God help Texas. Rick Perry won’t.

Politico reports that former president Bill Clinton lambasted Republican politicians who are in denial of global warming. “If you’re an American, the best thing you can do is to make it politically unacceptable for people to engage in denial” about climate change, the former president said. “I mean, it makes us – we look like a joke, right? You can’t win the nomination of one of the major parties in the country if you admit that the scientists are right? That disqualifies you from doing it? You could really help us there,” Clinton added.


Clinton was referring to the host of Republican presidential candidates who have adopted an anti-science agenda. This includes denial of global warming. In some cases (Michelle Bachmann) it includes begin duped by those who link autism with vaccinations. And in many cases (Rick Perry) it includes disbelief in evolution itself. The unwillingness of Republican leaders to accept science has frustrated even some Republicans — but the only presidential candidate willing to accept reality is John Huntsman, who recently said, “To be clear. I believe in evolution and trust scientists on global warming. Call me crazy.

Huntsman appears to be the only Republican candidate who isn’t crazy. Evidently, John Huntsman’s sanity disqualifies him for the Republican presidential nomination.

But Texas governor Rick Perry seems popular with the Tea Party and Republican hard-liners. His approach to global warming is to deny reality and blame scientists for faking data. It’s Rick Perry who’s faking the facts. Meanwhile, the state of Texas, back in June, set a new record for their hottest June ever. Then in July, they set a new record for their hottest month ever. But that didn’t last long. In August Texas set a new record for the hottest single month ever recorded by any state of the U.S.A.

They’re also in the grip of a tremendous drought. Rainfall over the last 12 months has been lower than any other 12-month period in Texas history. Crops are failing, livestock are in peril, wildfires have set new records for acreage burned, thousands of homes have burned to the ground, and Rick Perry’s “solution” is to ask the state to pray for rain while he cut the state budget for the firefighters who have to face the conflagration. The old saying is, “God helps those who help themselves.” That doesn’t include Rick Perry.

Texas state climatologist John Nielsen-Gammon highlights the combination of drought and heat with his excellent post spot the outlier. He begins with a scatterplot of summer (June through August) rainfall against summer temperature:

There’s a rather obvious correlation, with wetter summers tending to be cooler while dryer tends to mean hotter. Nielsen-Gammon also shows an approximate relationship between the two, plotting a quadratic fit of temperature to rainfall. But his first plot doesn’t include this year, so he adds 2011 data in his second plot:

Can you “spot the outlier”?

I reproduced his graph and got the same result:

Clearly we can blame some of the heat this summer in Texas on the drought. But just as clearly, we can’t blame it all on the lack of rainfall, because 2011 isn’t just on the line of the rainfall-temperature relationship, it’s far enough above that line (hotter) to be an “outlier.” And it’s not the only year since the turn of the millenium to be hotter than expected given the rainfall amount. Here’s the same graph with years since 2000 circled in red:

Note that 11 of 12 years are above the line — hotter — while 1 is (just barely) below.

We can even compute the difference between summer Texas temperature, and the expected temperature given the rainfall using Nielsen-Gammon’s quadratic model. We can call this the “excess summer temperature,” and here’s the time series of values:

If you wan’t to be worried, you can worry about the Texas drought. You can worry about the Texas heat. You can worry about the record-setting summer heat this year. But perhaps you should worry even more, not about this record-smashing year, but about the increasing trend in Texas summer heat.

Perhaps most of all, you should worry about how Texas will cope when their governor is in denial of a reality which threatens his home state. Or maybe you should worry about Perry becoming president of the United States. The president is “driving the bus” for the country — let’s not put a blind man in the driver’s seat.

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69 responses to “God help Texas. Rick Perry won’t.

  1. Seems like only seven months ago Texas was smashing cold records.

    [Response: Not only did you make it up, you've actually started to believe it. Unless of course ...]

    • Nope – not made up – I assume it was only local (not statewide) but Dallas, for one example, set record colds in February.

      [Response: Local daily records are broken all the time -- see for example here. Your attempt to equate that to, say, the hottest month on record for any state anywhere, shows how delusional you are.]

