# Similar estimates of temperature impacts on global wheat yield by three independent methods

Bing Liu, Senthold Asseng, Christoph Müller, Frank Ewert, Joshua Elliott, David B. Lobell, Pierre Martre, Alex C. Ruane, Daniel Wallach, James W. Jones, et al.

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► To cite this version:

Bing Liu, Senthold Asseng, Christoph Müller, Frank Ewert, Joshua Elliott, et al.. Similar estimates of temperature impacts on global wheat yield by three independent methods. Nature Climate Change, 2016, 6, pp.1130-1136. 10.1038/nclimate3115. hal-01604315

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Title: Similar estimates of temperature impacts on global wheat yield by three independent methods

Author: Bing Liu<sup>a,b</sup>, Senthold Asseng<sup>b</sup>, Christoph Müller<sup>c</sup>, Frank Ewert<sup>d</sup>, Joshua Elliott<sup>e,f</sup>,

David B. Lobell<sup>g</sup>, Pierre Martre<sup>h,i</sup>, Alex C. Ruane<sup>e,j</sup>, Daniel Wallach<sup>k</sup>, James W. Jones<sup>b</sup>,

Cynthia Rosenzweig<sup>e,j,t</sup>, Pramod K. Aggarwal<sup>l</sup>, Phillip D. Alderman<sup>m</sup>, Jakarat Anothai<sup>n</sup>,

Bruno Basso<sup>o,p</sup>, Christian Biernath<sup>q</sup>, Davide Cammarano<sup>r</sup>, Andy Challinor<sup>s,t</sup>, Delphine

Deryng<sup>e,f</sup>, Giacomo De Sanctis<sup>u</sup>, Jordi Doltra<sup>v</sup>, Elias Fereres<sup>w</sup>, Christian Folberth<sup>x</sup>, Margarita

Garcia-Vila<sup>w</sup>, Sebastian Gayler<sup>y</sup>, Gerrit Hoogenboom<sup>z</sup>, Leslie.A. Hunt<sup>aa</sup>, Roberto C.

Izaurralde<sup>bb,cc</sup>, Mohamed Jabloun<sup>dd</sup>, Curtis D. Jones<sup>bb</sup>, Kurt C. Kersebaum<sup>ee</sup>, Bruce A.

Kimball<sup>ff</sup>, Ann-Kristin Koehler<sup>s</sup>, Soora Naresh Kumar<sup>gg</sup>, Claas Nendel<sup>ee</sup>, Gary O'Leary<sup>hh</sup>,

Jørgen E. Olesen<sup>dd</sup>, Michael J. Ottman<sup>ii</sup>, Taru Palosuo<sup>jj</sup>, P.V. Vara Prasad<sup>kk</sup>, Eckart Priesack<sup>q</sup>,

Thomas A. M. Pugh<sup>ll,vv</sup>, Matthew Reynolds<sup>m</sup>, Ehsan E. Rezaei<sup>d</sup>, Reimund P. Rötter<sup>ij</sup>, Erwin

Schmid<sup>mm</sup>, Mikhail A. Semenov<sup>nn</sup>, Iurii Shcherbak<sup>o,p</sup>, Elke Stehfest<sup>oo</sup>, Claudio O. Stöckle<sup>pp</sup>,

Pierre Stratonovitch<sup>nn</sup>, Thilo Streck<sup>y</sup>, Iwan Supit<sup>qq</sup>, Fulu Tao<sup>rr,ij</sup>, Peter Thorburn<sup>ss</sup>, Katharina

Waha<sup>c</sup>, Gerard W. Wall<sup>ff</sup>, Enli Wang<sup>tt</sup>, Jeff W. White<sup>ff</sup>, Joost Wolf<sup>qq</sup>, Zhigan Zhao<sup>uu,tt</sup>, and

Yan Zhu<sup>a,*</sup>

Author affiliation:

<sup>a</sup> National Engineering and Technology Center for Information Agriculture, Jiangsu

Key Laboratory for Information Agriculture, Jiangsu Collaborative Innovation Center
for Modern Crop Production, Nanjing Agricultural University, Nanjing, Jiangsu
210095, China

<sup>b</sup> Agricultural & Biological Engineering Department, University of Florida,
Gainesville, FL 32611, USA

<sup>c</sup> Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany

<sup>d</sup> Institute of Crop Science and Resource Conservation INRES, University of Bonn,
53115, Germany

<sup>e</sup> Columbia University Center for Climate Systems Research, New York, NY 10025,
USA

<sup>f</sup> University of Chicago Computation Institute, Chicago, IL 60637, USA

<sup>g</sup> Department of Environmental Earth System Science and Center on Food Security
and the Environment, Stanford University, Stanford, CA 94305, USA

<sup>h</sup> INRA, UMR759 Laboratoire d'Ecophysiologie des Plantes sous Stress
Environnementaux, F-34 060 Montpellier, France

<sup>i</sup> Montpellier SupAgro, UMR759 Laboratoire d'Ecophysiologie des Plantes sous
Stress Environnementaux, F-34 060 Montpellier, France

<sup>j</sup> National Aeronautics and Space Administration Goddard Institute for Space Studies,
New York, NY 10025, USA

