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Nature Geoscience
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1159
nature geoscience
https://doi.org/10.1038/s41561-023-01302-3
Article
Global crop production increase by soil
organic carbon
Yuqing Ma
1,2,7
, Dominic Woolf
2,3,4,7
, Mingsheng Fan
1
, Lei Qiao
5
,
Rong Li
6
& Johannes Lehmann
2,3,4
Soil organic carbon sequestration has been promoted to combat climate
change while improving soil fertility. However, its quantitative contribution
to crop productivity has proven elusive. Using data from 13,662 controlled
field trials with 66,593 treatments across a broad range of soils, climates and
management practices, we here show that yields increase with increased
soil organic carbon, until no further increase (p < 0.05) occurs above mean
optimum soil organic carbon of 43.2–43.9 g kg
−1
for maize, 12.7–13.4 g kg
−1
for wheat and 31.2–32.4 g kg
−1
for rice. Sequestering soil organic carbon is
one-fifth as effective (that is, 80% less) as nitrogen fertilization for improving
crop yield where soil management is optimized. By increasing soil organic
carbon beyond current technology to optimum levels, global production
of the three most important staple crops increases by 4.3% (sufficient to
provide calories for 640 million people). However, currently available
management practices would increase crop production by only 0.7% once
other production constraints have already been addressed. Therefore, yield
improvements under currently available technologies are unlikely to drive
adoption of soil organic carbon sequestration globally, except in hot-spot
regions where crop production benefits most, or unless novel practices that
allow greater soil organic carbon sequestration beyond current limitations
can further increase yields cost-effectively.
With global greenhouse gas (GHG) emissions still rising
1
, the window of
opportunity to avoid dangerous climate change through emissions reduc-
tion alone has passed
2
. Carbon dioxide removal from the atmosphere is
therefore also expected to be required
2
, within a broader portfolio of
mitigation measures that must simultaneously reduce emissions from
energy and industry
3
. Sequestering photosynthetically fixed organic
carbon in soil organic carbon (SOC) has been suggested as a potentially
low-cost and highly scalable approach to carbon dioxide removal
4
. At a
global scale, SOC contains about three times more carbon than atmos-
pheric carbon dioxide (CO
2
)
5
. Therefore, a small fractional increase in SOC
stocks could have a substantial impact on CO
2
concentrations
6
. With most
of the potential to increase SOC located on agricultural soils, long-term
adoption of SOC sequestration practices depends on buy-in from farm-
ers
6
,
7
. The promise of improved soil health leading to higher crop yields
has been suggested as the most important driver of adoption because
this would support both farm productivity and food security objectives
7
.
However, although it has long been hypothesized that higher
SOC can increase crop yields
8
,
9
, the causal impact of SOC on yield at a
regional or global scale has still not been unequivocally demonstrated
or quantified
10
. The causal impact of SOC on crop yield at large scales
Received: 17 April 2023
Accepted: 21 September 2023
Published online: 30 October 2023
Check for updates
1
State Key Laboratory of Nutrient Use and Management, College of Resources and Environmental Sciences, China Agricultural University, Beijing, China.
2
Soil and Crop Sciences, School of Integrative Plant Science, Cornell University, Ithaca, NY, USA.
3
Cornell Institute for Digital Agriculture (CIDA), Cornell
University, Ithaca, NY, USA.
4
Cornell Atkinson Center for Sustainability, Cornell University, Ithaca, NY, USA.
5
Key Laboratory of Arable Land Quality Monitoring
and Evaluation, Ministry of Agriculture and Rural Affairs, Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural
Sciences (CAAS), Beijing, China.
6
Cultivated Land Quality Monitoring and Protection Center, Ministry of Agriculture and Rural Affairs of the People’s
Republic of China, Beijing, China.
7
These authors contributed equally: Yuqing Ma, Dominic Woolf. e-mail:
fanms@cau.edu.cn
;
CL273@cornell.edu
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We addressed the above issues by analysing data from a pro-
gramme of tens of thousands of controlled field trials with maize
(number of field sites, N
site
= 4,906), wheat (N
site
= 4,448) and rice
(N
site
= 4,308), distributed across all major cropping regions of China
covering a broad range of climate zones and soil types (Extended Data
Fig. 1). Yield variation due to differences in management between
farms was minimized by conducting recommended best management
practices based on consistent on-site guidance and recommendations
from local agricultural experts and trained extension personnel for key
operations including weed, pest and disease control, cultivar, tillage,
sowing date, seeding density, supplementary irrigation and harvest
(Methods; description of field trials). Each field trial site had treatments
with 0, 0.5, 1.0 and 1.5 times the optimum nitrogen (N) applications,
combined with optimum phosphorus (P
2
O
5
) and potassium (K
2
O) and
a treatment with no fertilization. Climatic, edaphic, management and
topographic covariates of SOC and yield were provided as explanatory
variables for machine learning (both random forest and causal forest)
models, thereby accounting for the most important confounding
variables. Thus, the partial dependence of yield on SOC was quantified
independently of such confounding variables and with variability in
farm management controlled for (Methods; causal effect of SOC on
crop yield). Field trials were almost ubiquitously conducted over a sin-
gle season by researchers at on-farm locations, ensuring that observed
has been difficult to quantify for several reasons. First, there are many
confounding factors that affect both yield and SOC that have been
difficult to fully control or account for. These include, for example,
climate, fertilization, land management, hydrology and soil proper-
ties. Second, the causal relationship between yield and SOC operates
in both directions, making the causal impact of SOC on yield difficult
to differentiate. For example, in addition to the expectation that SOC
may increase yields, the opposite is also true: that higher yields corre-
late with greater organic matter inputs to the soil (from crop residues
and belowground production), which in turn leads to higher SOC.
Third, many surveys omit metadata on important determinants of
yield, particularly in terms of farm management techniques such as
tillage, weed control, pest control, irrigation, varietal selection and
so on, which contribute to the large unexplained variance and a low
signal-to-noise ratio in SOC yield relationships
8
. These three types
of barrier have led to up to a half-century of ongoing debate about
the quantitative importance of SOC in determining crop yields
8
. The
resultant difficulty in quantitatively evaluating the SOC effect on yield
has been a limiting factor in understanding the potential importance
of SOC sequestration to global crop productivity, which therefore
introduces large uncertainty into cost–benefit estimations and discour-
ages risk-averse policymakers and farmers from adopting sustainable
agricultural practices to sequester SOC
7
.
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
−1.0
0
1.0
2.0
3.0
4.0
5.0
6.0
0
10
20
30
40
50
60
SOC (g kg
−1
)
SOC (g kg
−1
)
SOC (g kg
−1
)
SOC (g kg
−1
)
Normalized predicted yield
Normalized predicted SOC yield gap (%)
4,900
5,000
5,100
5,200
5,300
5,400
−120
−60
0
60
120
180
240
300
360
0
5
10
15
20
25
30
Mean predicted SOC yield gap (kg ha
−1
)
Mean predicted SOC yield gap (kg ha
−1
)
7,300
7,400
7,500
7,600
7,700
7,800
−70
0
70
140
210
280
350
420
0
10
20
30
40
50
Mean predicted yield (kg ha
−1
)
Mean predicted yield (kg ha
−1
)
Mean predicted yield (kg ha
−1
)
Mean predicted SOC yield gap (kg ha
−1
)
6,350
6,450
6,550
6,650
6,750
6,850
−120
−60
0
60
120
180
240
300
360
0
10
20
30
40
50
60
Three crops combined
Maize
Wheat
Rice
Mean predicted maximum SOC
yield gap = 334–349 kg ha
–1
Optimum SOC
= 43.2–43.9 g kg
–1
Mean predicted maximum SOC
yield gap = 206–216 kg ha
–1
Optimum SOC
= 12.7–13.4 g kg
–1
Mean predicted maximum SOC
yield gap = 174–180 kg ha
–1
Optimum SOC
= 31.2–32.4 g kg
–1
Mean partial dependence of crop yield on SOC
The effect of SOC on SOC yield gap
a
c
d
b
Fig. 1 | Causal effect of SOC on crop yield and SOC yield gap. a, Three crops
combined.
b, Maize. c, Wheat. d, Rice. The ribbons represent 95% confidence
intervals. Optimum SOC is the SOC level beyond which the rate of yield increase
is not different from zero (p < 0.05). The significance of the yield increase was
estimated by two-sided t tests. The SOC yield gap is defined as the amount by
which yield could be increased by increasing SOC. For three crops combined,
yield was normalized as the ratio of on-farm measured yield to predicted
minimum yield for each crop, and SOC yield gap was normalized relative to
minimum yield, expressed as percentage change. The grey bars at the bottom of
each panel represent the distribution of SOC.