      • Not completely made up, just totally misleading:
        Dallas was extremely cold for the first 4 days of February, and the maximum temperature of 20 on the 2nd was a new record low for the date. The minimum of 15 on the 10th was also a new low record. However, by the 13th, temperatures were above average for every day of the rest of the month except 1, and the month as a whole was . . .
        0.1 degrees above average

  2. Wow, that really *is* an alarming trend.

    Is similar data available for the temperature extremes? (i.e. maximum daytime temperature, and temp+humidity)

    I’m curious what the trend would be in, say, wet bulb temperature, which is quite relevent in the context of this:
    http://www.pnas.org/content/107/21/9552
    (freely available here [pdf])

    Of course, the extremely low rainfall implies very low humidity, but the fact that all of the last decade is above the trend line in the graph above suggests there’s been a measurable shift already.

  3. The quadratic term in that model looks unlikely to be significant. Would that be right?

    [Response: Yes. I'm not sure why Nielsen-Gammon included it, but it doesn't spoil the fit, and using a linear trend would make 2011 even *more* exceptional.]

  4. The drought this winter was also quite cold, but I think it was only a 1 in 10 or 1 in 20 cold year. It was quite cold, so there were a lot of dead 10 year old palm trees.

    • For the winter as a whole (Dec-Feb), Texas was only 42nd coldest (out of 116 years):
      http://www.ncdc.noaa.gov/sotc/service/national/Statewidetrank/201012-201102.gif?opt=final

      • There were 1 in 20 year extremes in terms of length of freezes and level. It is more obvious when there is a hard freeze for a few days when there never usually is one most years, this is what will have stood out for many Texans.

    • I know it snowed in Houston last winter, and Oklahoma broke its all-time record low. But you’re right, the heat of this summer is on a completely different level to the cold of last winter.

    • This or that record isn’t as significant to me as the fact that most ensemble runs of GCMs predict drought to be an increasing problem in various regions around the world. The American South West is one of those regions.

      In billiards or Horse when you call a difficult shot and make it, you’re given credit. With GCMs not only have climate scientists called the shot, they’ve demonstrated the reasons why. (A called event without a demonstration of the whys and wherefores is meaningless.)

      • I have homes in both Dallas and Houston, and have lived in Texas since 1980. This summer is unlike anything I have ever seen, and the drought hit Dallas later in the summer than most of the state. My neighbor purchased his house in the 1950s. He says the city had to supplement its water supply with water brought in from Oklahoma, which caused serious plumbing problems. But in terms of what this summer has been like, he does not think any summer in the 1950s compares.

        In April I started a cactus garden. Lol.

      • Admittedly, I’m not on top of everything, but from what I can find with a quick search (like, say, this paper) the ensemble model results for precipitation look sort of ambiguous for the American Southwest, which is sandwiched between regions of precipitation decrease to the south and increase to the north. Maybe the very southern edge of the U.S. (southern Texas included) falls in the zone where 66% of models predict winter precipitation decreases, but it’s not so clear for the Southwest as a whole.

        Perhaps you could say that individual models are “calling their shots” with regard to regional droughts (NOAA’s GFDL model projects precipitation decreases in the Southwest, for instance), but it’s not necessarily the bulk of them. My impression is that in the current state of climate modeling, predicting regional precipitation changes is still a tentative exercise at best, but regardless, the global patterns are clear (see this map from the first paper or this figure from the second): the latitudes around 30 degrees will experience the most drastic decreases. Southern Texas falls in that band, so…

        Anyway, I guess what I’m saying is that this seems less like calling a corner bank shot in the far right pocket and more like calling which quadrant of the table the ball will end up in, then sinking an extremely unlikely shot. Ensemble climate projections are by nature conservative, and the current drought is so far beyond those conservative expectations that it would be silly to say you called it ahead of time. But you did get the right corner of the table.

      • I’m going to say it was around 7 years ago that I started seeing articles in the Texas press about drought becoming a persistent problem, and one article in particular said that, unlike previous droughts, much of west Texas would eventually be in a very prolonged drought. But from memory, that was a mid-century prediction.

  5. Gavin's Pussycat

    Isn’t calling for prayer as a matter of state policy a violation of the 1st amendment? The US Constitution’s first amendment applies to a Texas governor, right?

    [Response: I'm no expert on constitutional law, but I think it's legitimate for a gov't. agency or official to appeal for prayer so long as they don't specify *which* deity is to be petitioned. And, the U.S. has a long history of "looking the other way" when it comes to the infiltration of Christianity into government.]

    • Horatio Algeranon

      The office of “Governor of Texas” (current and former) raises one above all law (including the physical kind).