<sup>k</sup> INRA, UMR1248 Agrosystèmes et développement territorial (AGIR), 31326

Castanet-Tolosan Cedex, France

<sup>l</sup> CGIAR Research Program on Climate Change, Agriculture and Food Security,
Borlaug Institute for South Asia. CIMMYT, New Delhi-110012, India
45 m CIMMYT Int. Adpo, D.F. Mexico 06600, Mexico

46 n Department of Plant Science, Faculty of Natural Resources, Prince of Songkla

47 University, Songkhla 90112, Thailand

48 o Department of Geological Sciences, Michigan State University East Lansing,

49 Michigan 48823, USA

50 p W.K. Kellogg Biological Station, Michigan State University East Lansing, Michigan

51 48823, USA

52 q Institute of Biochemical Plant Pathology, Helmholtz Zentrum München – German

53 Research Center for Environmental Health, Neuherberg, D-85764, Germany

54 r The James Hutton Institute Invergowrie, Dundee DD2 5DA, Scotland, UK

55 s Institute for Climate and Atmospheric Science, School of Earth and Environment,

56 University of Leeds, Leeds LS29JT, UK

57 t CGIAR-ESSP Program on Climate Change, Agriculture and Food Security,
58 International Centre for Tropical Agriculture (CIAT), A.A. 6713, Cali, Colombia.

59 u European Commission, Joint Research Centre, via Enrico Fermi, 2749 Ispra, 21027,

60 Italy

61 v Cantabrian Agricultural Research and Training Centre (CIFA), 39600 Muriedas,

62 Spain

63 w Dep. Agronomia, University of Cordoba, Apartado 3048, 14080 Cordoba, Spain

64 x Department of Geography, University of Munich, Germany

65 y Institute of Soil Science and Land Evaluation, University of Hohenheim, 70599

66 Stuttgart, Germany

67 z AgWeatherNet Program, Washington State University, Prosser, Washington 99350,

68 USA

69 aa Department of Plant Agriculture, University of Guelph, Guelph, Ontario, N1G 2W1,

70 Canada

71 bb Dept. of Geographical Sciences, Univ. of Maryland, College Park, MD 20742, USA

72 cc Texas A&M AgriLife Research and Extension Center, Texas A&M Univ., Temple,

73 TX 76502, USA

74 dd Department of Agroecology, Aarhus University, 8830 Tjele, Denmark

75 ee Institute of Landscape Systems Analysis, Leibniz Centre for Agricultural

76 Landscape Research, 15374 Müncheberg, Germany

77 ff USDA, Agricultural Research Service, U.S. Arid-Land Agricultural Research

78 Center, Maricopa, AZ 85138, USA

79 gg Centre for Environment Science and Climate Resilient Agriculture, Indian

80 Agricultural Research Institute, IARI PUSA, New Delhi 110 012, India

81 hh Landscape & Water Sciences, Department of Environment and Primary Industries,

82 Horsham 3400, Australia

83 ii The School of Plant Sciences, University of Arizona, Tucson, AZ 85721, USA
84 Environmental Impacts Group, Natural Resources Institute Finland (Luke), FI-03170 Vantaa, Finland.

85 Department of Agronomy, Kansas State University, Manhattan, KS 66506, USA

86 Institute of Meteorology and Climate Research, Atmospheric Environmental Research, Karlsruhe Institute of Technology, 82467 Garmisch-Partenkirchen, Germany

89 University of Natural Resources and Life Sciences, 1180 Vienna, Austria

90 Computational and Systems Biology Department, Rothamsted Research, Harpenden, Herts, AL5 2JQ, UK

91 PBL Netherlands Environmental Assessment Agency, 3720 AH, Bilthoven, The Netherlands

92 Department of Biological Systems Engineering, Washington State University, Pullman, Washington 99164, USA

93 Plant Production Systems & Earth System Science, Wageningen University, 6700AA Wageningen, The Netherlands

94 Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Science, Beijing 100101, China

95 CSIRO Ecosystem Sciences, Dutton Park QLD 4102, Australia

96 CSIRO Agriculture, Black Mountain ACT 2601, Australia

97 Department of Agronomy and Biotechnology, China Agricultural University, Yuanmingyuan West Road 2, Beijing 100193, China.

98 School of Geography, Earth & Environmental Science and Birmingham Institute of Forest Research, University of Birmingham, B15 2TT, UK.

99 Authors after C. Rosenzweig are listed in alphabetical order.

100

101 Keywords:

100 Global warming, wheat yield, climate impacts, impact method comparison, food security,

111 temperature

112
113 **Abstract**

114 The potential impact of global temperature change on global crop yield has recently been
115 assessed with different methods. Here we show that grid-based and point-based simulations
116 and statistical regressions (from historic records), without deliberate adaptation or CO2
117 fertilization effects, produce similar estimates of temperature impact on wheat yields at global
118 and national scales. With a 1℃ global temperature increase, global wheat yield is projected
119 to decline between 4.1% and 6.4%. Projected relative temperature impacts from different
120 methods were similar for major wheat producing countries China, India, USA and France, but
121 less so for Russia. Point-based and grid-based simulations, and to some extent the statistical
122 regressions, were consistent in projecting that warmer regions are likely to suffer more yield
123 loss with increasing temperature than cooler regions. By forming a multi-method ensemble, it
124 was possible to quantify 'method uncertainty' in addition to model uncertainty. This
125 significantly improves confidence in estimates of climate impacts on global food security.
126 Global demand for food is expected to increase 60% by the middle of the 21st century ¹.

