Explained variances (R2, in percent) are based on Pearson correlation coefficients derived from simulated and observed national time series of standardized crop yield anomalies (1980–2010), calculated as detrended (first quadratic polynom subtracted) and normalized (mean subtracted) yields, divided by the SD (hereinafter “yield anomalies”). To quantify residuals between the observed and simulated yield anomalies, we calculated RMSEs (unitless, as standardized anomalies are without unit). Note that the Pearson correlation coefficient is unaffected by the standardization of anomalies.

The composite analysis (Fig. 2 and fig. S8) was constructed by extracting a 7-year time window from historical national yield time series, centered on the respective “extreme year.” Extreme years were defined according to EM-DAT (13), which reports the country and year for various extreme event types from 1961 to 2010, if at least 10 people died, 100 or more people were injured, made homeless, or required immediate assistance, or a country declared a state of emergency, or called for international assistance. In this study, we considered all heat waves and droughts recorded between 1964 and 2007 (3 years before and after an extreme event required for the construction of the composite analysis), if the respective crop contributes more than 5% to the total cropland area in the affected country [based on Portmann et al. (27)]. For multiyear extreme events, we averaged consecutive extreme years into a single disaster year signal, so that the time window always consisted of seven entries, centered on the event signal.

This method creates a subset of 65 heat waves and 175 droughts for maize and 81 heat waves and 146 droughts for wheat (table S3). The extracted 7-year time series were divided by the average of the 3 years preceding and following the event to remove the absolute magnitude of national data from the signal. Any other data entry co-occurring with another extreme event was excluded from calculating the mean. Last, any linear trend was removed from the composite time series [in contrast to the study by Lesk et al. (14)], as model simulations are not expected to reproduce observed trends in yields driven by technological progress. The detrending was applied after compositing as it maintains the absolute event signal, which is thus directly comparable to previous studies (14). A discussion on potential type I and II errors associated with compositing sample size was presented in Lesk et al. (14).

Rainfall deficits in Fig. 3 were calculated as the relative difference of cumulative growing season precipitation in the respective year and the long-term average cumulative precipitation during the MIRCA2000 growing season.

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