Putting the Heat on Wheat

2008-09-24

Wherein I play with the lovely Google Charts API and expose my total incompetence in statistics, economics, agriculture, and geography. And quite possibly other things too.

So I was reading the Open Knowledge Foundation blog and came across this article featuring US wheat production, which points to this dataset of wheaty goodness. My recent work on Clear Climate Code had made me already aware of the availability of GISTEMP’s summary data products.

So it occurred to me that this could be used to answer the question “when the weather is warmer, does more wheat grow?”.

So the wheat data is US wheat production, including yields in bushels/acre, sigh. GISTEMP even do a dataset that shows the temperature anomaly for the US. I think this is incredibly parochial, but it happens to be just what I want.

So the wheat yield (volume of wheat per harvested unit area) has a general upward trend. At least from the mid 1930’s or so. Because I’m only interested in the local variation I have detrended the wheat data:

My hypothesis is that any deviation of the temperature from the long term average will lower wheat yields. I think this because I would expect that over the thousands of years of selection humans will have cultivated a variety of wheat that is optimised to grow at the average temperatures and it will do less well when temperatures deviate.

So what do we see? Here’s wheat yields and temperatures together:

Well, there’s no obvious correlation to eyeball. Scattergram:

(which is almost just changing ‘cht=lc’ to ‘cht=s’ in the above chart URL)

Bit of a blurry mess. If anything a slight negative trend, which would mean that colder temperatures gave a higher wheat yield. And indeed Pearson’s correlation is about -0.3 (assuming my calculations are correct) indicating a weak negative correlation.

There are problems. One problem is that I have no p-value. That’s partly because I haven’t read that far on the Wikipedia page (I’m not using some fancy stats package for my analysis; everything is hand-coded in Python), and partly because I have a degrees of freedom problem. Temperature is autocorrelated, so whilst I have 128 samples, that’s fewer than 128 degrees of freedom, so the standard assumption of independent variables is incorrect.

The other problem is that it looks like the detrending might have introduced a bit of an alarming feature into the wheat anomalies. There’s a gentle hump from 1866 to about 1940 and a similar one from about 1940 to 2000. This is almost certainly because I’ve used a cubic polynomial to fit to the data to detrend it. It looks like a two-leg linear fit would be better (with a kink around 1942), but I haven’t found how to do that. I have a sneaking suspicion I have some FORTRAN code lying around here to do it, but I’m too scared to look.

Final tiny problem almost too small to be worth mentioning: the wheat data is for the entire US, whereas the temperature data is for the contiguous 48. I’m guessing that Alaska and Hawaii make so little wheat contribution that it doesn’t matter.

In any case it doesn’t really look like fixing these problems would ever indicate a strong positive trend between temperature anomalies and wheat yields. So we can reject the notion that warmer weather means higher wheat yields. Of course warmer weather might mean we can grow more of something else (possibly just a different variety of wheat); it also might mean that the available belt of land for growing wheat is larger (but this is unlikely since it probably means the available belt of land for growing wheat has moved North).

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20 Responses to “Putting the Heat on Wheat”

  1. Francis Davey Says:

    Water (rainfall) is an important factor in the wheat production equation – which correlates to but in complicated ways to temperature, but so also are global prices which are an external factor that may be correlated with but not caused by global temperature – but you know all this.

    There’s a lot of land in Russia that could be farmed at higher temperatures of course.

  2. Devil's Advocate Says:

    Temperature has risen since the 1940s. Wheat yield has risen since the 1940s. Tell us again why you are detrending these numbers?

  3. Gareth Rees Says:

    I’m skeptical that this is going to be a useful avenue of research, since U.S. wheat production is an industrial process, not a natural one. Land is only one of the capital costs, and probably a fairly minor one, given how cheap land is in the U.S. midwest.

    You might find the National Agricultural Statistics Service useful.

  4. mathew Says:

    I think you need better climate statistics.

    Annual weather isn’t what counts; what you need to know is what the weather was like during the roughly 6 months of the year when wheat is actually growing. It doesn’t matter if winter is freakishly warm, that won’t alter wheat production at all.

    The second thing is that I strongly suspect sunlight hours are more important than temperature, though of course the two are correlated. Most of the energy transfer to the wheat, after all, is via photosynthesis.

  5. drj11 Says:

    @Devil’s Advocate: because there are several competing explanations for the long term trends of increasing wheat yields (such as increasing productivity which is true in almost any economic activity). By detrending I can see whether small perturbations in one variable lead to small perturbations in another. I think.

    I’m only playing this game as long you’re being a Devil’s advocate.

  6. drj11 Says:

    @Gareth: So are you suggesting that heat is not an important input into this industrial process? (I’m really not quite sure).

    Well, the data certainly support that suggestion.

  7. drj11 Says:

    @mathew: quite possibly yes. Though of course I would expect yearly average anomalies to have a good correlation with summer ones. I expect with a bit of effort I can get anomalies for just the growing season.

    Round here wheat is planted in August and harvested in August (well, September round here). Is it a summer crop in the US?