127 Climate change, and in particular rising temperatures, will impact food production ². For
128 global food security, it is important to understand how climate change will impact crop
129 production at the global scale to develop fact-based mitigation and adaptation strategies.

130 Many studies have shown a wide range of temperature impacts on yields of different crops in
131 different seasons at different locations ³, including Europe ⁴, China ⁵, India ⁶ and Sub-Saharan
132 Africa ⁷. A few studies have considered impacts on the entire globe⁸, ⁹, ¹⁰, ¹¹. However, the
133 methods used to make these assessments are based on very different premises and use
134 different methodological steps.

135 The uncertainty of estimates of global temperature impact on crop yields was analyzed
136 for the crop model component (i.e. model uncertainty) by using two different multi-model
137 ensemble approaches ⁸, ⁹. While both studies used process-based crop simulation models, the
138 scaling approach and input data differed greatly. The first study divided the globe into a
139 geographical grid cells defined by latitude and longitude and used climate and crop
140 management data integrated over each grid as input for seven crop models ⁹. This grid-based
141 system was used to estimate relative yield changes for rice, maize, wheat and soybean. The
142 second study used data from 30 individual field sites deemed to represent 2/3 of
143 wheat-producing areas worldwide ⁸. In this point-based approach estimates from sentinel sites
144 were scaled up and extrapolated to cover geographical areas with similar conditions.

145 In further contrast, statistical regressions based on global and country level data have
146 been used to quantify the impact of increasing temperatures on yields of wheat, maize, barley,
147 soybean, sorghum and rice ¹⁰, ¹¹. An important difference from the simulation models is that
statistical models do not directly consider processes inherent to crop growth. However, statistical models may include indirect effects of climatic variability, such as those related to pests and diseases, which are not well captured by simulation models¹². When assessing climate effects on crop yields, crop models can take into account autonomous adaptation and an increase in atmospheric CO₂ concentration. Also some statistical regressions include the yield effects associated with autonomous adaptation¹⁰. For the effects of gradual increase in CO₂ concentration in the past, statistical models may inherently include these within yield effects¹³, but for some regression models with a linear time term, effects of steady increase in CO₂ can be removed from yield impacts, just as the effects of technology improvement. In addition, upscaling methods influence the outcomes from regional assessments¹⁴. The statistical approach obtained global or regional impacts by aggregating county districts or countries¹⁰,¹¹. The grid-based system obtained global or regional impacts by aggregating 0.5° × 0.5° grid cells⁹, while the point-based approach employed 30 sites to represent global wheat regions⁸. Therefore, differences in upscaling could add uncertainties in the impact estimated in these studies.

In this letter, we compared three largely independent assessment methods used to estimate temperature impacts on wheat yields: grid-based simulations, point-based simulations, and statistical regressions. The details of each method are shown in Table S1.

The methods used independent different dynamic, statistical, up-scaling and source data approaches. The grid-based simulations used here were from the Agricultural Model Intercomparison and Improvement Project (AgMIP)¹⁵ as part of the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP). Wheat yields were simulated with seven global
gridded crop models during 1980-2099 under RCP 8.5, a greenhouse gas emissions scenario (here without CO₂ fertilization effects), over 0.5° × 0.5° grid cells⁹. The point-based simulations from the AgMIP-Wheat project⁸ consisted of simulations from 30 wheat models (including one statistical model) for 30 representative locations around the world from a baseline of the 1981-2010 period and a linear temperature increase. Temperature impacts determined by statistical regression methods were obtained directly from previously published data or our own statistical analysis (Table S1 and Supplementary methods).

## 177 Similar global impact from different methods

The average reductions in global wheat yield with 1°C global temperature increase estimated from grid-based simulations, point-based simulations, and statistical regressions at global level were all between 4.1% and 6.4% (Fig. 1). The average estimated temperature impact from all three methods (and four studies) was a 5.7% reduction in global yield per degree of global temperature increase. The estimated temperature effects on global wheat yield from the three different methods were similar.

A meta-analyses of mostly process-based crop model simulations, reported a 3.3 ± 0.8% decline in wheat yields with a 1°C increase in local temperature¹⁶. When adjusted to global temperature change (which is usually less than local wheat region temperature changes¹⁷), this impact amounts to respectively 3.9% yield reduction per degree of global temperature increase. Also, a summary of past regression and simulation studies reported an average of 5.9% wheat yield decrease with 1°C warming¹⁸. These values are very similar to the results obtained here for wheat using three different assessment methods.

The results here are presented for 1°C of global warming for consistency. However, the
estimated impacts do not increase linearly with increasing temperature and the disagreement
among method estimates become larger with more temperature change (Fig. S9).

Impacts for major wheat-producing countries

To understand how the different methods project such similar temperature impacts on
global wheat yields, we disaggregated the temperature impacts to the national scale.

