Overview of the global gridded crop models.

The model ensemble comprises six global gridded crop models (GGCMs) driven by daily climate data from five different global climate models (GCMs) under RCP 8.5 (ref. 3). The six GGCMs consist of:

the Environmental Policy Integrated Climate (EPIC) model28,29 (originally the Erosion Productivity Impact Calculator; ref. 30). the Geographic Information System-based Environmental Policy Integrated Climate (GEPIC) model30,31,32. the Lund-Potsdam-Jena managed Land (LPJmL) dynamic global vegetation and water balance model20,33,34. the Lund-Potsdam-Jena General Ecosystem Simulator (LPJ-GUESS) with managed land33,35,36. the parallel Decision Support System for Agro-technology Transfer (pDSSAT37,38; using the Crop Environment Resource Synthesis (CERES) models for maize, wheat, and rice and the Crop Template approach (CROPGRO) for soybean). the Predicting Ecosystem Goods And Services Using Scenarios (PEGASUS) model39,40.

These GGCMs can be grouped into two families spanning more than three decades of model development:

site-based crop models—extended for global analyses using a geographical information system (EPIC and GEPIC) and an advanced parallel simulation system (pDSSAT).

ecosystem models—initially developed to simulate the terrestrial carbon cycle for natural vegetation using downscaled global climate data and then extended to represent managed land (LPJmL, LPJ-GUESS and PEGASUS).

The site-based crop models tend to include a more detailed representation of cropping systems but necessitate substantial computing resources, whereas the ecosystem models typically include less detail on crop management but present the advantage of being run globally in a short fraction of time. In addition, because the ecosystem models simulate global carbon and water cycles, they are useful tools for assessing crop production in the context of global environmental change.

Model representation of biophysical processes.

Biophysical processes represented in GGCMs include light utilization, CO 2 effects (see next section for CO 2 ), environmental stresses, soil water dynamic and, for some, soil nutrient cycling. First, photosynthesis is described with either a simple radiation use efficiency (RUE) (for example, PEGASUS, described in ref. 40) or a detailed leaf-level photosynthesis respiration (PR) (ref. 41) (for example, LPJmL and LPJ-GUESS, described in ref. 42) approach. Representation of CO 2 fertilization effects on photosynthesis and transpiration rates thus follows either a descriptive (RUE-type models) or explanatory approach (PR-type models). Second, all GGCMs take into account temperature and water stress. Most models also include nitrogen stress (except the LPJ-type models). In addition, both EPIC-type models represent aluminium and oxygen stresses. PEGASUS represents heat stress effect at anthesis38, resulting in systematically strongest negative impacts (Supplementary Fig. 1). Third, GGCMs differ in respect to crop water demand and estimated evapotranspiration (ET): the EPIC-type models use the Penman–Monteith approach43,44, whereas the other GGCMs use the Priestley–Taylor approach45. In addition, the number of soil layers varies among GGCMs and roots are either linearly or exponentially distributed throughout the soil depth. Finally, crop phenology in GGCMs depends on temperature using growing degree-day accumulation, which varies with models’ definition of base and maximum temperature thresholds that are also crop specific (see Supplementary Table 3 in ref. 3 (accessible at http://www.pnas.org/content/suppl/2013/12/16/1222463110.DCSupplemental/sapp.pdf)).

Model representation and parameterization of crop response to [CO 2 ].

The choice of light utilization representation method (RUE versus PR) in GGCM determines that of CO 2 effects. In the RUE approach (followed by PEGASUS, EPIC, GEPIC and pDSSAT—for wheat/rice/maize), rising [CO 2 ] increases a RUE coefficient, which proportionally affects the rate of photosynthesis31,46. In PEGASUS, parameterization of the modified RUE coefficient was done by comparing grid-cell simulations and FACE results reported in ref. 12 using [CO 2 ] levels of 380 ppm for the baseline39. In EPIC and GEPIC, parameterization of the modified RUE coefficient uses pre-FACE data normalized around 330 ppm, as described in ref. 47. In the case of pDSSAT, Boote et al. (ref. 48) evaluated the CO 2 -responses of each DSSAT model, which was originally based on pre-FACE observations and normalized to 330 ppm. Evaluations for CERES-wheat and rice showed that the simulated responses to doubled CO 2 (27 and 32% response for wheat and rice, respectively) were sufficiently close to reported FACE data (31 and 30% response for wheat and rice, respectively). The review by Boote et al. (ref. 48) concluded that prior DSSAT parameterization to CO 2 effect for C 4 CERES-Maize, Sorghum, and Millet models was too high (based on old literature). Therefore, the response of these three C 4 crops in DSSAT was reduced to give a 4.2% grain yield increase for doubled CO 2 (350 to 700 ppm) beginning with DSSAT version V4.5 released in 2010, and in this study.

