The agrohydrological model LPJmL was used to show how (i) better representation of water constraints in irrigation and (ii) the implementation of spatially resolved crop cultivars based on observed and modeled growing seasons contribute to GGCM’s ability to explain observed interannual yield variability at the global scale (Table 1). An additional model run eliminating crop-water limitations in both currently rainfed and irrigated cropland areas was used to quantify the underlying contributions of water stress to observed crop yield variabilities.

By improving on a reference model version that does not account for water constraints in irrigation and based on a semistatic heat-unit parameterization not constrained by observations [LPJmL–Ref (33); details below], we first introduce an advanced representation of irrigation system functioning and water constraints (38) and then adjust PHU requirements to match spatially explicit information on sowing and harvesting dates.

Model versions were evaluated on the basis of national standardized yield anomalies (1980–2009) reported by the United Nations’ FAO (8) using the Pearson correlation (R2) and RMSE. In addition, we tested the ability to reproduce global average effects of heat waves and droughts on national crop yields between 1964 and 2007 (compositing) (14), where extreme events were derived from the International Disaster Database EM-DAT (13) (see the “Statistical analysis” section for more details).

Model simulations were forced by the three bias-corrected reanalysis climate datasets GSWP3 (34), PGFv2.1 (35), and WATCH + WFDEI (36). If not stated otherwise, results refer to the average of three crop model simulations forced by each climate dataset, respectively (fig. S6).

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