Climate impacts on global agriculture emerge earlier in new generation of climate and crop models

Abstract

Potential climate-related impacts on future crop yield are a major societal concern. Previous projections of the Agricultural Model Intercomparison and Improvement Project’s Global Gridded Crop Model Intercomparison based on the Coupled Model Intercomparison Project Phase 5 identified substantial climate impacts on all major crops, but associated uncertainties were substantial. Here we report new twenty-first-century projections using ensembles of latest-generation crop and climate models. Results suggest markedly more pessimistic yield responses for maize, soybean and rice compared to the original ensemble. Mean end-of-century maize productivity is shifted from +5% to −6% (SSP126) and from +1% to −24% (SSP585)—explained by warmer climate projections and improved crop model sensitivities. In contrast, wheat shows stronger gains (+9% shifted to +18%, SSP585), linked to higher CO2 concentrations and expanded high-latitude gains. The ‘emergence’ of climate impacts consistently occurs earlier in the new projections—before 2040 for several main producing regions. While future yield estimates remain uncertain, these results suggest that major breadbasket regions will face distinct anthropogenic climatic risks sooner than previously anticipated. Climate change affects agricultural productivity. New systematic global agricultural yield projections of the major crops were conducted using ensembles of the latest generation of crop and climate models. Substantial shifts in global crop productivity due to climate change will occur within the next 20 years—several decades sooner than previous projections—highlighting the need for targeted food system adaptation and risk management in the coming decades.

Full text

Articles
https://doi.org/10.1038/s43016-021-00400-y
1NASA Goddard Institute for Space Studies, New York, NY, USA. 2Columbia University, Center for Climate Systems Research, New York, NY, USA.
3Potsdam Institute for Climate Impacts Research (PIK), Member of the Leibniz Association, Potsdam, Germany. 4Center for Robust Decision-making on
Climate and Energy Policy (RDCEP), University of Chicago, Chicago, IL, USA. 5International Institute for Applied Systems Analysis, Laxenburg, Austria.
6Faculty of Natural Sciences, Comenius University in Bratislava, Bratislava, Slovak Republic. 7Agricultural & Biological Engineering Department, University
of Florida, Gainesville, FL, USA. 8Institut de recherche pour le développement (IRD) ESPACE-DEV, Montpellier, France. 9Department of Computer Science,
University of Chicago, Chicago, IL, USA. 10Department of the Geophysical Sciences, University of Chicago, Chicago, IL, USA. 11Institute of Meteorology
and Climate Research, Atmospheric Environmental Research, Karlsruhe Institute of Technology, Garmisch-Partenkirchen, Germany. 12Institute for
Sustainable Food Systems, University of Florida, Gainesville, FL, USA. 13Institute for Agro-Environmental Sciences, National Agriculture and Food Research
Organization, Tsukuba, Japan. 14Department of Atmospheric Sciences, University of Illinois, Urbana, IL, USA. 15Center for Agricultural Water Research
in China, College of Water Resources and Civil Engineering, China Agricultural University, Beijing, China. 16Multidisciplinary Water Management group,
University of Twente, Enschede, Netherlands. 17Center for Climate Change Adaptation, National Institute for Environmental Studies, Tsukuba, Japan.
18Department of Environmental Sciences, Rutgers University, New Brunswick, NJ, USA. 19Ludwig-Maximilians-Universität München (LMU), Munich,
Germany. 20Soil Science and Conservation Research Institute, National Agricultural and Food Centre, Bratislava, Slovak Republic. 21Leibniz Centre for
Agricultural Landscape Research (ZALF), Müncheberg, Germany. ✉e-mail: jonas.jaegermeyr@columbia.edu
Climate change already affects agricultural productivity world-
wide via many mechanisms, driven largely by warmer mean
and extreme temperatures, altered precipitation regimes and
drought patterns, and elevated atmospheric CO2 concentrations
([CO2])1. Uncertainties arising from greenhouse gas emission sce-
narios, climate model projections and the understanding and repre-
sentation of complex impact processes render estimates of future crop
yield highly uncertain2. A way towards improving yield projections
is the development of benchmarked multi-model ensemble simu-
lations driven by harmonized simulation protocols3. Facilitated by
the Agricultural Model Intercomparison and Improvement Project
(AgMIP)4 and the Inter-Sectoral Impact Model Intercomparison
Project (ISIMIP)5, here we present a new systematic assessment of
agricultural yield projections, based on a protocol similar to the one
used by the Coupled Model Intercomparison Project (CMIP) for
climate models6.
In 2014, AgMIP’s Global Gridded Crop Model Intercomparison
(GGCMI) provided the first set of harmonized crop model pro-
jections based on CMIP5 (GGCMI–CMIP5; hereafter ‘GC5’),
which identified substantial climate impacts on all major crops,
but also demonstrated that crop models might indeed introduce
larger uncertainty than climate models7. CMIP6 now provides new
Climate impacts on global agriculture emerge
earlier in new generation of climate and crop
models
Jonas Jägermeyr 1,2,3 ✉ , Christoph Müller 3, Alex C. Ruane 1, Joshua Elliott4, Juraj Balkovic5,6,
Oscar Castillo7, Babacar Faye8, Ian Foster 9, Christian Folberth 5, James A. Franke4,10,
Kathrin Fuchs 11, Jose R. Guarin 1,2, Jens Heinke3, Gerrit Hoogenboom 7,12, Toshichika Iizumi 13,
Atul K. Jain 14, David Kelly9, Nikolay Khabarov 5, Stefan Lange 3, Tzu-Shun Lin 14, Wenfeng Liu15,
Oleksandr Mialyk 16, Sara Minoli3, Elisabeth J. Moyer 4,10, Masashi Okada17, Meridel Phillips1,2,
Cheryl Porter 7, Sam S. Rabin11,18, Clemens Scheer11, Julia M. Schneider 19, Joep F. Schyns 16,
Rastislav Skalsky 5,20, Andrew Smerald 11, Tommaso Stella 21, Haynes Stephens 4,10,
Heidi Webber 21, Florian Zabel 19 and Cynthia Rosenzweig 1
Potential climate-related impacts on future crop yield are a major societal concern. Previous projections of the Agricultural
Model Intercomparison and Improvement Project’s Global Gridded Crop Model Intercomparison based on the Coupled Model
Intercomparison Project Phase 5 identified substantial climate impacts on all major crops, but associated uncertainties were
substantial. Here we report new twenty-first-century projections using ensembles of latest-generation crop and climate models.
Results suggest markedly more pessimistic yield responses for maize, soybean and rice compared to the original ensemble.
Mean end-of-century maize productivity is shifted from +5% to −6% (SSP126) and from +1% to −24% (SSP585)—explained
by warmer climate projections and improved crop model sensitivities. In contrast, wheat shows stronger gains (+9% shifted
to +18%, SSP585), linked to higher CO2 concentrations and expanded high-latitude gains. The ‘emergence’ of climate impacts
consistently occurs earlier in the new projections—before 2040 for several main producing regions. While future yield esti-
mates remain uncertain, these results suggest that major breadbasket regions will face distinct anthropogenic climatic risks
sooner than previously anticipated.
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Articles NATuRe FOOd
reference climate projections8,9, and improved bias-adjustment and
downscaling methods10 benefit the impact modelling community.
With improved and further harmonized inputs and cropping system
configurations, and an advanced ensemble of state-of-the-art
process-based crop models, GGCMI is able to provide a new stan-
dard in global crop yield projections for the twenty-first century
for several major crops using CMIP6 climate scenarios (GGCMI–
CMIP6; hereafter ‘GC6’).
Climate change impacts are usually quantified in terms of dif-
ferences over time, but especially in view of adaptation measures,
it is the amplitude of the change compared to the local background
variability and uncertainty of the recent past that is often more rele-
vant11. Time of climate impact emergence (TCIE)—the point in time
by which the yield levels of exceptional years (negative or positive)
have become the new norm—is a critical measure for risk assess-
ment. Time of emergence12 metrics have been applied to climate
variables including temperature13, precipitation14 and others15,16 and
demonstrate that major food-producing regions are increasingly
facing changing climate profiles in the near term. Here we introduce
the TCIE concept with respect to future agricultural risks.
Recent literature has focused on capturing the temperature
sensitivity of crops in isolation17–19. To quantify climate change
impacts more comprehensively, additional factors including pre-
cipitation changes, temperature–moisture feedbacks and [CO2]
need to be considered. The projections presented here dynamically
respond to these climate drivers and shed new light on the effects of
elevated [CO2], which are among the largest sources of uncertainty
in long-term crop yield estimates20–22.
As the first update since GC5 in 20147, the aims of this initial GC6
study are: (1) to provide latest-generation ensemble projections for
the productivity of major crops for the twenty-first century, (2) to
assess climate change impacts on crop yields from a risk perspec-
tive, employing the TCIE concept, (3) to improve understanding of
regional patterns of change and (4) to explore drivers of uncertainty
related to climate models, crop models and responses to [CO2].
Global production response of major crops
The simulation protocol is based on two representative concentra-
tion pathways (RCPs), RCP2.6 and RCP8.5 (hereafter ‘SSP126’ and
‘SSP585’; adaptation measures associated with the shared socio-
economic pathways are not considered)9, chosen to sample the
range of available scenarios and to make the results comparable
with GC5. Twelve GGCMs each simulated five GCM forcings,
resulting in about 240 climate–crop model realizations per crop
(GGCMs × GCMs × RCPs × CO2 settings). The climate projec-
tions from the five GCMs (Supplementary Table 1), bias-adjusted
and downscaled, are selected by ISIMIP based on benchmark per-
formance, equilibrium climate sensitivity and output availability
(Methods). All simulations are carried out globally on a 0.5° grid,
covering the time period 1850–2100 and we evaluate results based
on transient atmospheric [CO2] (that is, ‘default [CO2]’). This study is
based on temporally constant management assumptions, focusing on
the isolated climate change effect on current crop production systems.
