Looking at a little of the literature on the effect of climate change on agriculture, I noticed something that seems to be a mistake — perhaps someone here can explain why it isn’t.
Crop yields depend, among other things, on temperature, with an optimal average temperature for each crop — about 15°C for wheat, for example (Lobell 2012). If temperature goes up by a degree, yield in an area that used to be 15° and is now 16° goes down a little. This seems to be one of the effects that goes into estimates of reduced yield as a result of climate change.
But it shouldn’t. The same warming that shifts 15° up to 16° also, somewhere a little farther north in the northern hemisphere or south in the southern, warms 14° to 15°, 13° to 14°, and so on. If wheat was being grown between, say, 13° and 17°, the area of cultivation can shift by one degree towards the pole and continue to have a temperature range of 13°-17° and the same temperature-related yield as before.
I can see two possible objections to this argument. The first is that the land a little closer to the pole may be less well suited to growing wheat in respects other than temperature. That is obviously possible but why would you expect it? Is there any reason why land that happens to have the ideal temperature for growing wheat is also more likely than other land to have the ideal soil or the ideal amount of rain? If not, then on average the shift is to land about as well suited in other ways and now ideally suited in temperature. A more careful analysis might find a deviation from that in either direction, land a little closer to the poles a little better or a little worse, but why should we expect either?
The second objection is that shifting the area of cultivation is costly — wheat farms have irrigation systems suitable for growing wheat, appropriate farm machinery, are owned or managed by people experienced in growing wheat. You can’t just pick all that up and shift it a hundred miles further north.
How serious an issue this is depends in part on how fast the shift happens. Looking at maps showing average temperature, it seems to go down as you move towards the poles by about a degree every hundred miles, with a good deal of variation. At current rates of climate change, global temperature should be going up by about a degree every thirty years. So shifting the area of cultivation to keep the temperature at which wheat is being grown constant should require moving it by about three miles a year, with farms at the warm edge of the zone shifting to crops with a higher optimal temperature such as maize (18°) while farms at the cold edge are shifting from barley or vegetables to wheat.
The real pattern would, of course, be more complicated than this, but why isn’t it the right first approximation? If so, then reduced yield with warming should not be included in the effect of climate change on agriculture. What should be included is the large increase in total arable land as temperature contours shift towards the pole, since it is cold, not heat, that restricts the area of land suitable for agriculture.
Am I missing something? Alternatively, is all of this already being included in models of the effect of climate change on agricultural output? If so, perhaps someone can point me at examples.