Watch the food, ctd

This study on crop yields and warming has been all over the news recently, with great background here and great analysis here. These results compliment earlier research, which found:

Days above 30°C are particularly damaging. In otherwise normal conditions, every day the temperature is over this threshold diminishes yields by at least 1%. Moreover, days where the temperature exceeds 32°C do twice the harm of those at 31°C. And during a drought, things are worse still. Then, yields take a hit of 1.7% per day over 30°C.

This matters because increasing the average temperature only a bit can multiply the number of the hottest days a lot. The research predicts that a 1°C rise in average temperature will reduce yields across two-thirds of the maize-growing region of Africa, even in the absence of drought. Add drought and that effect spreads over the entire area.

The Economist, bless them, trust their readers know why a linear increase in temperatures produces an exponential increase in really hot days. But for the benefit of my fellow liberal arts majors, let me illustrate. Temperatures, like most quantities determined by the interaction of multiple factors (height and longevity are other examples, but this in fact applies to the behavior of most outputs of most systems) fall along a Gaussian distribution, aka a bell curve:



This is one of the more useful statistical concepts to get comfortable with. It's intuitively obvious, but often we make mistaken deductions about systems with the idea that the outcomes on the edge of the distribution are far more common and representative than they really are.

Does it really work? It really works:



So what happens to this curve if you warm things up a bit, if you shift the average?



(Don't you love it when the very image you want is right there waiting for you on Google images? Isn't the internet grand?)

One thing that happens when you increase the average temperature, shifting the curve to the right, is that the thin edge of the curve goes into new territory . . . and hence you get new temperature records. You also get a lot of days that are one or two degrees warmer than average, but you had a lot of those to begin with, right in the fat part of the curve. Where you are going to see a dramatic change is in the days that used to be in the wedge, but have now been pushed towards the middle. Because if you look just at that part of the curve, you see this:



But by shifting the curve to the right, we move our 30C or 32C day to the left, so if we flip the curve into the conventional orientation, rightward towards the future, we get:



And finally we have a picture of what is going to happen, and in fact is already happening, to the number of crop-wiltingly hot days.

Believe it or not, this is not the worst news in the climate realm this week. That honor goes to the UN study projecting further population growth through the rest of this century, peaking not at nine billion, but reaching ten billion and beyond. More on that anon.