Volcanoes and Drought In Asia

Guest Post by Willis Eschenbach

There’s a recent study in AGU Atmospheres entitled “Proxy evidence for China’s monsoon precipitation response to volcanic aerosols over the past seven centuries”, by Zhou et al, paywalled here. The study was highlighted by Anthony here. It makes the MADA overviewclaim that volcanic eruptions cause droughts in China. Is this possible? Sure. But have they made their case? … well, that is far from sure.

As is far too common, the authors have not archived either the data as used or the code as used. So, again as usual, I’ve gone to take a look at the data. Their main dataset is a reconstruction of the Palmer Drought Severity Index (PDSI) for China since the year 1300 … and how do they know what the PDSI was in China in the year say 1492?  

… Well … they are using a PDSI reconstruction called the Monsoon Asian Drought Atlas (MADA), by Cook et al. The MADA reconstruction and the description are here. Cook et al. say we can reconstruct the PDSI using tree rings. Now, this is a step above using tree rings for temperature, but still … they’re trying to reconstruct the PDSI on a 2.5° x 2.5° grid basis. Here’s the problem:

MADA overviewFigure 1. Cook et al. Figure 1B. ORIGINAL CAPTION: More detailed view of the MADA domain; the 534 grid points of instrumental PDSIs (red crosses) were reconstructed by the 327-series tree-ring chronology network (green dots).

As you can see, there are huge areas of both Asia in general and China in particular that do not have any trees within a long, long ways of the grid points. Cook discusses the various methods that were used to do the reconstruction, and you can read about them here, but I can’t claim that I was impressed. No matter how clever you are, you have more grid points with no data than grid points with data … sketchy.

In any case, I went to look at the MADA data. The study itself doesn’t show a graphic of the data … and given what the data looks like, I can’t say I’m surprised that they didn’t show it:

reconstructed PDSI from MADAFigure 2. Area-weighted average of the MADA reconstruction of the Palmer Drought Severity Index (PDSI). Negative numbers indicate drought. According to Zhou et al, “positive MADA values stand for wet conditions while negative values represent dry conditions; droughts develop while MADA values fall below 0.5.”

I’m sure that you can see the problem. According to the tree ring proxies, Asia is in the midst of the worst drought in seven hundred years … curious how that hasn’t made the headline news. How do Zhou et al. deal with that? Well … they don’t comment on it at all.

That alone would disqualify or at least raise serious questions about the validity of their study (and the MADA reconstruction) for me, but it gets worse. In the abstract, Zhou et al. say:

Results show a statistically significant (at 90% confidence level) drying trend over mainland China from year 1 to year 4 after the eruptions.

A 90% confidence level? Ninety percent?

Ninety percent confidence gives me no confidence at all. But it gets worse. Here are their results:

zhong stacked epoch analysis MADA dataFigure 3. Zhou et al. results of the stacked “Superposed Epoch Analysis” (SEA) of the MADA drought data, along with the Chinese Historic Index of droughts (CHI, panel b). INH2p shows northern hemisphere or global volcanoes twice the strength of Pinatubo, INH1p shows volcanoes the strength of Pinatubo or greater, INH1/2p shows volcanoes half the strength of Pinatubo or more, ISH shows volcanoes only affecting the southern hemisphere. Note that the sense of the MADA and CHI indexes are reversed, with positive CHI values indicating more drought and positive MADA values indicating wetter conditions.

They are using “stacked” data, what they call a “Superposed Epoch Analysis”. In this type of analysis, you align the data from the years surrounding each eruption at the dates of the eruptions, and then average them from five years before the eruptions to five years after the eruptions.

So what’s not to like?

Well, the first thing that I don’t like is that there are no error bars on the results. Bad scientists, no cookies. Considering that there are only six INH2p eruptions (Injections of sulfates in the Northern Hemisphere twice Pinatubo strength) in the IVI2 eruption dataset that they used, this is a huge omission.

Next thing I don’t like is that they’ve got data from 1300 to 2005, but they are only using data from 1400 to 1900 … not sure why they did that, but it does make me suspectful.

Next thing I don’t like is that the CHI index shows no effect at all the first year after the eruption, with the maximum effect of the NH volcanoes in the second year only, and things returning to pre-eruption values in the third year. But the MADA data shows the effects starting the year after the volcano, peaking during the third year, and not returning to normal until after the fifth year … there is no discussion of this difference.