Point-based and grid-based simulations were compared for 97 countries (Fig. 2a). Generally,
projected temperature impacts on wheat yields for most of the large wheat producers were
similar between the two simulation methods (with a R² of 0.64 for the top 20 producers,
Fig.S12), while differences were larger for small wheat-producing countries. Some large
differences occurred between point-based and grid-based simulation in irrigated semiarid
regions of Africa, which are mostly small wheat producers. The larger differences observed
for smaller producers have little weight in the global analysis. However, they are important
for regional economies. Method results were compared in more detail for the top five wheat
producing countries (Fig. 2b, Fig. 3). For China, India, USA, and France, the different
assessment methods resulted in similar values for temperature impacts on country wheat
yields. Additional country-level studies relying on other methods and data sources gave
similar estimates. For example, for China point-based simulations, grid-based simulations,
and two different regressions all concluded that yield reductions of about 3.0% are expected
with 1°C warming (Fig.3a). For India, country-level statistical regressions, grid-based and
point-based simulations all estimated about 8.0% yield declines per °C of global temperature
increase (Fig.3b). For Russia, the two simulation methods agreed well, but yield reductions
estimated from statistical regression were markedly higher (Fig. 3c). Another study using
statistical regression methods also showed higher negative temperature impacts on wheat yield than the two modeling methods used here for Rostov, a main wheat producing region in Russia <sup>19</sup>. Since wheat producing regions in Russia can experience relatively low temperatures (below optimal growth temperature) during early growing stages, a temperature increase during this stage (tillering), may have a positive yield impact, while at a later stage (booting or grain filling) an increase in temperature often reduces wheat yields <sup>19</sup>. As an average temperature over a growing season is usually used in statistical regressions, such in-season variability in temperature impacts would remain undetected. A dynamic crop simulation model takes in-season variability and impacts into account. This may explain the estimated larger impacts in Regression_A in comparison to the simulation results. For USA, a recent study using data from wheat variety trials from 1985–2013 in Kansas, USA reported a 7.3% decrease (corrected for global temperature change) in wheat yield with 1°C global temperature increase<sup>20</sup>. This result is similar to the other estimated temperature impacts on wheat yields for the USA (Fig. 3d). For France, yield reduction estimates from grid-based simulations, point-based simulations, and statistical regressions were 4.6%, 5.2%, and 4.2%, respectively (Fig. 3e). In an independent study, a 0.42t.ha<sup>-1</sup> reduction in wheat yields, which is a reduction of about 5.5% after correction for global temperature change, was reported in Northern France from 1998-2008 that included the planting of reference varieties in field experiments <sup>21</sup>. This is also in line with simulated impact response surfaces from a 26-wheat-model-ensemble across a European transect<sup>22</sup>.

With the different temperature impact methods used, despite some variation, there is a general similarity in the magnitude of negative effects of increasing temperature on wheat
yields for major wheat producing countries. As the five largest wheat producing countries have a combined total >50% of total global wheat production <sup>23</sup>, the similarity in method estimates of temperature impacts for these countries also dominates the similar negative temperature impacts computed at the global scale.

## Differences in model inputs

At the location scale, the yields from the point-based simulations were highly correlated to the yields from the grid-based simulations for the baseline and baseline+1°C periods (*P* < 0.001, R<sup>2</sup> > 0.5; Table S2), but simulated yields were generally higher in point-based than in grid-based simulations (Fig. 4 and Fig. S1). The average yields of the 30 locations in the point-based simulations were 3.2 (82%) and 3.0 (82%) t.ha<sup>-1</sup> higher than in the corresponding grid-based simulations under baseline and baseline + 1°C conditions, respectively. In both studies, mean temperatures were similar across sites for the 90 days period prior to maturity, except for three locations (Fig. S2). Seasonal temperature variability in the model input data differed slightly between methods and caused a larger seasonal yield variability in the grid-based simulations compared to the point-based simulations (Fig S7). Solar radiation inputs were 5% to 7% lower in the grid-based than in the point-based simulations (Fig. S3), which might have contributed slightly to the simulated yield difference <sup>24</sup>. Water stress was not considered in either study for the comparison of these 30 locations and any possible differences in precipitation inputs had no impact on the simulated results (Table S3). No nitrogen stress was assumed in the point-based simulations, but four of the seven crop models in the grid-based simulations did consider country-level average N fertilizer application which could explain why the grid-based model ensemble simulated generally
258 lower yields compared to the point-based simulations (Table S3).

259 Another important factor possibly contributing to yield differences between the
260 grid-based and point-based simulation at the local scale were the models used in the studies.

261 There were 29 crop models and one statistical regression in the point-based simulation
262 ensemble, whereas there were seven crop models in the grid-based simulations. Three models
263 (CERES, EPIC, and LPJmL) were common to both studies. These three models tended to
264 simulate lower yields than the 30-model ensemble average from the point-based study for the
265 30 locations, e.g., about 0.9 t·ha⁻¹ less in the baseline period (Fig. S4). This may have lowered
266 the average simulated yields in grid-based simulations. Differences in the calibration of the
267 crop models would also affect simulations²⁵. Some models in the grid-based simulations were
268 calibrated and some were not, and especially growing periods were not harmonized across
269 grid-based models ⁹, while in point-based simulations all models were calibrated for anthesis
270 and maturity dates with local phenology information ⁸. Hence, differences in models, solar
271 radiation and inputs like N fertilizer may explain some of the lower yields found in the
272 grid-based studies. Differences in cultivar calibration, particularly for phenology and growing
273 season, adds another source of differences between these two studies.

