temperature, precipitation, wind, ice extent, etc), it is probable that a climate change would affect the statistics of a number of different parameters simultaneously. Thus, the iid-test can be applied to a set of parallel series representing different aspects of one complex system to examine whether its general state is undergoing a change. Satellite observations tend to be too short for concluding whether they are consistent with null-hypothesis saying there is no climate change (i.e. it being iid) or the alternative hypothesis that the climate is in fact changing (or the observations are not independent). Nevertheless, the record-low sea ice concentration is consistent with a shrinking ice-cap due to a warming. Rainfall observations tend to be longer and therefore more appropriate for such tests, but, such an analysis has not yet been done on a global scale to my knowledge. Results of an iid-test on series of maximum monthly 24-hour rainfall within the Nordic countries (Norway, Sweden, Finland, Denmark & Iceland) could not rule out the null-hypothesis (i.e. the possibility that there is no change in the rainfall statistics), but this case was on the border line and the signal could also be too weak for detection. In a recent publication, however, Kharin & Zwiers (2005) analysed extreme values from model simulations of a changing climate and found that an enhanced greenhouse effect will likely lead to ‘more extreme’ precipitation. This would imply an anomalously high occurrence of record-high rainfall amounts. They discussed the effect of variables being non-iid on the extreme value analysis, and after taking that into account, propose that changes in extreme precipitation are likely to be larger than the corresponding changes in annual mean precipitation under a global warming. Thus, new record-high precipitation amounts are consistent with the climate change scenarios.

Theory for the mathematically minded

The simple theory behind the iid-test is that we have a number of N observations of the same object. If all the values represent a variable that follows the same distribution (i.e. exhibits the same behaviour), then the probability that the last observation is a record-breaking event (the highest number) is 1/N. It is then easy to estimate the expected number of record-events (E) for a series of length N: E = 1/1 + 1/2 + 1/3 + 1/4 + … + 1/N (the first observation being a ‘record-event’ by definition). It is also easy to estimate the likelihood that the number deviated from E by a given amount (i.e. using an analytical expression for the variance of E or so-called ‘Monte-Carlo’ simulations). The probability for seeing new record-events diminishes for an iid variable as the number N increases.

References

Benestad, R.E. (2004) Record-values, non-stationarity tests and extreme value distributions Global and Planetary Change vol 44, issue 1-4, p.11-26

Benestad, R.E. (2003) How often can we expect a record-event? Climate Research Vol 23, 3-13.

DIAG (2005) Detecting and Attributing External Influences on the Climate System: A Review of Recent Advances, J. Clim., vol 18, 1291-1313, 1 May

Kharin & Zwiers (2005), Estimating Extremes in Transient Climate Change Simulations, J. Clim., 18, 1156-1173


71 Responses to “On record-breaking events”

  1. 51
    Klaus Flemloese, Denmark says:

    How good are extreme meteorological events to falsify the greenhouse theory?

    The short answer: Very bad. There are too few extreme events to make the statistical testing and estimation to work efficiently.

    The long answer: Study the theory of extremes and statistical test theory.

    It is fascinating and frightening to observe extreme weather phenomena. From a statistical point of view a lot of information is lost by looking only on extreme events and the statistical test will not be very strong i.e. the probability to reject a false null hypothesis will be small.

    If you look at the graph of the average temperature in Denmark from 1873 to 2003, i.e.130 years

    http://www.dmi.dk/dmi/tr04-02.pdf

    and count the number of records, you will find 8 records over 130 years of observations. If one accept the hypothesis of iid temperature measurements one will expect 5.5 records and the probability of observing 8 or more records equals 15%. This is not significant in the statistical sense. Observing 11 or more records would have been significant on a 0.1% level of significance.

    Even if it is obvious that the temperature has increased systematically, this can not be verified in this case by testing on the number of records.

    Conclusion:
    Using the number of records is not a good way of testing the existence of global warming. I am afraid of, that this example and other similar examples might be used by the skeptical to prove that no global warming has taken place.

    I am very pleased that RealClimate has take “record-breaking events” up for discussion. However, please be carefull not to put to much weight on extreme events in the discussion on global warming and climate change even if extreme events may cause a lot of harm to many people world wide.