    Garh! I refer you all to my opening sentence. :)

  8. Devil's Advocate Says:

    Your reason for detrending seems like a good one. I have sent links to this post to Tamino and to Stoat (with whom I was discussing Google Charts over lunch).

  9. drj11 Says:

    @mathew: According to the USDA wheat is a winter crop in the US too: “Winter wheat production represents 70-80 percent of total U.S. production”.

    That leaves me with the problem of the other 25%, and also the fact that my years don’t match the wheat season (august to august, say). I need one of those lag correlation thingies.

  10. drj11 Says:

    @Gareth: Hold on, why are you referring me to another website? Are you suggesting I need more data in order to answer the question “when the weather is warmer, does more wheat grow?”. I have temperature anomalies, I have wheat yields. What more could I possibly need?

  11. Gareth Rees Says:

    You need to know many more specifics about the business of wheat production. You have data in the form of yield/acre, but are those the same acres from one year to the next? Maybe in warmer years farmers put their least productive fields into production, lowering the average yield but increasing total yield? Or maybe in warmer years farmers take advantage of the faster growth to reduce their input of fertilizers, keeping average yield roughly constant?

    With regard to the specific scientific question of how wheat is affected by temperature, then I think field studies are more likely to be reliable. But is that the question you are trying to answer?

  12. drj11 Says:

    @Gareth: I probably do need to learn more about those things, but I’m not asking “can more wheat grow”, I’m asking “does more wheat grow”.

  13. Gareth Rees Says:

    Given the data you’ve got so far, the question you can answer is, “do farmers increase their yield per acre in response to warmer temperatures?”

    Maybe this is what you mean by “does more wheat grow?” but I wouldn’t phrase it like that, as it seems rather misleading to omit to mention the farmers.

  14. drj11 Says:

    @Gareth: Yes, except for the “response to” bit. I have no idea whether farmers respond to the higher temperatures, or merely accidentally profit (or not) from them.

    My aim was not to mislead; wheat is a farmed crop, and I don’t think anyone would think otherwise.

    Obviously I am interested in the broader picture, and in particular the question of “can we grow more wheat”, but I never meant to imply that the data I had could address that. Mostly I was just playing around with the data.

    Though you have convinced that my analysis has no bearing on my “do less well when temperatures deviate” hypothesis.

  15. william Says:

    “Winter wheat” is just wheat planted in the autumn that overwinters, as opposed to spring wheat. I think. Winter climate is unlikely to have a huge effect on it? I think the idea that the yields are largely determined by summer climate is likely to be correct.

    At a rough guess, its also likely that precip has a bigger effect than temperature. Though the actual effect would be complex: witness summer here: depending on whether the rain falls during the growing or ripening season the effects could be good or bad.

    Top plot: I’m guessing that the lower, flatter, green line is the detrended data, and the raw data is the yellow line. But it doesn’t say so.

    Detrending: maybe your cubic isn’t such a good model. You might be better off taking anomalies from an n-year moving average, n about 10 perhaps. I agree though that you need to do something to take increasing tech out.

    People must have studied this to death though: its so economically important.

    I like google charts. Must find one to draw myself.

  16. Raymond Says:

    Your question is much too broad.

    First, there are two main kinds of wheat. Winter wheat has a complicated response to temperature. It is planted in autumn and requires a certain amount of time to sprout. Then it must go through a cold period (vernalization) in order to flower and produce grain after it resumes growth in the spring. Thus winter wheat needs a reasonably warm period to build energy for re-growth and then it needs a cold period so it will flower. Spring wheat is planted in — you guessed it — spring, and does not overwinter. One could well imagine a temperature regime that would be bad for winter wheat but neutral or positive for spring wheat, and vice versa.

    Second, the U.S. is a BIG country and different parts of the country experience different climates and year-to-year trends. So the average for the whole country isn’t very meaningful; for example, a year could seemingly have a normal temperature for the entire U.S. but with temperatures that are anomalously warm in some parts of the country and cold in others. It’s the old saying “if your hair is on fire and your feet are in a bucket of ice, your average temperature is OK.”

    My answer is that you need to ask a more focused question.

  17. Richard Simons Says:

    Wheat has to be pollinated before it can produce grain. Even though it normally self-pollinates, this process is temperature sensitive and high temperatures at pollination can drastically reduce grain yield. IIRC this has recently been a matter of concern in the southern US. This is also a major factor restricting wheat production in the tropics.

    Corn and rice pollination is also reduced by high temperature but they tolerate rather warmer conditions than does wheat.

  18. drj11 Says:

    @william: I like your anomalies-from-10-year-average idea for detrending, or something like that.

    Everyone: This is all very educational and interesting. You’re all very helpful.

  19. Luke Warmer Says:

    You should check out Herschel’s use of Adam Smith’s data to compare wheat prices and sunspot activity – also taken up by Jevons of Peak coal fame and more recently by some astrophysics bods.

  20. drj11 Says:

    @Luke: Should I? Why is that?


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