NorESM1‐M) selected to span the CMIP5 range of global mean temperature changes and relative precipitation changes (Warszawski _et al._ , 2013). Of the five GCMs, ISI‐MIP retained HadGEM2‐ES as the reference model, and we do the same in this study. Under RCP8.5, HadGEM2‐ES projects a global temperature increase for 2050 of about 2.5 °C and an average increase in precipitation of about 3 percent. This ranks HadGEM2‐ES as the hottest and driest of the five GCMs, with potentially the most negative effects on agricultural production.

For this paper, we focus on the two most extreme RCPs: RCP2.6 and RCP 8.5. This choice appears the most practical as it allows to infer the effect of the intermediate emission pathways impacts by approximate interpolation. Effects of different RCPs are then compared to a situation without additional forcing, here represented by the historical climate observed between 1980 and 2010.

In the first scenario, RCP 2.6, a radiative forcing of 2.6 W/m<sup>2</sup> is assumed by the end of the century, after peaking at 3 W/m<sup>2</sup> before 2050. In terms of GHG concentration, this scenario is equivalent to about 450 ppm of CO2 equivalent in the atmosphere by 2100. It corresponds to a limited level of climate change, at about +1 ±0.3 °C by 2046‐2065 and +1 ±0.4 °C by 2081‐2100 on the earth surface, compared to 1980‐2010 levels. On emerged land, the temperature increase is on average +1.2 ±0.6 °C by 2081‐ 2100 (Collins _et al._ , 2013).

The second scenario, RCP 8.5, corresponds to a high increase in radiative forcing, reaching 8.5 W/m<sup>2</sup> by the end of the century. Under this scenario, GHG concentration in the atmosphere increases up to 1370 ppm of CO2 equivalent by 2100. This leads to significant magnitude in climate change at about +2 ±0.4 °C by 2046‐2065 already and +3.7 ±0.7 °C by 2081‐2100, compared to 1980‐2010 level. On emerged land, anticipated temperature increase is even higher, at +4.8 ±0.9 °C by 2081‐2100 (Collins _et al._ , 2013). This scenario can be seen as an extreme climate change situation; however the recent emission developments exceed even the RCP8.5 emission levels for the corresponding years (Peters _et al._ , 2013).

The level of uncertainty in temperature and precipitation change comes from the uncertainty related to the impact of GHGs atmospheric concentration on climate, as predicted by general circulation models (GCMs). For the same level of radiative forcing, GCMs tend to broadly agree on magnitude of temperature changes, but notably disagree on the regional patterns, and on evolution of precipitation patterns. Considering different sets of possible impacts is therefore crucial to reflect the model projection diversity. Therefore, for each RCP, we look at the impacts of GHG concentration on climate according to five different GCMs: HadGEM2‐ES, IPSL‐CM5A‐LR, GFDL‐ESM2M, MIROC‐ESM‐CHEM and NorESM1‐M. These provide spatially explicit results for temperature and precipitation changes that are then used in the EPIC crop model on a global grid (see section 2). As a standard assumption, we keep the default modeling of the CO2 effects as represented in the EPIC model, which includes crop response in terms of photosynthesis (fertilization effect) as well as the impact on water‐use efficiency resulting from decreased evapotranspiration. Because the resulting yield impact of these CO2 effects is an important source of uncertainty, we also consider one additional scenario as a sensitivity analysis on RCP8.5 where CO2 effects are disabled. This scenario, labelled RCP8.5* in the paper, is run with the HadGEM2‐ES climate change projections. Under RCP8.5, HadGEM2‐ES projects a global temperature increase for 2050 of about 2.5 °C and an average increase in precipitation of about 3 percent. This ranks HadGEM2‐ES as the hottest and driest of the five ISI‐MIP models, with potentially the most 12