      • Horatio Algeranon

        “Unbridled Stallions”
        — by Horatio Algeranon

        The Texas Governor isn’t bound
        By petty Constitutions
        He’s unrestrained by contracts
        And new years resolutions

        In fact, he rises high above
        The laws that govern masses
        Of Jefferson and Hamilton
        Newton and the gases.

    • Gavin's Pussycat

      OK (LOL) thanks! Not very inclusive of atheists then…

  6. One point about the choice of a quadratic, or even linear, fit is the fact that negative precipitation is impossible. This would suggest that any underlying temp v precip relationship must significantly change shape as precip approaches zero. If we continue to assume that increased temperatures are associated with decreased precipitation, then the curve should become very steep at low precipitation levels, which should result in 2011’s “excess heat” being somewhat less extreme.

    Another concern is my suspicion that this relationship probably isn’t causal – dry conditions don’t generally cause warming, and warming doesn’t generally cause decreased precipitation. It seems more likely to me that the dry conditions are associated with warmer temperatures because of a third factor (for example, sea surface temperature patterns and/or the dynamics of upper atmosphere phenomena like the jet stream).

    Finally, it would be interesting to know if GCMs tend to reproduce this general relationship (decreasing summer rain with increasing summer temperature) in the Texas region. I know that GCMs tend to strongly predict the opposite in my part of the world (Canadian Prairies).

    [Response: The correlation is certainly significant. And it strikes me as quite plausible that it's causal, because evapotranspiration is such an important cooling mechanism. The lack of water on the ground, in lakes and rivers, in the soil, in plant tissues, seems plausibly a cause of reduced evaporation and therefore reduced cooling.]

    • I certainly font doubt that it’s significant, but I still strongly doubt that much of the correlation is causal (although I agree that latent heat can explain at least part of this correlation, and that would be a causal link).

      The main problem I have is that regional precipitation is almost always heavily influenced by larger scale phenomena, particularly sea surface temperature patterns. This makes your choice of “excess temperature” problematic, if only on academic grounds.

      But this still leaves the more problematic issue of the form of the best fit equation. Again, negative precipitation is physically meaningless. The T vs P relationship should be highly non-linear at low P. This has significant implications when you try to apply the derived curve to low precipitation levels. You’re essentially extrapolating here because 2011 is such an outlier – the derived relationship is almost entirely determined from the 1895-2010 data. Extrapolating with a curve that ignores physics is always problematic.

      • Oh, and I’ll gladly shut up about all of this if it can be shown that latent heat can explain the magnatude of the slope of the derived T v P relationship.

      • OK, time to shut up I think.

        That slope is about 1 deg C per 100 mm. After allowing for about 30% runoff, 100 mm over three months translates to about 20 W/m2 of latent heat. That seems to be enough to produce a 1 deg C temp rise.

        I think I was thrown off by the imperial units.

        0.5 deg F per inch sounds so much steeper than 0.01 deg C per mm.

      • Nice job on the evapotranspiration estimate. It’s the sort of “no wait, my initial guess was wrong and here are the numbers to prove it” that one never sees on the “other side”.

        So, given that direction of the causality, would you agree there’s no strong reason to expect the T vs P relationship to be highly non-linear at low P? While T will continue to go up over the coming decades at all values of P, I don’t see any reason for the P=0 intercept of the general relationship to be radically higher than casual extrapolation would suggest.

      • Yeah, mine line of thinking was something like this:

        1) the slope is too steep to be explained by latent heat alone so something else must be the explanation

        2) that something else must be a third factor that controls both T and P

        3) the resulting relationship shouldn’t be able to cross the T axis, otherwise there would be a maximum value for T

        4) this implies a T v P relationship should be asymptotic to the T axis

        This all falls apart if the relationship is causal and the extra temperature is directly due to the extra sensible heating made possible by less latent heat loss.

        That’s my current take on it anyway.

    • The feedback between surface dryness and high temperatures has long been recognized in meteorology as a strong factor in the prolongation of drought.

      • The feedback…. Higher temperature increases the rate of evaporation, drying out the soil. Drier soil means less moist air convection, and normally more heat is transported from the surface by moist air convection than by any other process. Higher temperatures over land also mean reduced relative humidity and thus reduced precipitation. I presume.