The ensemble response across the new generation of climate and
crop models to the SSP126 and SSP585 forcing is markedly more
pronounced than in GC5 (ref. 7) (Fig. 1). Wheat results are more
optimistic, while maize, soybean and rice results are decisively more
pessimistic. For maize, the most important global crop in terms
of total production and food security in many regions, the mean
end-of-century (2069–2099) global productivity response is ∼10%
–6.4
+4.9
–24.1
+1.3
e
b
c
a
d
3
9
4
612
2
1
10 5
8
11
7
Maize
–
60
–
40
–
20
0
20
40
60
Global productivity change (%)
Global productivity change (%)
+8.8
+5
+17.5
+9.9
b
e
c
a
d
2
7
4
5
6
10
3
8
9
11 12
1
Wheat
+2
+6.5
–2.1
+15.3
e
b
c
a
d
3
2
6
7
10
5
9
12
1
8
11
Soybean
+3.4
+7.7
+1.7
+23.3
80
e
b
d
a
c
2
3
9
510
67
8
1
11
Rice
–
60
–
40
–
20
0
20
40
60
Rosenzweig et al.
7
(CMIP5)
SSP126
SSP585
Climate model range
Crop model range
Climate models
a GFDL-ESM4
b IPSL-CM6A-LR
c MPI-ESM1-2-HR
d MRI-ESM2-0
e UKESM1-0-LL
Crop models
1 ACEA
2 CROVER
3 CYGMA1p74
4 DSSAT-Pythia
5 EPIC-IIASA
6 ISAM
7 LandscapeDNDC
8 LPJmL
9 pDSSAT
10 PEPIC
11 PROMET
12 SIMPLACE-LINTUL5
Fig. 1 | Ensemble end-of-century crop productivity response. Global productivity changes (2069–2099 compared to 1983–2013) for SSP126 and SSP585
are shown as the mean across climate and crop models for the four major crops (highlighted by numbers in circles underneath each plot). Whiskers indicate
the range of individual climate model realizations (dashed line, as the mean across crop models), and the range across crop models (solid line, as the mean
across climate models). Individual model results are indicated by the bullets along the whisker lines (for SSP585 only); violin shades additionally highlight the
model distribution. For context, grey bars and whiskers reference previous GGCMI simulations based on CMIP5 (GC5; Rosenzweig et al.7) in the same way,
without specifying individual models. Data are shown for the default [CO2]. Not all crop models simulate all crops, see Supplementary Table 3 for details.
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(SSP126) and ∼20% (SSP585) lower than in GC5. This shifts the
SSP585 estimate from +1% (interquartile range (IQR) of crop–cli-
mate model combinations: −10% to +8%) to −24% (IQR: −38% to
−7%) and for SSP126 from +5 to −6%.
For wheat, the second largest global crop in terms of produc-
tion, the SSP585 ensemble estimate is shifted upwards from +10%
(IQR: −1% to +15%) to +18% (IQR: −2% to +39%), and under
SSP126 from +5% to +9%. The SSP585 ensemble estimates for
soybean are revised downward from +15% (IQR: −8% to +36%)
to −2% (IQR: −21% to +17%) and for rice from +23% (IQR: +1%
to +33%) to +2% (IQR: −15% to +12%). Overall, the new climate
and crop model combinations narrow the range of crop yield pro-
jections for soybean and rice, but disagreement among crop mod-
els remains substantial and is largely indecisive about the sign of
change at the global level (t test: P > 0.5 for both crops). The maize
and wheat responses are robust and became more distinct since
GC5. While the range of crop projections somewhat increased,
85% of model combinations indicate negative maize changes and
73% project positive wheat changes under SSP585. Both responses
are now statistically significant (P < 10−5); the maize response
in GC5 was not (P > 0.6). There is larger agreement on positive
change for wheat under SSP126 (89%) than under SSP585, indicat-
ing peak-and-decline trajectories for parts of the ensemble under
high-emissions scenarios (Supplementary Fig. 1).
As a C4 crop, maize has a smaller capacity to benefit from
elevated [CO2] (ref. 23), and is also grown across a wider range of low
latitudes that are projected to experience the largest adverse impacts
due in large part to current proximity to crop-limiting temperature
thresholds24. As a C3 crop, the positive wheat response is explained
by its relatively stronger CO2 response and the fact that global
warming leads to wheat yield increases in high-latitude regions that
are currently temperature-limited19.
Three factors explain the more pronounced crop yield response
in GC6. First, CMIP6 has markedly higher [CO2] than CMIP5
(Fig. 2), with year 2099 concentrations increased from 927 ppm
(RCP8.5) to 1,122 ppm (SSP585)9. Second, CMIP6 has higher aver-
age end-of-century warming levels than CMIP5, adequately rep-
resented in the five GCMs sampled here (Supplementary Tables 1
and 2). While both RCP2.6 and RCP8.5 are on average ∼0.3 °C
warmer in CMIP6 than in CMIP5 over land and oceans, the
difference is even more pronounced (>0.5 °C) across the main
maize-producing regions (Fig. 2). Third, the new crop model ensem-
ble features advanced versions of previous models, several new
members and improved input data, which resulted in more realistic
sensitivities to climate and [CO2] changes (see details below).
Emergence of the climate change signal in agriculture
The TCIE describes the point in time when average climate change
impacts are projected to occur outside the envelope of historical
variability and uncertainty (‘noise’). We define TCIE as the year
in which the multi-model 25 yr moving-average crop production
change (‘signal’) emerges from the noise (that is, the standard devia-
tion of simulated variability across all GCM × GGCM combinations
in 1983–2013).
Maize consistently shows emerging negative productivity
changes (‘negative TCIE’) among major producer regions. The
ensemble median signal emerges from the noise at the global level
in the year 2032 under SSP585 and in the year 2051 under SSP126
(Fig. 3). Of all individual GCM × GGCM realizations, 84% show a
negative TCIE by 2099 under SSP585 (52% under SSP126) and the
IQR spans from 2014 to 2056, indicating sizeable agreement among
models. This is a substantial shift away from the GC5 simulations in
which the ensemble median shows no emergence by 2099 under any
emission pathway, only seen in 46% of individual GCM × GGCM
combinations under RCP8.5 (IQR: 2044–2080). Overall, the TCIE
signal at the global level is shifted earlier and is more pronounced in
the new generation of climate and crop model projections (Fig. 4).
By the end of the century, 10% (SSP126) to 74% (SSP585) of
current global maize cultivation areas are projected to undergo
negative TCIE (Fig. 5). Under SSP585 this trajectory is markedly
earlier, with higher late-century fractions of cropland area affected
compared to the respective 47% in GC5 (RCP8.5). Crop models
indicate early negative maize TCIE before 2040 even under SSP126
in Central Asia, the Middle East, southern Europe, the western
United States and tropical South America. Projections referencing
the 1983–2013 period suggest that the mean yield signal is already
starting to emerge in some of these regions (Figs. 3e and 5), patterns
largely in line with recent observations14,25,26.
The standard deviation of grid-level TCIE estimates under
SSP585 ranges between 25 and 35 yr across most breadbasket
421
927
447
1,122
2020 2040 2060
Year
2080 2100
400
600
800
1,000
1,200
[CO2] (ppm)
a
SSP126 (CMIP6)
RCP2.6 (CMIP5)
SSP585 (CMIP6)
RCP8.5 (CMIP5)
0.32
n = 12,141
0.59
n = 658
0.31
n = 12,141
0.53
n = 658
–0.5
0
0.5
1.0
1.5
2.0
Temperature change difference (°C)
b
SSP126–RCP2.6
SSP126–RCP2.6 (high-producing regions)
SSP585–RCP8.5
SSP585–RCP8.5 (high-producing regions)
Fig. 2 | Comparison of [CO2] and temperature changes between CMIP5 and CMIP6. a, [CO2] pathways for RCP2.6 and RCP8.5 in CMIP5 compared to
SSP126 and SSP585 in CMIP6. b, Box-and-whisker plots showing the difference of the average maize growing season temperature changes (2069–2099
versus 1983–2013) between the CMIP6 and CMIP5 ensembles. Each ensemble is represented by the mean of five GCMs (Supplementary Tables 1 and 2)
in each grid cell. CMIP6 and CMIP5 differences are separated for SSP126 (green) and SSP585 (yellow) for all maize-producing grid cells (lighter shade)
and for the highest-producing grid cells that together account for 50% of global production (darker shade).
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regions, with slightly higher values under SSP126 (Supplementary
Fig. 2). Such uncertainty ranges are in line with time of emergence
estimates for climatological variables, yet somewhat higher due to
the additional layer of crop model uncertainties12,13. Clearest emer-
gence signals, that is, largest signal-to-noise ratios with values <−2,
are found among lower latitudes in the tropics but also in Central
Asia, the Middle East and the western United States (Supplementary
Fig. 2e). As internal variability—and thus total noise—decreases
with averaging, earlier TCIE is generally found for larger spatial
scales.
For wheat, ensemble projections indicate TCIE of positive pro-
ductivity changes (‘positive TCIE’) at the global level (Fig. 3b) and
across large parts of currently cultivated areas (Fig. 5). While also
found in GC5 simulations, TCIE is shifted ∼10 yr earlier in GC6,
0
a
–10
–20
–30
–40 GGCMI–CMIP5: >2099
2032
>2099
2051
2033
2023
2033
2025
50
40
30
20
10
0
GGCMI–CMIP6:
–50
60
40
20
0
–20
60
40
20
0
30
20
10
0
10
–10
–30
–50
10 50
30
20
0
–20
–40
10
–10
Temperature limited Temperature limited
Subtropical
Temperate Temperate
Tropical Subtropical Tropical
0.3% 1.4%
23.1% 0.9%
74.7%
81.3%
9.1%9.2%
2013 2012
2017
2017
>2099 >2099
2020
2021
2034
2037
>2099
2037
2017 2018
2022
2021
2081
2039
>2099
2083
2033 2039
2029
2026
–10
–30
–50
0
–20
–40
1980 2000 2020 2040
Year Year
Year Year
Maize Wheat
2060 2080 2100
2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100
2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100
2000 2020 2040 2060 2080 2100
2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100
1980 2000 2020 2040 2060 2080 2100
Global productivity change (%)
Productivity change (%)
Global productivity change (%)
Productivity change (%)
< –40 –30 –20 –10 –5
Yield change (%)
5 10 20 30 40 >
b
cd
ef
SSP126
SSP585
IQR of climate and crop models
Model mean, 30 yr average
Model mean
Yield variability and uncertainty (1983–2013)
Fig. 3 | Projections of global crop productivity for the twenty-first century. a,b, Productivity time series for maize (a) and wheat (b) shown as relative
changes to the 1983–2013 reference period under SSP126 (green) and SSP585 (yellow). Shaded ranges illustrate the IQR of all climate–crop model
combinations (5 GCMs × 12 GGCMs). The solid line shows the median response (and a 25 yr moving average). Horizontal dashed lines mark the standard
deviation of historical yield variability and model uncertainty (that is, ‘noise’ from individual climate–crop model combinations) and open circles highlight
the TCIE, the year in which the smoothed climate change response emerges from the noise. For context, the TCIE calculated from GC5 (ref. 7) simulations
is indicated in lighter shades above the TCIE based on GC6 (>2099 if no TCIE occurs by 2099). c,d, Maps showing median yield changes (2069–2099)
for maize (c) and wheat (d) under SSP585 across climate and crop models for current growing regions (>10 ha). Hatching indicates areas where <70%
of the climate–crop model combinations agree on the sign of impact. e,f, Regional productivity time series for maize (e) and wheat (f) similar to a, but
stratified for the four major Koeppen–Geiger climate zones (temperature limited, temperate/humid, subtropical and tropical). The percentage of the total
global production contributed by each zone is indicated in the top right corner of the insets. All data are shown for the default [CO2] (see Supplementary
Fig. 3 for all four crops).
