Warming temperatures tend to damage crop yields, yet the influence of water supply on global yields and its relation to temperature stress remains unclear. Here we use satellite-based measurements to provide empirical estimates of how root zone soil moisture and surface air temperature jointly influence the global productivity of maize, soybeans, millet and sorghum. Relative to empirical models using precipitation as a proxy for water supply, we find that models using soil moisture explain 30–120% more of the interannual yield variation across crops. Models using soil moisture also better separate water-supply stress from correlated heat stress and show that soil moisture and temperature contribute roughly equally to historical variations in yield. Globally, our models project yield damages of −9% to −32% across crops by end-of-century under Shared Socioeconomic Pathway 5-8.5 from changes in temperature and soil moisture. By contrast, projections using temperature and precipitation overestimate damages by 28% to 320% across crops both because they confound stresses from dryness and heat and because changes in soil moisture and temperature diverge from their historical association due to climate change. Our results demonstrate the importance of accurately representing water supply for predicting changes in global agricultural productivity and for designing effective adaptation strategies.
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All data used in this analysis are from free, publicly available sources and are publicly accessible from Zenodo at https://doi.org/10.5281/zenodo.7041431.
Replication code is publicly accessible from Zenodo at https://doi.org/10.5281/zenodo.7041431.
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We thank seminar participants at the University of California Santa Barbara, Harvard University, the University of British Columbia, the Woods Hole Oceanographic Institution, the Gordon Research Conference on Climate Engineering, the American Geophysical Union, the Planetary Health Colloquium, and the Seminar on Planetary Management for useful comments. Funding for this project was provided by the Harvard Google Data+Climate Project.
The authors declare no competing interests.
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Average of yield data (2007–2018, hg/ha) from the Food and Agricultural Organization of the United Nations.
Extended Data Fig. 2 Reconstructions of U.S. yield anomalies using a model accounting for water supply and temperature stress.
Observed yield anomalies from the trend, along with predicted climate-induced yield anomalies from the trend using the TS model. The individual temperature and soil moisture components of this prediction are also plotted. 95% confidence intervals around the predictions, relative to a growing season with average conditions, are shown as dotted lines.
Extended Data Fig. 3 The influence of temperature, soil moisture and precipitation on barley, oats and wheat yield.
Identical to Fig. 2 but estimated for barley, oats and wheat. These crops were omitted from the primary analysis due to them commonly being planted as either a spring or winter crop, as the FAO does not differentiate yield by winter versus spring planting. The findings from these three crops are consistent with those of maize, soybeans, sorghum and millet. Barley, oats and wheat also show moderated effects of extreme heat and improved performance in the TS model relative to the TP model. Out-of-sample within-R2 is 0.125 for barley, 0.172 for oats, and 0.122 for wheat in the TS model and 0.095 for barley, 0.154 for oats and 0.106 for wheat in the TP model.
Extended Data Fig. 4 Correlation of daily temperature, soil moisture and precipitation during the maize, soybean, sorghum and millet growing season over cropped areas.
The Pearson’s correlation coefficient is calculated weighting daily observations across crops by cropped fraction for each 50km x 50km pixel with harvest area greater than 100 hectares.
Extended Data Fig. 5 Omitting measures of water supply biases estimated effects of temperature on crop yield in simulation.
(A) Simulated daily temperature and soil moisture. (B) Estimated temperature response curves where simulated yields are a linear function of daily growing season temperature and soil moisture. The prescribed true response (black) is shown along with estimated responses modelling temperature (red), temperature and precipitation (yellow), and temperature and soil moisture (blue). (C) Similar response curves to (A) except that yield is simulated and modelled as a quadratic, rather than linear, function of temperature. (D) Similar to (C) except that instead of soil moisture having a linear influence on yield, soil moisture has a nonlinear influence whereby increasing soil moisture at low values increases yield but increasing soil moisture at high values has little effect. This produces larger bias at high temperatures than at low temperatures in the models that omit soil moisture, which is consistent with what we observe in Fig. 2. (E) Similar to (A) but with a stronger simulated relationship between daily soil moisture and temperature in hot and dry conditions. (F) Similar to (D) but with additional bias at high temperatures relative to low temperatures due to the strengthened soil-moisture temperature relationship in (E).
Extended Data Fig. 6 Irrigation modifies the influences of climatic factors on crop yield and validates empirical separation of water supply and temperature stresses.
Identical to Fig. 3 except that responses are estimated separately for each of the four crops rather than pooled. Grey backgrounds indicate models where either allowing for heterogeneity with respect to irrigation does not improve performance or where the response function is not significantly different from the null of zero effect at the p < 0.10 level (see Extended Data Table 1 for model performance when neither T nor S is interacted with irrigation or when both T and S are; when only T is interacted with irrigation, within-R2 = 0.097 for maize, 0.141 for soybeans, 0.034 for sorghum and 0.028 for millet; when only S is interacted with irrigation, R2 = 0.106 for maize, 0.136 for soybeans, 0.054 for sorghum and 0.022 for millet). Outliers are winsorized for display to their 0.5 and 99.5 percentiles for temperature and soil moisture and 1 and 99 percentiles for precipitation.
Extended Data Fig. 7 Estimated influence of soil moisture and temperature on global crop yields allowing for interaction effects.
Response surfaces show the influence on yield of changing a day in the growing season from 25 ∘C and 0.2 cm3cm−3 to a given temperature and soil moisture. (A) Shows the estimated response surface, allowing the nonlinear influence of temperature and soil moisture to depend nonlinearly on the level of the other (Methods). (B) Shows the estimated response surface allowing for nonlinear effects of temperature and soil moisture, but no interaction between the two (that is the same model as in Fig. 2). Black contours show the cropped-area-weighted distribution of daily growing season values across crops in the pooled surface and for each crop in their respective plots. Response functions are shown over the 95th percentile contour of the underlying distribution of daily values. White lines show contours of the estimated response surfaces to aid display. P-values for the null of no interaction effect are 0.738 for the pooled model, 0.295 for maize, 0.461 for soybeans, 0.956 for sorghum, and 0.141 for millet. See Supplementary Discussion 4.
Extended Data Fig. 8 Projected influence of climate change on maize, soybean, sorghum and millet yields due to changes in temperature and soil moisture.
(A) Projected influence of changes in temperature stress due to climate change on crop yield using the TS model (SSP5-8.5, 2015–2035 to 2080–2100, averaged across six CMIP6 models, see Methods). (B) Projected influence of changes in water-supply stress due to climate change on crop yield using the TS model. Locations where five out of six of the models agree on the sign are not stippled.
Extended Data Fig. 9 Distribution of observed (black) and CMIP6 simulated (coloured) daily growing season temperature and soil moisture over cropped areas before and after debiasing.
Observations have been winsorized to 10∘C and 55∘C and to 0.5 cm3cm−3 for display. Light colours show near-future (2015-2035) values and dark colours show end of century (2080-2100) values. Middle and right columns show distributions after pixel-wise mean and mean and variance debiasing approaches were applied (Methods).
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Proctor, J., Rigden, A., Chan, D. et al. More accurate specification of water supply shows its importance for global crop production. Nat Food 3, 753–763 (2022). https://doi.org/10.1038/s43016-022-00592-x