Consistent negative response of US crops to high temperatures in observations and crop models

High temperatures are detrimental to crop yields and could lead to global warming-driven reductions in agricultural productivity. To assess future threats, the majority of studies used process-based crop models, but their ability to represent effects of high temperature has been questioned. Here we show that an ensemble of nine crop models reproduces the observed average temperature responses of US maize, soybean and wheat yields. Each day >30 °C diminishes maize and soybean yields by up to 6% under rainfed conditions. Declines observed in irrigated areas, or simulated assuming full irrigation, are weak. This supports the hypothesis that water stress induced by high temperatures causes the decline. For wheat a negative response to high temperature is neither observed nor simulated under historical conditions, since critical temperatures are rarely exceeded during the growing season. In the future, yields are modelled to decline for all three crops at temperatures >30 °C. Elevated CO2 can only weakly reduce these yield losses, in contrast to irrigation.

the three crops maize, soybean and wheat under irrigated and rainfed conditions. All 172 pairwise t-tests for mean difference are highly significant (p = 0); relative differences are 173 shown in Supplementary Table 3. three crops maize, soybean and wheat under irrigated and rainfed conditions. All pairwise t-177 tests for mean difference are highly significant (p = 0); relative differences are shown in 178 Supplementary Table 3. (fixed present/increased) combinations. All pairwise t-tests for mean difference are highly 207 significant (p = 0); relative differences are shown in Supplementary Table 4. irrigation pattern, and "Irrigated" is full irrigation on all cultivated areas. Outliers above 5 221 were removed for visual clarity (0.4% of the data). Only counties were considered where 222 yields were available for both historical and future simulations (removed 24% of the data). fixed growing season is split into three equally sized parts. For maize and soybean these are 243 March-April (part 1), May-June (part 2) and July-August (part 3). For wheat the parts are 244 October-January (part 1), January-April (part 2) and April to July (part 3); months are split on 245 day 15 as the fixed winter growing season is from October 15 to July 15. and wheat (c). Observed yields are shown in red, while predicted yields are shown in green.

301
The box plots show the median (black line within the box) and the first and third quartile 302 (boxes). Whiskers extend to approx. the 1. 6 Figures 1-3)). 377 Additionally, a modified Principal-Component-Regression yields no different results than the 378 multiple linear regression applied in the main paper (Supplementary Figure 4). This proves 379 that multi-collinearity between the temperature exposure times is not influencing the For more details of the method please refer to ref. 2 . This piecewise linear approach, where 391 only two temperature-dependent slopes are estimated, exhibits the same yield response as 392 the step-function regression applied in the main paper -which indicates that the response is 393 stable and independent from the regression method. 394 395 A modified Principal-Component-Regression was applied to the data set to control for 396 multicollinearity between temperature variables. We kept precipitation, county-fixed effects 397 and state-time trends in the data matrix, but selected only those temperature bins that a 398 principal component analysis yielded as most important (a standard deviation larger than 399 two was used as cutoff, then representative temperature variables were selected for each 400 component). Afterwards the standard multiple regression analysis as described in the main 401 paper was applied to the reduced data set. For all crops the temperature coefficients are 402 comparable to the original regression results (Supplementary Figure 4). Note that a 'classical' 403 Principal-Component regression of all explanatory variables (i.e. regressing yield on 404 transformed orthogonal components) yields similar results, but does not provide 405 information on standard errors -this is why we resorted to the modified approach. for maize and soybean (but 117% for wheat) and EPIC-Boku simulates 67% of mean yields for 417 wheat. The low average yields seem to reduce the signal-to-noise ratio through an increased 418 coefficient of variation, which results in an unexpected temperature response. confirms that there is no detectable response of historical wheat yields to high temperature. 431 These plots are useful for telling whether there is a difference between irrigated and rainfed 432 yield responses, for all coefficients at once rather than for single coefficients. The R 2 433 correlation values (in the legends) are inconclusive for the modelling capacity as there is 434 little difference between the rainfed and the irrigated comparisons, due to the close 435 clustering of values around 0. temperature; all coefficients (except one for maize and two for soybean) are insignificant.

