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# Different uncertainty distribution between high and low latitudes in modelling warming impacts on wheat

## Abstract

Global gridded climate–crop model ensembles are increasingly used to make projections of how climate change will affect future crop yield. However, the level of certainty that can be attributed to such simulations is unknown. Here, using currently available geospatial datasets and a widely employed simulation procedure, we created a wheat model ensemble of 1,440 global simulations of 20 climate scenarios, 3 crop models, 4 parameterization strategies and 3 management inputs of sowing date. We quantified the contributions of climate, model, parameterization and management to the overall uncertainty to predicted responses of yield to warming, then related the results to the latitude of the grid cells. For all warming scenarios, the total uncertainty for mid- and high latitudes is much larger than for low latitudes. Uncertainty arising from crop models was larger than that from the other sources combined. Parameterizing crop models with grid-specific information on wheat cultivars tended to decrease the crop model uncertainty, particularly for low latitudes. Crop model improvements and better-quality spatial input data more closely representing the wide range of growing conditions around the world will be needed to reduce the uncertainty of climate change impact assessment of crop yields.

## Main

In the global gridded crop model (GGCM) approach, the world is divided into grid cells defined by latitude and longitude, and crop yield for the landmass in each grid cell is simulated1,2,3,4. To estimate the potential impact of climate change on food production, researchers aggregate simulated results into nations, regions or the world to aid economic analysis and inform policymaking at different scales5,6. To be deemed trustworthy, GGCM results must provide accurate estimates of yield–climate relationships, or otherwise give explicit information of the uncertainty of projections. Current crop models produce different results due to underlying differences in climate projections, model structure, inputs and parameterization, so overall there is a large degree of uncertainty in crop yield projections1. An effective way to quantify this uncertainty is to compare multiple climate–crop simulations of the same climate change problem7,8. Most current impact assessments are conducted for just a few well-characterized sites9,10,11,12, so while model accuracy can be improved through understanding where and how uncertainty arises in a multimodel ensemble13, the uncertainty of predictions across the mass of diverse arable lands around the world is difficult to estimate.

Estimating impact consistently across the globe by applying a GGCM ensemble is expensive and difficult in terms of labour, timing, computational ability and resources, and expertise. Compared with crop modelling at individual sites, GGCMs introduce additional sources of uncertainty such as those that arise from geospatial data and data processing. For example, recent GGCM ensemble studies compared simulation results from different research groups14. Even when committed to following a common simulation protocol15, groups adopted their unique ways of processing data and parameterizing the models for the globe. A further aspect that has received insufficient attention in GGCMs is model parameterization and how it can affect the uncertainty of global-scale predictions, particularly for parameters describing local-scale spatial variation in the use and performance of cultivars, varieties or hybrids.

Here we present a range of global wheat yield responses to future warming scenarios based on a large simulation ensemble. The ensemble was composed of 1,440 global simulations, with combinations of 20 climate projections (5 climate models under 4 representative concentration pathways (RCPs) for greenhouse gas emissions), 3 crop models, 4 parameterization strategies and 3 management inputs of sowing date (Supplementary Fig. 1). We linked the uncertainty of gridded predictions to the latitude of grid cells. To include the uncertainty of crop yield predictions due to CO2 fertilization, we conducted two sets of simulations: the first accounted for the effects of both increased CO2 as projected by the RCPs and changes in climate (CC w/CO2); the second accounted for changes in climate at 360 ppm CO2, assuming CO2 concentration would remain constant at its 1995 value (CC w/o CO2). We estimated wheat yield changes for each ensemble member for the period from 2011 to 2099 relative to the mean yield of the corresponding simulations for the baseline from 1981 to 2010. There were 72 baselines by the combination of 3 crop models, 4 parameterization strategies, 3 management inputs of sowing and 2 CO2 effects. Simulated yield responses are shown as a function of global mean temperature change during the wheat growing seasons so the results can be readily compared across emissions scenarios and periods. Differences in the responses of yield to warming calculated by ensemble members were used as an estimate of uncertainty. The goal of this study was to quantify the uncertainties arising from different sources in the global modelling procedure, namely climate projection, crop model, parameterization strategy and critical model input such as sowing date. All information required for the ensemble was extracted or estimated from currently available databases (Supplementary Table 1).