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variations in yield do not affect SOC whereas SOC can affect yield, thus
providing confidence that the partial dependence of crop yield on SOC
represents a causal effect that is distinct from a spurious correlation.
The causal effects of SOC and fertilizer on yield
On average, crop yields increased with SOC and levelled off as SOC
approaches a threshold level, confirming the existence of an optimum
SOC concentration beyond which little to no additional yield gains
accrued from further increases in SOC
8
,
11
(Fig.
1
). We define the SOC
yield gap as the difference between yield at the optimum SOC and
yield at current SOC (SOC yield gaps were defined as zero when current
SOC is above the optimum). The optimum SOC (in grams of organic
carbon per kilogram of soil) was estimated as the SOC concentration
beyond which the rate of increase in yield is not different from zero
(p < 0.05). The mean optimum SOC was different for the three crops,
namely 43.2–43.9 g kg
−1
(95% confidence interval (C.I.)) for maize,
12.7–13.4 g kg
−1
for wheat and 31.2–32.4 g kg
−1
for rice (Fig.
1
). These
results expand previous studies that suggested 20 g kg
−1
as a universal
average optimum SOC
8
,
12
, underscoring the need to adopt specific
optimum SOC levels for each cropping system, which also varies with
soil and climate (Extended Data Fig. 2). Effect sizes estimated by the ran-
dom forest model were in the same range as those estimated by causal
forest, supporting that the random forest-based results are unbiased by
heterogeneous treatment effects (Supplementary Text 1 and Table 1).
Nitrogen fertilizer input was, not surprisingly, the best predictor
of yield for all three studied crops combined. Importantly, however, we
found that SOC contributes to yield, with a relative prediction impor-
tance of around 3%, which is, on average, one-fifth that of nitrogen ferti-
lization. The relative importance of nitrogen fertilization as a predictor
of maize yield was half (8%) compared to wheat (16%) and rice (19%)
(Fig.
2
). This could be attributed to the lower nitrogen fertilizer use effi-
ciency of maize compared with wheat and rice
13
. Previous studies have
suggested that mineral fertilizers compensate to sustain yield even at
low SOC levels
14
. We found that even though addition of more nitrogen
AWC
Soil type
Slope
Bulk density
Clay
Crop variety
Sand
Silt
Cropping frequency
AP
pH
AK
SOC
PK fertilization
PRE
Tmin
Tmax
PET
Aridity index
RAD
GDD
Growing days
Rotational systems
N fertilization
0
4
8
12
16
20
Relative importance (%)
AWC
Clay
Bulk density
Sand
Silt
Slope
AK
Cropping frequency
pH
SOC
GDD
Tmax
Crop variety
Irrigation
PK fertilization
Previous crop type
AP
PRE
RAD
Growing days
Tmin
Rotational systems
PET
Soil type
Aridity index
N fertilization
0
3
6
9
12
15
18
Relative importance (%)
AWC
Crop variety
Bulk density
Clay
Sand
Silt
Cropping frequency
Irrigation
AK
Slope
Rotational systems
PK fertilization
Previous crop type
AP
pH
SOC
GDD
Growing days
PRE
Tmax
Soil type
N fertilization
PET
RAD
Aridity index
Tmin
0
2
4
6
8
10
12
Relative importance (%)
AWC
Bulk density
Clay
Sand
Cropping frequency
Silt
Slope
AK
Crop variety
PK fertilization
pH
SOC
AP
Irrigation
PRE
PET
Soil type
GDD
Rotational systems
Previous crop type
Tmax
Growing days
RAD
Tmin
Aridity index
N fertilization
0
2
4
6
8
10
12
Relative importance (%)
b
d
a
c
Three crops combined
Driver
Driver
Driver
Driver
Maize
Wheat
Rice
Fig. 2 | Drivers of crop yield. a, Three crops combined. b, Maize. c, Wheat.
d, Rice. Bar charts indicate the relative importance (by permutation method;
Methods) of variables as predictors of the crop yield. NPK fertilization = nitrogen,
phosphorus and potassium fertilizer rate; PET = potential evapotranspiration;
GDD, RAD, PRE, Tmax and Tmin = growing degree days, radiation, precipitation,
maximum mean temperature and minimum mean temperature during the
growing days; AP = plant-available phosphorus; AK = plant-available potassium;
AWC = available water capacity; SOC is highlighted in red for ease of reading.
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fertilizer (up to optimum rates) always contributed to higher crop
productivity, crop productivity simultaneously increased with SOC
up to the SOC optima under any nitrogen input rate (Extended Data
Fig. 3 and Supplementary Text 2). This suggests that SOC increases may
serve as a complementary strategy to nitrogen fertilizer amendments.
Feature importance for prediction of the SOC
yield gap
The predicted maximum SOC yield gap (that is, difference between
yields at the optimum SOC and the lowest SOC per climate zone) was
generally higher in dry compared to moist climates. With maize, for
example, the yield gap was fourfold greater in warm–temperate–
dry compared to warm–temperate–moist climates (Extended Data
Fig. 4 and Supplementary Text 3). This underlines the important role
of aridity in controlling SOC yield gaps. Indeed, using a random forest
model trained to predict SOC yield gaps rather than yield (Methods;
drivers of soil organic carbon yield gap), aridity index was the most
important parameter in determining this yield gap, explaining 12% of
the variability in the SOC-derived yield gap for maize, 17% for wheat,
13% for rice and 14% for the three crops combined (Fig.
3
). Most vari-
ation of the yield gap with aridity was found in dry climates (defined
as an aridity index lower than unity) where this SOC-derived yield gap
increased as soils became drier (Fig.
3
). This indicates that improved
plant-available water capacity (AWC) with greater SOC
15
is the most
important mechanism underlying observed increases in crop yield
with higher SOC in the current large dataset. Indeed, SOC is known to
contribute to the formation of aggregation and greater volume of pore
spaces
16
, providing more space to store water from rainfall or irrigation
to sustain crop yields during drought
17
. This result expands previous
evidence of only a small increase in AWC for plants from SOC increase
18
,
as our results demonstrate that changes in AWC in response to a SOC
increase can provide more moisture for crops to sustain 0.4–1.5% higher
yield (16–45% of the SOC yield gap) under water-limited conditions.
Although most of the SOC yield gap response to aridity occurs in
dry climates, a smaller increase was also observed (especially in rice)
in moister and wetter climates, where water availability is less limiting
to crop production (Fig.
3
). This response observed for rice in moist
climates could be explained by higher SOC decreasing cation leaching
in wet regions via improved cation exchange capacity, which might
therefore increase crop yield
10
.