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suggesting that climate-related increases might occur globally
within the next few years (year 2023 under SSP585, year 2025 under
SSP126; IQR, 2014–2029 and 2015–2029) and across major bread-
basket regions within the next two decades (Fig. 5). In some regions
we already detect a TCIE signal today, which is in line with the
range of time of emergence estimates for temperature and precipita-
tion13,14. Such effects are difficult to distinguish from rapidly chang-
ing management practices in observational data, but climate change
impacts have been documented, for example, in Central and South
Asia, northern China and the United States25,27. The TCIE estimates
for wheat show high consistencies across the model ensemble—76%
(SSP126) and 88% (SSP585) of individual model combinations
show positive TCIE by 2099. As for maize, the TCIE signal is shifted
earlier and is more pronounced in GC6 than in GC5 (Fig. 4).
Year
Maize Wheat
Sum = 84%
Sum = 46%
a
2000 2020 2040 2060 2080 2100
0
5
10
15
20
25
30
35
Fraction of ensemble (%)
0
5
10
15
20
25
30
35
Fraction of ensemble (%)
Year
Sum = 88%
Sum = 69%
b
2000 2020 2040 2060 2080 2100
GGCMI
–
CMIP6
GGCMI
–
CMIP5
Fig. 4 | Shift towards earlier and more pronounced climate impact emergence. a,b, Density plots of individual TCIE estimates across the GCM × GGCM
ensemble under SSP585 are shown for global maize productivity (a; negative TCIE) and global wheat productivity (b; positive TCIE). Histogram counts are
smoothed with a locally weighted fit (LOESS; span, 0.5) and shown as the fraction of the respective ensemble size. The GGCMI–CMIP6 ensemble includes
12 crop models, GGCMI–CMIP5 includes seven crop models; both comprise five GCMs. The total ensemble fraction that shows TCIE by 2099 is indicated
by ‘Sum’. The ensemble median TCIE is highlighted with vertical dashed lines. See Supplementary Fig. 4 for soybean and rice.
SSP126
a
< 2099 2080
Emergence of negative change (year) Emergence of positive change (year)
GC6 SSP585
GC6 SSP126
GC5 RCP8.5
GC5 RCP2.6
2060 2040 2016 2040 2060 2080 2099 >
SSP585 80
60
40
20
0
2020 2060
Year
Year
2100
2020 2060 2100
37
9
10
47
74
22
88
Area with negative TCIE (%)
80
60
40
20
0
Area with positive TCIE (%)
MaizeWheat
b
cd
e
f
Fig. 5 | Geographic patterns in TCIE. a–d, Maps showing TCIE estimates for maize (a,b) and wheat (c,d) under SSP126 (a,c) and SSP585 (b,d)—calculated
as the median of individual TCIE estimates from each climate–crop model combination. Hatching indicates areas in which <70% of the crop models agree
on the emergence signal by 2099. See Supplementary Fig. 2 for the associated standard deviation of TCIE estimates and the signal-to-noise ratio. e,f,
Illustration of the annual percentage of the respective global cropland area affected by negative TCIE (e, maize) and positive TCIE (f, wheat) under SSP126
and SSP585, separated for results from GC5 (ref. 7) and GC6. Vertical bars indicate the IQR of all climate–crop model combinations, with the median value
in the circle. The maps show the first TCIE occurrence, even if the signal is reversed by late century (for example, parts of India for wheat; compare with
Supplementary Fig. 2); estimates of the affected areas in e and f account for signal changes.
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The share of wheat cultivation areas projected to see positive
TCIE increased substantially in GC6, from 8% (GC5, RCP8.5) to
37% (GC6, SSP585; Fig. 5f). This share levels off by midcentury,
a result of peak-and-decline trajectories seen in some crop models
(compare Fig. 5d and Supplementary Fig. 2f for regions that show
TCIE early on but not by late century). Wheat also exhibits negative
TCIE among important growing regions in South Asia, the southern
United States, Mexico and parts of South America around midcen-
tury. The uncertainty among grid-level TCIE estimates is generally
higher for wheat than for maize and the extent of areas with very
high signal-to-noise ratios (that is, >2) is smaller (Supplementary
Fig. 2f).
Ensemble median soybean and rice productivity peak midcen-
tury and decline towards the end of the century at the global level
(Supplementary Fig. 3). The soybean response exhibits late-century
negative TCIE (year 2096) under SSP585; rice, on the other hand,
shows early positive TCIE (year 2030, SSP585) but late-century
declines are not projected to reach the level of negative TCIE at the
global level (38% of GCM × GGCM combinations under RCP8.5
indicate negative TCIE by 2099; Supplementary Fig. 4). Rice is the
only crop in this study that indicates positive TCIE in the tropics,
which drives early net global gains before productivity is simu-
lated to decline again by about 2060 (Supplementary Fig. 3c). As
for maize and wheat, the TCIE signal is shifted earlier and is more
pronounced in GC6 than in GC5 (Supplementary Fig. 4).
Regional patterns of yield change
Projections of crop yield changes include regions of losses and
gains for all crops (Fig. 3 and Supplementary Fig. 3). Global average
responses can hide important regional changes, which are supported
by strong crop model agreement. Maize projections show spatially
homogeneous losses especially among main growing regions in
North America, Mexico, West Africa, Central Asia and China, where
crop model agreement is high (Fig. 3c). The high-latitude gains
found in GC5 are not as prevalent in GC6 and are associated with
high crop model uncertainty and low baseline yields. Wheat shows
distinct geographic gradients with losses in spring wheat regions in
Mexico, the southern United States, South America and South Asia,
supported by good model agreement. Sizeable wheat gains are pro-
jected by many models for the North China Plains, Australia, Central
Asia, the Middle East and for the winter-wheat-growing regions in
the northern United States and Canada (Fig. 3d). Soybean shows
the greatest losses in the main-producer regions—the United States,
Brazil and Southeast Asia—paired with large gains across parts of
China and generally higher latitudes (Supplementary Fig. 3). Major
declines in rice yields are simulated in Central Asia, and gains in
South Asia, northeastern China and South America. Both soybean
and rice yield changes must be interpreted in view of the wide range
in crop model ensemble results (Fig. 1 and Supplementary Fig. 3).
A breakdown of yield responses for the top-ten producer countries
per crop highlights a wide range of CO2 effects embedded in the
signal (Supplementary Figs. 5 and 6).
A latitudinal profile of yield changes under SSP585—simulated
in all grid cells irrespective of the current cropland distribution—
indicates that losses are most prevalent among low-latitude tropical
regions with highest gains found at higher latitudes beyond 50° N
and 30° S for all crops (Fig. 6). Maize exhibits widespread losses
between 50° N and 30° S, while losses for the other crops are more
concentrated in the tropics with a less distinct signal for soybean
and rice. Major wheat breadbaskets are generally located at higher
latitudes than maize, which further contributes to overall wheat
gains when aggregated across currently cultivated areas. Although
more than 90% of maize and wheat is currently produced in the
temperate and subtropical climate zones, major yield losses will
affect the livelihoods and food security of many smallholder farm-
ers in the tropics. Overall, our results show that lower latitudes face
the largest losses for all crops, while higher latitudes see potential
gains. These conclusions are in line with the IPCC AR5 (ref. 28) and
recent studies7,29,30 and such uneven distribution of impacts may
further increase regional disparities that are a ‘reason for concern’31
regarding climate change risks.
Drivers of more pronounced ensemble response
It is difficult to determine to what degree the differences in crop
yield projections between GC6 and GC5 can be explained by the
new atmospheric forcing, the new crop model ensemble or new
input data. A subset of GC6 and GC5 crop models that participated
in both ensembles (albeit in different versions) shows very similar
responses compared with the respective full ensemble, suggesting
that the crop model selection does not explain the differences (Fig. 7).
Further, standardized comparisons of crop model responses to
specific mean temperature increases over cropland areas (‘warm-
ing sensitivity’; under constant [CO2] conditions, but including
changes in other climate variables) from 1 to 2 °C and from 2 to
3 °C, respectively, highlights that the isolated warming sensitivity in
GC6 has substantially increased for maize (from 2–3% in GC5 to
8–9% in GC6) and decreased for wheat (from 7% to 3–6%; Fig. 7).
With higher overall warming levels in CMIP6, net warming-related
maize losses by 2069–2099 thus increased from 12% (4.6 °C maize
cropland warming) to 30% (5 °C maize cropland warming) in GC6.
Moreover, the CO2 sensitivity at 500 and 700 ppm, but also net
effects by the end of the century, have decreased for both maize and
wheat. In summary, the more pessimistic maize response in GC6
can largely be attributed to a higher sensitivity to warming and a
lower compensating effect due to CO2 fertilization in the crop mod-
els, and to a smaller extent to the higher absolute warming levels in
CMIP6. For wheat on the other hand, the more optimistic response
in GC6 can be explained by lower losses per degree warming
(with stronger temperature-related gains in high-latitude regions),
overcompensating for a lower CO2 fertilization effect than in GC5
(despite higher total [CO2] levels). For soybean and rice, in contrast,
the more pessimistic response in GC6 is largely attributed to higher
warming levels in CMIP6 compounded by a higher crop model sen-
sitivity to warming, with similar sensitivities to changes in [CO2]
(Supplementary Fig. 7).