## Results

### Simulating historical wheat yield by generic to specific parameterization of GGCM ensemble

A range of parameterization strategies has been employed separately in previous studies for global simulations5,6,16, reflecting the different levels of complexity and data required to calibrate models so that they can reproduce historical observations. Four parameterization strategies (PS) were used here with increasingly specific information on wheat cultivar use across the globe. They are PS1, one universal cultivar for the entire globe; PS2, 17 current wheat cultivars from previous calibrations; PS3 and PS4, gridded specific cultivars that calibrated in a 10 yr historical simulation (1996−2005), part of the baseline period, under fully irrigated conditions (Supplementary Fig. 2).

Figure 1 shows the distribution of simulated biases of days to maturity and yield for the baseline, compared with reported gridded values (Supplementary Fig. 4). With increasingly detailed parameters, simulated bias decreased gradually from PS1, with no explicit calibration, to PS4, with the most detailed calibration, as indicated by decreases in the median and the narrowing of the variation ranges. The median of simulated biases of all models moved from PS1 (6.5% for days to maturity and 10% for yield) to nearly zero in PS4. From PS1 to PS4, the full range of the biases decreased 92% for days to maturity and 40% for yield. These substantial reductions demonstrate that more heterogeneous spatial data with detailed biological calibration can be an efficient approach to increase simulation agreement with historical observations. Simulation of crop maturity date, a critical indicator for crop–climate relationships, was particularly improved by more specific cultivar parameters (Supplementary Figs. 69).

### Sources of uncertainty in wheat GGCM ensemble

The simulated impact of warming on global wheat yield varied considerably between ensemble members. The total uncertainty of simulated yield response to warming is from 20.8% to 54.8%, depending on the warming level and whether CO2 levels are constant or increasing (Fig. 2 and Supplementary Table 4). Uncertainty is in a range from 20.8% to 48.5% in CC w/o CO2 simulations, exhibiting similar directions of yield change (Fig. 2a). By comparison, the CC w/CO2 simulations were more uncertain at most warming levels, with a range of 21.8% to 54.8% and opposite directions of yield change, particularly in mid–high latitudes. The difference in projection range between CC w/o CO2 and CC w/CO2 simulations reveals that the uncertainty from 1% to 6.3% is due to simulating increasing CO2 concentration responses for the globe, depending on the warming extent and CO2 concentration (Fig. 2b). Taking all simulations together by averaging the ensemble members and attributing uncertainty to their sources (Methods), including different warming levels and constant or increasing CO2 concentrations, the crop models generate most uncertainty (17.5%), followed by climate projections (6.6%), parameterization strategy (5.8%) and management input of sowing (4.8%).

### Variation in GGCM uncertainty for different latitudes

The results of the gridded simulations were plotted according to the latitude of individual grid cells (Fig. 3). This spatial analysis of the predicted yield changes produced a U-shaped yield response for all levels of temperature change. There was close agreement among simulations that warming would have a strong negative effect on wheat yield in tropical and subtropical regions. The uncertainty at mid- and high latitudes is substantially higher than that at low latitudes. At mid- and high latitudes, small negative to substantial positive effects were predicted but with a large degree of uncertainty (Fig. 3 and Supplementary Figs. 10 and 11). Using the latitudes of 40° N and 40° S as arbitrary boundaries, the total uncertainty averaged across latitudes outside the boundaries (that is, from mid-latitudes towards the poles) and all warming levels is 116%, more than twice the 56% uncertainty for areas inside the boundaries (that is, encompassing the tropics and the Equator). Averaged across warming levels and constant or increasing CO2 concentrations, the primary uncertainty was from the crop model for 62% of wheat growing areas, mainly those concentrated in the mid- and high latitudes of the Northern Hemisphere across Europe and northern Asia. Climate projection was the primary uncertainty source for approximately 30% of wheat growing areas, mainly those in the Southern Hemisphere, low latitudes of the Northern Hemisphere and the central part of North America. Parameterization was the highest uncertainty source for only 7% of wheat growing areas that were scattered around the world, while crop management (sowing date inputs) was mostly a negligible uncertainty source except for 1% of the wheat growing area (Supplementary Figs. 10 and 11, and Supplementary Table 5).