Final thing I don’t like? I can’t replicate their results. Here’s what I get for the MADA data (I haven’t bothered with the CHI data).

stacked epoch analysis MADA dataFigure 4. My results for the Superimposed Epoch Analysis of the MADA drought data. Error bars show the 95% confidence interval for each point. Points are offset slightly to show the individual error bars.

This shows the importance of error bars. Out of the 44 points in the four analyses, there are only two which are significantly different from zero. With forty-four data points, random chance alone should give us up to 5 data points which are “significant” at a 95% confidence level … so they’re not doing better than random.

One final issue. They say:

Results obtained from the above methods are based on the assumption that there is no temporal correlation of the precipitation proxies. CHI is obtained from historical documents and thus is independent in time and space. MADA is reconstructed from the tree ring data which should be determined largely by the meteorological conditions of the individual growing season so the data should have no correlation in time.

Autocorrelation is very important in assessing the statistical significance of a result. As a consequence, it seems to me that these assumptions about the autocorrelation of the reconstructions need to be tested and verified rather than assumed and asserted … especially given that the PDSI for the US 1895-2009 has a lag-1 autocorrelation of about 0.5.

CONCLUSIONS:

• The MADA reconstruction of the Palmer Drought Severity Index shows a very strange dropoff at the end (see Figure 2), which indicates that there is something seriously wrong with or omitted from either the proxy data, with the reconstruction method, or with the underlying assumption of linearity. Curiously, it appears to be a version of the “divergence problem” seen in other tree-ring reconstructions, and which no one has ever satisfactorily explained. In temperature reconstructions the narrow rings are said to represent cool temperatures in recent years, despite the acknowledged slight warming. If the same narrow rings appear in a drought reconstruction, on the other hand, it would be interpreted as dry conditions.

• The lack of error bars renders their results meaningless.

• The differences between the MADA and the CHI results indicates further problems with their datasets. Strangely, they show no direct comparison of the MADA and CHI data.

• In my analysis including error bars, only two of the forty-four data points resulting from the SEA analysis are significantly different from zero at the 95% level.

• They use a very low 90% significance level for their overall results.

• They have assumed a lack of autocorrelation of the MADA and CHI data, but apparently have made no effort to actually calculate the autocorrelation.

• I am unable to replicate their results.

• Since they have not posted either their data as used or their code as used, I am unable to determine the reason for the difference between their results and mine. It may be my error entirely, perhaps my foolish error, but without their data and code I can’t tell. However, even if I could replicate their results, the other errors invalidate the study on their own.

There are other problems with the study, but I downloaded the data last night in Salem, Oregon, and I’ve done this entire analysis on a train rolling south to the middle of California. Right now it’s 11:45PM, and I can’t be bothered to mess with this nonsense any more. I gotta say, these kinds of pseudo-scientific studies are getting old … in any case, at present their results are useless.

Best regards to all, and don’t believe everything that you read in the “scientific” journals,

w.

THE USUAL: If you disagree with someone, please QUOTE THEIR EXACT WORDS THAT YOU DISAGREE WITH. Don’t just reference their entire comment, quote only and exactly where you think they went off the rails. This avoids all manner of problems and misunderstandings.

DATA AND CODE: The source for the MADA data is given above. That data, plus the IVI2 volcano data used in the study and the R code, is in a folder called “MADA folder.zip“.

48 thoughts on “Volcanoes and Drought In Asia

  1. Too many factors affect tree-ring growth so why use them? If you have a theory it’s the perfect pick because somewhere you will find tree-ring data that support it?

  2. This looks like another form Briffa’s divergence problem. A notable deviation since c. 1960.

    Maybe this tells us something about trees and the problems of their use as thermometers.

    Whether this geographically representative or not , there are large number of site which, while unevenly placed cover some widely spaced sites. There is a clear signal of something after 1960.

    Are these tree rings showing a variation in the same physical measurement as the Briffa tree proxies?

    Apparently it’s not drought. It went the wrong way for temperature rise. So what is the variable trees are so strongly responding to ?

    CO2 or something more subtle ?

    I have other things to do today but this may be worth looking into.

  3. the Earth is interring a cool down, a reversion to the mean. Buy stocks in coal companies. CAGW adherents are about to find that Mother Nature calls the shots, not mankind’s CO2.