        As for why Texas is experiencing this, it is my understanding that the Hadley cells have been expanding as the result of global warming. With Hadley Cells, moist air rises in the tropics, gives up its moisture as it cools with increasing altitude, then subsides once it has given its moisture at roughly 30 N/S of the equator. Dallas is at about 32 N.

      • “Namias (1955) suggested that the soil moisture in the Great Plains of the U.S. played an important role in the Great Plains drought by varying the heat input to the overlying atmosphere. That is, heat could be used for sensible heating of the soil or for producing long period lags in the general circulation. This paper also stressed that the drought-producing upper level high-pressure cell over the Great Plains is dependent upon similar anomalous cells over both the North pacific and North Atlantic, operating through teleconnections. Once this triple cell pattern was established, soil moisture deficits could feed back to help maintain the continental high cell. These effects were later exploited by Van den Dool and others and are still being explored in modern coupled (air-land) hydrologic experiments started by GEWEX (Global Energy and Water Cycling Experiment). ”
        http://ecpc.ucsd.edu/general/namias.html

  7. Alastair McDonald

    When thinking about cold winters, it should be remembered that CO2 is not the only greenhouse gas. Water vapour also acts to provide a “warm blanket” preventing exceptionally cold nights. If the Texan soils have now dried out there will be lower humidity and colder winters. OTOH, less water in the soils to evaporate will lead to hotter ground temperatures and record summer temperatures.

    As Bern says it would be interesting to see see humidity plotted against summer temperatures and winter temperatures.

    The worry about an outlier is that it may signify that a tipping point has been passed.

    Cheers, Alastair.

  8. Perhaps my question is very misleading, but, anyway, I ask. Could we assess the probability of finding by chance 10 years above the line in a set of contiguous 11 years? Sort of application of the binomial distribution … I guess. The problem is to properly take into account autocorrelation and so on when determining p. If the probability is very low (I hope so), perhaps it could be assessed from GCM runs under 20C3m scenario. Thinking about it, just that.

  9. In England, the three month period from the Central England Temperature record for March, April and May 2011 was the warmest in the 353 years since records began in 1659, see:
    http://www.metoffice.gov.uk/hadobs/hadcet/ssn_HadCET_mean_sort.txt

    Indeed, April 2011 was the warmest April since 1659, but it followed December 2010, which was the second coldest December in the series! see:
    http://www.metoffice.gov.uk/hadobs/hadcet/mly_cet_mean_sort.txt

    These recent events are set against a general, though erratic, CET warming trend over the last century or so. It does appear that we are witnessing not just warmer but increasingly erratic weather, and not only with respect to temperature, but also precipitation (rate and amount) and perhaps wind speed also.
    So, a relatively steady increase in atmospheric CO2 gives rise to a (presumably) less steady increase in heat content of the oceans/atmosphere/land surface syatem, which produces an even less steady increase in global temperatures, which results in even more variable regional and local effects: at each step the variability increases and the longer the time required to recognise any trend.
    If outliers in regional weather, such as the Texas heat/drought and English temperatures, are becoming more common, then how can this be shown statistically? Is it possible to develop an ‘Index of Variability’ whereby we can say that this region’s climate has become, not only warmer, but also more variable? And what is the correlation between rate/amount of regional warming and regional variability?

    Meanwhile, I observe the manifestations of the Tea Party (along with all the other anti-science denialist clap-trap) and I shudder. I am reminded of some words of Yeats, written just after WW1:

    “TURNING and turning in the widening gyre
    The falcon cannot hear the falconer;
    Things fall apart; the centre cannot hold;
    Mere anarchy is loosed upon the world,
    The blood-dimmed tide is loosed, and everywhere
    The ceremony of innocence is drowned;
    The best lack all conviction,
    While the worst are full of passionate intensity.”

    Though at least that penultimate line is not yet so, as witnessed here. And may it long remain so.

  10. Unusually cold last winter? It is easy to check at National Weather Service. I am attaching the link for College Station, and it is easy to see that Jan-Feb were normal, and since that time we have been riding above…I wish someone would put together a similar set of graphs for US regions.
    http://www.srh.noaa.gov/hgx/?n=climate_cll

  11. The first comment looks like a case of D’aleo Regional Syndrome. In the space of two posts, Texas shrank to Dallas and monthly averages shrank to daily extremes. Presumably, the next iteration narrows things to the back alley at 15:02:37.

    • My tea cup is cold.

