Friday, January 18, 2013

Blame it on the rain?

One of the things I’ve been puzzling over lately is why so many agronomists and others in agriculture seem to have the mantra that July rainfall makes the corn crop. These are generally smart people whose opinion I respect. For example, I’m a fan of Scott Irwin and Darrel Good’s blog over at Farmdoc daily, where they recently discussed the prospects for next July’s rainfall. They are definitely not the only ones to focus on rainfall. Whenever I present empirical work on weather and yield to a group of agronomists, at least one will invariably argue that the strong temperature effects are just an artifact of temperature tending to be high when rainfall is low. One problem with that argument is that a lot of the recent empirical work shows temperature as being important, and not all of it uses datasets with high correlations between temperature and rainfall.

Usually I try to explain the various mechanisms that link temperature to yields. And these discussions can often lead to interesting studies about which mechanisms matter more, such as one paper we have coming out soon. But I never really delved into the reason that rainfall is given so much credit for good or bad years. One likely reason is it’s just a lot easier to see whether or not it rains than to detect a shift in temperatures. So people will tend to remember dry years more than hot years. But there’s also some analysis that appears to support the rainfall hypothesis.

A lot of the work on US corn and weather traces back to Louis M. Thompson’s work 30 years ago. These were basically time series models at the state level, looking for instance at how Illinois yields changed over time in relation to weather. More recent work has updated this type of analysis, and emphasizes the role of July rainfall and temperature, but with a bigger role for rainfall. To recreate that type of analysis, I plot below detrended corn yields for Illinois (detrended by fitting a linear slope to represent gradual technology change, and then adjusting all years to 2006 technology) versus July rainfall (prec) and average maximum temperature (Tmax). I also plot prec and Tmax against each other. (Correlation coefficients are given in the bottom panels). Thanks to Wolfram for providing updated data.

You can see that yields are clearly low at low levels of rainfall, and that yields are also low at high Tmax. But you can also see that Tmax and rainfall have a strong negative correlation, which makes it hard to say whether Tmax, rainfall, or some combination (or neither) is the actual cause of yield loss. I also show three recent years in color (red = 2009, green = 2010, blue = 2011). What’s mildly interesting about these years is they don’t follow the normal correlation between Tmax and rainfall. 2009 was especially cool but with medium rainfall, and 2010 and 2011 were both unusually warm for the given amount of rainfall.

The main point, though, is that the colinearity issue cuts both ways. You can’t just decide it’s rainfall and say that temperatures are less important, no more than you can decide it’s all temperature. Many empirical studies try to move beyond these simple time series specifically because of the colinearity problem. One way to reduce colinearity between Tmax and rainfall is to restrict yourself to looking over a narrow range of one of the variables, so that it is essentially being held fixed while the other one is varying. This is hard to do with a time series that is about 50 years long in total, because you quickly run into problems with small sample sizes.

But it’s easier to do this if we look at time series from lots of counties at the same time, or a so-called panel analysis. As a simple illustration, the plot below shows all points for 1950-2011 for counties in the “three I” states: Illinois, Iowa, and Indiana. The left-hand plot just shows the same scatter as before between Tmax and rainfall. Notice there is still a strong negative correlation. But we can now select only points that are within a narrow range of rainfall (shown as green points) or a narrow range of temperature (shown as red). Then we can take the red points and see how rainfall matters when holding temperature constant (middle panel). Or we can take the green points and see how temperature matters when holding precipitation constant (right panel). The black lines in the right two panels show local polynomial fits to the data (using loess in R).

What do we see? Well, at least for these particular places and values of Tmax and rainfall, there does not appear to be much effect of changing rainfall when July Tmax is constant (at around 30C). But temperature changes do appear to be important when rainfall is held constant (at around 100mm).

Now, there are obviously lots of other combinations we could try, and the point isn’t that rainfall is always and completely unimportant. For example, if we hold Tmax constant at a higher level, where I’d expect rainfall to be more critical, we do in fact see a bigger effect of rainfall at low levels (see below).  But if nothing else, it should be clear that a lot of the credit given to July rainfall for US corn is not necessarily well deserved. Coincidentally, the singers of “blame it on the rain” also got a lot of underserved credit!

In future posts, I’ll try to get more into the reasons that temperature can dominate the effects of rainfall, even in a rainfed system. 


  1. Thought provoking analysis. I look forward to seeing your future posts on the topic. Personally, I have always found a simple argument to be persuasive regarding the dominance of rainfall over temperature on corn yield. It is commonplace to produce very high corn yields under irrigation in places where summer temps can be very high (Nebraska). This tells me that water availability is the key limiting factor, which is also consistent with all of the biological simulation models that I have seen. Perhaps an interesting way to identify the max temp impact would be to look at irrigated yields only. The USDA publishes long series of irrigated corn yields for a few states. The most important is Nebraska, with about 60% of US irrigated corn production.

    Scott Irwin

    1. thanks for the comment Scott. i agree irrigated corn is a lot less sensitive to T - wolfram and mike had a plot in their PNAS paper appendix to this effect. there is no doubt having irrigation raises yields and reduces variability in the western US. i think the difference is irrigation is adding a lot more water that the typical difference between a high and low rainfall year. but i'll delve into this a little more when i have some time.