  4. Odd, I just sent a post with nothing questionalbe in it but it disappeared, no moderation tag. Just gone. More WordPress magic :(

  5. This inverse hockeystick should be compared to Briffa’s divergence problem. Could tell us what trees are responding to since 1960.

  6. ” Cook discusses the various methods that were used to do the reconstruction, and you can read about them here, but I can’t claim that I was impressed.”

    That’s paywalled. Did you manage to actually get the paper?

    BTW I love the contact address:
    E-mail: drdendro@ldeo.columbia.edu

  7. Ah, I missed this bit:
    As a service to the community, AAAS/ Science has made this article free with registration.

    As soon as I see a log-in I tend to back out pronto.

  8. The mid–18th-century Strange Parallels drought
    over Southeast Asia (Fig. 2B) coincided with a
    time of substantial societal upheaval and political
    reorganization across Southeast Asia and simul-
    taneously across the Siberian plains (17). This
    drought was first identified from a teak ring-
    width record from northwest Thailand (20) and
    later corroborated in a northern Vietnamese cy-
    press chronology (21).

    Googling Strange Parallels drought does not seem to give anything but refs to this paper or citations thereof.

    The two refs that identified this “dought” were also tree rings ( from individual trees ).

    Those tree ring “droughts” are then taken to be corroboration of Cook’s “Strange Parallels drought”.

    Having read the paper I still don’t know what physical measurement they are using and how they correlate it to rainfall, whether they take density or tree age into account. …..

    In fact I have not found any tree-ring data.

  9. Willis,
    You probably know the following, but there is an error that has become endemic in climate change style statistics that acts to mask potentially serious consequences.
    Your calculated ‘error bars’ do not show total error because they lack a component of accuracy errors. What you and the authors have shown is a numerical estimate of variability of the numbers, or a rough estimate of precision. Total error includes both precision and accuracy errors.
    Accuracy errors can be larger than precision errors in earth science data.
    (If you get picky, precision error calculations could be wrong if they rely on the assumptions that certain distributions of the numbers apply and possibly that the numbers need to be shown as i.i.d., meaning independent and identically distributed, as you no doubt know.)
    That aside, your quick analysis of this paper shows problems, no argument. These problems can be found in other work. For example, Ed Cook’s work on Tasmanian Huon Pine trees, Lagarostrobos franklinii, can also be criticised for lack of a proper temperature record for proxy calibration.

  10. A new book by Timothy Brook (Harvard University Press) attributes the fall of the Ming dynasty to Climate Change! The publisher’s blurb reads:

    ‘The Mongol takeover in the 1270s changed the course of Chinese history. The Confucian empire—a millennium and a half in the making—was suddenly thrust under foreign occupation. What China had been before its reunification as the Yuan dynasty in 1279 was no longer what it would be in the future. Four centuries later, another wave of steppe invaders would replace the Ming dynasty with yet another foreign occupation. The Troubled Empire explores what happened to China between these two dramatic invasions.

    If anything defined the complex dynamics of this period, it was changes in the weather. Asia, like Europe, experienced a Little Ice Age, and as temperatures fell in the thirteenth century, Kublai Khan moved south into China. His Yuan dynasty collapsed in less than a century, but Mongol values lived on in Ming institutions. A second blast of cold in the 1630s, combined with drought, was more than the dynasty could stand, and the Ming fell to Manchu invaders.’

    Nah, couldn’t be – current climate change is unprecedented, The Guardian says so every day!

  11. Willis said;
    “Next thing I don’t like is that the CHI index shows no effect at all the first year after the eruption, with the maximum effect of the NH volcanoes in the second year only, and things returning to pre-eruption values in the third year.”

    Actually I wouldn’t expect the tree rings to be affected much the first year of the drought depending on whether the drought hit during the springtime portion of the year or not. The vast majority of the tree ring growth occurs in just a few months out of the year.

    Tree rings generally sample just a couple of months out of the year. So ‘yearly’ precision seems problematical.

  12. Thank you Willis, very entertaining. What is the purpose of publishing a paper at a 90% confidence?

  13. Seeing this same drop in tree ring size after 1960 is very interesting. I wonder if smaller tree rings always mean less growth or is it possible to have denser wood make the tree ring narrow?