442
The yield drop at elevated temperatures above 30°C is absent in particular for maize and 443 soybean. The positive coefficient for soybean at temperatures above 39°C may be a 444 regression artefact due to few days with this temperature and the insignificance of 12 of the 445 other 13 coefficients, but does not contradict our findings. The negative responses of 446 pDSSAT wheat (panel c, brown curve) to all except two temperature bins are insignificant 447 (confidence intervals contain 0) and underline the independence of irrigated yields from 448 temperature. Additionally, the sample size for irrigated wheat is small with only 10 counties 449 in Arizona containing sufficient data. Why pDSSAT responds differently than the other 450 models in this case has not been investigated here but would require further data on 451 irrigated wheat. 452 The models generally show a slightly higher responsiveness to temperature than the 453 observations do. This might indicate that some management decisions apart from irrigation 454 are reflected in the observed but not in the simulated yields. The low relative abundance of extremely high temperatures above 36°C could lead to a 459 lower sensitivity of the statistical model to detect yield effects of these temperatures. We 460 tested this sensitivity by artificially reducing simulated yields at each grid cell for each day 461 above different temperature thresholds. We used 33, 36 and 39°C as thresholds, above 462 which each day reduced crop yields by 2%. Thus, 10 days at e.g. 33°C or above reduce crop 463 yields by a factor of 0.98^10 = 0.817. The reduction was additionally applied to simulated 464 historical ensemble yields in rainfed counties. Reductions were applied to yields in grid cells 465 and then aggregated to counties.

466
The statistical approach shows correct quantitative responses to artificially induced 467 "temperature stress" by log(0.98) = -0.02 lower coefficients at and above the thresholds 468 (Supplementary Figure 25). Thus we conclude that the regression is sensitive to extremely 469 high temperatures, independent of their relative abundance, and that the aggregating from 470 grid cells to counties does not conceal these events. All coefficients below the threshold 471 temperatures are unchanged, which shows the robustness of the approach and the 472 specificity towards temperature bins.

474
The distribution of exposure times differs across different parts of the historical growing 475 season (Supplementary Figure 26). Earlier parts of the (fixed) growing season contain cooler 476 average temperatures and less high temperature events. Most of the high (above 30°C) and 477 extremely high (above 36°C) temperature events expectably occur in the last part of the 478 growing season. But for maize and soybean already a substantial number of these events 479 occur in the middle part of the growing season. For wheat high temperature events occur 480 only in the third part. It is evident that many crops experience (extremely) high 481 temperatures already in the middle part of the growing season. Crop anthesis dates for 482 maize (June/July), soybean (June/July) and wheat (May) usually lie at the end of part 2 or in 483 part 3 of the growing season 1 . Grain filling mostly occurs in the last part, which experiences 484 the highest temperatures. Both anthesis and grain filling are known to be very sensitive to 485 high temperatures 6,7,8,9,10,11,12  The AgMERRA 13 climate data used in this study are one order of magnitude coarser (0.5° x 495 0.5°) than those used by Schlenker & Roberts at a 2.5-mile resolution (about 0.04°) 2 . We 496 decided to use the AgMERRA data instead as the GGCMs from the AgMIP ensemble were 497 also forced by them. The temperature distribution of the fine-scale data set is slightly shifted 498 with lower densities below about 27°C and higher densities in the temperature range from 499 27°C to 37°C (Supplementary Figure 29). The fine-scale climate data are constructed from 500 monthly and daily data; this is described in the supplement of Schlenker & Roberts 2 . The 501 comparison between the two climate data sets therefore shows differences between these, 502 but not necessarily differences between AgMERRA and the "true" climate. 503 504 We also analyzed the spatial agreement of the two temperature distributions by comparing 505 the numbers of days with maximum temperature above certain thresholds (30°C and 32°C) 506 for dot corresponds to one grid cell), with R 2 values of 94% and 91%, respectively. The AgMERRA 512 data tend to include even more hot days than the fine-scale climate data in the very hot 513 regions.

515
To test the sensitivity of the coefficients to the deviations of the temperature distributions 516 we compare our scaling coefficients based on the AgMERRA data to the ones originally 517 derived by Schlenker & Roberts. Both estimates for observed rainfed yields agree closely 518 (Supplementary Figure 31), in particular also in the temperature range above 30°C. There is 519 no hint for a significant divergence of the regression coefficients based on the higher 520 resolution temperatures and the ones based on the AgMERRA data for both maize and 521 soybean (the two crops considered by both Schlenker & Roberts and also simulated by our