Crop and climate model uncertainty
The range of crop model responses under SSP585 (mean across cli-
mate models) is substantially larger than the range introduced by the
five climate models (mean across crop models; Fig. 1). However, for
all crops and RCPs, the uncertainty associated with the five CMIP6
climate models has increased compared to the five climate models
sampled in GC5. In turn, the fraction of total variance induced by
the crop models is substantially reduced for all crops in GC6 (for
maize from 97% to 69%; Fig. 8), which highlights that the crop
response became more consistent, despite the fact that the number
of crop models increased. Absolute variance induced by the climate
models has increased for all crops (Fig. 8), which is explained by a
wider distribution of climate sensitivities tracked by the five CMIP6
GCMs (Supplementary Tables 1 and 2), but also by higher [CO2]
assumed in CMIP6 (Fig. 2). In this sample, UKESM1 is the most
pessimistic GCM for both RCPs and all crops, the global mean
warming level by 2099 is ∼2.6 °C higher than in GFDL-ESM4, and
the transient climate response is 1.2 °C higher (see Supplementary
Table 1 for more details)6. Generally, the least pessimistic crop
impacts are found with MRI-ESM2 (Fig. 1).
Higher emission scenarios inflate the crop model uncertainty
(SSP585), while the overall climate- and crop model-induced uncer-
tainty range in GC6 is of comparable size under SSP126 (Fig. 1).
Uncertainty in the CO2 effect causes much of the crop model
uncertainty for wheat, soybean and rice (Supplementary Fig. 8), yet
the range of maize responses is not fundamentally reduced without
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the CO2 effect. In line with physiological knowledge23, crop mod-
els mostly show the smallest CO2 effects for C4 crops (maize) and
much larger responses for C3 crops (wheat, soybean, rice). However,
the CO2 effects differ widely across crop models; the ensemble
median rainfed response is 19% for maize, 33% for wheat, 48% for
soybean and 37% for rice by the year 2099 (Supplementary Fig. 8),
which is generally in line with field experiments given that model
simulations include nutrient limitations20,23. CYGMA and CROVER
exhibit a strong peak-and-decline CO2 response for some crops,
resulting in negative CO2 effects for maize in CYGMA after 2090
(Supplementary Fig. 8). This is driven by increased water use effi-
ciencies under elevated [CO2], eventually leading to adverse excess
moisture effects in humid regions—a new feedback represented
primarily in CYGMA and underexplored in previous studies32.
In addition to the CO2 effect, climate change affects simulations
of crop growth and development in various ways. These include, for
example, changed precipitation patterns, extreme heat and drought
events, and importantly, accelerated maturity. Higher temperatures
lead to faster phenological development and substantial reductions
in the growing season length in all crop models, which in turn lead
to complex processes affecting yield, including shorter grain-filling
periods, smaller canopies and reductions in photosynthesis. This
effect varies across models and additional work is needed to further
narrow the range of crop model responses33. After all, the standard
deviation of simulated yield variability matches observational data
to a much higher degree in GC6 (R = 79%) than in GC5 (R = 44%),
adding to more realistic yield responses (Supplementary Fig. 9).
Discussion
We introduce the concept of climate impact emergence to the field
of agriculture impacts, highlighting that major shifts in global crop
productivity due to climate change are projected to occur within the
next 20 yr, several decades sooner than estimates based on previous
model projections. The impact on crop productivity under SSP126
and SSP585 is largely similar for the coming decade, which leaves
little room for climate mitigation efforts. In light of the much larger
climate and crop model agreement for these short-term projections
than for the late century, the findings highlight challenges for food
system adaptation faced with noticeably shorter lead times.
These CMIP6 multi-model crop yield projections suggest that cli-
mate change impacts on global agriculture will be more pronounced
than in GC5, with substantially larger losses for maize, soybean and
rice and additional gains for wheat. This is supported by a generally
more consistent crop model ensemble. However, large uncertainties
remain, particularly in TCIE estimates—the standard deviation for
global maize TCIE is 24 yr (SSP585), which is similar to estimates of
temperature emergence12. Yet the signal is robust: more than 80% of
the GCM-GGCM combinations indicate TCIE for maize and wheat
by late century across major breadbaskets (SSP585). TCIE esti-
mates based on different metrics qualitatively agree (for example,
multi-model ensemble mean TCIE for maize is found in the year
2032, the median of individual GCM × GGCM estimates in the year
2027, and the mean in the year 2036). Leaving one crop model out at
a time introduces a TCIE standard deviation of only 1.5 yr for both
maize and wheat (SSP585). That said, time of emergence estimates
are sensitive to the underlying definitions (for example, noise, pre-
industrial or recent climate, smoothing approach, threshold selec-
tion) and can push the emergence date earlier or later in time12–14.
Absolute TCIE estimates are therefore more challenging to interpret
than relative comparisons among regions, crops and especially the
two ensemble projections GC5 and GC6.
Wheat yield increases are projected to level off by midcentury
and part of the climate–crop model ensemble indicates net losses
under SSP585 by 2099 (Fig. 1 and Supplementary Fig. 1). Maize
yield, on the other hand, is projected to decline steadily, supported
by higher model agreement than for wheat. These general response
differences are also in line with previous findings34. The more pro-
nounced response of the new projections can be explained primar-
ily by higher equilibrium climate sensitivities, higher [CO2] and
different crop model sensitivities per degree warming and [CO2]
changes. With regard to CMIP6, higher and wider-ranging climate
sensitivities are critically discussed and associated with differing
parameterizations of cloud feedback and cloud–aerosol interac-
tions35–38. While better simulations of cloud liquid water contents
Cropland extent
Yield decline
Yield increase
–
40
–
20 0 20 40
Yield change (%)
10 5 0 5 10
Fraction of global cropland (%)
60° S
30° S
0°
30° N
60° N
90° N
Latitude
Maize
a
–
40
–
20 0 20 40
Yield change (%)
10 5 0 5 10
Fraction of global cropland (%)
Wheat
b
–
40
–
20 0 20 40
Yield change (%)
10 5 0 5 10
Fraction of global cropland (%)
Soybean
c
–
40
–
20 0 20 40
Yield change (%)
10 5 0 5 10
Fraction of global cropland (%)
60° S
30° S
0°
30° N
60° N
90° N
Latitude
Rice
d
Fig. 6 | Latitudinal profile of crop yield changes. a–d, Yield changes (SSP585, 2069–2099) are shown as latitude averages for maize (a), wheat (b),
soybean (c) and rice (d), based on crop simulations in all grid cells, unconstrained by current cropland extent (bottom x axis). For context, the current
cropland extent is shown across latitude bands as fractions of the crop-specific global extent (top x axis; mirrored to allow overlaps with both positive and
negative yield changes). Yield data are shown as the climate and crop model median (marginal areas with yield lower than the 20th percentile per crop
are excluded).
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and their radiative behaviour render the climate models more
realistic, it is unclear whether these improvements translate into
more accurate estimates of equilibrium climate sensitivity (ECS) and
overall warming levels. Additional improvements of the GCMs, and
the bias-adjustment and downscaling methods used, result in bet-
ter representations of extreme events and internal variability10,39–41,
1
2
5
7
GC5
subset
–1.2
5
8
9
10
GC6
subset
–19.8
1
2
3
4
5
6
7
GC5
–0.6
1
2
3
4
5
6
7
8
9
10
11
12
GC6
–22.4
–60
–40
–20
0
20
40
Global productivity change (%)
End-of-century response
GGCMI–CMIP5
GGCMI–CMIP6
Maize
a
1
2
3
4
5
6
7
–3.1
2
3
5
6
7
8
9
10
11
12
–7.5
From 1 to 2 °C
cropland T change
–20
–15
–10
–5
0
5
Global productivity change (%)
Warming sensitivity
(constant CO
2
)
c
1
2
3
4
5
6
7
–1.9
2
3
5
6
7
8
9
10
11
12
–7.4
From 2 to 3 °C
cropland T change
1
2
3
4
5
6
7
–11.9
2
3
5
6
7
8
9
10
11
12
–30.2
(2069–2099)
4.6 °C 5 °C
–60
–40
–20
0
20
40
1
2
3
4
5
6
7
4.6
2
3
5
6
7
8
9
10
11
12
2.3
500
ppm
1
2
3
4
5
6
7
10.3
2
3
5
6
7
8
9
10
11
12
7.4
700
ppm
1
2
3
4
5
6
7
12.7
2
3
5
6
7
8
9
10
11
12
10.3
(2069–2099)
794
ppm
921
ppm
0
10
20
30
Global productivity change (%)
CO
2
sensitivity
e
1
2
5
7
GC5
subset
6.1
5
8
9
10
GC6
subset
11.3
1
2
3
4
5
6
7
GC5
2.6
1
2
3
4
5
6
7
8
9
10
11
12
GC6
9.8
–20
0
20
40
Global productivity change (%)
Wheat
b
1
2
3
4
5
6
7
–5.6
2
3
5
6
7
8
9
10
11
12
–4.7
From 1 to 2 °C
cropland T change
–10
–5
0
Global productivity change (%)
d
1
2
3
4
5
6
7
–5.7
2
3
5
6
7
8
9
10
11
12
–4.4
From 2 to 3 °C
cropland T change
1
2
3
4
5
6
7
–13.6
2
3
5
6
7
8
9
10
11
12
–15.3
(2069
–
2099)
4.9 °C 5.2 °C
–40
–30
–20
–10
0
10
1
2
3
4
5
6
7
14.1
2
3
5
6
7
8
9
10
11
12
8.3
500
ppm
1
2
3
4
5
6
7
28.3
2
3
5
6
7
8
9
10
11
12
20.3
700
ppm
1
2
3
4
5
6
7
32.6
2
3
5
6
7
8
9
10
11
12
28.8
(2069–2099)
794
ppm
921
ppm
0
20
40
60
80
Global productivity change (%)
f
GC5 crop models
1 EPIC
2 GEPIC
3 IMAGE
4 LPJ-GUESS
5 LPJmL
6 PEGASUS
7 pDSSAT
GC6 crop models
1 ACEA
2 CROVER
3 CYGMA1p74
4 DSSAT-Pythia
5 EPIC-IIASA
6 ISAM
7 LandscapeDNDC
8 LPJmL
9 pDSSAT
10 PEPIC
11 PROMET
12 SIMPLACE-LINTUL5
Fig. 7 | Driver attribution of crop model responses. a,b, Projected end-of-century global productivity changes for maize (a) and wheat (b) under RCP8.5
(climate model mean) are shown for all members of the crop model ensembles GGCMI–CMIP5 (GC5) and GGCMI–CMIP5 (GC6), and for a subset of
crop models that participated in both rounds (note substantial differences between model versions). c,d, The sensitivity to global mean warming of the
full ensembles is shown for temperature (T) changes over maize (c) and wheat (d) cropland areas from 1 to 2 °C, from 2 to 3 °C, and for the total change
between 1983–2013 and 2069–2099. The warming sensitivity is based on [CO2] held constant at the 2015 level but includes changes in other climate
variables. e,f, The CO2 sensitivity for maize (e) and wheat (f) in GC5 and GC6 is shown at specific [CO2] and for the 2069–2099 mean concentrations.