Global and regional contribution of SOC to crop
production
Crop yield models were obtained by random forest regression and used
to estimate crop production increases across global maize-, wheat- and
rice-producing regions for two scenarios. The first scenario corresponds
to an unconstrained increase in SOC up to its yield-maximizing opti-
mum (Methods; global extrapolation of SOC yield gap). Note that this
optimum level varies with crop, climate and soil (Extended Data Fig. 2).
Although there is no known pathway to achieving this optimum SOC
in most locations, the unconstrained scenario allows us to bracket the
maximum theoretical yield impact from SOC should future advances
allow SOC to be increased far beyond the current technical potential.
Such advances could include, for example, enhanced phenotypes
19
or
higher photosynthetic efficiency
20
. The unconstrained scenario also
allows us to locate the greatest impacts of improved SOC, recogniz-
ing that although achieving this unconstrained potential everywhere
simultaneously may not be feasible, understanding where the greatest
positive effects from organic matter additions to soil can be realized
may assist in optimizing spatial application of transportable organic
AWC
Soil type
N fertilization
Slope
Cropping frequency
Clay
Bulk density
Rotational systems
Crop variety
Silt
Sand
AP
pH
Growing days
AK
Aridity index
0 2 4 6 8 10 12 14
Relative importance (%)
AWC
N fertilization
Slope
Crop variety
Cropping frequency
Bulk density
Clay
Sand
Silt
Rotational systems
Driver
Driver
Driver
Driver
AP
AK
pH
Soil type
Growing days
Aridity index
0 2 4 6 8 10 12 14
Relative importance (%)
1.00
1.05
1.10
1.15
1.20
1.25
0
0.5
1.0
1.5
2.0
Aridity index (mm mm
−1
)
Aridity index (mm mm
−1
)
Aridity index (mm mm
−1
)
Aridity index (mm mm
−1
)
Normalized predicted SOC
yield gap
AWC
N fertilization
Crop variety
Cropping frequency
Irrigation
Bulk density
Clay
Slope
Sand
Silt
AP
Previous crop type
AK
pH
Rotational systems
Growing days
Soil type
Aridity index
0 2 4 6 8 10 12 14
Relative importance (%)
N fertilization
AWC
Cropping frequency
Crop variety
Slope
Previous crop type
Rotational systems
Bulk density
Clay
Irrigation
Sand
Silt
Soil type
AK
AP
pH
Growing days
Aridity index
0 3 6 9 12 15 18
Relative importance (%)
310
330
350
370
390
410
430
0
0.5
1.0
1.5
2.0
Predicted SOC yield gap (kg ha
−1
)
Predicted SOC yield gap (kg ha
−1
)
Predicted SOC yield gap (kg ha
−1
)
160
180
200
220
240
260
0
0.5
1.0
1.5
2.0
150
160
170
180
190
200
0
0.5
1.0
1.5
2.0
Three crops combined
Maize
Wheat
Rice
Three crops combined
Maize
Wheat
Rice
Dry
Moist
Dry
Moist
Dry
Moist
Dry
Moist
a
b
c
d
e
f
g
h
Fig. 3 | Drivers of SOC yield gap. a–d, Bar charts indicate relative importance of
variables as predictors of SOC yield gap for three crops combined (
a), maize (b),
wheat (
c) and rice (d). N fertilization = nitrogen fertilizer rate; AP = plant-available
phosphorus, AK = plant-available potassium. AWC = available water capacity.
e–h, Solid lines represent the mean partial dependence of the predicted SOC
yield gap on the aridity index for three crops combined (
e), maize (f), wheat
(
g) and rice (h) (lower aridity index values correspond to a drier climate). For
three crops combined, the predicted SOC yield gap was normalized relative to
the predicted minimum SOC yield gap for each crop. The ribbons represent the
95% confidence interval. The dashed lines indicate the aridity index = 1.0 line,
which differentiates dry versus moist climates; aridity index in panels
a–d are
highlighted in red for ease of identification; the grey bars at the bottom of panels
e–h represent the distribution of aridity index data.
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resources. The second scenario corresponds to the technical potential
by which SOC stocks could be increased from current levels using cur-
rently available management options including a combination of high
organic matter inputs (from cover crops and crop residue retention)
and zero tillage
21
(Methods; global extrapolation of SOC yield gap).
Raising SOC to optimum levels (the unconstrained scenario), were
it achievable, would increase global maize, wheat and rice potential
production (once other management and fertilization constraints
have already been eliminated) by 120 Tg yr
−1
in aggregate (Table
1
), with
the global crop production increasing by 4.3%. This is equivalent to
700 million people’s cereal demand and the energy needs for 640 mil-
lion people (420 × 10
12
kcals yr
−1
). The unconstrained SOC yield gap
was greatest in dry climates, being on average 1.3–2.2 times greater
than in moist and wet climate zones (Supplementary Table 2). Spe-
cifically, the US maize belt; Central, South and Southeast Asia; eastern
Asia; maize-producing regions in Canada; South America; Europe;
sub-Saharan Africa and Russia have the largest quartile of SOC-derived
maize yield gaps, with 549–1,016 kg ha
−1
. For wheat, the 25% largest
SOC-derived yield gaps are observed in the southwestern United
States; northern Mexico; North Mediterranean basin; North China
Plain; wheat-producing regions in South America; sub-Saharan Africa;
Central, South and Southeast Asia and Australia, with 407–898 kg ha
−1
.
Rice-producing regions demonstrate only a slight increase in yield
when increasing SOC in an unconstrained way, with the 25% largest
yield increase of 192–291 kg ha
−1
found in southern and eastern South
America; Central, West and South Asia; eastern Asia; rice-producing
regions in sub-Saharan Africa and Australia (detailed regional distribu-
tion of the 25% highest SOC yield gaps is listed in Fig.
4
, Extended Data
Fig. 5 and Supplementary Table 3, respectively). The low SOC yield
gaps for rice can be explained by the current SOC levels in flooded rice
systems already approaching yield-optimizing levels.
The technical potential for SOC sequestration is, however, sub-
stantially smaller than the unconstrained scenario, with potential
global maize, wheat and rice production increasing by only 0.7%
(20 Tg yr
−1
), once other management and fertilization constraints
have also been addressed (Table
1
). The average weighted global SOC
yield gap for the technical potential is 41 (±4; one standard error,
estimated by the jackknife method in Extended Data Fig. 6) kg ha
−1
for all three crops (Methods; uncertainty analysis of global extrapo-
lations). However, this SOC yield gap is somewhat higher for specific
crops in specific regions (Fig.
4
), with the 25% highest SOC yield gaps
ranging from 73 ± 2 kg ha
−1
for rice in Central, West and Southeast
Asia to 231 ± 4 kg ha
−1
for maize-producing regions in sub-Saharan
Africa (detailed regional distribution with the 25% highest SOC yield
gaps is listed in Extended Data Fig. 5 and Supplementary Table 3).
Closing yield gaps by improving SOC to the technical potential, once
other constraints have been removed, could contribute to an annual
increase of 71 × 10
12
kcals energy for the three crops globally, which
would meet 120 million people’s cereal demand, or caloric needs of
110 million people.