274 More yield reduction at warmer regions

275 Interestingly, when comparing the grid-based and point-based simulations, no obvious
276 bias was observed in the simulated relative yield impacts between point-based and grid-based
277 simulations (Fig. 4c and Fig.S1c), even though simulated absolute yields with point-based
278 simulations were much higher than grid-based simulations. This was still true when the
279 outlier location in Fig. 4c was removed from calculations. Temperature impacts at the local
scale in grid-based and point-based simulations were highly correlated. With 1°C global temperature increase, higher yield reductions were observed at locations with higher baseline temperatures than locations with lower baseline temperatures in both point-based and grid-based simulations (Fig. 4c). For example, at Aswan in Egypt, point-based and grid-based simulations showed about 11% and 20% decline in yield with 1°C temperature increase, while for Krasnodar in Russia, point-based and grid-based simulations estimated about 4% and 7% yield decline with 1°C global increase. The spatial pattern of temperature impacts at the location scale was also consistent with that at the country scale (Fig. 2a, Fig. 2b, and Fig.S11), which indicated that warmer regions (e.g. India) are likely to suffer more wheat yield reductions than cooler regions (e.g. China). The exception is for statistical regression estimates for Russia, a generally cooler region (Fig. 2b). The effects of temperature on wheat yields are consistent with reports of impacts on other crops, such as maize, soybean, and cotton<sup>26, 27, 28</sup>. An increase in extreme temperature events with increasing mean temperatures<sup>29</sup> are likely to further contribute to yield decline in wheat<sup>30, 31</sup>. Several crop models used in point-based simulations (tested against warming experiments) and Regression_A (using a nonlinear regression method), also considered the impacts of extreme temperature<sup>8, 10</sup>.

## Effects of up-scaling methods

To assess climate impacts on global or country-level crop production, both process-based crop modeling approaches and statistical regressions need to be upscaled from locations to regions and then to the entire globe<sup>32</sup>. In the point-based simulations, a range of local information (e.g. local sowing dates, cultivar, anthesis and maturity date) was used for the 30 locations selected to represent about 70% of current global wheat production, which was then
302 upscaled via FAO statistics ⁸. Much less local information was available for each of the 0.5° ×

303 0.5° grid cells which were aggregated to country and global scales in the grid-based

304 simulations ⁹. However, very similar estimated temperature impacts on relative global yield

305 changes were simulated with both approaches. This was surprising as Ewert, van Bussel ¹⁴

306 showed that scaling methods can add significant uncertainties to simulated outcomes.

307 Although uncertainties are known to be reduced with multi-model ensembles, these results

308 might also indicate that the selected 30 locations in the point-based study ⁸ were indeed

309 representative of agro-climatic variability of wheat growing conditions throughout the world.

310 The results also suggest that global grid-based models, despite having limited local

311 information, are on a par with point-based approaches, while providing greater coverage of

312 regional heterogeneity.

313 In the statistical regression methods, yield and weather data from different scales were

314 used to obtain global and country-level temperature impacts. For example, both global ¹¹ and

315 country ¹⁰ level regressions, observed yield records were used to conduct global assessments,

316 and both country-level yields and county (or similar) level yields were used for country

317 assessments (e.g. for China, India, and USA). Generally, regressions with different spatial

318 scales resulted in similar temperature impacts on yields.

319 **Advantage of different assessment methods**

320 Compared with process-based crop models, statistical regressions are simpler and require

321 less input information. However, other important growth factors which change with climate

322 change, such as radiation or the combined effects of heat, water and nutrient stresses, vary

323 over the period of a crop growing cycle, but are often not directly considered in statistical
regressions. Some of these factors might also be confounded in a statistical regression
analysis. While there have been attempts to include more factors in statistical impact methods
³³, detailed process-based, dynamic crop simulation models may be more suitable to simulate
the more complex climate change scenarios, beyond the single impact of temperature change.
However, process-based models, like statistical methods, often do not account for many other
important factors required for holistic climate change impact assessment. Such factors include
impacts from frost, pests, weeds, diseases, and floods, and also dissimilar impacts between
day and night temperatures ³⁴, or extreme temperature events at different growth stages,
which are all likely to change with future climates. However, process-based models are
capable of accounting for the effects of elevated CO₂ ³⁵, even though this effect is not
considered here, but large uncertainties exist not only with respect to the general effects on
crop yields ³⁶, ³⁷ but also with respect to model implementation ⁹, ³⁸.
Field or environment-controlled experiments are independent ways to estimate
temperature impacts on wheat yields⁸, ¹⁶. For example, 2% to 8% reductions in wheat yield for
every 1°C increase of post-anthesis temperature above an optimum season-average
temperature of 15°C (i.e. local temperature) have been measured for a range of cultivars under
controlled ³⁹ and field experiments ⁴⁰. Considerable variations of wheat yield impacts with
increasing temperature have been found in a 4-growing season warming experiments ⁴¹.
However, while measured temperature impacts on yields can guide other impact estimation
methods, they are often specific to a particular location, cultivar, crop management or
experimental treatment and are not representative of a larger region, which makes it difficult
to extrapolate such measurements to regional or global impacts.
346 **Applying multi-method ensembles**