Warming and CO2 sensitivities are calculated based on crop model responses over a 21 yr window centred on the year in which a certain temperature change
or [CO2] occurs in each climate model. Filled circles indicate the median crop model response, additionally highlighted by circled numbers underneath each
plot. Black bars show the IQR and individual models are indicated by numbers. Note that both c and d include two different legends. See Supplementary Fig.
7 for soybean and rice results. ACEA and DSSAT-Pythia have not submitted simulations for the constant [CO2] setting and are excluded from c–f.
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which are critical for crop modelling. Higher [CO2] in CMIP6 are
due to a revised trade-off between [CO2] and [CH4] resulting from
updated observations and assumptions in the MAGICC7.0 model42.
The GGCMI crop model ensemble has substantially changed
and consists of revised and new members. For example, LPJmL
contributed to GC5 and has since been fundamentally improved
with the addition of the nitrogen cycle43 and heat unit parameter-
ization44. In addition, input data and model harmonization have
been improved, including growing season harmonization based on
a new crop calendar developed for this study (Methods). A com-
prehensive attribution of crop response differences between GC5
and GC6 to changes in climate forcing, crop model selection and
sensitivities, and input data is not feasible. But standardized com-
parisons of changes in cropland warming and [CO2] indicate that,
for maize and wheat, changes in crop model ensemble sensitivities
dominate the response, and for soybean and rice, higher warm-
ing levels and warming sensitivity explain much of the differences
(Fig. 7 and Supplementary Fig. 7).
The new GCM bias adjustment, crop model advancement,
improved input data and a new crop yield bias correction serve to
substantially reduce the amount of variance induced by the crop
models compared to the climate models, rendering the new GC6
ensemble more balanced and consistent than GC5 despite a larger
ensemble size (12 crop models in GC6, 7 in GC5; Fig. 8). In a similar
vein, Müller et al.45 comprehensively compared crop yield uncer-
tainties under all CMIP5 and CMIP6 GCMs based on GGCMI crop
model emulators46, confirming that CMIP6 int ro duces a wider range
of yield responses with more pessimistic average impacts. In view of
improved model harmonization, inputs and GGCM versions and
performance, we consider GC6 more reliable than GC5—despite
ongoing discussions on the temperature sensitivity in CMIP6.
The uncertainty in the mechanisms and overall size of the effects
of CO2 fertilization manifested in farmers’ fields are reflected in a
wide range of CO2 sensitivities among the crop models contributing
to the GGCMI archive20. Average simulated CO2 fertilization effects
are generally in line with field experiments20,47,48, but the wide range
of this effect merits more rigorous model testing at the process
level, which in turn requires better reference data, especially at high
[CO2] levels. Moreover, elevated [CO2] boosts crop yield, but may
also affect the nutritional content of the crops49,50. Impacts related
to excess moisture, water resource limitations and new distributions
of pests and diseases may lead to additional regional biotic stresses
requiring follow-on analysis.
Cropping system adaptation can substantially reduce and even
outweigh adverse climate change impacts, for example, by switch-
ing to other crops51 or better-adapted varieties52. Integrated into
ISIMIP’s wider cross-sector activities, GGCMI will systematically
evaluate farming system adaptation and changes in yield variability
and extreme event impacts in subsequent efforts.
In conclusion, the new generation of AgMIP’s GGCMI provides
the most comprehensive ensemble of process-based future crop
yield projections under climate change to date. The degree to which
even high mitigation climate change scenarios are projected to push
global farming outside of its historical regimes suggests that cur-
rent food production systems will soon face fundamentally changed
risk profiles. Despite prevailing uncertainties, these ensemble pro-
jections spotlight the need for targeted food system adaptation and
risk management across the main producer regions in the coming
decades.
Methods
Time of emergence metric. We dene TCIE as the year in which the smoothed
climate change signal (‘signal’) exceeds the underlying internal variability and
model uncertainty (‘noise’). e signal is the multi-model ensemble mean crop
productivity change against the 1983–2013 reference period (smoothed with a
25 yr moving window). Noise is dened as the standard deviation of simulated
historical variability of crop productivity across all individual GCM × GGCM
combinations (1983–2013). TCIE is the rst year in which the signal emerges
from the noise, that is, when the signal-to-noise ratio becomes greater than 1.
Similar time of emergence denitions have been used in previous studies (for
example, refs. 12,14,53,54). Historical productivity time series are not detrended as we
hold all management factors constant throughout the simulations. To assess TCIE
uncertainties, we calculate TCIE also for each individual climate–crop model
realization as suggested by Hawkins and Sutton12, and we analyse the distribution
of the individual estimates (including mean, median, IQR and s.d.). We nd that
the multi-model ensemble mean TCIE usually occurs between the median and the
mean of individual TCIE estimates. For example, global-level maize production
under RCP8.5 shows a multi-model ensemble mean TCIE in year 2032, the
median of individual estimates occurs in year 2027 and the mean in year 2036.
Wheat shows the same pattern and results are qualitatively the same across the
dierent methods. To test the robustness of results in another way, we calculate the
0.31
0.69
0.03
0.97
95 119
42 3
Absolute
variance:
GGCMs
GCMs
0
0.5
1.0
GC6 GC5
Maize
0.12
0.88
0.08
0.92
165 96
24 9
GC6 GC5
Wheat
0.3
0.7
0.08
0.92
175 422
75 38
GC6 GC5
Soybean
0.34
0.66
0.02
0.98
63 300
32 5
0
0.5
1.0
GC6 GC5
Rice
Variance induced by GCMs
Variance induced by GGCMs
Fig. 8 | Variance decomposition of ensemble projections. Stacks show the fraction of total variance of midcentury crop production changes (2030–2070
mean) induced by the climate model ensemble (GCMs; yellow) and by the crop model ensemble (GGCMs; pink), for GGCMI–CMIP6 (GC6) and GGCMI–
CMIP5 (GC5) under RCP8.5, respectively. Variance fractions are normalized by the variance cross-term to be additive. The absolute variance introduced
by GGCMs and GCMs is indicated at the base of each stack. The GCM ensemble has five members in both cases, the GGCM ensemble has 12 members in
GC6 and seven members in GC5, which further highlights that the crop model response became more consistent in GC6 compared to the climate model
uncertainty.
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multi-model ensemble mean TCIE iteratively while removing one crop model at a
time. e s.d. of this distribution at global level is marginal; 1.5 yr for both maize
and wheat under RCP8.5. As a nal metric, we also compare the number of climate
and crop model combinations that show an emergence signal by the end of the
century. We calculate TCIE at global level, for dierent Koeppen–Geiger climate
zones, and for individual grid cells. Earlier TCIE is generally found for larger
spatial scales as the variance of internal variability decreases with averaging. For
additional discussions see, for example, refs. 11–13.
ISIMIP climate input datasets. GGCMI simulation efforts for CMIP6 impact
assessment are aligned with the ISIMIP5 activity in which GGCMI represents the
agriculture sector. Key modelling inputs such as information on climate, land
use, fertilizer input, soils, among others, are harmonized across various research
sectors. CMIP6 climate model outputs are centrally bias-adjusted and downscaled
by the ISIMIP framework to provide climate-input datasets on a daily regular
0.5° × 0.5° global grid. The bias-adjustment method employs a quantile mapping
approach and uses the observational W5E5 v.1.0 dataset55,56. This historical
dataset compares favourably with climatic forcing datasets that have been used
previously by AgMIP GGCMI57. The new quantile-mapping method adjusts
biases and preserves trends in all quantiles of the distribution of simulated daily
climate model outputs; for more details see Lange10. To lower the barrier for
participation in this study we provide climate input data for five CMIP6 GCMs:
GFDL-ESM4, IPSL-CM6A-LR, MPI-ESM1-2-HR, MRI-ESM2-0 and UKESM1-
0-LL (see Supplementary Table 1 for further details). The GCM selection is
based on data availability at the time of selection, performance in the historical
period, structural independence, process representation and equilibrium climate
sensitivity (ECS). The five GCMs are structurally independent in terms of their
ocean and atmosphere model components and overall they represent the range of
ECS across the full CMIP6 ensemble, including three models with below-average
ECS (GFDL-ESM4, MPI-ESM1-2-HR and MRI-ESM2-0) and two models with
above-average ECS (IPSL-CM6A-LR and UKESM1-0-LL)8. ECS and transient
climate response (TCR) for all GCMs used are listed in Supplementary Table 1. The
mean and s.d. of both ECS (mean, 3.7 °C; s.d., 1.1) and TCR (mean, 2.0 °C; s.d., 0.5)
across the five GCMs used here precisely match the mean and s.d. across the full
CMIP6 ensemble with 38 members (Supplementary Tables 1 and 2), much better
than in GC5, although the range of ECS in the CMIP6 ISIMIP models is larger
than in the CMIP5 ISIMIP models.
The daily weather variables at a 0.5° spatial resolution that are used as input
for the crop models include: daily mean, minimum, and maximum 2 m air
temperature (T, Tmin and Tmax, respectively (°C)), daily total precipitation (P (mm)),
and daily mean shortwave and longwave radiation (SR and LR (W m−2)).