We noted that there is large uncertainty in projections at mid- and high latitudes, with corresponding wide ranges of impact estimates spanning from positive to negative (Fig. 3). This relationship is particularly marked for temperate zones of the Northern Hemisphere, coinciding with a large portion of the world’s wheat-producing regions (43.5%). This lack of certainty poses a real problem for designing future adaptation strategies. The large uncertainty at mid- and high latitudes is mostly from crop model differences and is more accentuated when warming is the highest. For example, where local warming was the largest across the wheat growing areas north of 40° N (at all warming levels), crop model uncertainty was as high as 50% on average, substantially more than the 24% average within the 40° N and 40° S boundaries. However, even when warming was the same across latitudes, crop models produced larger disagreement between yield responses at high latitudes than at low latitudes (Supplementary Fig. 12). This large inconsistency among crop models suggests they have varying skills in predicting the response of yield in temperate wheat areas in the mid- and high latitudes.

To investigate the reason for the large model uncertainty in mid–high latitudes, we compared our gridded warming–yield relationship (Fig. 3) with site-scale results from a multimodel intercomparison study17. The site-scale intercomparison covers most wheat areas from 37.75° S to 60.8° N, comprising 34 locally well-calibrated wheat models, including the three models used in our study. Although the mean of estimated warming–yield response across latitudes was similar between the site and gridded values, particularly under the irrigated condition, the site values did not show a clear larger uncertainty across models in high latitudes than in low latitudes, indicated by insignificant (P < 0.05) difference in models’ standard deviation between the low and high latitudes (Supplementary Fig. 13). This difference in estimated uncertainty between the site and grid simulations suggests that geospatial data or model parameterization rather than model might be the key reason for the large uncertainty in high latitudes.

### Reducing uncertainty of GGCM projections with spatially resolved wheat cultivar data

Grouping the results according to the parameterization strategies shows that parameterization with improved spatial data can substantially reduce the simulation uncertainty (Fig. 4 and Supplementary Fig. 14). For all warming levels, the combined uncertainty of climate projection, crop model and management input of sowing decreases with increasingly detailed parameterization from PS1 to PS4 across latitudes. This decrease suggests that the uncertainty of a global ensemble simulation for future yield estimates can be effectively reduced by improving simulation performance in reproducing the spatial pattern of historical production. This approach works particularly well for the wheat growing areas within the latitudes of 40° N–40° S. The crop model uncertainty averaged across wheat growing areas within the latitudes of 40° N–40° S decreases substantially from between 19% and 24% for PS1 to between 11% and 14% for PS4. This 45% decrease brings crop model uncertainty down to a level that is equal to or less than the sum of the uncertainties caused by climate projection and management input. However, decreases in crop model uncertainty among the parameterization strategies were insignificant for wheat areas in both hemispheres beyond 40° N and 40° S (P < 0.05; Fig. 4 and Supplementary Fig. 14). The spatial variability in the effectiveness of parameterization in reducing model uncertainty is partly due to the inaccuracy or unavailability of reported data such as crop phenology for mid- and high latitudes. For example, the reported value of days to maturity was homogeneous and ambiguous in northern Eurasia (Supplementary Fig. 4), leading to calibration errors in models for many regions (Supplementary Fig. 6 and 7). Information on critical phenological stages such as flowering is important for temperate wheat cultivars in determining their warming–yield responses13 but is lacking in most global simulations, making it difficult in our simulation to parameterize models sufficiently to increase the agreement between them for historical production at mid- and high latitudes (Supplementary Fig. 15). In addition, in temperate climates, the duration of wheat growth varies according to photoperiod and vernalization. The difference in model structure can result in large discrepancies in modelling these aspects, also likely contributing to the disparate projections of warming effects between crop models at mid- and high latitudes. Crop models and observation data at mid- and high latitudes would thus benefit from comprehensive quality analysis, particularly for the Northern Hemisphere.

The simulation results demonstrate that improved parameterization strategies tend to decrease the uncertainty caused by ambiguous model inputs. In the absence of the localized information, we chose a universal rule to set up the planting date, and the estimated uncertainty due to the different planting dates was relatively small, ranging from 7% to 12%. However, applying regionalized and localized crop cultivar parameters as in PS4 reduced this uncertainty by up to 80%, down to an uncertainty of just 2%. This reduction in uncertainty is especially evident at low latitudes where the simulation discrepancy in reproducing historical phenology is already generally small. The reduction in uncertainty due to management input of sowing is also pronounced at mid- and high latitudes when more localized information on crop cultivars and parameters is applied. At a warming of 6 °C, parameterization reduces uncertainty arising from management input of sowing by up to 30%. The strong influence of parameterization on uncertainty suggests that new parameterization approaches are needed when crop management information is lacking or insufficiently detailed.