    Also, only two large things (maybe a few more) have happened that I can think of around mic-century. A large increase in CO2 is one, the atomic bomb tests all over the world is another. I guess a few more would be increase in jet aviation, chlorofluorocarbons, etc. Just thinking of things that really increased and could have a world-wide effect, now that the same pattern is seen in SE Asia as in N. hemisphere tree rings.

    CO2 (all else equal) make plants grow more, so unless the tree rings were more dense, this seems the opposite of what you would see from CO2. Of course, a decrease in temperature world wide (during growing season) could explain it. Seems to me that this is something that should be studied intensely rather than hiding the data. Very interesting mystery. Could even be anthropogenic.

  14. More dubious science and one has to wonder at the low standards seen in climate science.
    Too bad, because events such as prodigious volcanic eruptions are topics worthy of exploration.

  15. Bill-W

    I agree, it is a topic most worthy of examination. There is a fair chance that it is anthropogenic. It is a mystery why no one has delved into this intriguing question.

  16. I’m more concerned about geoengineered aerosols than volcanic aerosols. Like manmade stratospheric seeding with refractory metallic particles,like Colloidal Silica, Silica gel, aluminium oxide, thorium oxide gel and god knows what else.

  17. The only reliable data from tree rings is that they grew more in some years than in others. What it doesn’t and can’t tell is why.

    It could be any combination of so many different things – temperature, rainfall, CO2 levels, cloud cover, leaf disease, flash floods removing nutrient rich soil, a species becoming more or less dominant compared to competitors, or even bush fires.

    I don’t understand how any reputable scientists can make any claims based on tree ring data that go beyond stating they grew more in this year than in that – but maybe a big fat check (cheque) for researching ‘climate change’ would free my mind from such scientific rigor (rigour) ……

  18. We lost a huge white oak a couple of years ago. Counting the rings it was about 165 yrs old.

    The interesting part was how tightly the rings were packed until 1927, then all of a sudden the tree took off. My house was originally built in 1927. Coincidence or climate change??

  19. “We lost a huge white oak a couple of years ago. Counting the rings it was about 165 yrs old.

    The interesting part was how tightly the rings were packed until 1927, then all of a sudden the tree took off. My house was originally built in 1927. Coincidence or climate change??”

    Maybe the tree-rings are the cause for modern experienced global warming?

  20. Maybe the downward curve shows people are limbing trees for firewood but using more live wood than dead because there isn’t enough dead wood (not like Washington DC at all). Stripping younger trees would also impact growth. If it keeps them warm people will burn anything they can. The missing data point in this analysis is population – you don’t get to a billion people by sitting in the lotus position all day. Someone has to gather (from farther afield and from ever higher bows) wood for the hearth. Transportation also improved substantially thanks to better carts and wagons, draft horses large and small, and other beasts of burden that secondarily were tasty. http://soulontigerhorse.com/body_index.html

  21. “Thank you Willis, very entertaining. What is the purpose of publishing a paper at a 90% confidence?”

    what is the purpose of 95%. both are arbitrary.

    it would be better just to report the observed significance.

  22. Quick, Willis! Chop off those inconvenient trees at the end of the graph and replace them with “real” data. No-one will notice. It works every time!
    Or, if you don’t have the time, just flip the Y axis.

  23. So tree-ring data can reflect temperatures AND/OR precipitation?

    Don’t disagree but I sure would like to see the study that disentangled the two variables
    .

  24. dp says:
    August 10, 2014 at 8:08 am
    Mosh – meaningless low-confidence papers can be counted to advantage in Lewandowsky polls.
    ==========================================================================
    Also very valuable for global warming propaganda

  25. Coincidence or climate change??
    ================
    clearing the land in 1927 to build your house changed the climate of the world. the dust bowl era of the 1930’s was the result. a similar effect continues today. every time I pee in the ocean sea level rises. if I don’t stop drinking beer, pretty soon Gore’s, Flannery’s and Suzuki’s houses will be all be awash.

    So strange these climate apocalypse guys buying houses near the ocean. Could it be that all the hype over sea level rise drove down prices, make waterfront a good investment? Could it be that the market is the most efficient way to deal with climate change? That all that governments need do is simply get our of the way?