It is important to note that the global extrapolation assumes opti-
mum management practices where the yield constraints derived from
inadequate nutrition, hydration, pest, weed and disease have already
been addressed. Nonetheless, addressing management and soil quality
constraints are complementary approaches, whereby increasing soil
quality without improving management or vice versa is expected to
give lower absolute yield improvements
22
. Furthermore, although the
field trial data were collected from a diverse geographic extent that
includes seven of eight climate zones, ten of the 12 soil texture classes
used by the US Department of Agriculture (USDA) and three of the four
major soil orders (Alfisols, Inceptisols, Mollisols and Untisols) where
global maize-, wheat- and rice-producing regions are located, a few
of the climate and soil regions where these crops are produced had
only a few or no field trial data, especially in tropical dry and tropical
montane climate zones and Alfisol regions. Extrapolations to these
underrepresented regions should therefore be treated with more
caution than those regions with more data. Nonetheless, because the
field trials cover the most important climate zones for these crops
globally (Extended Data Fig. 7) and soils with 10 out of 12 USDA soil
texture classes, pH values of 3–9, SOC of 1–58 g kg
−1
exceeding the
average range observed for global producing regions of these crops,
the overall conclusions are well supported.
Implications for global soil organic carbon
sequestration
Despite the expectation expressed in earlier publications that SOC
can make large (up to 10–23%) contributions to crop production
increases
8
,
23
and that crop yield increases would be therefore be a driv-
ing force behind the adoption of SOC sequestration at a global scale
6
,
7
,
our finding that the technical potential provides less than a 1% increase
in global crop production challenges this assumption and rather sug-
gests adopting a more nuanced regional focus. The negligible increase
in global average crop production is probably lower than previous esti-
mates both as a result of considering currently available technologies to
improve SOC and also because we have isolated the causal effect from
an overall correlation. Although crop yields under the technical poten-
tial increase only by a global average of 41 kg ha
−1
, within countries that
have a weak or moderate food security, the mean impact is higher (for
example, 71 kg ha
−1
in sub-Saharan Africa, 106 kg ha
−1
in Central America,
89 kg ha
−1
in the Caribbean and 72 kg ha
−1
in South America) (Extended
Data Fig. 8c and Supplementary Text 4). Notably, yield improvements
derived from SOC, once other constraints have been addressed, vary
from 26% (technical potential) to 86% (unconstrained potential) of
current food deficits in food-insecure countries (Extended Data Fig. 9
and Supplementary Text 4). Because the SOC impacts on yield reported
here are derived from a dataset where optimum management and fer-
tilization were already implemented, the extent to which food deficits
could be alleviated by SOC under current situations in food-insecure
countries remains an open question. Importantly, SOC benefits accrue
gradually over decades. Therefore, adoption of integrated nitrogen
fertilizer, pest, weed and SOC management strategies may be the most
promising means to improve crop production in food-insecure coun-
tries because their benefits are both more immediate and larger.
Although unconstrained increases in SOC up to their
yield-maximizing level would provide a much more compelling
yield benefit, being six times larger than the technical potential,
such large increases in SOC are not achievable using agricultural prac-
tices that can currently be applied at scale. This remaining SOC yield
Table 1 | Global production increase and calories provided from closing SOC yield gaps for three studied crops
Global production
increase for maize
(Tg yr
−1
)
Global production
increase for wheat
(Tg yr
−1
)
Global production
increase for rice
(Tg yr
−1
)
Total production
increase for the three
crops (Tg yr
−1
)
Energy provision from
production increase for the
three crops (kcal yr
−1
)
Technical potential
10
6
4
20
71 × 10
12
Unconstrained
50
58
12
120
420 × 10
12
Technical potential represents yield gains when SOC increased to levels that are achieved using a combination of high organic matter inputs and zero tillage; unconstrained increase in SOC
represents yield gains when SOC increased to optimum levels.
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gap, beyond what can be achieved with current scalable practices,
provides a strong rationale to investigate how much further we can
extend the envelope of achievable SOC sequestration through use
of novel practices beyond cover cropping, zero tillage and residue
returns. Other possible options for sequestering greater amounts of
organic carbon in soils include biochar
24
; plant breeding for increased
photosynthetic efficiency
25
and increased belowground produc-
tion
20
; or changing the soil microbiome to favour carbon-stabilizing
taxa
26
. Furthermore, the large geographic variation in SOC yield gaps
with climate and soil types in the unconstrained scenario suggests
potentially realizable benefits from redistributing available carbon
resources to regions with the greatest yield increases or with large
food security co-benefits. However, such a practice would need to
be balanced against the possibility of soil degradation in areas from
which organic matter is removed and the logistic cost of transporting
large quantities of material.
Carbon dioxide removal practices, such as SOC sequestration,
must be implemented and scaled up rapidly if we are to reach net zero
GHG emissions by mid-century. According to our analysis, improving
soil fertility using currently available technologies is unlikely to be a
major driver for adoption of SOC sequestration in much of the world,
and other policy measures would need to be explored if the full poten-
tial for SOC to address climate change is to be achieved. Nonetheless,
the motivation of enhancing crop production in certain regions or the
promise of SOC to help address food deficits in food-insecure countries
could prove more likely to drive SOC sequestration policy in some
regions. Furthermore, novel practices that extend the boundary of
achievable SOC sequestration to optimum levels are important areas
of further research that could drive climate policy by bringing larger
yield benefits within reach.
Online content
Any methods, additional references, Nature Portfolio reporting sum-
maries, source data, extended data, supplementary information,
acknowledgements, peer review information; details of author contri-
butions and competing interests; and statements of data and code avail-
ability are available at
https://doi.org/10.1038/s41561-023-01302-3
.
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≤10
20
50
100
200
500
1,000
2,000
Technical potential
Unconstrained
Maize
Maize
Wheat
Wheat
Rice
Rice
Yield increase when increasing soil organic carbon (kg ha
–1
)
a
b
c
d
e
f
Fig. 4 | Global potential to increase yields by increasing SOC. a,c,e, Technical
potential indicates the amount by which crop yields could be increased by
increasing SOC to its current technical potential SOC levels for maize (
a), wheat
(
e) and rice (e). Current technical potential SOC levels indicate the levels of
SOC that can be achieved using a combination of high organic matter inputs
(including cover crops and crop residues) and zero tillage.
b,d,f, Unconstrained
indicated the amount by which crop yields could be increased by increasing SOC
to its soil- and climate-specific optimum levels for maize (
b), wheat (d) and rice (f)
(Extended Data Fig. 2). Basemap reproduced from ArcGIS/Esri.
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terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Springer Nature Limited
2023
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Methods
Description of field trials
Field trials were conducted from 2005 to 2013 during the National
Soil Test and Fertilizer Recommendation Projects, which were previ-
ously described in ref.
27
. In the current study, field trials from a total
of 13,662 sites (number of field sites are 4,906 for maize, 4,448 for
wheat and 4,308 for rice) were collected (Extended Data Fig. 1), and the
dataset was established by expanding multiple biophysical factors and
management measurements to quantify the causal effect of SOC on
crop yield. All trials were designed and managed by local agricultural
experts and/or trained extension personnel and were implemented in
on-farm fields based on a stratified randomized sample of local farms
according to a series of criteria including selection of local typical soil
types, a broad range of soil fertility gradients and fertilization levels
and crop type. Nearly all field trials were conducted over a single season
(less than 3% of the trials were conducted for two or three seasons). Five
nitrogen fertilizer application rates were used in each trial, including
0, 0.5, 1.0 and 1.5 times the optimum nitrogen rate at optimum phos-
phorus and potassium rates; and a zero-fertilization treatment without
nitrogen, phosphorus or potassium additions (control). Optimum
nitrogen, phosphorus and potassium rates were recommended by
local agricultural experts and/or trained extension personnel based
on an integrated nutrient management strategy
28
, with the target to
maximize both nutrient-use efficiency and crop yield for a given site.