## Conclusion

Our study is an explicit assessment of the heterogeneous uncertainty inherent in the processes, components or practices of simulating crop responses with a wheat GGCM ensemble. Our analysis focuses on the uncertainties arising from the sources in conducting the GGCM ensemble, including the utilization of publicly available datasets, crop models and their parameterization. Some important uncertainty sources, such as the diverse fertilizer and water management, may have large effects on simulated yield–warming response for the future but were excluded in the study due to the data unavailability. We pinpointed how much uncertainty comes from different sources for all latitudes around the globe. This is a step forward as uncertainty is usually confounded in ensemble simulations. We also demonstrated that a more thorough and consistent parameterization approach across multimodels has the potential to reduce uncertainty.

The results are based on three dynamic wheat models embedded in a crop modelling platform18. It is interesting to note that even with similar structures, the same input and a consistent calibration method, the crop models generated most of the uncertainty, more than climate projection, parameterization strategy and management input of sowing dates combined. To improve models, researchers should pay particular attention to how increased CO2 and high temperatures may interact, especially regarding the effect of extreme temperatures and compensation with higher CO2 concentration. For example, extreme high temperature can reduce crop yield by damaging plant reproductive organs and hastening senescence19,20. These mechanisms are a source of discrepancy between NWHEAT and the other two crop models, CERES and CROPSIM. This is particularly urgent with the likelihood of increasing growing season temperatures and more frequent heat stress21. The larger uncertainty due to the crop models for mid- and high latitudes strongly underscores the current limitations of global crop simulations, particularly the gap in understanding phenological responses for wheat planted under low temperatures. Data availability and quality need to be improved to facilitate model parameterization for temperate wheat regions. At mid- and high latitudes, wheat has to adjust its growth duration according to daylength and vernalization to avoid low-temperature stresses, but this mechanism is dealt with differently across crop models and leads to a large degree of uncertainty for the baseline and also under a warmer climate.

Our study highlights that to achieve robust projections of a global crop response to future climate change requires careful model parameterization. As parameters are estimated with detailed field observations, scaling-up site-specific models usually produce ambiguous parameter estimates22,23,24. Using better-quality geospatial data, for instance, from remote sensing25,26,27, could equip models with improved input data across a wider range of conditions. Even though the global data infrastructure is advancing, innovative approaches to calibrate model parameters for multiple crop models in a consistent manner are still needed to reduce uncertainties for future climate change impact assessment studies.

## Methods

### Crop models

The three crop models are the Cropping System Model-CERES-Wheat28 (referred to as CERES), CROPSIM-Wheat29 (referred to as CROPSIM) and NWHEAT30. These three wheat models are well-known crop growth models and have been used in AgMIP (Agricultural Model Intercomparison and Improvement Project) wheat model intercomparison studies9,13. The models have similar complexity and model structure, but a different representation of some of the physiological processes (that is, abiotic stress) (Supplementary Table 2). They are embedded in the crop modelling platform Decision Support System for Agrotechnology Transfer (DSSAT (v4.7))18, which is a suite of crop models that have a common soil water and nitrogen component enabling crop rotation simulation and designed to estimate production, resource use and risks associated with crop production practices. The same input requirement and file format among models facilitate the ensemble to exclude certain uncertainty sources such as model type (for example, site-based crop models or ecosystem models), data inputs and processing.