347 Understanding and quantifying uncertainty of impact assessments has been a key aspect
348 in assessing climate impacts on crop production in recent studies²⁵, ⁴², ⁴³. Most previous studies
349 have focused on uncertainties arising from crop models or climate models²⁵. Here the
350 uncertainties in both point-based and grid-based simulations were quantified by multi-model
351 ensembles. Uncertainties due to crop models, expressed as error bars in the grid-based
352 simulations, were relatively large at both global and country scales (Fig. 1 & Fig. 3), which
353 was due to the limited number of models and relatively wide spread of model results in this
354 study. The differences in model inputs (e.g. nitrogen application, sowing dates, cultivars),
355 calibration methods and model ⁹ explain some of the variability between the point and
356 grid-based simulations. Many crop models do not simulate temperature interactions with
357 canopy temperature variation under different soil water conditions, which could result in
358 simulated differences of temperature impacts ⁸. However, multi-model ensemble medians
359 have been shown to be more consistently accurate than individual models when comparing
360 measurements across locations and growing environments, adding confidence to the estimates
361 here⁴⁴. Bootstrap resampling methods were employed to estimate the uncertainty of
362 temperature impacts calculated in the two global scale statistical regressions. Thus different
363 assessment approaches have independent methods of quantifying uncertainty. Multi-method
364 ensembles can enable the quantification of method uncertainty, similar to how multi-model
365 ensembles enable estimation of model uncertainty. The uncertainty range of wheat yield
366 reduction with 1°C global temperature increase from the multi-method ensemble calculated
367 from the median of the four methods analyzed here was between 4.0% and 6.9% at the global
scale (95% confidence interval). While this absolute difference is still substantial, this is
narrower than the uncertainty due to the models in the multi-model ensembles from the
simulations or the boot-strapping method in the statistical regressions. Therefore, applying
multi-method ensembles can improve reliability of the assessment of climate impacts on
global food security.

However, the consistency of negative global yield impacts of increasing temperature
quantified here at global level should not be applied to local or regional scale. As previous
studies have found, there were considerable large variations of increasing temperature
impacts on wheat yields at local and regional scale<sup>8, 45</sup>, and the spatial variation of temperature
impacts has also been observed in the two modeling approaches here among different
locations.

Adaptation to global warming, e.g. farmer's autonomous adaptation through changing
sowing dates or cultivars, has been suggested in several studies to compensate negative
impacts of increasing temperature<sup>46</sup>. At global scale, point-based simulations did not consider
adaptation. Also a panel regression approach attempted to exclude adaptations<sup>10</sup>. In the
grid-based simulations, four of the seven models did allow cultivar and sowing date
adaptation with a changing climate (Table S3), and the simulated impacts tended to be lower
with simulated adaptation (Fig.S10). However, temperature impacts from models with
adaptation varied largely. Temperature impacts with and without adaptation were estimated
from different models in grid-based simulations, which added considerable uncertainty in the
results. The adaptation effects on temperature impacts should be further studied with more
consistent protocols for multi-model assessments. Other future adaptation, e.g. wheat
390 cultivation shifting to marginal regions in higher latitudes, could offset some of the negative impacts.
391

392 Assessing climate change impacts on crop production is a key aspect in determining appropriate global food security strategies ⁴². Reliable estimates of climate change impacts on food security require an integrated use of climate, crop, and economic models¹⁵. Applying multi-method ensembles further improves the estimated impact precision and confidence in assessments of climate impacts on global food security. The consistent negative impact from increasing temperatures confirmed by three independent methods warrants critical needed investment in climate change adaptation strategies to counteract the adverse effects of rising temperatures on global wheat production, including genetic improvement and management adjustments ⁴⁷, ⁴⁸. However, some or all of the negative global warming impacts on wheat yield might be compensated by increasing atmospheric CO₂ concentrations under full irrigation and fertilization²⁵.

403

404 **Corresponding author**

405 Correspondence and requests for materials should be addressed to Y.Z.

406 **Yan Zhu**

407 Tel: +86-25-84396598

408 Fax: +86-25-84396672

409 E-mail: yanzhu@njau.edu.cn

410 **Address:** No.1 Weigang Road, Nanjing, Jiangsu 210095, P. R. China

411

412 **Acknowledgements**
413 This work was supported by the National High-Tech Research and Development
414 Program of China (2013AA100404), the National Natural Science Foundation of China
415 (31271616, 41571088 and 31561143003), the National Research Foundation for the Doctoral
416 Program of Higher Education of China (20120097110042), the Priority Academic Program
417 Development of Jiangsu Higher Education Institutions (PAPD), and the China Scholarship
418 Council. We would like to acknowledge support provided by IFPRI through the Global
419 Futures and Strategic Foresight project, the CGIAR Research Program on Climate Change,
420 Agriculture and Food Security (CCAFS), the CGIAR Research Program on Wheat and the
421 Agricultural Model Intercomparison and Improvement Project (AgMIP).