No organic amendments or straw were applied during the trials. In
total, there were 66,593 treatments (number of treatments are 24,107
for maize, 20,932 for rice and 21,554 for wheat) recorded during the
project when missing treatments were removed (1,717 treatments were
removed due to missing yield data because of recording issues or bad
weather). Local agricultural experts and/or trained extension officers
provided direct and consistent on-site guidance and recommended
management advice during key farming operations, including weed,
pest and disease control; cultivar selection; tillage; sowing date and
density; irrigation (only in irrigated systems, and all rice trials were
flood-irrigated) and harvest, to minimize the impact of management
variability other than fertilization on variation in crop yield. Thus, the
field trial design minimized both management constraints to yield and
variability in yield due to management. Prior rotational systems, crop-
ping frequency and previous crop type were recorded by local agricul-
tural experts and/or trained extension officers through interviews with
farmers before the trial. Previous crop type was not recorded for rice.
Metadata characterizing the site and management during the field
trials were collected by the local experts conducting the trials. The
information recorded included irrigation, crop variety, slope, planting
and harvest dates. Yield was measured at crop physiological maturity
and was standardized to an assumed 14% moisture content for maize
and rice and 13% for wheat. Climatic data during crop growing peri-
ods, including daily average maximum (Tmax) and minimum (Tmin)
temperatures, precipitation (PRE) and sunshine duration (SSD), were
collected for each field trial by using the daily climatic data from the
Chinese Meteorological Administration in the county or municipality
where the trial was implemented. Daily Solar Radiation (RAD) was calcu-
lated based on SSD using the WeatherAid module in the Hybrid-Maize
model
29
. Growing degree days (GDD) were calculated as the annual sum
of days in which the daily mean temperature exceeded 10 °C for maize
and rice and 0 °C for wheat. Aridity index was calculated as mean annual
precipitation divided by mean annual potential evapotranspiration
(PET) using data for the year of the trial collected from the Climate
Research Unit (CRU) Time-Series version 4.04 of high-resolution grid-
ded data of month-by-month variation in climate
30
.
Soil sampling for analysis of SOC and other soil indicators
Soil samples were collected from a depth of 0–0.3 m. Five soil samples
were collected from each field trial and then combined for laboratory
measurements of soil properties, including soil organic carbon (SOC),
soil pH, plant-available potassium (AK) and plant-available phosphorus
(AP), based on standard methods
31
. Specifically, SOC was measured by
the potassium dichromate volumetric method. Soil pH was measured
with a glass electrode in a 1:2.5 soil/water suspension. AK was analysed
by a flame photometer after extraction with 1 M ammonium acetate. AP
was analysed by the Olsen method. Soil type was classified according
to the Chinese soil taxonomy system
32
. Soil bulk density and relative
proportion of clay, silt and sand in the topsoil for each field trial were
estimated geospatially using SoilGrids version 2.0
33
. Available water
capacity (AWC) was estimated with texture pedotransfer functions
34
in the topsoil.
Causal effect of SOC on crop yield
Random forest regression models were established for each of the
three crops (maize, wheat and rice) separately, using the R package
‘ranger’
35
, with the above climatic, edaphic, topographic, fertilization
and management variables as independent predictors. Additionally, a
combined random forest model for normalized yield of all three crops
was derived using the same independent variables, with normalized
yield calculated by dividing in-field measured crop yield by predicted
minimum yield of the crop type (that is, when SOC is at the low end of
the range for each crop) in Fig.
1
(7,365 kg ha
−1
for maize, 5,033 kg ha
−1
for
wheat, 6,472 kg ha
−1
for rice). The independent variables for fertilization
rates were expressed relative to optimum rates, with values of 0, 0.5,
1 and 1.5 for N and values of 0 and 1 for P and K. Parameter importance
was calculated using the permutation method
36
. We set the ‘respect.
unordered.factors’ parameter in ranger equal to ‘TRUE’ to ensure that
unordered categorical data are not assumed to be ordered relative to
regression results. Coefficients of determination (R
2
, estimated using
the internal out-of-bag samples) and index of agreement (d) were used
to assess model performance. The performance of the yield models
(both R
2
and d) refers to part 1 in Supplementary Table 4.
Partial dependence of the random forest was adopted to eliminate
confounding factors, which established the mean causal effect of SOC
on crop yield for each separate studied crop and the three crops com-
bined. Partial dependence was calculated using the R package ‘pdp’
37
and smoothed using Tikhonov regularization (ridge regression)
38
.
Leave-one-out cross validation was adopted to adjust the regulariza-
tion parameter used for smoothing the partial dependence curves.
Partial dependence variance and standard error were calculated using
bootstrap sampling of model predictions. The optimum SOC was
determined by the concentration beyond which the rate of increase
in yield with SOC is not different from 0 (p < 0.05). The significance
of yield increases was estimated by two-sided t test. The 95% C.I. of
the optimum SOC was determined by bootstrapping. A causal forest
regression model was used to validate the partial dependence of the
random forest method by comparing the average treatment effect
size of SOC on crop yield for the two methods (Supplementary Text 1
provides results of the causal forest validation). The causal forest was
derived using the R package ‘grf’
39
. Furthermore, scatter plots of the
measured data for SOC and crop yield of the three crops are provided
in Supplementary Fig. 1.
Partial dependence of the random forest was also used to investi-
gate the causal effect of SOC on crop yield for each crop under differ-
ent nitrogen fertilizer rates based on above steps and above climate,
soil and management variables. For the three crops combined under
different nitrogen fertilization rates (Extended Data Fig. 3), predicted
yield was normalized to predicted minimum yield for each crop under
the same treatment.
Causal effect of SOC on crop yield under climate zones
Field trials were grouped based on the Intergovernmental Panel on
Climate Change (IPCC) climate zone definitions
40
classified according
to elevation and climatic data
30
. Partial dependence of the random
forest was used to investigate the causal effect of SOC on crop yield
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for each crop under different climate zones based on above steps and
above climate, soil and management variables. For each climate zone
(Extended Data Fig. 4), normalized predicted yield was calculated
as the ratio of predicted yield from partial dependence to predicted
minimum mean yield for each crop under each climate zone, which
facilitated comparisons between climate zones.
Drivers for the SOC yield gap
The above maize, wheat and rice yield random forest models were used
to estimate the SOC yield gaps disaggregated into specific crop, soil
and climate combinations, rather than the mean SOC yield gap across
all locations derived from Fig.
1
. In each field trial, the SOC yield gap was
defined as the difference between predicted maximum yield at optimum
SOC level and predicted yield at the current SOC level. The climate, soil
and management independent variables in the dataset were provided
as inputs to the random forest yield models to estimate crop yield at cur-
rent SOC for each trial. The predicted maximum yield at optimum SOC
was calculated for each field trial as the maximum yield when increasing
SOC while holding other independent variables constant.
Random forest yield models were trained to predict the SOC yield
gap for each trial of maize, wheat and rice systems separately and
the normalized yield gap for all crops combined, using R ranger as
described above for the yield models. The normalized SOC yield gap
of all three crops in the combined random forest model was calculated
by dividing estimated SOC yield gap in each of the field trials by the
predicted minimum SOC yield gap of the crop type (that is, when aridity
index is at the low end of the range for each crop) from Fig.
3
(322 kg ha
−1
for maize, 169 kg ha
−1
for wheat, 157 kg ha
−1
for rice). Coefficients of
determination (R
2
, estimated using internal out-of-bag samples) and
index of agreement (d) were used to assess SOC yield gap model per-
formance (part 2 in Supplementary Table 4). Partial dependence of
the SOC yield gap for which the highest-importance predictor (aridity
index) was calculated as described for partial dependence in the yield
model above. For partial dependence of the SOC yield gap on aridity
index, parameters that showed a strong correlation with aridity index
(that is, GDD, RAD, PET, Tmax, Tmin and PRE) were removed from the
models, because varying aridity index while holding these strongly
correlated variables constant would lead to inaccurate predictions.