    For sure, the immigration problem on the US southern border is a result of climate change. As the climate heats up south of the border, all the kids are heading north to the US so they wont fry in 100 years. Luckily Barry Oh and his buddies are moving to outlaw demon coal, guaranteeing big oil a monopoly on US energy production. What could possible go wrong there? It isn’t like the US has every experience an oil crisis. Along with global cooling, the 1970’s oil embargo never happened.

    Even more amazing, the US maintains a Strategic Petroleum Reserve, with a whopping 36 days worth of oil, but apparently has no need for a Strategic Coal Reserve. Even though coal is the number 1 source of electricity in the US. Could it be that the US has plenty of Coal, so must make it illegal to burn coal, while oil which is in short supply, will become the fuel of choice? All the coal burning electric cars, doing their bit to stop global warming. Only in Amerika.

  26. The other Ren says:
    August 10, 2014 at 7:03 am
    ==================================================
    Was that oak tree somewhat close to the house? Did it start to receive extra water from the residents of the house?

    I worked in the woods in the logging trade during the 1970s. I had the opportunity to look at many tree stumps. I also had 80 acres in the mountains in the mid 1970s. The Douglas fir trees on the property were almost all second growth trees. They were around 90 to 120 foot in height, and when I logged around 10% of them the rings showed their age to range between 70 to 110 years old. They were fast growing with ring patterns of 6 to 8 rings per inch. Although, it could be seen that in their early years the rate of growth was slower, around 12 to 15 rings/inch. That would correspond to what is being noted by others here that around the early 1900s tree growth accelerated. I did have one old tree that I harvested. It was 6′ by 9′ on the stump, and yielded 18,000 bd/ft. The tree was 175 foot tall, and a ring count showed that the tree was around 360 years old. It had very tight grain through most of the wood, around 25 rings/inch. The outer rings showed a faster rate of growth of around 12 rings/inch, which corresponded to an increase in rate of growth around 1900. It would be interesting to take another look at that stump.

  27. Curiously, it appears to be a version of the “divergence problem” seen in other tree-ring reconstructions, and which no one has ever satisfactorily explained.
    =========
    the Team of Manniacs explained it at the time. Increased CO2 made trees grow slower, giving a false impression that solar intensity dropped off after 1960, so they truncated the data. The notice was on display in the bottom of a locked filing cabinet stuck in a disused lavatory with a sign on the door saying ‘Beware of the Leopard’.”

  28. Well a quick look on Google Earth suggests that most of their trees are in the Himalayan foothills, or in hill ranges bordering the Gobi and Takimakan deserts. Not sure you could grid those over the whole of china… Admit it you are trying to wind us up for a bet…..I mean 10% significance level, YGBSM, right…..:-)

  29. Another thing not to like about the result:
    Figure 1b, blue and cyan lines seem to show an ability for the CHI to respond a year before the eruptions. That’s hard to explain. It is in fact, evidence of the size of the error bars in their analysis.

  30. ‘When I use a word,’ Humpty Dumpty said, in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

    A tree ring means just what a climate scientist chooses it to mean.

  31. The superposed epoch analysis code isn’t included in the zip file, so we cannot tell what’s been done differently. Since the significance test is based on a Monte Carlo procedure, it might be misleading to show error bars on the plot. The Monte Carlo procedure can take care of temporal autocorrelation – the author of the method are explicit about this.

  32. People get ill from the air pollution in China and India, perhaps some of the same consequences happens to trees. I think that tree rings could be interesting, and that much good work have been done with the method, but perhaps the necessary analysis is not developed yet to interpret exactly what you find. What do chemical analysis show?

  33. richard telford says:
    August 10, 2014 at 1:01 pm

    The superposed epoch analysis code isn’t included in the zip file, so we cannot tell what’s been done differently.

    Hi, Richard. If you mean my zip file, the SEA code is indeed there. It’s a portion of the R code entitled “chinese droughts.R”. It’s not all that elegant, I could likely do it as a very short function, but I used a loop instead.

    Since the significance test is based on a Monte Carlo procedure, it might be misleading to show error bars on the plot.

    The more items that you average, the more accurate the mean value becomes. With only 6 data points, e.g. the six eruptions that are twice as strong as Pinatubo, the average is not all that accurate. Thus the blue results in Figure 4 have a large error bar and the The category that includes all known eruptions, on the other hand, will have a more accurate average.