    [Response:
    I think that we should not be afraid of discussing difficult matters. Extremes is a wide and very complicated topic, and I do agree in general that extremes are not suitable for testing whether there is a climate change. However, the iid-test tests just that: whether the data conform to being independent and identically distributed. It’s very simple, but can also be very powerful. You can test it on other data, and I have been surprised about it being so unversial. But results from the iid-test is certainly not the reason for why we think there is an ongoing climate change: it’s to my mind firstly our physical understanding and secondly the multitude of empirical evidence. When it comes to skeptics, I don’t think we should let them decide what we discuss just because we worry of how they may twist and spin the issue.
    ]

  2. 52
    Armand MacMurray says:

    I’m just curious about what happened to the Muscheler guest topic posting and threads that were here on the site until yesterday. Was there a system crash?

    [Response: Was accidentally deleted due to a technical glitch. We’ve restored it now, though some comments were lost. Our apologies to our readers! ]

  3. 53
    TCO says:

    Answer me or send me to a good GW site. palm trees and alligators in VA? How long? I’m not talking Florida. Something like Cape Hatteras.

  4. 54
    TCO says:

    Please don’t ban me. I already got kicked off (and comments deleted) from the climate auditor site. And I wasn’t misbehaving. If anything I was more on their side than yours, but I just wanted to dig a little into the methodology (well wanted them to do a first cut reanalysis…not of your work…but starting from scratch). Even if they are right and you are wrong, it seems a little wierd how much time they spend on someone else’s work. you would think with all the effort exerted, they would get interested and start doing original work.

    Anyhow…if you ban me too, I will feel really bad. How about puitting a word in for me instead with your colleagues over there?

    And I’m not really a troll. Well…actually I have an AWFUL tendancy to troll. But I thought I didn’t really do any…yet.

  5. 55

    Re #43

    There may have been a few record warm days this year on Svalbard, but one need to check the facts, before believing the jumping to conclusions of the journalist…

    Glaciers on Svalbard are shrinking, but that is already (at least) since the 1920’s. Yearly average temperatures up to 2004 are app. 0.5 °C lower in the last decades than in the period 1930-1960 (be it that there is a non-overlapping switch in stations), but summer temperatures are app. 0.5 °C higher than periods in the 1920-1930’s. See the temperature trends of the Svalbard stations.

    Thus Svalbard is not “dangerously warming” and the link with man-made greenhouse gases is not evident, as these should have their highest influence in winter, not in summer…

  6. 56
    Michael Jankowski says:

    Re#50,

    Try this http://www.usgcrp.gov/usgcrp/Library/nationalassessment/overviewlooking.htm

    Basically, both models say Virginia will be warmer thru 2100, albeit by differing amounts. The Canadian model suggests a drop in precipitation of about 10% and a drop in summer soil moisture content of 25-50%. The Hadley Centre mode suggests an increase in precipitation of about 30-40% and an increase in summer soil moisture content of up to 25%.

    It looks like the gators will have to wait-out and see which model gets the closest.

  7. 57
    Stephen Berg says:

    A story on climate change and its potentially disastrous effects on butterfly species:

    http://www.sciencedaily.com/releases/2005/08/050805175531.htm

  8. 58
    Joseph O'Sullivan says:

    The discussion of record weather events and climate change is very interesting and considering the press these events get is very informative.

    I am learning more about climate change science and trying to keep up with recent developments. The toughest part is the mathematical/statistical part of the science so the discussion of statistics in this post is very helpful. I did well in the statistics courses when I was an undergraduate but I retained very little of what I learned. I thought those classes were boring. I wished I had taken them more seriously, but since I did not I hope to see more mathematical/statistical explanations on RealClimate!

    It is also good to see RealClimate cover topics that could be controversial and twisted by contrarians. I fully agree with the response to #51 about not avoiding discussions of some scientific topics and letting skeptics decide what the discussion should be.

  9. 59
    TCO says:

    I’m fascinated by the gators. I’ve done some reading on them and googled as much as I can. The very far extent of their northern range is in the north edge of the albemarle sound almost to the VA border). However, I’ve read some other stuff that says that they are only up to SC. And then, other stuff that says that they were only in northern NC in last century. one other site says that they had a historical range up to NJ! But I can’t get any confirmation of that. It seems that they have mostly recovered their natural range (from endangered to millions of them). But I still wonder if there is any chance that they have a natural range up to VA and will come on up to the dismal swamp. There have been a few critters killed in VA recently (Richmond and Chesapeake). but hypothesis is that they were released and would not survive a winter. Wonder how many average degrees warmer a winter would be needed to let gators live in the Dismal Swamp (VA side of the line).

  10. 60
    TCO says:

    56: I looked at that site now. The good part is the most increase in temp will be nighttime winter lows. That might be enough to swing things into gatorland. I figure if we split the difference on the two, precip will be same. And the Dismal Swamp is pretty damp regardless.

