Methods - Climate Stabilization Targets - page 281

5.1 FOOD PRODUCTION, PRICES, AND HUNGER

Methods summary for food figure

Left-hand panel:

For broad regions, yield losses per °C of local warming were taken from
Figure 5.2 in the Working Group 2 reports of the Fourth Assessment Report
of the IPCC (Easterling et al., 2007). These estimates include estimates of
CO 2 effects but without explicit modeling of adaptation. The mean and one
standard error for each level of warming were approximated from the figure.
Local temperature changes were converted to global temperature levels us-
ing a value of 1.5°C local per global °C for mid-to-high latitudes and 1.2°C
local per global °C for low latitudes.
Note that since several of these studies are based on experiments where
climate is allowed to equilibrate with doubled CO 2 levels, while others
were taken from transient simulations (e.g., based on SRES scenarios), the
CO 2 levels for different amounts of warming likely varied by study, with the
equilibrium studies likely underestimating CO 2 levels for a given warming
amount.

Right-hand panel:

Yield losses per °C of local warming were taken from the follow-
ing studies: U.S. maize and soybean (Schlenker and Roberts, 2009); Asia
rice (Matthews et al., 1995); India wheat (Lal et al., 1998); Africa maize
(Schlenker and Lobell, 2010). For each region, global temperatures were
converted to local temperature change based on the patterns in Section 4.2.
The yield effects of higher CO 2 were estimated based on a recent meta-
analysis (Ainsworth et al., 2008). CO 2 levels for each temperature value
were based on the values reported in Section 3.2, and assuming a ratio of
CO 2 to CO 2 -equivalent equal to the average of the SRES scenarios (ratio is
1.05 for 1°C, 0.93 for 2°C, and 0.8 for 3°C and warmer).
Standard errors were estimated by propagating estimates of standard
errors for (1) local temperature change for a given global temperature; (2)
crop yield response to temperature; (3) CO 2 levels for a given global tem-
perature; and (4) yield response at a CO 2 level. Propagation was done with
the standard equations:

Var (a × b) = E[a] 2 × Var (b) + Var(a) × E[b] 2 + Var(a) × Var(b) [1]

Var(f(X)) ≈ ( f' (E[X])) 2 × Var(X) [2]