    The Monte Carlo procedure can take care of temporal autocorrelation – the author of the method are explicit about this.

    Of course the “Monte Carlo procedure can take care of temporal autocorrelation” as you say. The question is not whether it can, that’s a given. The question is whether in this case it DOES take care of temporal autocorrelation … and we don’t know whether it does or not.

    Without their code, I fear that you have absolutely no way of determining whether that is true.

    Without their code, we have no idea how well they have been able to emulate the real data. Heck, their code could contain some simple but not obvious bug. Thus, their claims of significance are the output of a black box. That’s not science, that’s just using “Monte Carlo, Monte Carlo, Monte Carlo” as a magical incantation.

    Your comment has made me think of an alternate way to look at the data, kind of an expanded Superposed Epoch Analysis. I’ll take a look.

    Regards,

    w.

  34. Furthermore, what’s special about 95%? Are you going to be completely convinced of significance at 95.0%, but completely unconvinced at 94.9%?

  35. Old England says:

    August 10, 2014 at 6:47 am

    “The only reliable data from tree rings is that they grew more in some years than in others. What it doesn’t and can’t tell is why.

    It could be any combination of so many different things – temperature, rainfall, CO2 levels, cloud cover, leaf disease, flash floods removing nutrient rich soil, a species becoming more or less dominant compared to competitors, or even bush fires.”
    ———
    I do agree with the first paragraph of your comment. However in the 2nd paragraph, I would also add insect predation on the leaves, bark beetles, and other things that are easy to speculate upon.
    But speculation or not, they could affect tree ring widths.
    Thanks for your comment, made me remember when I first started reading tree ring papers it seemed they were almost always used for precipitation proxies, which of course, also had all the problems you mentioned.
    Good comment.

  36. Some thoughts about tree rings: http://www.air-quality.org.uk/15.php
    “How Acid Rain Harms Trees
    Acid rain does not usually kill trees directly. Instead, it is more likely to weaken the trees by damaging their leaves, limiting the nutrients available to them, or poisoning them with toxic substances slowly released from the soil. The main atmospheric pollutants that affect trees are nitrates and sulphates. Forest decline is often the first sign that trees are in trouble due to air pollution.
    Scientists believe that acidic water dissolves the nutrients and helpful minerals in the soil and then washes them away before the trees and other plants can use them to grow. At the same time, the acid rain causes the release of toxic substances such as aluminium into the soil. These are very harmful to trees and plants, even if contact is limited. Toxic substances also wash away in the runoff that carries the substances into streams, rivers, and lakes. Fewer of these toxic substances are released when the rainfall is cleaner.
    Even if the soil is well buffered, there can be damage from acid rain. Forests in high mountain regions receive additional acid from the acidic clouds and fog that often surround them. These clouds and fog are often more acidic than rainfall. When leaves are frequently bathed in this acid fog, their protective waxy coating can wear away. The loss of the coating damages the leaves and creates brown spots. Leaves turn the energy in sunlight into food for growth. This process is called photosynthesis. When leaves are damaged, they cannot produce enough food energy for the tree to remain healthy.
    Once trees are weak, diseases or insects that ultimately kill them can more easily attack them. Weakened trees may also become injured more easily by cold weather.”

    This has been a problem in many forests, I think. Together with the Asian black smoke and Ozon and other pollutants, this must have an effect.

  37. And it was this fish death in small lakes and rivers in the 60-ies and 70-ies which is well known, at least in Nothern Europa.

  38. The tree ring network cannot realistically be extended to provide data for the points in the PDSI grid, no matter what cunning data manipulation system one might have at hand.

    If trends can be observed across the tree ring network they could possibly be applied across east Asia but only in a very general sense. And what trends ? Do tree ring widths provide information about rainfall, temperature, CO2, cloud cover, effects of volcanic dust, tree age or other things I haven’t thought of or a combination of all the previous variables ?

    Volcanic eruptions causing drought in China ?

    Possibly but Zhou et all will need more than tree rings to make the case.

  39. “Furthermore, what’s special about 95%? Are you going to be completely convinced of significance at 95.0%, but completely unconvinced at 94.9%?”

    What was special was that in the days before computers did this for you and the calculation was a PITA you used to do your test and look the value up in the relevant book of tables, which typically were calc’ed out at 10%, 5%, 2.5%,1%,0.5%….

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