Transpiration in PEGASUS, EPIC and GEPIC increases with CO 2 , following a logarithmic equation as in refs 31,46, and is identical for all crops39. Transpiration in pDSSAT follows the approach of leaf resistance, increasing as a function of rising CO 2 —one equation for C 3 and one for C 4 . Then, the daily transpiration is reduced as a function of rising CO 2 , where the relative transpiration effect ratio is computed in a Penman–Monteith-style equation that considers the psychrometric constant, gamma, the two canopy resistances (at reference CO 2 and at present CO 2 ), and boundary resistance. The effect is modest, and has not been tested with any transpiration data (see ref. 48 for more information).

The PR approach in pDSSAT-soybean (that is, CROPGRO-soybean) uses an analytical derivation, for example, RuBP-limiting side of the rubisco kinetics of ref. 49, as described in refs 50,51. Farquhar and von Caemmerer (ref. 49) developed an analytical solution for quantum efficiency that depends on the RuBP-limiting (light-limiting) phase, with no need to consider rubisco enzyme parameters. The approach is applied to make quantum efficiency and light-saturated photosynthesis (Amax) sensitive to temperature and CO 2 within asymptotic exponential equations for sunlit and shaded leaf classes. As a replacement for rubisco enzyme, the Amax term is strongly dependent on specific leaf nitrogen. The CO 2 response for soybean is an emergent outcome of this parameterization and was shown to give yield response to doubled CO 2 comparable to metadata48. Similarly, in the PR approach followed by the two LPJ models, potential photosynthesis rate is calculated as a function of co-limitation by light and the rubisco enzyme, considering the influences of photosynthetically active radiation, temperature and [CO 2 ]42. Note that, although rubisco capacity is not prescribed but maximized daily, photosynthesis rate is not acclimated in response to a possible downregulation of rubisco activity at elevated [CO 2 ]. In case of a soil moisture deficit, both photosynthesis and transpiration (canopy conductance) are reduced nonlinearly52.

Model representation of agricultural management practices.

Representation of farm management practices is also a source of difference in GGCM results: whether and how fertilizer application, irrigation, crop residue management, crop cultivar selection and planting date decision are simulated strongly influence yield and other outputs. The site-specific models (that is, EPIC, GEPIC and pDSSAT) apply fertilizer dynamically through the crop growing season: application occurs at specific stages of the crop development to take into account the role of both application quantity and timing. PEGASUS applies fertilizer as a daily stress function and thus does not simulate effect of fertilizer application timing39. LPJmL and LPJ-GUESS do not represent fertilizer application. Also, although ISI-MIP provided harmonized climate data, models generally used differing input data/methods for soil characteristics and national fertilizer application rates3.

Planting date decision and choice of crop cultivars also vary among GGCMs. Supplementary Tables 2 and 4 in ref. 3 provide a detailed description of GGCMs assumptions (accessible at http://www.pnas.org/content/suppl/2013/12/16/1222463110.DCSupplemental/sapp.pdf). Chiefly, PEGASUS and GEPIC allow for adaptation in planting window whereas the other GGCMs assumed planting window fixed to present day. LPJ-GUESS and PEGASUS also allow for adaptation in crop cultivars (growing degree-day requirements) whereas the other GGCMs use fixed crop cultivars.

Model calibration.

Finally, GGCM calibration methods differ significantly between site-specific and ecosystem models. Ecosystem models are calibrated to global crop yield data (for example, PEGASUS, ref. 39) and FAO national statistics (for example, LPJmL, ref. 33) by tuning a limited number of parameters, whereas the site-specific models use a large set of parameters previously calibrated at various study sites3. Given all these differences, we found models from similar origins, such as EPIC/GEPIC and LPJmL/LPJ-GUESS differ enough to be considered each as an independent GGCM within the ensemble.

Climate inputs.

All GGCMs were run at 0.5° latitude × 0.5° longitude spatial resolution using bias-corrected climate scenarios resulting from five GCMs under RCP 8.5 for the period 1971–2099. Hempel et al. (ref. 23) provides a detailed description of the GCMs used and downscaling methods. The five GCMs include:

HadGEM2-ES (developed at the Hadley Centre for Climate Prediction and Research in the UK). IPSL-CM5A-LR (developed at the Institut Pierre Simon Laplace in France). MIROC-ESM-CHEM (cooperatively developed at the Center for the University of Tokyo, the National Institute for Environmental Studies, and the Frontier Research Center for Global Change in Japan). GFDL-ESM2M (developed at the Geophysical Fluid Dynamics Laboratory in the United States). NorESM1-M (developed at the Norwegian Climate Centre in Norway).

