Non-linear relationships between daily temperature extremes and US agricultural yields uncovered by global gridded meteorological datasets

The study investigates whether newly available global daily/hourly meteorological datasets (ERA5-Land and GMFD) can accurately recover the non-linear effects of temperature, especially extreme heat, on agricultural yields relative to a fine-scaled, country-specific dataset (PRISM) in the United States. The motivation is that global commodity prices depend on aggregate supply, necessitating globally comparable weather inputs for estimating production responses and climate impacts. A key challenge is that temporal or spatial aggregation can mask non-linearities in temperature–yield relationships, and coarse measurements can introduce attenuation bias, particularly around critical thresholds where effects switch from beneficial to harmful. The paper tests model performance and estimated response functions across datasets using US county-level yield data (corn and soybeans) and then evaluates predictive power in a data-sparse region (Sub-Saharan Africa) using satellite-based EVI as a yield proxy, comparing ERA5-Land and GMFD to the monthly CRU dataset.

Prior research has established that temperature extremes, particularly extreme heat, are major determinants of agricultural yields and that the capacity for adaptation to extreme heat critically shapes climate impacts. Studies show that incorporating the full daily temperature distribution (between daily minima and maxima) improves prediction of heat-related yield losses, while averaging over time (monthly) or space (coarser grids) obscures the non-linear exposure–response relationship. Historically, many global analyses relied on monthly datasets (e.g., CRU, University of Delaware), which cannot capture daily extremes. The paper also notes similar non-linear temperature response functions have been documented in other sectors (e.g., energy demand and mortality), highlighting the broader relevance of correctly modeling temperature extremes.

Data and scope: The US analysis links county-level yields for corn and soybeans (USDA NASS, 1950–2019; dryland counties east of the 100° meridian, excluding Florida) to weather from three sources: PRISM (fine-scale, 1/24° ≈ 4 km, daily T_min/T_max, precipitation; 1950–2019), ERA5-Land (0.1° ≈ 11 km, hourly temperature, total precipitation; 1950–2019), and GMFD (0.25° ≈ 28 km, daily T_min/T_max, precipitation; 1950–2010). Panels result in 128,169 observations for corn and 102,674 for soybeans; approximately 14,000 observations are dropped when restricting to GMFD years.

Weather construction and aggregation: For PRISM and GMFD, within-day temperatures are approximated with a sinusoidal curve between daily minima and maxima to compute time spent within each 1°C interval and degree-days above thresholds. ERA5-Land’s hourly temperature enables direct construction of daily exposure distributions; supplementary tests show little difference versus sinusoidal interpolation. All weather variables are constructed at the daily grid-cell level to preserve non-linearities, then aggregated to counties for March–September growing seasons. Aggregation weights use a high-resolution cropland mask (USDA CDL), averaging crop masks from 2008–2021 at 30 m, and, for ERA5-Land and GMFD, additional weights based on the fraction of a grid cell overlapping county boundaries.

Econometric models (US): Log yield is modeled against non-linear temperature exposure with controls for county fixed effects, state-specific quadratic time trends (technological change), and a quadratic in total growing-season precipitation. Standard errors are clustered at the state level, with robustness checks (year fixed effects, alternative clustering, Conley SEs) in supplementary materials. Three temperature functional forms are estimated for each crop and dataset: (1) piecewise linear “degree-day” model with a data-driven cross-validated threshold (breakpoint) chosen separately by crop and dataset; (2) an 8th order Chebyshev polynomial in temperature; and (3) semi-parametric 3°C bins up to 36°C. Models are interpreted in relative terms (county fixed effects), with response functions normalized at 10°C.

Model evaluation and projections (US): Predictive performance is assessed via repeated cross-validation: 1000 repetitions that randomly sample 85% of years for estimation and predict the remaining 15%, computing the reduction in RMS error relative to a baseline with only county fixed effects and state quadratic time trends (no weather). Comparisons include models using daily extremes versus a quadratic in growing-season average temperature. Climate impact projections are generated by applying spatially uniform warming scenarios of +1°C to +4°C to the historical temperature distribution, propagating uncertainty via 1000 draws from the estimated response function covariance.

Sub-Saharan Africa analysis: In the absence of reliable sub-national yield data, the study uses the log of total growing-season Enhanced Vegetation Index (EVI) from Landsat as a yield proxy over a 10-year panel, aggregating to ERA5-Land’s 0.1° grid and masking by FAO GAEZ harvested area for maize. Degree-days are constructed from ERA5-Land and GMFD as in the US analysis; for CRU (monthly), degree-days are estimated using Thom’s formula. Growing seasons are defined by subregional crop calendars. The analysis compares out-of-sample predictive performance of piecewise linear EVI–temperature models using ERA5-Land, GMFD, and CRU, separately for grids containing an NCDC weather station and grids without stations.

Additional diagnostics: A resampled PRISM model (spatially aggregated to 0.1° prior to county aggregation) assesses the role of spatial resolution in predictive skill gaps versus ERA5-Land. Temporal aggregation tests compare ERA5-Land hourly versus daily T_min/T_max-derived measures.