Effects of P and K fertilization were also removed, due to their negligi-
ble importance (less than 0.1% explanation of the SOC yield gap). The
maximum contribution of aridity index on the SOC yield gap (or the
contribution of AWC to the SOC yield gap) was calculated for each crop
as the difference between maximum and minimum SOC yield gap in the
line charts of Fig.
3
, which was then used to estimate the contribution to
the absolute crop yield and total SOC yield gap. The scatter plot of the
individual data for aridity index and SOC yield gap of the three crops
is provided in Supplementary Fig. 2.
Global extrapolation of SOC yield gaps
SOC yield gaps were extrapolated to global maize-, wheat- and
rice-producing regions. Gridded global data on cropped area for each
of these crops were from ref.
41
(at 0.08° spatial resolution). Climate
and soil data were resampled to this same target resolution using
bilinear interpolation. Annual climate data (PRE, Tmax, Tmin, aridity
index and PET) were from the CRU Time-Series version 4.04
30
. The
yield model for global extrapolation was trained using annual mean
CRU TS4.04 climate data corresponding to the specific years in which
each field was conducted. For global prediction, we used climate data
averaged over the years 2011–2019. Soil properties (bulk density, clay,
silt, sand, pH) were from SoilGrids v2.0
33
. AWC was estimated with
texture pedotransfer functions
34
.
Both current SOC in croplands and its technical potential to be
increased under currently available technologies using high organic
matter inputs (residue retention and cover crops) and no till were
estimated using the SOC Tier 1 model of the 2019 revisions to the IPCC
guidelines for national GHG inventories
21
, according to the method
of ref.
42
.
These climate and soil independent variables were provided as
inputs to the random forest yield models (the random forest yield mod-
els having been trained using field trial data) to predict the increase in
yield of each crop as SOC is increased from current to either optimum
or technical potential values. Optimum SOC (Extended Data Fig. 2)
values were defined as the SOC level at which crop yield is maximized
when increasing SOC in the global extrapolation section. Because the
training data are from field trials that used best management practices
to minimize variance from management, it was assumed that optimum
fertilization and management would be used globally. Thus, the global
extrapolation estimates the additional yield that could be achieved
through higher SOC once yield gaps from suboptimal fertilization or
management have already been addressed. Coefficients of determina-
tion (R
2
, estimated using the internal out-of-bag samples) and index
of agreement (d) were used to assess model performance (part 3 in
Supplementary Table 4). The yield gap was defined as zero if the yield
at unconstrained SOC levels was less than the yield at current levels
because only yield increases from increasing SOC were considered.
Global total SOC yield gaps were calculated as the sum of the yield
gaps multiplied by the harvested area per crop in each pixel
41
. The
contribution of yield increase for the three crops to the global crop
production was estimated by using the yield increases under the two
scenarios, divided by the global annual production of the sum of the
three studied crops (2.8 Pg on a dry mass basis) in 2021
43
. The additional
per capita cereal supply was calculated assuming an annual cereal con-
sumption of 171 kg per capita
44
. The SOC yield gap was also converted
to energy equivalents, assuming calorific values of 3.65 kcal g
−1
(maize),
3.39 kcal g
−1
(wheat) and 3.60 kcal g
−1
(rice)
45
on a moist mass basis. The
number of additional people’s energy needs that could be provided
was then calculated assuming a mean daily energy requirement of at
least 1,800 kcal per capita
46
.
Crop production increases in each country were calculated as the
total yield increase of maize, wheat and rice as a result of both technical
potential and unconstrained increases in SOC. The country-level crop
production increase from SOC increases were then expressed relative
to annual current production of the three crops in each country to
total harvested areas of the three crops in each country and to annual
production of the three crops at optimum management. Annual cur-
rent production of the three crops was calculated as the mean yield per
hectare multiplied by the sum of country-level harvested areas of the
three crops, where the unit yield was the mean of values from 2018 to
2020
43
, and the country-level harvested areas were calculated as the
sum of the harvested areas
41
in a country.
Uncertainty analysis of global extrapolations
To investigate prediction uncertainty, standard errors from predic-
tion for maize, wheat and rice yield models were estimated using the
jackknife method (leave-one-out cross validation), with a random
forest model trained separately on each data iteration. Each of these
jackknife random forest models was then used to predict the yield gap
with the parameter values of the omitted data point at each SOC value
from zero to 50 g kg
−1
(in 0.1 g kg
−1
steps). Finally, mean predictions and
their standard errors were calculated for each of the SOC values. The
maximum standard errors for prediction of the SOC yield gap via SOC
changes was 4 kg ha
−1
for maize, 3 kg ha
−1
for wheat and 2 kg ha
−1
for
rice (Extended Data Fig. 6).
Benchmarking of yield potential against current food deficits
Annual total caloric food deficit in each country was calculated using
the depth (size) of the food deficit (kcal per capita per day) multiplied
by the number of the undernourished population and the number
of days in a year. The energy content of in-country crop production
increase of the three crops (under either the technical potential or the
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unconstrained SOC increase) was compared to food deficits by dividing
by the total per country food deficit.
The undernourished population in each country was calculated as
the prevalence of undernourishment (2018–2020)
47
multiplied by the
total population (2018–2020)
48
. Prevalence of undernourishment or
food deficit in each country was defined as the undernourished popu-
lation as a proportion of the total population. The depth of daily food
deficit (per capita per day) in each country was estimated as the differ-
ence between the daily minimum dietary energy requirement and the
daily mean dietary energy consumption of the undernourished popula-
tion
49
. These are the most recent published data providing global per
country values for depth of food deficit. Because these data provide the
depth of food deficit per malnourished person, they are constrained
by human physiology to lie in the range of up to a few hundred calories
per capita per day below the minimum dietary energy requirement.
Food deficits greater than this cannot be sustained for longer than
short periods during famine, which is not considered in our model.
Our estimates based on year 2000 data are, accordingly, expected to
be conservative rather than over-estimates in most countries, as the
general trend since then has been towards increased production. In
contrast to the depth of food deficit, the prevalence of undernourish-
ment changes greatly over time and is the most dominant factor that
influences total food deficit and is the value for which the most recent
data (2018 to 2020) are available
47
.
For this benchmarking of SOC yield increases against food defi-
cits, only in-country production and deficits were considered, rather
than imports and exports. For countries where the additional caloric
production exceeded the food deficit, the fraction of food deficit
addressed was capped at 100%. Countries were classified using their
food security level based on the Global Food Security Index
50
, with five
cohorts corresponding to ‘weak’, ‘moderate’, ‘good’ and ‘very good’
food security environments and a cohort of countries for which food
security levels were not provided. The countries for which food security
levels were not provided were then reclassified into above four classes
based on the quartile according to prevalence of undernourishment
(Supplementary Table 6). Finally, only the countries with ‘weak’ and
‘moderate’ food security levels were defined as food-insecure countries
(for all cohorts in Supplementary Table 6), because the food deficits
are not considered a major issue in these countries with ‘good’ and
‘very good’ food security levels (the prevalence of undernourishment
in those countries are recorded as less than 2.5%).
Data availability
Data that support these findings are available via figshare (
https://doi.
org/10.6084/m9.figshare.24137280
).
Code availability
Codes for processing the data are available via figshare (
https://doi.
org/10.6084/m9.figshare.24137280
).
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41. Monfreda, C., Ramankutty, N. & Foley, J. A. Farming the planet: 2.
geographic distribution of crop areas, yields, physiological types,
and net primary production in the year 2000. Glob. Biogeochem.