Modelling protocol.

All GGCMs simulated maize, wheat, rice and soybean except PEGASUS, which does not simulate rice. In the case of wheat, PEGASUS simulated spring variety everywhere, as it does not simulate winter wheat, assuming a spring variety was planted in areas where a winter variety is typically grown. Each GGCM–GCM combination was run with (w/) and without (w/o) CO 2 from 1971 to 2099 according to the modelling protocol developed within the framework of the Agricultural Model Intercomparison and Improvement Project (AgMIP) and the Inter-Sectoral Impacts Model Intercomparison Project (ISI-MIP)3. In the CC w/o CO 2 simulations, [CO 2 ] were kept constant to 380 ppm, corresponding to concentrations in the year 2000. For this analysis, simulations under CC w/o CO 2 have been updated from the original set of simulations presented in ref. 3 to ensure all models used the same [CO 2 ] baseline—that is, 380 ppm in 2000. We analyse GGCM outputs of crop yield and AET and calculate crop water productivity (CWP in kg m−3) for a specific year following the equation: CWP = 100Y /AET where Y is the crop yield in ton ha−1 yr−1 and AET is the total actual evapotranspiration in mm over the growing season of that specific year. Each year of crop yield data is averaged over a 30-year or a 10-year period according to the ISI-MIP protocol. GGCMs perform simulations over the entire land surface according to their own agroclimatic suitability indices. We then mask out results to current cropland rainfed and irrigated areas using the MIRCA data set25. Global average estimates of yield, AET and CWP consist in weighted mean values across all grid cells, weighted by crop rainfed and irrigated harvested areas. Two irrigation scenarios were considered: no irrigation (that is, rainfed) and fully irrigated assuming no water stress (the specific threshold for water stress was independently selected by each GGCM modelling team). We calculate global average CWP from actual yield combining both fully irrigated and rainfed yields according to the MIRCA data for irrigated cropland areas25. We further disaggregated our results by climatic regions, following the Köppen–Geiger system to distinguish between tropical, arid, temperate and cold regions53. An extensive description of the GGCMs that participated in the AgMIP/ISI-MIP fast-track exercise is also published in the Supplementary Appendix of ref. 3.

Comparison to FACE observations.

To assess the performance of GGCMs against current observations, we compiled available results from FACE experiments reporting on CWP identified at several locations across the world (wheat in Arizona, USA54,55,56,57, Germany11,58 and Australia59; rice in China60 and Japan61; soybean in Illinois, USA62; and maize in Germany63). Supplementary Tables 1 and 2 summarize FACE site characteristics and GGCMs results. We compared GGCM simulations against these FACE observations (that is, at the grid-cell level) for rainfed and/or irrigated conditions (Supplementary Tables 1 and 2). We selected corresponding yield and AET values from the GGCM simulations at grid cells matching the coordinates of FACE observations to calculate the relative change in CWP between CC w/ CO 2 and CC w/o CO 2 . Ambient atmospheric [CO 2 ] in the FACE experiments varied between 360 and 380 ppm and elevated CO 2 corresponds to 550 ppm. We thus used 10-year average estimates around the year 2050, which corresponds to the same increment of [CO 2 ] level rise relative to the baseline (550 ppm in 2050 to 380 ppm in 2000, respectively). In most FACE experiments reported here, temperatures are held constant. We thus estimate the relative change between w/ and w/o CO 2 around the year 2050 to single out effects of CO 2 from those of temperature and precipitation changes relative to the year 2000.

Sources of differences in simulated CWP.

Model evaluation against FACE measurements show median simulated CO 2 effects on CWP tend to be slightly greater than observation for maize (Fig. 1 and Supplementary Fig. 1) owing to stronger simulated effects on ET (Supplementary Fig. 3). Overall, we find CO 2 effects on maize yield are minimal for both simulated and observed data (Supplementary Fig. 2). However, the choice of a descriptive rather than explanatory representation of light utilization (that is, radiation use efficiency—RUE—versus leaf-level photosynthesis and respiration—PR; see Methods) slightly overestimates the CO 2 effects on maize yield at the ‘wet’ FACE site (Supplementary Fig. 2), and thus partly contributes to greater simulated CO 2 effects on CWP in the ensemble (Fig. 1). In contrast, in drier agroclimatic conditions, the greater responsiveness of crop yield and CWP to elevated [CO 2 ] appears independent of the choice of light utilization representation method but rather sensitive to model calibration and parameterization method (Supplementary Fig. 8).