    • It wouldn’t be the first time. I’ve seen serious–well, apparently seriously intended–comments based upon how someone’s back yard looked that morning. Part of what I parodied in my “When Did Global Warming Stop?” article.

    • spilgard: I’m quite well aware that significant trends are much harder to spot when you look at daily extremes, given the amount of variability there. If you read the paper I linked, though, you’ll understand why I asked that question – while the monthly / seasonal averages tell the story of how climate is changing, the extent of the impact on humans is determined more by the daily extremes.

      • I agree. My reference is to the first comment of the thread (KenM) which began as a suggestion that the state of Texas plunged to record monthly lows last winter, and by the next post became a couple of really cold February days in Dallas.

  12. If I’m not mistaken what Texas is experiencing now with the help of la nina will become the norm when temps hit the +2 degree mark. So one important thing to me is how much or many of our resources go to buy band-aids to fix the problems. Wet-bulb temp is an interesting topic but I think we are looking at something there that will be farther into the future in states like MS, AL, GA. and will be an intermittent problem. So I think we will have bigger problems.

  13. “. . .something there that will be farther into the future in states like MS, AL, GA. . .”

    Interesting, as I live in the Atlanta area. Models forecast no strong tendency to drought, as we are expected to receive enough moisture from the Gulf, on average, even as things continue to warm.

    On the other hand, personal observation over the last four years shows a strong apparent correlation between drought and La Nina conditions. We had a very severe three-year drought from 2007-2009–heating up the GA vs. FL & AL water wars, currently in litigation (again)–and only remitting during the El Nino of 2010. Now much of the state is back in “extreme drought” officially. With La Nina resurging, apparently, I’m expecting some more crispy lawn throughout the winter.

    Combine the personal observations with the known inadequacy of current modeling on regional and sub-regional scales, and I can’t help wondering if perhaps the future for Georgia is now.

    • “Interesting, as I live in the Atlanta area. Models forecast no strong tendency to drought, as we are expected to receive enough moisture from the Gulf, on average, even as things continue to warm.”

      And that’s where the wet bulb temperature comes in – it’s the combination of temperature and humidity that causes problems. Humans can withstand temperatures of 50ºC or more, so long as the humidity is low. But a wet bulb temperature of 35ºC is enough to cause serious heat stroke in just a few hours, with death likely to follow for a significant portion of the population.

      The relationship between dry and wet bulb temperatures depends on the humidity, of course. The easiest way to see the relationship is on a psychrometric chart. Areas above a wet-bulb temp of 35ºC are restricted to the top right portion of the chart – high temperature combined with high humidity.

  14. This NOAA image of ‘Texas Standard Precipitation’ is quite striking. The temp graph is no fun either.

  15. Philippe Chantreau

    I wouldn’t be surprised if 2011 CONUS temps clock in higher than 1934. Will be interesting to see how the denialosphere changes its message on that one (although I kinda have an idea how that’s going to proceed).

    • Adam, I live in a Houston high rise that looks out over a golf course. There are a bunch of dead trees in the part I can see – guessing around 20 mature trees

      The is a big cluster across from the Houston Zoo. Driving from Houston to Dallas, dead trees – lots of dead trees.

  16. Horatio Algeranon

    What’s the standard deviation of “excess summer temperature” for the given time period?

    How many SD’s “out” is the 2011 value?

    What’s the slope of the least squares line for excess temp since about 1970?

    what’s the estimate for 2 sigma uncertainty?

  17. What is it with humans and the burying of heads in the sands of ideology and superstition, when scientific pragmatism taps them on the collective shoulder with carefully-considered words of caution?

    The US has Perry running hot for the presidential candidacy, and here in Australia it is almost certain that the odious denier of science, Tony Abbott, will walk into the next Prime Ministership on the back of a campaign of dog-whistling and hysteria-whipping over a string of faux issues.

    It’s enough to reduce one to tears of abject dismay at the insufficiency of human understanding.

  18. And a trivial observation – from 2012 onward for several years there will be many postings by the Denialati claiming that “Texas is cooling, cooling I tellz ya – just look at this graph starting from 2011!”….

  19. Tamino,

    In the text after the first scatterplot did you intend to say:

    “There’s a rather obvious correlation, with wetter summers tending to be cooler while dryer tends to mean hotter.”

  20. I have been following John Nielsen-Gammons blog this summer as the relation of AGW, drought and food production impact is a subject of great interest to me. This post here is an excellent addition to JNG discussion.