422

423 Author contributions

424 B.L., S.A., C.M., F.E., J.E., D.B.L., P.M., A.C.R., D.W., J.W.J., C.R. and Y.Z. motivated
425 the study, S.A. coordinated the study, B.L. S.A., C.M., F.E., J.E., D.B.L., P.M., A.C.R., and
426 D.W. analyzed data, P.K.A., P.D.A., J.A., B.B., C.B., D.C., A.J.C., D.D., G.D.S., J.D., E.F.,
427 C.F., M.G-V., S.G., G.H., L.A.H., R.C.I., M.J., C.D.J., K.C.K., A-K.K., C.M., S.N.K., C.N.,
428 G.O'L., J.E.O., T.P., E.P., T.A.M.P., E.E.R., R.R.P., E.S., M.A.S., I.S., E.S., C.O.S., P.S.,
429 T.S., I.S., F.T., P.J.T., K.W., E.W., J.W., Z.Z. and Y.Z. carried out crop model simulations
430 and discussed the results, C.M., J.E., B.A.K., M.J.O., G.W.W., J.W.W., M.P.R., P.D.A.,
431 P.V.V.P. and A.C.R. provided experimental data, B.L., S.A., C.M., F.E., J.E., D.B.L., P.M.,
432 A.C.R., D.W., J.W.J., C.R. and Y.Z. wrote the paper. All other authors gave comments on the
433 earlier version of this manuscript.

434
435 Competing financial interests

436 The authors declare no competing financial interests.

437

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617

618
619 **Figure legends**

620 **Figure 1 | Impacts of 1°C global temperature increase on global wheat yield**
621 **estimated by different assessment methods.** The grid-based (0.5° x 0.5° grid cells)
622 method is an ensemble median from seven global gridded crop models, averaged over
623 30 years and aggregated over all simulated grid cells (after Ref. 9). The point-based
624 method is an ensemble median from 30 models, averaged over 30 years and
625 aggregated over 30 global locations (after Ref. 8). Regression_A is based on a
626 country-level statistical regression from Ref. 10. Regression_B is based on a global
627 level statistical regression from Ref. 11. The error bars for four different methods
628 indicate the 95% confidence intervals based on multi-model ensembles in the
629 simulations and bootstrap resampling in the statistical regressions. The mean of the
630 method_ensemble is shown with error bar indicating the 95% confidence intervals
631 based on medians of individual methods.

632

633 **Figure 2 | Comparison of wheat yield changes with 1°C global temperature**
634 **increase for 97 wheat producing countries estimated using three different**
635 **methods.** (a) Median simulations of a grid-based (0.5° × 0.5°) ensemble of seven
636 models (after Ref. 9) versus a point-based (30 locations over 30 years) ensemble of 30
637 models (after Ref. 8). (b) Country level statistical regression for China, India, USA,
638 France and Russia, the top five wheat producing countries, from Ref. 10 versus
639 point-based simulations for these countries (after Ref. 8). Note, only data on these five
640 countries were supplied in Ref. 10. Circle color indicates the wheat growing season
641 temperature (from Ref. 10). Circle size indicates the amount of wheat production for
642 each country according to FAO statistics 23. The solid line is the 1:1 line and dashed
643 lines represent 0% yield change.

644

645 **Figure 3 | Estimated impacts of 1°C global temperature increase on wheat yield**

646 (a) China, (b) India, (c) Russia, (d) USA, and (e) France using different assessment
647 methods. The grid-based (0.5° × 0.5°) method produced an ensemble median from
648 seven global gridded crop models (after Ref. 9). The point-based method produced an
649 ensemble median from 30 models from 1 to 3 country locations (after Ref. 8).

650 Regression_A is a statistical regression based on country statistics after Ref. 10.

651 Regression_C is a statistical regression based on 0.5° × 0.5° grid statistics after Ref.

652 45. Regression_D is county level statistical regressions produced by two different
653 regression methods from Ref. 50. Regression_E is a county level regression produced
654 for this study. The error bars indicate the 95% confidence interval based on
655 multi-models for the simulations and bootstrap resampling (Regression_A,
656 Regression_B, and Regression_D) or t-tests (Regression_E) for the statistical
657 regressions. No error bar was provided for Regression_C in Ref. 45.

658

659 **Figure 4 | Comparison of simulated multi-model median wheat yield and yield
660 changes.** Absolute wheat yields for (a) baseline and (b) baseline + 1°C periods, and (c)
661 relative yield change with 1°C global temperature increase from grid-based
662 simulations (0.5° × 0.5°) (from Ref. 9) of cells centered around the 30 locations from
663 the point-based study versus that from the point-based simulations (from Ref. 8). Note

664 in (c), regression line is drawn without outlier (location in Sudan).

