Research: Higher temperatures TERRIBLE for staple crops

I knew Michael Roberts had a good blog; I didn't know he was working on monumentally important and relevant research on the impact of temperature on staple crop yields:
We set out to develop a better statistical model linking weather and U.S. crop yields for corn, soybeans and cotton, the largest three crops in the U.S. in production value. Our major new finding is that (by far) the best predictor of yield is a measure of extreme heat: how much temperatures exceed about 29C (84F) during the growing season. The threshold varies somewhat by crop--29C is the threshold for corn. Below this threshold, warmer temperatures are more beneficial for yields, but the damaging effects of temperatures much above 29C are staggeringly large.
They introduce a measure I had not seen before, but makes a lot of sense - "degree days above 29C".
A good measure extreme heat is degree days above 29C. This is calculated as (Degrees Above 29C x Days) summed up for all time (including fractions of days) at each temperature above 29C. The more degree days above 29C, the lower are corn yields. Historically, average degree days above 29C during the growing season were about 57. Under the slow warming scenario (we cut emissions to 50 percent of 1991 levels by 2050) this number is projected to rise to 194 by 2070-2099 and corn yields are estimated to decline by 46 percent [emphasis mine]. Under the fast-warming (business as usual) scenario, degree days above 29C are projected to increase to about 413, and estimated corn yields decline 82 percent [emphasis mine].
Their findings on adaptation are particularly troubling:
Somewhat surprisingly, we find no evidence that farmers in the warmer south have been successful in adapting to the higher frequency of temperatures above 29C. This is troublesome as we hoped to learn from warmer regions how farmers might adapt to more frequent temperature extremes.
What are the implications?
These big estimated impacts are important because the U.S. is by far the largest producer and exporter of agricultural commodities. This is especially true for corn and soybeans, which are two out of the world's four most important staples (the other two are wheat and rice). If U.S. yields go down a lot, it drives up prices of staple food commodities all around the world. Almost surely the poor in other parts of the world, particularly developing countries that import food, would suffer far more than the U.S. would.
And the caveats?
There are three major caveats: (1) CO2 fertilization may offset some of these negative effects--something still under significant debate; (2) Seed companies (Monsanto) might develop more heat tolerant crops in the future (but we find little evidence of adaptation in the past); and (3) Farmers will be able to offset some of the losses by shifting where they grow different kinds of crops.
There are more detailed findings in his post. I'll say again that this appears to be critical research that highlights the consequences of climate change for both the broad world food system and U.S. farmers in particular. In fact, it would be great if this were publicized more broadly and were able to shift the opinions of some obstinate agricultural states on the importance of addressing climate change.

Update: He answers my question on longer growing seasons:
R: Great research - love your approach and the conclusions are frightening (but better that we know, and have our eyes wide open).

One other mitigating factor I can imagine is longer growing seasons - any idea how much this could counterbalance the fall in yields? (probably not much, just curious)

Michael: R,

Thanks for your comment and good questions.

We did investigate adjusting growing seasons by moving everything back one month (see the supplement). This does offset damages a little (I recall about about 10 percentage points in the long-run worst-case scenario, but see the supplement for a precise number). We were wary about moving things much earlier since the sunlight and sun orientation would shift so much and the the model implicitly holds these fixed.

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