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Atmospheric opacity has a nonlinear effect on global crop yields


Agricultural impacts of air pollution, climate change and geoengineering remain uncertain due to potentially offsetting changes in the quantity and quality of sunlight. By leveraging year-to-year variation in growing-season cloud optical thickness, I provide nonlinear empirical estimates of how increased atmospheric opacity alters sunlight across the Earth’s surface and how this affects maize and soy yields in the United States, Europe, Brazil and China. I find that the response of yields to changes in sunlight from cloud scattering and absorption is consistently concave across crops and regions. An additional day of optimal cloud cover, relative to a clear-sky day, increases maize and soy yields by 0.4%. Changes in sunlight due to changes in clouds have decreased the global average maize and soy yields by 1% and 0.1% due to air pollution and may further decrease yields by 1.8% and 0.4% due to climate change.

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Fig. 1: Clouds alter the global optical environment.
Fig. 2: Empirical estimates of the sunlight-mediated effect of cloud opacity on crop yield.
Fig. 3: Empirical estimates of the effect of total and diffuse sunlight on crop yield.
Fig. 4: The sunlight-mediated influence of anthropogenic changes in clouds on global crop yield.

Data availability

All data used in this analysis are from free, publicly available sources, other than the Chinese yield data. Replication data are available at as well as upon request from the corresponding author.

Code availability

Replication code is available at as well as upon request from the corresponding author.


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I thank M. Auffhammer, J. Burney, T. Carleton, W. Collins, M. Fowlie, S. Hsiang, A. Hultgren, P. Huybers and seminar participants at Berkeley, Harvard, Minnesota and Stanford universities and the American Geophysical Annual Meeting for useful comments. This material is based on work supported by the National Science Foundation Graduate Research Fellowship under grant no. DGE 1752814.

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Correspondence to Jonathan Proctor.

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Peer review information Nature Food thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Sample averages of maize and soy yield and some of their climatological determinants.

Maize and soy growing-season-average yield, cloud OD, photosynthetically active radiation, temperature, and precipitation in the subnational areas included in the analysis (1985-2009).

Extended Data Fig. 2 Correlation of cloud OD with other climatological determinants of yield.

The estimated deviation-from-average of temperature, precipitation, wind speed and aerosol OD correlated with increases in cloud OD in the pooled sample. Regressions for each of the four variables include the other three climate variables and administrative level-2 fixed effects and quadratic time trends as controls to mirror the identifying variation in the estimation of cloud impacts on yields. Dotted lines represent the 95% confidence interval, which is calculated allowing for arbitrary temporal and spatial correlation within administrative level-1 (e.g. state) units.

Extended Data Fig. 3 Estimated climate control functions from the model of cloud opacity impacts on maize and soy yield.

Regional climate response functions from the pooled model (Supplementary Information Eqn. 14) for maize (a) and soy (b). Responses show the effect of changing a day’s precipitation, temperature, wind speed and aerosol OD on growing season yield.

Extended Data Fig. 4 The effect of adding controls to the estimated effect of cloud opacity on maize and soy yields.

The estimated effect of cloud opacity on maize and soy yields in the pooled and regional samples adding controls in one-at-a-time. Generally, adding precipitation (P) and temperature (T) into the model decrease the benefits of cloudiness while adding aerosol OD (A) and wind speed (W) have little effect. Dotted lines show the 95% confidence interval for the cloud response in the model with no controls. The confidence interval is calculated allowing for arbitrary temporal and spatial correlation within administrative level-1 (e.g. state) units.

Extended Data Fig. 5 Marginal limitation of yield due to the realized optical environment, relative to the ideal optical environment.

Maps show sunlight-mediated maize and soy yield gains from changing 1% of the growing season from the observed (1985-2009) distribution of cloud OD to the empirically estimated ideal optical conditions (that is OD = 15). a shows the total gain, and b,c decompose that total into parts due a) to increasing cloud OD when opacity is less than optimal (OD < 15) and b) to reducing opacity when cloud OD is higher than optimal (OD > 15). Note that much of the yield gain from increasing opacity is from increasing cloud amount (that is raising OD from 0 to 15) rather than increasing the OD of existing clouds that are optically thin (Supplementary Information Section III.8).

Extended Data Fig. 6 Including cloud OD increases out of sample model fit.

Bars show the average within R2 across folds from a 10-fold cross-validation experiment. Red bars show validation-set performance for the primary specification (Supplementary Information Eqn. 13); the other bars show validation-set performance when cloud OD, temperature, precipitation, aerosol OD, and wind speed are individually removed and the model is re-trained and evaluated via cross-validation. The within R2 is calculated on the validation set for each fold, and the displayed within R2 is the average of within R2 values across the 10 folds.

Extended Data Fig. 7 Robustness of empirical estimates of the sunlight-mediated effect of cloud opacity on crop yield.

Each curve shows the estimated effect of increasing the cloud OD of cloudy areas from zero to a given value for three hours during the growing season in the pooled sample. In all panels, dotted lines represent the 95% confidence interval for the pooled effect. a, Climatic controls in the primary specification (‘BASE’, black) (Supplementary Information Eqn. 14) are altered to use a different precipitation dataset (red), model temperature non-parametrically using bins (green), model temperature using degree days calculated from a sinusoidal interpolation of daily maximum and minimum temperature (yellow), control for nighttime cloud cover (grey) and for vapor pressure deficit (blue) (Supplementary Information, Section III.4). b, The fixed-effects in the primary specification (black) are changed from administrative unit level-2 specific quadratic trends, to administrative unit level-2 cubic trends (yellow) and administrative unit level-1 quadratic trends (blue). c, The functional form used to calculate the cloud response is altered from the preferred specification which uses a restricted cubic spline with four knots (black) to a restricted cubic spline using 3 knots (blue) and 5 knots (yellow) as well as a cubic polynomial (green), and non-parametric bins of OD (red). d, The observational weights are changed from standard OLS weights to planted-area weights (red).

Extended Data Fig. 8 Empirical estimates of the response of maize and soy yields to PAR at three diffuse fractions.

The estimated effect of changing PAR on maize and soy yields for an hour during the growing season in the pooled sample (black), Brazil (green), China (red), the European Union (yellow), and the United States (blue). The effect of changing PAR is evaluated at (a) a diffuse fraction of 0, (b) the average diffuse fraction of 0.4, and (c) a diffuse fraction of 1 (Supplementary Information Section IV). Dotted lines represent the 95% confidence interval for the pooled effect, which is calculated allowing for arbitrary temporal and spatial correlation within administrative level-1 (e.g. state) units.

Extended Data Fig. 9 Changes in cloud distributions due to anthropogenic aerosol and carbon dioxide emissions.

Simulated changes in cloud amount (CA) for nine cloud types (Supplementary Information Section III.7) in the air pollution and climate changes scenarios. Growing season changes are averages over 5 climate models and 30 years of data (Supplementary Information Section V).

Extended Data Fig. 10 Model spread of the projected effect of air pollution and climate change on crop yields due to cloud-induced changes in sunlight.

Maps show the pixel-wise minimum and maximum of the impacts projected by the 5 climate models for maize and soy yields.

Supplementary information

Supplementary Information

Supplementary Methods, Figs. 1–4 and Table 1.

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Proctor, J. Atmospheric opacity has a nonlinear effect on global crop yields. Nat Food 2, 166–173 (2021).

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