Sowing dates and harvest dates in all model versions except for LPJmL–PHU were internally derived per crop on the basis of local climatic conditions (37). In contrast, LPJmL–PHU was additionally constrained by reported information about growing seasons under rainfed and irrigated conditions around the year 2000 at 0.5° spatial and monthly temporal resolution according to MIRCA2000 (27). The first day of a reported planting month was used as the planting date and the last day of a harvest month as the harvest date. MIRCA2000 differentiates between up to five different seasons per grid cell and crop. Grain and silage maize were distinguished neither in MIRCA2000 nor in LPJmL. MIRCA2000 was originally released at the 5–arc min spatial resolution, aggregated to 0.5° for the use in global crop models. However, the underlying information about growing seasons has a much lower spatial resolution with 402 units, where, for example Russia, Spain, France, Ukraine, Nigeria, Mexico, and Argentina are single spatial units without distinguishing subnational regions. An alternative global crop calendar (52) has been published, but it relies on largely similar data sources and does not distinguish rainfed and irrigated crops and was therefore not considered in this study. Given the limited spatial resolution of reported data, we complemented the MIRCA2000 information with LPJmL–internally derived growing seasons based on local climatic conditions (37). For each therefore available growing season, we derived grid cell–specific heat units required to match targeted harvest dates (fig. S4). Per country, we selected the season that leads to the highest correlation between simulated and observed crop-yield anomalies when used as input in LPJmL–PHU. Figure S4 shows individual model performances of all seasons, for simulations solely based on LPJmL-derived growing seasons but with spatially resolved heat units, and also for simulations with growing seasons exclusively based on MIRCA2000 information. For final LPJmL–PHU simulations as described in Table 1, MIRCA2000 information was used across 80 and 59% of total main producers’ cropland area for maize and wheat, respectively (see the map in fig. S5).

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