  11. 61
    Robert Fawcett says:

    Stephen Luntz (comment #21) appears to be referring to some work done by my colleague David Jones and I. This work was presented at the 16th Australia New Zealand Climate Forum in November 2004. The abstract of our presentation is contained within the volume of abstracts, available here (pages 50-51), or separately here. A media release on this, with a regrettable and inaccurate headline, was issued at the time
    (available here), and attracted some local media interest. This work has not yet appeared in any form in the refereed scientific literature,
    so our results should be treated with some caution.

    We followed the IID null hypothesis approach of Benestad and others (as noted above, there is plenty of relevant statistical literature on rates of record setting outside the fields of meteorology, climatology, hydrology and oceanography), and some of the time series we investigated are available here.

    If we look at the global annual mean temperature anomaly time series (as derived from the University of East Angliaâ??s
    monthly anomaly time series), we find the number of new high records (14) is well above the expected number (5.6) under the IID null hypothesis for a time series of length 148. The results we obtained from various Australian time series were naturally considerably less extreme than this,
    but generally consistent with the warming trend observed over Australia during the 20th Century (reported on here).

  12. 62
    Michael Jankowski says:

    Re#44 (rasmus comment),

    Maybe my post wasn’t clear. I wasn’t referring simply to gaps in data, but portions where the data exists. If you have a reconstruction of annual average temperatures at a location over the past 1000 yrs with an error range of, say, +/-0.3 deg C in the proxy data, and the net temperature change over that time period is 1.0 deg C from the proxy data, your counts and timing of records are going to be heavily dependent on errors. For instance, you can have a “false high” early in the data that is +0.3 deg C higher in the data reconstruction than it was in actuality, and then you’d have fewer record highs subsequent to that than you should have.

    Records are often exceeded by 1/10ths of a degree. If the level of accuracy in the proxies isn’t much smaller than that, there will be plenty of both false and missed records. I don’t think it’s necessarily a good assumption that these would balance out.

    [Response:True, but as long as the errors themselves are iid, then you are still testing for a signal if you have many parallel series (the noise cancels in a similar way to taking the mean over many measurements). Try it with a synthetic numerical example and see!(see http://cran.r-project.org for free analytical tool) -rasmus]

  13. 63
    Stephen Berg says:

    Another story from ScienceDaily. This time on the damage caused by ice shelf disintegration:

    http://www.sciencedaily.com/releases/2005/08/050804123855.htm

  14. 64
  15. 65
    Ian Smith says:

    Re #4
    Michael Jankowski commented: “I can also find recent quotes from a Dr. Ian Smith of CSIRO claiming that climate changes in the south-western portion of Western Australia are “most likely due to long-term natural climate variations.”

    That is still the case with regard to the observed winter rainfall decline since about 1970 although, to be precise, I would now add:
    ” however, we cannot rule out the possibility that that the enhanced greenhouse effect has contributed to the decline.”

    In other words, while it is very difficult to demonstrate that the enhanced greenhouse effect could be the sole, or even major, reason for the decline, we cannot rule it out entirely. This simply reflects the fact that our knowledge of how the climate system behaves is not perfect.

  16. 66
    Mike Doran says:

    http://www.nytimes.com/aponline/science/AP-Fire-and-Ice.html

    Report: Icier Clouds Make More Lightning
    E-Mail This
    Printer-Friendly
    By THE ASSOCIATED PRESS
    Published: August 11, 2005
    Filed at 7:27 p.m. ET

    WASHINGTON (AP) — Poet Robert Frost once pondered whether the world would end in fire or in ice. Weather researchers say where you find ice you find fire — at least in the form of lightning.

    Whether the storm was over land, ocean or coastal areas, clouds with more ice produced more lightning, researchers studying satellite radar images report in the journal Geophysical Research Letters.

    ”The new thing is that when you look at different areas of the planet … the hypothesis about the importance of ice holds up,” Walter A. Petersen of the University of Alabama at Huntsville said Thursday.

    He said weather scientists have known there was a relationship between ice and lightning, but were learning new details by studying the National Aeronautics and Space Administration satellite images which can look at both the number of lightning strikes and the volume of ice in a cloud at the same time.

    Crucial is what is called precipitation-sized ice, particles of a millimeter or so which sometimes can be seen falling as small hail. ”Where you have more of that, you tend to have more lightning,” Petersen said.

    These particles crash into smaller ice particles in the swirling winds inside storm clouds, resulting in a separation of electrical charge.