Cycles
22
, GB1022 (2008).
42. Roe, S. et al. Land-based measures to mitigate climate change:
potential and feasibility by country. Glob. Change Biol.
27
,
6025–6058 (2021).
43. FAOSTAT: Crops and Livestock Products (FAO, 2021);
https://www.
fao.org/faostat/en/#data/QCL
44. Alexandratos, N. & Mernies, J. in World Agriculture: Towards
2015/2030 An FAO Perspective: Prospects for Food and Nutrition
(Ed. Bruinsma, J.) Ch. 2 (FAO, 2003).
45. Nuss, E. T. & Tanumihardjo, S. A. Maize: a paramount staple crop in
the context of global nutrition. Compr. Rev. Food Sci. Food Saf.
9
,
417–436 (2010).
46. Rome Declaration on World Food Security and World Food Summit
Plan of Action (FAO, 1996).
47. FAOSTAT: Suite of Food Security Indicators (FAO, 2022);
https://
www.fao.org/faostat/en/#data/FS
48. Department of Economic and Social Affairs World Population
Prospects (United Nations, 2019);
https://population.un.org/wpp
49. The State of Food Insecurity in the World (FAO, 2000).
50. Global Food Security Index: Exploring Challenges and Developing
Solutions (Economist Impact, 2021);
https://impact.economist.
com/sustainability/project/food-security-index/
Acknowledgements
We thank the National Key Research and Development Program
of China (2017YFD0200108) and the National Natural Science
Foundation of China (31972520) for providing financial support
to Y.M., M.F. and L.Q. We thank the Cornell Institute for Digital
Agriculture (CIDA RIF2019) for supporting D.W. and AI-CLIMATE (NIFA-
2023-67021-39829) for supporting J.L. on this project. We thank the
China Scholarship Council for providing funds to Y.M. to pursue his
study at Cornell University. We thank L. M. Johnson from the Cornell
Statistical Consulting Unit for supporting the data analysis work.
We thank all agricultural scientists and extension personnel who
provided local technical assistance and management during the
project.
Page 11
Nature Geoscience
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Author contributions
Y.M., D.W., M.F. and J.L. designed the research; Y.M., D.W., M.F., L.Q.,
R.L. and J.L. collected field and other research data; Y.M., D.W., M.F.
and J.L. contributed to methodology and data analysis; Y.M. and D.W.
contributed to visualization; D.W., M.F. and J.L. supervised the work;
Y.M. and D.W. wrote the first manuscript; Y.M., D.W., M.F. and J.L. edited
the manuscript; all authors read and approved the final manuscript.
Competing interests
The authors declare no competing interests.
Additional information
Extended data
is available for this paper at
https://doi.org/10.1038/s41561-023-01302-3
.
Supplementary information
The online version
contains supplementary material available at
https://doi.org/10.1038/s41561-023-01302-3
.
Correspondence and requests for materials
should be addressed to
Mingsheng Fan or Johannes Lehmann.
Peer review information
Nature Geoscience thanks Marcel van der
Heijden and the other, anonymous, reviewer(s) for their contribution
to the peer review of this work. Primary Handling Editor: Xujia Jiang, in
collaboration with the Nature Geoscience team.
Reprints and permissions information
is available at
www.nature.com/reprints
.
Page 12
Nature Geoscience
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Extended Data Fig. 1 | Distribution of field trials for maize, wheat and rice.
a–c, Maize (a), wheat (b) and rice (c). The round symbols on the three top panels
represent the locations of field trials. The bottom panel indicates the eight IPCC
climate zones (large fractions of climate zones where the three studied crops
distribute are covered by field trials). Numbers in brackets under the climate
name indicate the number of field trials for each climate zone of each crop.
Numbers in brackets under the crop name indicate the total number of field trials
for each crop. Basemap reproduced from Resource and Environment Science and
Data Center, Institute of Geographic Sciences and Natural Resources, Chinese
Academy of Sciences.
Page 13
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0
10
20
30
40
50
60
(a) Maize
(b) Wheat
(c) Rice
Optimum soil organic carbon concentrations (g kg
-1
)
Extended Data Fig. 2 | Distribution of climate-and-soil specific optimum SOC for maize, wheat and rice. a–c, Maize (a), wheat (b) and rice (c). The optimum SOC is
the value above which no additional increase in crop yield can be achieved by increasing SOC. Basemap reproduced from ArcGIS/Esri.
Page 14
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7100
7200
7300
7400
7500
7600
7700
7800
0
20
40
60
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
7500
7600
7700
7800
7900
8000
8100
8200
0
20
40
60
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
5500
5600
5700
5800
5900
6000
6100
6200
0
20
40
60
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
5700
5800
5900
6000
6100
6200
6300
6400
0
5 10 15 20 25 30
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
5900
6000
6100
6200
6300
6400
6500
6600
0
5 10 15 20 25 30
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
4050
4150
4250
4350
4450
4550
4650
4750
0
5 10 15 20 25 30
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
8300
8400
8500
8600
8700
8800
8900
9000
0
10
20
30
40
50
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
8450
8550
8650
8750
8850
8950
9050
9150
0
10
20
30
40
50
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
7650
7750
7850
7950
8050
8150
8250
8350
0
10
20
30
40
50
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
6550
6650
6750
6850
6950
7050
7150
7250
0
10
20
30
40
50
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
0.98
1.00
1.02
1.04
1.06
1.08
0
20
40
60
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.98
1.00
1.02
1.04
1.06
1.08
0
20
40
60
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.98
1.00
1.02
1.04
1.06
1.08
0
20
40
60
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.98
1.00
1.02
1.04
1.06
1.08
0
20
40
60
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.99
1.01
1.03
1.05
1.07
1.09
0
20
40
60
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
5550
5650
5750
5850
5950
6050
6150
6250
0
10
20
30
40
50
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
3400
3500
3600
3700
3800
3900
4000
4100
0
5 10 15 20 25 30
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
5000
5100
5200
5300
5400
5500
5600
5700
0
5 10 15 20 25 30
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
4900
5000
5100
5200
5300
5400
5500
5600
0
20
40
60
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
6700
6800
6900
7000
7100
7200
7300
7400
0
20
40
60
SOC
(
g kg
−
1
)
Pr
ed
ic
te
d
yi
el
d
(
kg
ha
−
1
)
(a) Three crops combined
(b) Maize
(c) Wheat
(d) Rice
Control
N0
N0.5
N1.0
N1.5
Control
N0
N0.5
N1.0
N1.5
Control
N0
N0.5
N1.0
N1.5
Control
N0
N0.5
N1.0
N1.5
Normalized predicted
maximum SOC yield
gap = 0.07
Normalized predicted
maximum SOC yield
gap = 0.05
Normalized predicted
maximum SOC yield
gap = 0.05
Normalized predicted
maximum SOC yield
gap = 0.02
Normalized predicted
maximum SOC yield
gap = 0.03
Predicted maximum
SOC yield gap
= 503 kg ha
-1
Predicted maximum
SOC yield gap
= 395 kg ha
-1
Predicted maximum
SOC yield gap
= 387 kg ha
-1
Predicted maximum
SOC yield gap
= 153 kg ha
-1
Predicted maximum
SOC yield gap
= 176 kg ha
-1
Predicted maximum
SOC yield gap
= 220 kg ha
-1
Predicted maximum
SOC yield gap
= 145 kg ha
-1
Predicted maximum
SOC yield gap
= 196 kg ha
-1
Predicted maximum
SOC yield gap
= 308 kg ha
-1
Predicted maximum
SOC yield gap
= 313 kg ha
-1
Predicted maximum
SOC yield gap
= 255 kg ha
-1
Predicted maximum
SOC yield gap
= 290 kg ha
-1
Predicted maximum
SOC yield gap
= 222 kg ha
-1
Predicted maximum
SOC yield gap
= 74 kg ha
-1
Predicted maximum
SOC yield gap
= 165 kg ha
-1
Extended Data Fig. 3 | Causal effect of soil organic carbon (SOC) on crop yield
under different nitrogen input rates. a, three crops combined. b, maize.
c, wheat, d, rice. The solid lines represent mean partial dependence of crop
yield on SOC, and the ribbons represent 95% confidence intervals. N0, N0.5,
N1.0 and N1.5 indicate 0, 50%, 100% and 150% of optimum nitrogen input rates,
respectively, with optimum phosphorus and potassium input rates. Control
means no fertilizer inputs. For three crops combined, predicted yield was
normalized as the ratio of on-farm measured yield in each trial to predicted
minimum SOC yield gap for each crop under the same treatment. Predicted
maximum SOC yield gap is the difference between predicted yield under
optimum SOC and predicted minimum yield.