• All datasets (PRISM, ERA5-Land, GMFD) recover similar non-linear, asymmetric temperature–yield relationships for US corn and soybeans: yields rise with moderate temperatures and decline sharply at high temperatures. Cross-validated thresholds (piecewise models) differ modestly by dataset (e.g., corn thresholds from ~27°C ERA5-Land to ~30°C GMFD; soybeans ~28°C ERA5-Land to ~30°C PRISM).
• Table 1 effects (relative to a full day at 10°C): Replacing a full day at 10°C with 36°C reduces corn yields by approximately 3.2% (SE 1.2%, ERA5-Land) to 3.8% (SE 1.0%, PRISM), and soybean yields by roughly 2.7% (SE 0.32%, ERA5-Land) to 3.5% (SE 0.38%, PRISM). Replacing a 10°C day with the yield-maximizing temperature increases corn yields by 0.64% (SE 0.16%, ERA5-Land) to 0.87% (SE 0.23%, GMFD) and soybean yields by 1.04% (SE 0.20%, ERA5-Land) to 1.28% (SE 0.19%, GMFD).
• Out-of-sample predictive performance (RMS reduction vs. baseline): For corn, PRISM averages 14.9% RMS reduction versus 12.1% (ERA5-Land) and 12.0% (GMFD); for soybeans, PRISM averages 15.7% versus 13.1% (ERA5-Land) and 13.2% (GMFD). Differences PRISM vs. global datasets are statistically significant (Welch tests, P < 0.01), while ERA5-Land vs. GMFD differences are insignificant (P > 0.1). Across all datasets, daily-extremes models (piecewise, polynomial, 3°C bins) outperform models using a quadratic in growing-season average temperature.
• Uniform warming projections (US): For +2°C, projected aggregate yield losses are 11–16% for corn and 9–11% for soybeans across daily-specification models and datasets; for +4°C, losses are 30–35% (corn) and 25–29% (soybeans). Models using seasonal average temperature project smaller impacts, missing the asymmetric damages from extreme heat.
• Sub-Saharan Africa (EVI proxy): ERA5-Land and GMFD (daily) exhibit significantly better out-of-sample predictive power than CRU (monthly). ERA5-Land shows particularly strong performance and is largely unaffected by proximity to weather stations; GMFD exhibits a small but statistically significant improvement near stations. Overall differences due to station proximity are small relative to the gains from daily datasets.
• Diagnostics: Aggregating PRISM to ERA5-Land’s spatial scale reduces PRISM’s lead in RMS over ERA5-Land by about 55%, attributing much of the predictive advantage to finer spatial resolution. Temporal aggregation from hourly to daily (ERA5-Land) has negligible effect on performance.

The study’s core question—whether global daily meteorological datasets can reliably capture the non-linear effects of temperature extremes on crop yields—is answered in the affirmative: ERA5-Land and GMFD reproduce key non-linear response shapes, thresholds, and climate-impact magnitudes similar to those from fine-scale PRISM, despite somewhat lower predictive skill. The findings emphasize that correctly modeling daily temperature extremes (functional form) is more consequential for predictive power and impact projections than the choice among these datasets. Reduced performance from seasonal-average temperature models highlights the importance of accounting for asymmetric damages from extreme heat.

Differences in predictive skill are partly explained by spatial resolution and reanalysis/interpolation methods. Spatial aggregation accounts for roughly half the PRISM advantage over ERA5-Land, while temporal resolution (hourly vs. daily min/max) adds little. Reanalysis approaches may smooth extremes, potentially diminishing precision around critical thresholds.

In data-sparse regions, daily global products still outperform monthly data: ERA5-Land and GMFD significantly surpass CRU in predicting EVI-based yield proxies in Sub-Saharan Africa, with minimal dependence on station proximity (especially for ERA5-Land, which uses satellite-based reanalysis). These results support the use of globally consistent daily datasets for productivity estimation, climate impact assessment, and downstream applications such as trade modeling, climate policy analysis, and index insurance design.

ERA5-Land and GMFD, despite coarser spatial resolution than PRISM, successfully uncover the non-linear temperature–yield relationships driven by daily extremes for US corn and soybeans across multiple model specifications. While PRISM yields the best out-of-sample performance, the two global datasets produce comparable response functions and similar climate impact projections under uniform warming scenarios. Models that incorporate daily temperature extremes substantially outperform those relying on seasonal-average temperatures. Thus, the appropriate functional form is more critical than the specific choice among these daily datasets. Future research should examine how observational unit scale affects estimated relationships, further evaluate performance in regions with sparse station networks, and leverage emerging high-resolution yield datasets to refine climate-yield modeling.

Key limitations include: (1) Absence of sub-national yield data in Sub-Saharan Africa necessitates use of EVI as a proxy, which may be influenced by non-weather factors; (2) Shorter panel and limited out-of-sample years in the Africa analysis increase sensitivity to idiosyncratic shocks (e.g., pests), skewing RMS distributions; (3) Potential measurement error from spatial aggregation and reanalysis/interpolation, which may smooth extreme events critical for yield prediction; (4) The US models assume additive separability of temperature effects over the growing season, which may not capture timing-specific sensitivities; (5) GMFD’s dependence on ground stations could reduce accuracy in station-sparse regions, and PRISM’s superior performance may not generalize where station networks are weak; (6) Uniform warming scenarios simplify spatially heterogeneous climate change and do not incorporate precipitation or humidity changes beyond the modeled precipitation control.