    The charge separated between smaller and larger particles, with the smaller carrying a positive charge to the top of the thundercloud and the larger ones with the negative charge sinking to the bottom, he explained in a telephone interview.

    ”You effectively make a big battery with positive and negative ends,” he said, with the charge building up until it is discharged as lightning.

    The relationship between ice volume and lightning held true over such varied locations as the Himalaya Mountains, Central Africa, Madagascar, northern Australia and Florida, the researchers reported.

    They found small areas of subtropical South America where lightning flash density seemed slightly less than would have been expected for the measured ice amount. Since they could find no physical reason for this the researchers said it may be a sampling error. They are doing more research on those areas.

    The work was funded by the NASA’s Earth Observing System and Earth Science Enterprise programs.

    ^——

    On the Net:

    Geophysical Research Letters: http://www.agu.org/journals/gl/

    [Response:Thanks! There is little doubt that electric charges play a role in lightning and there is a relationship between ice crystals and charge separation. But this is not the same as to say that the exact state of the ionosphere has strong influence on particular cases. Yes, the ionosphere plays a role, but I believe more as setting the stage (eg the fair weather electric field). -rasmus]

  17. 67
    Almuth Ernsting says:

    Re 14 and 23:
    Here is a very interesting report about ‘excess winter deaths’ in Europe:

    It pretty much demolishes the idea that excess winter mortality is linked to people living in countries with particularly low temperatures, or to a wide annual temperature range.

    It states that excess winter mortality is particularly high in the UK, but also in Ireland, Italy, Spain and Portugal. It is lower in most parts of northern Europe, ie in countries with a greater annual mean temperature range. A considerable number of those deaths is linked to influenza (and nobody has shown that flu, or infectious diseases will diminish under GW). Influenza alone cannot explain the number of winter deaths in the UK, but it would be interesting to see whether it can explain them in those many northern European countries with much lower winter death rates. Deaths from hypothermia in the UK are rare.

    Housing conditions have been blamed widely for those deaths, and given that I used to work for a housing charity in Scotland this is not in the slightest surprising – we have many thousands of properties which are below tolerable standard, hard or impossible to heat, with single-glazed windows in rotting window frames, draughty doors, and above all extreme condensation and rising damp (and they are dreadfully unhealthy in a mild, wet, windy winter too). Over recent years, there has been some (though not enough) progress with regard to housing standards, insulation and fuel poverty and you would expect to see lower winter death rates as a result.

    In short, UK mortality rates really give no evidence that GW will mean less deaths worldwide – it is a particular housing and social problem we have which can be fixed quite easily with some decent housing and public health investment and does not require us to heat the whole planet!

  18. 68

    NOAA just reported July 2005 as the warmest in history for the Northern Hemisphere.

    http://lwf.ncdc.noaa.gov/oa/climate/research/2005/jul/global.html#Temp

    Contrairians will easily postulate that this is caused by concrete cities or some likewise lame esoteric explanation. There is no vast big cities in the Arctic (except for a couple in Russia). For students of our world climate this event is extraordinary giving that El-Nino is inactive. I would be interested in reading comments from Climatologists about this phenomena. AGW is certainly the cause, but the driving force behind this years spike is surely the Arctic Ocean, which had much broken ice seen as early as February 05. This transpired in an Arctic Ocean which can be sailed from Nordcapp Norway Eastwards all the way back to Nordcapp by way of the Russian Northeast and Alaska-Canadian Northwest passages.

  19. 69
    Stephen Berg says:

    To further #68,

    “The average global temperature anomaly for combined land and ocean surfaces for July (based on preliminary data) was 1.1 degrees F (0.6 degrees C) above the 1880-2004 long-term mean. This was the second warmest July since 1880 (the beginning of reliable instrumental records). The warmest July was in 1998 with an anomaly of 1.2 degrees F (0.7 degrees C) above the mean. There were warmer than average conditions in Scandinavia, much of Asia, North Africa and the western U.S., while below-average temperatures occurred in northern Canada and northern Alaska. Ocean temperatures were also second highest on record.”

    http://www.noaanews.noaa.gov/stories2005/s2489.htm

  20. 70
    Stephen Berg says:

    “Sea Ice May Be On Increase In The Antarctic: A Phenomenon Due To A Lot of ‘Hot Air’?”:

    http://www.sciencedaily.com/releases/2005/08/050819093118.htm

  21. 71
    Stephen Berg says:

    #70 (continued):

    However, “Arctic Ocean Could Be Ice-free In Summer Within 100 Years, Scientists Say”:

    http://www.sciencedaily.com/releases/2005/08/050824081334.htm


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