GGCMI phase 3 crop modelling protocol. Bias-adjusted climate model
projections are used to drive transient crop model simulations, that is,
uninterrupted runs for the historical (1850–2014) and future (2015-2100) time
periods. Potential future trajectories are represented by SSP1 with RCP2.6 (here
SSP126) and SSP5 with RCP8.5 (here SSP585). Therefore, each crop model
performs 20 future simulation runs for each crop (5 GCM × 2 RCP × 2 [CO2]
settings). Note that in this study any socioeconomic forcing or adaptation effort
associated with the SSP storylines is held constant at the year 2015 level to isolate
the climate signal (that is, year 2015 land-use, fertilizer application, growing
seasons, crop cultivars, but also NO3 and NH4 deposition rates, are used in years
after 2015). To help isolate yield effects associated with the CO2 fertilization
effect, all crop model simulations are run for two separate assumptions:
(1) transient [CO2] in line with the respective RCP (‘default [CO2]’), and
(2) [CO2] concentration held constant at the 2015 level at 399.95 ppmv (‘constant
[CO2]’). Differences between the two [CO2] levels are not a measure of [CO2]
uncertainty, as there is no plausible climate change scenario without increasing
[CO2]22. Instead, this set-up is used to quantify the size of the CO2 fertilization
effect and for climate change factor attribution. All simulations are carried out
at the 0.5° global grid. In addition to the GCM forcing, we include historical
simulations based on the reanalysis product GSWP3-W5E5 v.1.055,56 for each
crop model and crop to better evaluate crop model performance against
observational data.
We focus on the four major global grain crops, that is, maize (Zea mays L.),
wheat (Triticum sp. L.), rice (Oryza sativa L.) and soybean (Glycine max L. Merr.).
Wheat is simulated as winter and spring wheat individually; grain and silage maize
are not distinguished. These four main crops contribute 90% of today’s global
caloric production of all cereals and soybean58.
All crops are simulated under both rainfed conditions and full irrigation
(where soil moisture is set to field capacity every day, without constraints on water
availability) in all grid cells—independent of the current cropland distribution. The
physical cropland extent is applied in postprocessing based on the MIRCA2000
(Monthly Irrigated and Rainfed Crop Areas around the year 2000) reference
dataset59 and irrigated fractions are adapted from Siebert et al.60; both are held
constant over time.
Soil moisture and soil temperature for various soil layers are calculated by most
crop models in a transient way, that is, without reinitializing at the beginning of
each year. All models use a classic phenological heat sum approach to determine
physiological stages between planting and maturity. Heat unit accumulation can
be modified by the sensitivity to day length (photoperiod) and for winter wheat is
stalled until vernalization requirements are reached, that is, the exposure to cold
temperatures before anthesis. Planting dates (Crop calendar and crop varieties) are
constant over time but the heat sum approach leads to different growing season
lengths depending on the daily temperature distribution in each growing season.
Except for rice, we simulate only one growing season per calendar year. The first
and last years of the transient runs are removed from crop model simulations due
to partially incomplete growing seasons. Simulations in grid cells with a growing
season length <50 d are removed, as are simulations resulting in premature harvest
(that is, accumulated heat units <80% of required heat units; this applies only to
those models that can provide such outputs).
The harmonization of crop models includes the required use of a central crop
calendar product (new development for this study, see below), fertilizer inputs and
soil information. Additional protocol characteristics are recommended but not
required, as not all models can address all features (see below).
Simulation protocols determine mineral and organic fertilizer (kgN ha−1)
inputs per crop and grid cell. Mineral fertilizer (ammonium nitrate; NH4NO3)
application is crop specific and is derived from the LUH2 product61, harmonized
by ISIMIP and GGCMI. Manure application inputs (C:N ratio, 14.5) are grid
cell specific, but constant across crops62. All other nutrients are considered
non-limiting. Fertilizer scheduling follows a simple assumption with 20% applied
at sowing and 80% applied when 25% of the heat units required to reach maturity
are accumulated. As for all other management aspects, fertilizer application is held
constant throughout the simulation period. Atmospheric nitrogen deposition is
considered, separating NHx and NOy, based on Tian et al.63 and held constant at the
2015 level.
Soil input is harmonized across crop models for the first time in GGCMI,
derived from the Harmonized World Soil Database (HWSD)64. While the same
HWSD dataset is used across ISIMIP sectors, in this study we employ a different
algorithm to aggregate the data to 0.5° in order to be cropland specific. The
pDSSAT model uses the Global Soil Data set for Earth system modelling (GSDE)65
and DSSAT-Pythia uses the Global High-Resolution Soil Profile Database for Crop
Modelling Applications66 due to difficulties in retrieving all soil parameters from
HWSD.
Finally, the following management aspects are encouraged to be harmonized
across crop models, but are not accounted for by all teams: tillage (two tillage
events, planting day and harvest day, 200 mm depth, full inversion), residues (70%
of above-ground residues removed), no pest and disease damage, no soil erosion
and no cover crops. Except for rice and wheat, which are simulated for two separate
growing seasons, we do not consider multicropping systems or crop rotations.
Inputs are provided for 18 different crops globally, but most crop models can only
simulate the major crops, which we focus on in this study. All socioeconomic and
farm management input data are publicly available via www.isimip.org.
Participating GGCMI crop models. Twelve process-based global crop models
participate in this study: ACEA, CROVER, CYGMA1p74, DSSAT-Pythia,
EPIC-IIASA, ISAM, LandscapeDNDC, LPJmL, pDSSAT, PEPIC, PROMET
and SIMPLACE-LINTUL5 (see Supplementary Table 3 for further details and
references). The full ensemble, therefore, consists of roughly 240 future crop model
simulations per crop plus one historical reference run for each crop and climate
model and one historical reanalysis run per crop model. Due to computational
constraints, ACEA has only run GCMs UKESM1-0-LL and MRI-ESM2-0 so far,
and DSSAT-Pythia has not yet run UKESM1-0-LL. ACEA and DSSAT-Pythia have
not yet finished simulations for the constant [CO2] setting.
All crop models are considered independent. LPJmL, pDSSAT, EPIC-IIASA,
PROMET and PEPIC have participated in previous GGCMI protocols7,67–69, but the
individual models and their parameterizations have substantially advanced. This
is especially the case for those models that participated in GC5 and GC6 (LPJmL,
pDSSAT, EPIC-based models) and a comprehensive account of changes in the
model code, parameters, inputs and the modelling protocol is beyond the scope
of this study. The main structural differences for LPJmL include the addition of
a nitrogen cycle, crop residue and tillage management, and manure application;
PEPIC and EPIC-IIASA in GC6 used the Penman–Monteith method to estimate
PET, GEPIC and EPIC in GC5 used the Hargreaves method and more generally
a substantially different model parameterization and spin-up protocol. In GC5
pDSSAT used DSSAT4.0 and different yield and cultivar calibrations. As opposed
to GC6, in GC5 fertilizer application rates and timing, planting and harvest dates,
soil information, irrigation and soil erosion were not harmonized across modelling
teams.
While the other models are new GGCMI ensemble members, they have been
thoroughly evaluated individually (see references in Supplementary Table 3). To
participate in this study, each model was required to go through a benchmark
performance evaluation for the historical period based on GSWP3-W5E5
reanalysis data (results available upon request). An overview of the degree to which
the GC6 crop models explain observed interannual yield variability is presented
in Supplementary Fig. 10. For the top five producer countries per crop, the
ensemble mean generally shows higher performance in terms of correlation and
root-mean-square error than the bulk of individual models. Generally, explained
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Articles
NATuRe FOOd
variability in individual models is satisfactory for most maize, wheat and soybean
main-producer countries. The metrics are lower for rice which also links to the
fact that the weather signal in (largely irrigated) rice is smaller than in other crops,
and the overall observed interannual variability in these rice producer countries
is smaller than for the other crops. Since management decisions (planting dates,
crop rotations and areas, fertilizer application, irrigation and so on) are held
constant over time, the crop models can only capture the interannual weather
signal in reported yields, which in general is much smaller in the tropics compared
to mid- to high-latitude regions. Additional in-depth GGCMI model comparison
and evaluation is presented by Müller et al.67. Overall, crop model performance
evaluation based on historical yield variability provides limited insight into the
models’ capability to project future yield impacts70.
Since GCM-based crop model simulations are difficult to compare with
observed interannual yield levels (for example, the 1988 drought does not
necessarily occur in 1988 in the GCM), we compare the overall range of simulated
and observed yield variability across the historical reference period. The standard
deviation of observed national yield variability is matched to a substantially higher
degree in GC6 (R = 79%, r.m.s.e. = 0.11) than in GC5 (R = 44%, r.m.s.e. = 0.17),
which is indicative of more realistic yield responses in GC6 (Supplementary Fig. 9).
These improvements are linked to a combination of factors, including different
internal variability in CMIP6, new GCM bias-adjustment method, improved
crop model ensemble, new crop yield bias-correction and improved crop model
inputs. The match with observed yield variability using GC6 simulations based
on GSWP3-W5E5 reanalysis data is only slightly better (R = 87%, r.m.s.e. = 0.09)
than with GCM-forced simulations, which highlights that the CMIP6 GCMs
do not introduce substantial errors in terms of historical variability
(Supplementary Fig. 9).
While the models generally reproduce yield declines in extreme years, adverse
impacts of excess water on crop growth due to lower aeration, waterlogging
and nitrogen leaching are generally underrepresented in current global crop
models32. As an exception, the crop model CYGMA accounts for effects due to
excess moisture stress71. ACEA, EPIC-based, and DSSAT-based crop models also
have processes related to waterlogging and root aeration but associated stresses
occur rarely and foremost on sensitive soils72. Many models do not handle
direct effects of extreme heat (for example, on leaf senescence, pollen sterility;
see Supplementary Table 3)3. Individual model responses to elevated [CO2] are
shown in Fig. 7 and Supplementary Fig. 8 and discussed in the main text. The
ISAM model requires sub-daily weather data and therefore uses CRU–National
Centers for Environmental Prediction (CRUNCEP) diurnal factors to convert
daily bias-adjusted climate model data to diurnal data. The PROMET model also
requires sub-daily weather data and uses ERA5-derived diurnal factors to convert
climate model data to diurnal inputs; it also uses WFDE5 instead of GSWP3-W5E5
for reanalysis simulations.
All models use spin-up simulations of various lengths to reach soil and carbon
pool equilibrium. EPIC-IIASA uses dynamic soil handling during spin-up to
generate soil attributes. Subsequently these are used as an input in the actual
simulations with static soil handling, that is annual reinitialization of all soil
attributes (including soil organic matter fractions and soil texture among others)
except mineral nutrient pools, temperature and soil moisture. The models do not
account for human management intervention other than fertilizer application,
irrigation, seed selection, growing periods and basic field management such as
tillage and residue removal.
