Crop Yields Under Global Warming

Up until now I thought that global warming would have a significant impact on crop yields, both in the US and elsewhere.

But I've gathered some numbers, and I'm so sure anymore -- at least for US farmers/farming corps.

My understanding was taken from papers like this one:

“For wheat, maize and barley, there is a clearly negative response of global yields to increased temperatures. Based on these sensitivities and observed climate trends, we estimate that warming since 1981 has resulted in annual combined losses of these three crops representing roughly 40 Mt or $5 billion per year, as of 2002.”
-- “Global scale climate–crop yield relationships and the impacts of recent warming," David B Lobell and Christopher B Field 2007 Environ. Res. Lett. 2 014002 doi:10.1088/1748-9326/2/1/014002
http://iopscience.iop.org/1748-9326/2/1/014002

and this one

“With a 1°C global temperature increase, global wheat yield is projected to decline between 4.1% and 6.4%. Projected relative temperature impacts from different methods were similar for major wheat-producing countries China, India, USA and France, but less so for Russia. Point-based and grid-based simulations, and to some extent the statistical regressions, were consistent in projecting that warmer regions are likely to suffer more yield loss with increasing temperature than cooler regions.”
- B. Liu et al, “Similar estimates of temperature impacts on global wheat yields by three independent methods, Nature Climate Change (2016) doi:10.1038/nclimate3115, http://www.nature.com/nclimate/journal/vaop/ncurrent/full/nclimate3115.html 

But -- again, for the US -- these turn out to be quite small numbers, because the market sizes are so big and yields are increasing year-after-year.

So how do crop yields (again, US-only) vary with temperature? Here are some data from the National Climate Assessment (2014), Figure 18.3, p 421

These data are, admittedly, rather scattered and a straight-line trend will have errors. (I don't have the underlying data to calculate those here.) But by eye, I estimate the trends to be, for corn: -0.39 t/ha/°F, and, for soybeans: -0.08 t/ha/°F.

So what are the current yields, and how fast are they increasing? Here is the current yield and trend in corn yields, and the same for soybean yields.

So, plugging in the data, the trend in corn yields = 1.9 bu/acre/yr, and the trend in soybean yields = 0.5 bu/acre/yr. Relative to 2017, these are 1.1%/yr and 1.0%/yr, respectively.

From the same source, 2017 yields are, for corn: 176.6 bu/acre, and for soybeans, 49.1 bu/acre. "bu" is bushels.

I need to know the density of corn and of soybeans: 39.3680 bu/t and 39.7740 bu/t, respectively, from this source.

Translating into metric units: 2017 corn yield = 11.1 t/ha, 2017 soybean yield = 3.1 t/ha.

OK, now we can put things together.

Let's assume the surface warming trend is +0.20°C/decade. That's one degree Celsius in 50 years. (Results for other trends will scale linearly.)

Assuming the current trend in yields continues (iffy?), in 50 years (a long time, granted), yields will have increased by 170% (for corn), and 165% (for soybeans).

But in that time, yields will only decrease due to higher temperature by -6% (corn) and -5% (soybeans).

So agricultural technology will, even if trends continue at only a fraction of their current value, swamp any losses due to global warming.

And it won't take much increase in yields in developing countries for them to cancel out any loses due to higher temperatures, either.

--

Of course, there's no inherent reason to believe that yield increases will continue at their rate of the last 30 years for the next 50 years. Nor will warming stay linear, probably. And we'll need more food to feed ever more people, about 10 B by the middle of this century. And warming won't be limited to just one degree Celsius (we're already at that value anyway).

But I don't anymore see a big problem here. Am I missing something?