### Data sources

We used the gridded formatted inputs to drive the crop models, including daily weather, soil parameters, crop calendar and fertilizer application information. Descriptions of the datasets are in Supplementary Table 1. Historical daily weather data (1981−2010) were from AgMERRA dataset. AgMERRA is a post-processing of the NASA Modern-Era Retrospective Analysis for Research and Applications (MERRA) suitable for agricultural modelling31. For future years (2010–2099), we used the climate scenarios data extracted from output archives of five GCMs under four RCPs retrieved from World Climate Research Programme (WCRP) Coupled Model Intercomparison Project (CMIP) website (http://www.wcrp-climate.org/wgcm-cmip/wgcm-cmip5). The wheat crop calendar came from ref. 32. Observed wheat yield and area in 2000 were from the Spatial Production Allocation Model33. Wheat management information including chemical fertilizers was from ref. 6. Only the weather data have the same resolution as the simulation that we defined; therefore, we resampled all other datasets into 0.5º × 0.5º grid resolution. Soil parameters (including texture, bulk density, pH, organic carbon content and the fraction of calcium carbonate for each of five 20-cm-thick soil layers) were obtained from the International Soil Profile Data set (WISE)34. Soil parameters were allocated to each simulation grid cell based on the spatially dominant soil type taken from the digital Soil Map of the World (DSMW)35. Soil retention and hydraulic parameters were calculated using pedotransfer function36. Soil parameters for organic soils missing in WISE dataset were adopted from ref. 37.

### Parameterization strategies for the simulation

The selection of crop genotype/cultivar contributes to simulation uncertainty in predicting yield–climate relationships. We investigated this uncertainty by designing four parameterization strategies to develop a set of cultivar coefficients and the way to apply them for the globe. In PS1, just one universal cultivar was used for each of the three wheat types (spring, winter and facultative) and applied to the entire globe. In PS2, 17 current wheat cultivars from previous calibrations38 were used and applied to grid cells based on their respective mega-environments defined by International Maize and Wheat Improvement Center39. In PS3, grid-specific cultivars were used and simulated maturity dates were calibrated to observed maturity dates32 (Supplementary Fig. 4a,b). In PS4, grid-specific cultivars were used and simulated maturity dates and yield were calibrated to observed maturity dates32 and yield33 (Supplementary Fig. 4c,d).

Calibration in PS3 and PS4 was conducted based on a global optimization algorithm—differential evaluation39—with a short historical simulation of 1996–2015. The optimization was operated for each grid under a full irrigated condition as irrigated yields are better than rainfed yield to represent the growth potential of a cultivar. The optimization was operated for each grid in parallel in a high-performance computer system by linking the differential evaluation with the DSSAT core. For PS3, we only optimized model phenology coefficients to match the reported days to maturity32. In PS4, we optimized additional coefficients of the yield component to match the reported grain yield33. Details for the four PS and coefficients that were adjusted in the calibration are described in the Supplementary Methods, Supplementary Fig. 2 and Supplementary Table 3.

### Simulations

There are three types of wheat grown worldwide—spring, winter and facultative wheat (Supplementary Fig. 3)—but we categorized the facultative into winter type in the ensemble simulation. Therefore, for each global run (includes future and baseline), we simulated either spring or winter wheat for most grid cells under both rainfed and irrigated conditions. There were less than 10% of grid cells (in mega-environment (ME)7, ME8 and ME9) with a mix of spring and winter wheat types, mostly in Asia–Europe between 43° and 53° N; therefore, we conducted two simulations for both spring and winter types, but extracted yield of winter wheat only if the yield of winter wheat exceeded spring wheat by more than 200%. Rainfed and irrigated cropping area for the year 2000 was from ref. 33. For irrigated conditions, we used the middle point of the reported sowing window32 as the irrigated sowing date. Irrigation (20 mm) is triggered whenever soil water content is less than 80% of the soil water holding capacity. For rainfed conditions, the initial sowing date was the day when the 3 d accumulative rainfall amount before the day exceeds 25 mm, or the last day of the reported window, if no day meets the condition. We applied current input rates of fertilizer applications and assumed no change in the future. Nitrogen was applied twice at sowing (60%) and 60 d after sowing (40%) with a sum of value in the nitrogen raster in ref. 6. Phosphorus and potash were assumed unlimited for the crop because of the limitation of the models in simulating such effects40,41 and missing information on phosphorus and potassium in the Harmonized World Soil Database42. Current crop simulations have limited skill in predicting large-scale pest/disease effects due to insufficient knowledge and information related to the pest/disease epidemic and their interactions with crop and management, even though the observed data the models have been calibrated on implicitly contain such effects. Therefore, we assumed that there were no pest and disease effects (or they were unchanged) for wheat growth in the baseline and future. The size of the simulation grid cells is 0.5º × 0.5º, which is roughly a 50 km × 50 km square cell at the Equator.