All models follow a phenology calibration with respect to grid cell-specific
cultivar parameterizations (that is, phenological heat units) based on the respective
crop calendar and weather forcing (Supplementary Table 3). Yield calibration
is not harmonized across crop models and each team follows their individual
protocol, including grid cell-specific calibration against SPAM73 reference yields
(for example, pDSSAT), various site-specific efforts based on field experiments
(for example, ISAM) and calibrations with national FAO58 statistics (for example,
PEPIC).
Crop yield bias correction. Crop production is calculated as yield times harvested
area of the respective crop. We omit grid cells with <10 ha cropland area for each
crop. To compare results across crop models, but also to represent realistic overall
crop production estimates and spatial pattern, we calculate fractional yield changes
from each individual crop model simulation between the historical reference
period (1983–2013) and the respective future projection and multiply these with
a spatially explicit (0.5°) observational yield reference dataset (see Supplementary
Fig. 14 in ref. 74). SPAM (Spatial Production Allocation Model)73 is used as the
main reference yield data as it separates rainfed and irrigated systems. Grid cells
with missing SPAM yield data but with >10 ha MIRCA2000 harvested area are
gap-filled with Ray et al.75 yield data; both SPAM and Ray et al. represent the time
period 2003 to 2007.
Crop calendar and crop varieties. We provide planting and maturity dates for
each crop in each grid cell, separate for rainfed and irrigated systems, based on a
new observational crop calendar product. See Supplementary Information section
GGCMI crop calendar and Supplementary Figs. 11-14 for details. Growing season
inputs are static over time throughout the historical and future time period to
avoid confounding trends. Each model calculated required reference heat units to
reach physiological maturity for each crop in each grid cell by averaging annual
heat sums over all growing seasons between 1979 and 2010.
Map projection and smoothing. Global maps are based on the Robinson
projection and grid-level data are smoothed to improve clarity and visual
appearance. Smoothing is done by first resampling the raw data to five times finer
resolution, followed by a 5 × 5 grid cell focal mean window aggregation. Map
smoothing is done for visualization purposes only and all analyses are based on the
raw data.
Reporting summary. Further information on research design is available in the
Nature Research Reporting Summary linked to this article.
Data availability
All data needed to evaluate the conclusions in the paper are present in the paper
and/or the Supplementary Information. Model inputs are publicly available via
https://www.isimip.org/ or from the corresponding author. The GGCMI crop
calendar is accessible at https://doi.org/10.5281/zenodo.5062513; fertilizer inputs
are available at https://doi.org/10.5281/zenodo.4954582. Crop model simulations
will be made publicly available under the CC0 license pending publication.
Code availability
Details and code for each crop model can be requested from the contact persons
listed in Supplementary Table 3. Code developed for data analysis and figures is
available from the corresponding author upon request.
Received: 5 November 2020; Accepted: 29 September 2021;
Published: xx xx xxxx
References
1. Mbow, C. et al. in Special Report on Climate Change and Land (eds Shukla, P.
R. et al.) 437–550 (IPCC, 2019).
2. Asseng, S. et al. Uncertainty in simulating wheat yields under climate change.
Nat. Clim. Change 3, 827–832 (2013).
3. Wang, E. et al. e uncertainty of crop yield projections is reduced by
improved temperature response functions. Nat. Plants 3, 17102 (2017).
4. Rosenzweig, C. et al. e agricultural model intercomparison and improvement
project (AgMIP): protocols and pilot studies. Agric. For. Meteorol. 170, 166–182
(2013).
5. e Inter-Sectoral Impact Model Intercomparison Project (ISIMIP, 2021);
https://www.isimip.org/
6. Eyring, V. et al. Overview of the Coupled Model Intercomparison Project
phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev. 9,
1937–1958 (2016).
7. Rosenzweig, C. et al. Assessing agricultural risks of climate change in the 21st
century in a Global Gridded Crop Model intercomparison. Proc. Natl Acad.
Sci. USA 111, 3268–3273 (2014).
8. Meehl, G. A. et al. Context for interpreting equilibrium climate sensitivity
and transient climate response from the CMIP6 Earth system models. Sci.
Adv. 6, eaba1981 (2020).
9. O’Neill, B. C. et al. e Scenario Model Intercomparison Project
(ScenarioMIP) for CMIP6. Geosci. Model Dev. 9, 3461–3482 (2016).
10. Lange, S. Trend-preserving bias adjustment and statistical downscaling with
ISIMIP3BASD (v1.0). Geosci. Model Dev. 12, 3055–3070 (2019).
11. Hawkins, E. et al. Observed emergence of the climate change signal: from the
familiar to the unknown. Geophys. Res. Lett. 47, e2019GL086259 (2020).
12. Hawkins, E. & Sutton, R. Time of emergence of climate signals. Geophys. Res.
Lett. 39, L01702 (2012).
13. Kirtman, B. et al. in Climate Change 2013: e Physical Science Basis
(eds Stocker, T. F. et al.) 953–1028 (IPCC, Cambridge Univ. Press, 2013).
14. Rojas, M., Lambert, F., Ramirez-Villegas, J. & Challinor, A. J. Emergence of
robust precipitation changes across crop production areas in the 21st century.
Proc. Natl Acad. Sci. USA 116, 6673–6678 (2019).
15. Raymond, C., Matthews, T. & Horton, R. M. e emergence of heat and
humidity too severe for human tolerance. Sci. Adv. 6, eaaw1838 (2020).
16. Park, C. E. et al. Keeping global warming within 1.5 °C constrains emergence
of aridication. Nat. Clim. Change https://doi.org/10.1038/s41558-017-0034-4
(2018).
17. Liu, B. et al. Similar estimates of temperature impacts on global wheat yield
by three independent methods. Nat. Clim. Change 6, 1130–1136 (2016).
18. Zhao, C. et al. Temperature increase reduces global yields of major crops in
four independent estimates. Proc. Natl Acad. Sci. USA https://doi.org/10.1073/
pnas.1701762114 (2017).
19. Asseng, S. et al. Rising temperatures reduce global wheat production.
Nat. Clim. Change 5, 143–147 (2014).
20. Toreti, A. et al. Narrowing uncertainties in the eects of elevated CO2 on crops.
Nat. Food 1, 775–782 (2020).
NATURE FOOD | www.nature.com/natfood

Articles NATuRe FOOd
21. Ahmed, M. et al. Novel multimodel ensemble approach to evaluate the sole
eect of elevated CO2 on winter wheat productivity. Sci. Rep. 9, 7813 (2019).
22. Leakey, A. D. B., Bishop, K. A. & Ainsworth, E. A. A multi-biome gap in
understanding of crop and ecosystem responses to elevated CO2. Curr. Opin.
Plant Biol. https://doi.org/10.1016/j.pbi.2012.01.009 (2012).
23. Kimball, B. A. Crop responses to elevated CO2 and interactions with H2O, N,
and temperature. Curr. Opin. Plant Biol. https://doi.org/10.1016/j.pbi.2016.
03.006 (2016).
24. Zabel, F. et al. Large potential for crop production adaptation depends on
available future varieties. Glob. Change Biol. https://doi.org/10.1111/gcb.15649
(2021).
25. Ray, D. K. et al. Climate change has likely already aected global food
production. PLoS ONE 14, e0217148 (2019).
26. Lobell, D. B., Schlenker, W. & Costa-Roberts, J. Climate trends and global
crop production since 1980. Science 333, 616–620 (2011).
27. Ahmad, S. et al. Climate warming and management impact on the change of
phenology of the rice–wheat cropping system in Punjab, Pakistan. Field Crops
Res. 230, 46–61 (2019).
28. Porter, J. R. et al. in Climate Change 2014: Impacts, Adaptation, and Vulnerability
(eds Field, C. B. et al.) 485–533 (IPCC, Cambridge Univ. Press, 2014).
29. Levis, S., Badger, A., Drewniak, B., Nevison, C. & Ren, X. CLMcrop yields
and water requirements: avoided impacts by choosing RCP 4.5 over 8.5.
Clim. Change 146, 501–515 (2018).
30. Falconnier, G. N. et al. Modelling climate change impacts on maize yields
under low nitrogen input conditions in sub‐Saharan Africa. Glob. Change
Biol. 26, 5942–5964 (2020).
31. O’Neill, B. C. et al. IPCC reasons for concern regarding climate change risks.
Nat. Clim. Change 7, 28–37 (2017).
32. Li, Y., Guan, K., Schnitkey, G. D., DeLucia, E. & Peng, B. Excessive rainfall
leads to maize yield loss of a comparable magnitude to extreme drought in
the United States. Glob. Change Biol. 25, 2325–2337 (2019).
33. Zhu, P., Zhuang, Q., Archontoulis, S. V., Bernacchi, C. & Müller, C.
Dissecting the nonlinear response of maize yield to high temperature stress
with model-data integration. Glob. Change Biol. 25, 2470–2484 (2019).
34. Iizumi, T. et al. Responses of crop yield growth to global temperature and
socioeconomic changes. Sci. Rep. 7, 7800 (2017).
35. Sherwood, S. C. et al. An assessment of Earth’s climate sensitivity using
multiple lines of evidence. Rev. Geophys. 58, e2019RG000678 (2020).
36. Nijsse, F. J. M. M., Cox, P. M. & Williamson, M. S. Emergent constraints on
transient climate response (TCR) and equilibrium climate sensitivity (ECS)
from historical warming in CMIP5 and CMIP6 models. Earth Syst. Dyn. 11,
737–750 (2020).
37. Zelinka, M. D. et al. Causes of higher climate sensitivity in CMIP6 models.
Geophys. Res. Lett. 47, e2019GL085782 (2020).
38. Tokarska, K. B. et al. Past warming trend constrains future warming in
CMIP6 models. Sci. Adv. 6, eaaz9549 (2020).
39. Fan, X., Miao, C., Duan, Q., Shen, C. & Wu, Y. e performance of CMIP6
versus CMIP5 in simulating temperature extremes over the global land
surface. J. Geophys. Res. Atmos. 125, e2020JD033031 (2020).
40. Xin, X., Wu, T., Zhang, J., Yao, J. & Fang, Y. Comparison of CMIP6 and
CMIP5 simulations of precipitation in China and the East Asian summer
monsoon. Int. J. Climatol. 40, 6423–6440 (2020).