665

666
<figure><img src="image_3.png" /><figcaption>Figure 1.</figcaption></figure>

668

669

670
<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /><figcaption>675 Figure 3.</figcaption></figure>

676

677
<figure><img src="image_6.png" /><figcaption>679
680</figcaption></figure>
681 Methods

682 *Grid-based simulations.* Seven global gridded models simulated $0.5^\circ \times 0.5^\circ$ grid cells across
683 all wheat growing regions of the world from 1980 to 2099 under a RCP8.5 scenario with a
684 statistically-downscaled version of HadGEM2-ES $^{49}$, with only a small trend in solar radiation
685 at some locations (Fig. S6). Here, a set of simulation experiments without effects of elevated
686 CO$_2$ and under full irrigation treatments were used. Among the seven global gridded models,
687 adaptation through cultivars, sowing dates or growing season had been employed in four of
688 the models (Table S3). The global yield impacts from models with and without adaptation are
689 compared in Fig. S10. Only one climate model and RCP were used as there was limited data
690 available for grid-based simulations. The period 2029-2058 was selected as being on average
691 $2^\circ$C warmer globally than the baseline period of 1981-2010 and the impact was halved to
692 adjust the temperature change to $+1^\circ$C for the analysis here. The temperature change
693 considered here is $1^\circ$C warming of the global mean temperature, including land and ocean
694 surface. The change in simulated grain yields between these two temperature periods was
695 used to estimate temperature impacts on wheat at global and national scales. Grid-based
696 simulations for the direct comparison to point-based simulations were extracted from
697 simulations assuming full irrigation. For national and global scale results, grid-based
698 simulations were aggregated by area-weighted means, using rain-fed and irrigated wheat
699 areas per pixel of MIRCA2000 $^{50}$ combining simulations under irrigated and rain-fed
700 conditions. To make projections between the different grid-based models comparable, yield
701 simulations were bias-corrected to national FAO levels by using FAO mean yields and
702 superimposing projected relative changes. More details about the grid-based simulations can
703 be found in Ref. 9.
704 Point-based simulations. Thirty models, 29 crop simulation models and one statistical
705 regression model, were used to simulate wheat grain yields for 30 representative locations in
706 high rainfall and irrigated wheat growing regions around the world (together representing
707 about 70% of global wheat production) with the estimated baseline period of 1981-2010 and
708 baseline + 2°C. Three models (CERES, EPIC, and LPJmL) in point-based simulations were
709 used in grid-based simulations. No CO₂ fertilization effects or any adaptation was considered
710 in the point-based simulations. The impact was halved to adjust the temperature change to
711 +1°C for the analysis here. Local temperature impacts on yields were adjusted to global
712 temperature change and upscaled via FAO statistics. Temperature impacts on national scales
713 were assessed for 125 countries. Each country was assigned as being similar to one or more
714 representative locations, so the temperature impacts of each country were the average impacts
715 of the corresponding representative locations. More details can be found in Ref. 8.
716 Statistical regressions. All estimated temperature impacts from statistical regressions were
717 from literature reports¹⁰, ¹¹, ⁴⁵, ⁵¹, except for one new statistical regression analysis for the USA
718 that we present here (Supplementary Methods). All temperature impacts were adjusted to
719 global temperature change following the approach by Ref. 8. Details of these regression
720 studies and impacts adjustments are summarized in Table S1.
721 Meta-analysis and experimental data. Meta-analysis and experimental data from the literature
722 are cited here for further comparison after adjusting them to global temperature change where
723 possible. Meta-analysis and experimental data from the literature were cited here for further
724 comparison after adjusting them to global temperature change. An adjustment factor to global
725 temperature used for the statistical regressions was also used here. The temperature factors
726 are listed in Table S1.

727 *Comparison at a national scale.* Temperature impacts for 97 countries from both grid-based
728 and point-based simulations were compared. Due to the limited number of country-scale
729 estimates of temperature impacts on wheat yields with statistical regression analysis, we
730 compared the regression results with the two simulation approaches for the top five wheat
731 producing countries (Table S1).

732 *Comparison at local scales.* Yield simulations from 30 single grid cells from the grid-based
733 method were chosen that were centered around the 30 global representative locations from the
734 point-based method. Full irrigation treatments were applied in point-based and grid-based
735 simulations. The baseline and increased temperature periods for the 30 grid cells were
736 determined individually by matching the 30-year average annual temperature of each grid to
737 the 30-year average annual temperature of the corresponding location from point-based
738 simulations. The baseline and increased temperature periods for each of the 30 grid cells and
739 temperature differences between the two methods are shown in Table S4. Most locations had
740 very similar temperature input data in the two comparison periods for grid-based and
741 point-based simulations. Outliers (Table S4) were found where the input data differed
742 substantially but these did not cause outliers in yield impacts. The yield impact outlier at the
743 Sudan location was caused by very low simulated yields (Fig. 4). The simulated yields for
744 baseline and increased temperature periods were used to calculate temperature impacts at the
745 local scale. These were also adjusted to global temperature change with the same method at
746 global and national scales. The temperature and radiation data from the critical growing
747 period of wheat from 90 days before maturity to maturity were compared. Maturity dates

748 were the dates supplied from observations for each location in the point-based method ⁸.

749

750