    While wading through the complexities of the statistical analysis I could help but be distracted by this comment:

    “But Texas governor Rick Perry seems popular with the Tea Party and Republican hard-liners. His approach to global warming is to deny reality and blame scientists for faking data. It’s Rick Perry who’s faking the facts. Meanwhile, the state of Texas, back in June, set a new record for their hottest June ever.”

    In fact the loop here can be closed a bit more. In this article at PoliticusUSA on the wealth of the Koch brothers they indicate (citing Think Progress):

    “the Koch boys have made their money by aggressively speculating in energy markets, “Koch uses legitimate hedging products to create price stability. However, the documents reveal that Koch is also participating in the unregulated derivatives markets as a financial player, buying and selling speculative products that are increasingly contributing to the skyrocketing price of oil.”

    and they continue:

    “In other words, every time the price of gas goes up for no particular reason other than the vague energy speculators excuse, the Koch brothers just made themselves more money. Charles and David Koch are profiting by artificially raising the price of energy futures.”

    and:

    “What makes the Koch brothers different is that they have taken some of their vast fortune and used it to fund candidates and elected officials in the Republican Party who will allow them to keep making money while the rest of America winces when they have to fill up the gas tank.”

    http://www.politicususa.com/en/koch-brothers-wealth

    And Rick Perry? Below is a link to a document published by American Progress citing Rick Perry as the recipient of $76,000 from Koch towards his gubernatorial fund.

    So Perry is bought and paid for by Koch Industries and clearly his job will be to clear the path to any obstructions to the Koch brothers increasing their wealth which by the way, the politicus article states jumped 43% in about a year. The brothers combined wealth is not far behind Gates (richest) and both are on the top 10 richest list in the country.

    http://www.americanprogressaction.org/issues/2011/04/pdf/koch_brothers.pdf

    • Sooo…, since Perry has been duped by the Bros, are you saying he’s a [edit]

      [Response: Perhaps a little restraint would be a good idea.]

      • Ray,

        Duped? I don’t know. That doesn’t seem exactly correct.

        I will say this though. Do you recall in a recent debate when Perry expressed his indignation at Romney for suggesting that he could be bought for $5000? I think the articles referenced provide some context as to the source of his indignation.

      • Ray just couldn’t resist a good straight line. . . so to speak.

        I can relate.

      • PJKar,
        Kevin is correct. The edited portion featured the family name of the brothers mentioned above, along with a common American English epithet for a rube or one who has been duped. When combined, they form one of the 7 words that the late George Carlin told us we could not say on the airwaves.

      • Kevin,
        One of the joys of getting older is that it presents so many more options for the ages one can act… about Jr. High in this case, I’d estimate. ;-)

  21. Well I have to say I agree with Bernard J above. Looking at the graphs mouncounter referred to, unless my calculator is wrong, TX temp has remained relatively stable the last 100 years. I don’t think la nina will become a semi permanent system so in a year or so TX could return to normal. Then I have to wonder will a step increase occur when the Hadley Cell becomes the driving influence and will TX look like Somalia does now. I will return to lurking now as I’m much better at that than commenting.

  22. Further analysis here:
    http://blog.chron.com/climateabyss/2011/09/texas-drought-and-global-warming/

    Of relevance: extending the time period to include antecedent precipitation maintains explained variance while making 2011 less of an outlier. In the present context, it’s more similar to the past 12 years in the extent to which it departs from the best fit line, though still implicating global warming as a factor.

    Also, for more peer-reviewed stuff on the precip-temperature relationship in the central United States, and its fundamental nonlinearity, there’s Koster et al. 2009: http://journals.ametsoc.org/doi/abs/10.1175/2009JCLI3075.1

    • John,

      Thank you providing the link to Koster to this forum. I saw it in your list of references and tried to access it last night (and again today) but unfortunately I can’t get it even though I am a member of AMS.

  23. John, the point is that 11 of those 12 years ARE ABOVE THE LINE.

  24. Pete Dunkelberg

    Often Google scholar or plain google will have the answer. At times either may fail but the other succeed.
    http://gmao.gsfc.nasa.gov/pubs/docs/Koster394.pdf

  25. Thanks to Timothy Chase and Pete Dunkelberg for providing that NASA link.

  26. Give a man a fish, and he eats for a day. Teach him to fish, and he will spend all day in a boat drinking beer.