41. Ridder, N. N., Pitman, A. J. & Ukkola, A. M. Do CMIP6 climate models
simulate global or regional compound events skilfully? Geophys. Res. Lett.
https://doi.org/10.1029/2020gl091152 (2020).
42. Meinshausen, M. et al. e shared socio-economic pathway (SSP) greenhouse
gas concentrations and their extensions to 2500. Geosci. Model Dev. 13,
3571–3605 (2020).
43. Von Bloh, W. et al. Implementing the nitrogen cycle into the dynamic global
vegetation, hydrology, and crop growth model LPJmL (version 5.0). Geosci.
Model Dev. 11, 2789–2812 (2018).
44. Jägermeyr, J. & Frieler, K. Spatial variations in crop growing seasons pivotal
to reproduce global uctuations in maize and wheat yields. Sci. Adv. 4,
eaat4517 (2018).
45. Müller, C. et al. Exploring uncertainties in global crop yield projections in a
large ensemble of crop models and CMIP5 and CMIP6 climate scenarios.
Environ. Res. Lett. 16, 034040 (2021).
46. Franke, J. A. et al. e GGCMI Phase 2 emulators: Global Gridded Crop
Model responses to changes in CO2, temperature, water, and nitrogen
(version 1.0). Geosci. Model Dev. 13, 2315–2336 (2020).
47. Allen, L. H. et al. Fluctuations of CO2 in free-air CO2 enrichment (FACE)
depress plant photosynthesis, growth, and yield. Agric. For. Meteorol. 284,
107899 (2020).
48. Durand, J. L. et al. How accurately do maize crop models simulate the
interactions of atmospheric CO2 concentration levels with limited water supply
on water use and yield? Eur. J. Agron. https://doi.org/10.1016/j.eja.2017.01.002
(2018).
49. Myers, S. S. et al. Increasing CO2 threatens human nutrition. Nature 510,
139–142 (2014).
50. Zhu, C. et al. Carbon dioxide (CO2) levels this century will alter the protein,
micronutrients, and vitamin content of rice grains with potential health
consequences for the poorest rice-dependent countries. Sci. Adv. 4, eaaq1012
(2018).
51. Rising, J. & Devineni, N. Crop switching reduces agricultural losses from
climate change in the United States by half under RCP 8.5. Nat. Commun. 11,
4991 (2020).
52. Asseng, S. et al. Climate Change impact and adaptation for wheat protein.
Glob. Change Biol. 25, 155–173 (2019).
53. Hawkins, E. & Sutton, R. e potential to narrow uncertainty in regional
climate predictions. Bull. Am. Meteorol. Soc. 90, 1095–1107 (2009).
54. Giorgi, F. & Bi, X. Time of emergence (TOE) of GHG-forced precipitation
change hot-spots. Geophys. Res. Lett. 36, L06709 (2009).
55. Lange, S. WFDE5 Over Land Merged with ERA5 Over the Ocean (W5E5).
V. 1.0 (GFZ Data Services, 2019); https://doi.org/10.5880/pik.2019.023
56. Cucchi, M. et al. WFDE5: bias-adjusted ERA5 reanalysis data for impact
studies. Earth Syst. Sci. Data 12, 2097–2120 (2020).
57. Ruane, A. C. et al. Strong regional inuence of climatic forcing datasets on
global crop model ensembles. Agric. For. Meteorol. 300, 108313 (2021).
58. FAOSTAT (United Nation’s Food and Agricultural Organization, 2019);
http://www.fao.org/faostat/
59. Portmann, F. T., Siebert, S. & Döll, P. MIRCA2000—Global monthly irrigated
and rainfed crop areas around the year 2000: a new high-resolution data set
for agricultural and hydrological modeling. Global Biogeochem. Cycles 24,
GB1011 (2010).
60. Siebert, S. et al. A global data set of the extent of irrigated land from 1900 to
2005. Hydrol. Earth Syst. Sci. 19, 1521–1545 (2015).
61. Heinke, J., Müller, C., Mueller, N. D. & Jägermeyr, J. N application rates from
mineral fertiliser and manure Zenodo https://doi.org/10.5281/zenodo.4954582
(2021).
62. Zhang, B. et al. Global manure nitrogen production and application in
cropland during 1860–2014: a 5 arcmin gridded global dataset for Earth
system modeling. Earth Syst. Sci. Data 9, 667–678 (2017).
63. Tian, H. et al. e global N2O model intercomparison project. Bull. Am.
Meteorol. Soc. 99, 1231–1251 (2018).
64. Nachtergaele, F. et al. Harmonized World Soil Database (version 1.2) (FAO
and IIASA, 2012).
65. Shangguan, W., Dai, Y., Duan, Q., Liu, B. & Yuan, H. A global soil data set
for Earth system modeling. J. Adv. Model. Earth Syst. 6, 249–263 (2014).
66. Hengl, T. et al. SoilGrids1km—global soil information based on automated
mapping. PLoS ONE 9, e114788 (2014).
67. Müller, C. et al. Global Gridded Crop Model evaluation: benchmarking, skills,
deciencies and implications. Geosci. Model Dev. 10, 1403–1422 (2017).
68. Franke, J. A. et al. e GGCMI Phase 2 experiment: Global Gridded Crop
Model simulations under uniform changes in CO2, temperature, water, and
nitrogen levels (protocol version 1.0). Geosci. Model Dev. 13, 2315–2336 (2020).
69. Elliott, J. et al. e Global Gridded Crop Model Intercomparison: data and
modeling protocols for Phase 1 (v1.0). Geosci. Model Dev. 8, 261–277 (2015).
70. Ruane, A. C. et al. Multi-wheat-model ensemble responses to interannual
climate variability. Environ. Model. Sow. 81, 86–101 (2016).
71. Wang, R., Bowling, L. C. & Cherkauer, K. A. Estimation of the eects of
climate variability on crop yield in the Midwest USA. Agric. For. Meteorol.
216, 141–156 (2016).
72. Folberth, C., Gaiser, T., Abbaspour, K. C., Schulin, R. & Yang, H.
Regionalization of a large-scale crop growth model for sub-Saharan Africa:
model setup, evaluation, and estimation of maize yields. Agric. Ecosyst.
Environ. 151, 21–33 (2012).
73. Global Spatially-Disaggregated Crop Production Statistics Data for 2010 Version
1.0. Harvard Dataverse, V1 (International Food Policy Research Institute,
2019); https://doi.org/10.7910/DVN/PRFF8V
74. Jägermeyr, J. et al. A regional nuclear conict would compromise global food
security. Proc. Natl Acad. Sci. USA 117, 7071–7081 (2020).
75. Ray, D. K., Ramankutty, N., Mueller, N. D., West, P. C. & Foley, J. A. Recent
patterns of crop yield growth and stagnation. Nat. Commun. 3, 1293 (2012).
Acknowledgements
J.J., A.C.R., C.R. and M.P. were supported by NASA GISS Climate Impacts Group
and Indicators for the National Climate Assessment funding from the NASA Earth
Sciences Division. J.J. and J.R.G. received support from the Open Philanthropy Project
and thank the University of Chicago Research Computing Center for supercomputer
allocations to run the pDSSAT model. Ludwig-Maximilians-Universität München
thanks the Leibniz Supercomputing Center of the Bavarian Academy of Sciences and
Humanities for providing capacity on the Cloud computing infrastructure to run the
PROMET model. J.M.S. was supported by the German Federal Ministry of Education
and Research (grant number 031B0230A: BioNex—The Future of the Biomass Nexus).
O.M. and J.F.S. were supported by funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme (Earth@
lternatives project, grant agreement number 834716). J.A.F. and H.S. were supported
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Articles
NATuRe FOOd
by the NSF NRT programme (grant number DGE-1735359). J.A.F was supported
by the NSF Graduate Research Fellowship Program (grant number DGE-1746045).
RDCEP is funded by NSF through the Decision Making Under Uncertainty programme
(grant number SES-1463644). T.I. was partly supported by the Environment Research
and Technology Development Fund (2-2005) of the Environmental Restoration and
Conservation Agency and Grant-in-Aid for Scientific Research B (18H02317) of the
Japan Society for the Promotion of Science. A.K.J and T.-S.L. were supported by the US
National Science Foundation (NSF - 831361857). M.O. was supported by the Climate
Change Adaptation Research Program of NIES, Japan. S.L. was supported by the German
Federal Office for Agriculture and Food (BLE) in the framework of OptAKlim (grant
number 281B203316). S.S.R. acknowledges funding from the German Federal Ministry
of Education and Research (BMBF) via the ISIpedia project.
Author contributions
J.J. and C.M. conceived the paper and coordinated GGCMI. J.J., C.M. and S.S.R.
developed the simulation protocol. A.C.R. and C.R. coordinated AgMIP integration.
C.M., J.J., J.B., O.C., B.F., C.F., K.F., G.H., T.I., A.K.J., N.K., T.-S.L., W.L., S.M., M.O., O.M.,
C.P., S.S.R., J.M.S., J.F.S., R.S., A.S., T.S. and F.Z. conducted crop model simulations.
S.L. prepared climate data inputs. J.J. conducted the data analysis, and developed the
manuscript and figures. All coauthors supported manuscript writing.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s43016-021-00400-y.
Correspondence and requests for materials should be addressed to Jonas Jägermeyr.
Peer review information Nature Food thanks Bin Peng and the other, anonymous,
reviewer(s) for their contribution to the peer review of this work.
Reprints and permissions information is available at www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
© The Author(s), under exclusive licence to Springer Nature Limited 2021
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nature research | reporting summary April 2020
Corresponding author(s): Jonas Jägermeyr
Last updated by author(s): 9/3014/21
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Data collection Crop models contributing data to the study are written in various languages including C, Python, Fortran, etc. Details and code for each model
can be requested from the respective contact person listed in the Supplement.
Data analysis All data analyses and the preparation of figures are done using R version 3.6.2 (Copyright (C) 2019 The R Foundation for Statistical Computing,
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nature research | reporting summary April 2020
Field-specific reporting
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Ecological, evolutionary & environmental sciences study design
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Study description Five climate models provide inputs for an ensemble of harmonized global crop models to simulate potential responses of crop
productivity to climate change.
Research sample Five global climate models from the Coupled Model Intercomparison Project (CMIP) phase 6 are bias-adjusted and downscaled by
ISIMIP. The ensemble of GGCMI global process-based crop models samples a range of state-of-the-art dynamic modeling approaches.
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