### Estimation of uncertainties

For each ensemble member, we calculated yield change for each year from 2011 to 2099 at both the global and grid levels. For each grid, yield change is the percentage change of the yearly yield, compared with the mean yield of 1981–2010 from the corresponding baseline driven by historical weather of AgMERRA. Yield change for the globe is the percentage change of area-weighted yearly yield, compared with the mean yield of the baseline. The global wheat area was kept unchanged from the value of 2000. For each CP, we estimated the changes in temperature during the wheat growing season. To take into account the actual diverse planting practices, we used the span from the first day of sowing to the last day of harvest reported by ref. 32 to define the growing season. Global temperature change in the wheat growing season is the gridded value weighted by reported wheat area33 and relative to the value of the baseline.

We distinguished the uncertainties for predicted yield change from four sources: climate projection (CP), crop model (CM), model parameterization strategy (PS) and crop management, that is sowing date input (MA). To measure the uncertainty, we used a simple method by plotting estimated yield change against the corresponding growing season warming (at both global and regional levels) and computing the uncertainty directly from the distribution of simulated yield change (Supplementary Fig. 5). For example, in the case of CC w/CO2 simulations that include 720 global runs (20 CP × 3 CM × 4 PS × 3 MA), the relationship between simulated yearly yield change and growing season warming is shown in Supplementary Fig. 5a. For any given warming extent, the total uncertainty (Ut) is the difference between the highest and lowest projections of the ensemble distribution (Pmax(y) − Pmin(y)), excluding the outliers (points that lie more than one and a half times the interquartile range of the data). For uncertainty of specific sources i (i= 1, ... 4: CP, CM, PS, MA), we averaged all ensemble members into the elements j of the sources i (for example, in the case of source CM, we have three elements j (CERES, CROPSIM and NWHEAT) $$(\bar y_{ij})$$ and the uncertainty (Ui) is the value range of the three elements $$({\mathrm{max}}(\bar y_{ij})-{\mathrm{min}}(\bar y_{ij}))$$ (Supplementary Fig. 5b)).

We also estimated the uncertainty across the latitudes to examine the spatial variation of uncertainty. By doing so, we first grouped all simulated yearly yield change into the latitudes and different warming levels based on the global temperature change during wheat growing season (2 °C: up to 2 °C; 4 °C: 2 °C to 4 °C; 6 °C: 4 °C to 6 °C). We then estimated the uncertainty for the overall and each source based on the yield change distribution with the above method.

### Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

All data supporting the simulation and analysis in this study are publicly available from open sources. The historical weather data (1981–2010) are available at https://data.giss.nasa.gov/impacts/agmipcf/; the future climate scenario data (2010–2099) are available at https://esgf-node.llnl.gov/projects/esgf-llnl/. Wheat mega-environment and definition are from https://data.cimmyt.org/dataset.xhtml?persistentId=hdl:11529/10625. The spatial data of harvest area, yield, crop calendar and irrigation portion are available at http://mapspam.Info/ (SPAM) and http://www.sage.wisc.edu (SAGE). Historical chemical nitrogen input of wheat is available at http://www.earthstat.org/nutrient-application-major-crops/. The soil data are available from the WISE database (https://www.isric.online/index.php/) and the Digital Soil Map of the World (DSMW). All other generated data (that is, model coefficients for the three crop models), simulation outputs (yield and phenology) and processed data for plotting the figures are available from the corresponding author on request.

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## Acknowledgements

We thank J. Yang for help analysing data, and J. Yang and U. A. Schulthess for helpful comments. This work was directly supported by The National Science Foundation of China (grant nos 4147104 and 41171093). This study was also indirectly supported by the CGIAR research programme on wheat agri-food systems (CRP WHEAT) and the CGIAR Platform for Big Data in Agriculture, the World Bank and the Mexican government through the Sustainable Modernization of Traditional Agriculture (MasAgro) project. R. Robertson’s contributions were supported by the CGIAR Research Program on Policies, Institutions, and Markets.

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W.X. and S.A. conceived the study. W.X., I.H.-O., R.R., K.S., D.P., M.R. and B.G. implemented the experiment, W.X., S.A. and G.H. drafted the paper, and all contributed to the writing.

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Correspondence to Wei Xiong.

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Xiong, W., Asseng, S., Hoogenboom, G. et al. Different uncertainty distribution between high and low latitudes in modelling warming impacts on wheat. Nat Food 1, 63–69 (2020). https://doi.org/10.1038/s43016-019-0004-2

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