Page 15
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0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
5
10
15
20
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
10
20
30
40
50
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
10
20
30
40
50
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
0
5
10 15 20 25 30
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
5
10 15 20 25 30
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
or
ed
ic
te
d
yi
el
d
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
5 10 15 20 25 30 35
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
5
10 15 20 25 30
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
10
20
30
40
50
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ci
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
5
10 15 20 25 30
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
10 20 30 40 50 60
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
0
10
20
30
40
50
SOC
(
g kg
−
1
)
No
rm
al
iz
ed
pr
ed
ic
te
d
yi
el
d
(a) Cool dry
(b) Cool moist
(c) Warm dry
(d) Warm moist
Wheat cool
temperate dry
Maize cool
temperate dry
Maize cool
temperate moist
Maize warm
temperate dry
Wheat warm
temperate dry
Rice warm
temperate dry
Wheat warm
temperate moist
Maize warm
temperate moist
Maize tropical
moist
Rice warm
temperate moist
Rice tropical
moist
Normalized predicted
maximum SOC yield gap
= 0
Normalized predicted
maximum SOC yield gap
= 0.06
Optimum SOC
= 43 g kg
-1
Normalized predicted
maximum SOC yield gap
= 0
Optimum SOC
= 15 g kg
-1
Normalized predicted
maximum SOC yield gap
= 0.06
Optimum SOC
= 12 g kg
-1
Normalized predicted
maximum SOC yield gap
= 0.02
Optimum SOC
= 17 g kg
-1
Normalized predicted
maximum SOC yield gap
= 0.08
Normalized predicted
maximum SOC yield gap
= 0
Normalized predicted
maximum SOC yield gap
= 0.02
Normalized predicted
maximum SOC yield gap
= 0
Optimum SOC
= 19 g kg
-1
Normalized predicted
maximum SOC yield gap
= 0.04
Optimum SOC
= 36 g kg
-1
Normalized predicted
maximum SOC yield gap
= 0.02
Optimum SOC
= 19 g kg
-1
Extended Data Fig. 4 | Causal effect of soil organic carbon (SOC) on crop yield
across climate zones for maize, wheat and rice. a-d, cool dry (a), cool moist
(b), warm dry (c), and warm moist (d). The solid lines represent the mean partial
dependence of normalized crop yield on SOC, and the ribbons represent 95%
confidence intervals. Optimum SOC is the SOC level beyond which no significant
(p < 0.05) yield increases were observed. The significance of the yield increase
was estimated by two-sided t-tests. Normalized predicted yield was calculated as
the ratio of predicted yield from partial dependence to predicted minimum mean
yield for each crop under each climate zone. Normalized predicted maximum
SOC yield gap is the difference between normalized predicted yield under
optimum SOC and normalized predicted minimum yield.
Page 16
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0−25%
25−50%
50−75%
75−100% (25% highest)
Technical potential
Unconstrained
(a) Maize
(b) Maize
(c) Wheat
(d) Wheat
(e) Rice
(f) Rice
Extended Data Fig. 5 | Distribution of yield increases derived from soil
organic carbon (SOC) for three studied crops. Regions on the maps are derived
from Fig.
4
and classified into quartiles.
a, c, e, technical potential represents
yield gains when SOC is increased to current technical potential SOC levels for
maize (a), wheat (c), and rice (e). Current technical potential SOC levels can be
achieved using a combination of high organic matter inputs and zero tillage;
b, d, f, unconstrained represents yield gains when SOC increased to optimum
levels for (b), wheat (d), and rice (f). Basemap reproduced from ArcGIS/Esri.
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1.0
1.5
2.0
2.5
0
10
20
30
40
50
SOC
(
g kg
−
1
)
St
an
da
rd
er
ro
rs
of
SO
C
yi
el
d
ga
p
(
kg
ha
−
1
)
0.5
1.5
2.5
3.5
0
10
20
30
40
50
SOC
(
g kg
−
1
)
St
an
da
rd
er
ro
rs
of
SO
C
yi
el
d
ga
p
(
kg
ha
−
1
)
1
2
3
4
0
10
20
30
40
50
SOC
(
g kg
−
1
)
St
an
da
rd
er
ro
rs
of
SO
C
yi
el
d
ga
p
(
kg
ha
−
1
)
AWC
PK fertilization
Ssilt
Bulk density
Clay
Sand
SOC
PH
N fertilization
PET
Aridity index
PRE
Tmax
Tmin
0
3
6
9
12 15 18
Relative Importance (%)
AWC
Bulk density
Sand
Clay
Silt
PK fertilization
SOC
PH
Tmax
Tmin
PRE
Aridity index
N fertilization
PET
0
3
6
9
12 15 18
Relative Importance (%)
AWC
Bulk density
Clay
Silt
Sand
PK fertilization
SOC
PH
PET
Aridity index
Tmax
Tmin
PRE
N fertilization
0 3 6 9 12 15 18 21
Relative Importance (%)
(a) Maize
(b) Wheat
(c) Rice
(d) Maize
(e) Wheat
(f) Rice
Extended Data Fig. 6 | Relative importance (%) of variables for the global
extrapolation of yield models and its predicted standard errors for each
model. a,b,c, bar charts indicate relative importance (permutation method; see
Methods) of variables as predictors of random forest extrapolation yield models.
d,e,f, line charts represent the predictions of standard errors for maize (d), wheat
(e), and rice (f) estimated by the jackknife method (See methods; Uncertainty
analysis of global extrapolations). NPK fertilization = nitrogen, phosphorus
and potassium fertilizer rate; PET = potential evapotranspiration; PRE, Tmax
and Tmin = precipitation, maximum mean temperature and minimum mean
temperature; AWC = available water capacity.
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(a) Maize
(b) Wheat
(c) Rice
Warm temperate dry (Ntreat = 8,049)
Warm temperate moist (Ntreat = 4,777)
Tropical moist (Ntreat = 236)
Cool temperate moist (Ntreat = 145)
Cool temperate dry (Ntreat = 10,890)
Warm temperate dry (Ntreat = 17,292)
Warm temperate moist (Ntreat = 3,273)
Tropical moist (Ntreat = 40)
Cool temperate dry (Ntreat = 949)
Warm temperate dry (Ntreat = 1,559)
Warm temperate moist (Ntreat = 16,631)
Tropical moist (Ntreat = 2,649)
Tropical wet (Ntreat = 63)
Extended Data Fig. 7 | Correspondence of distributions of climate zones
where the majority of field trials are located and producing regions of the
three studied crops. a, maize, b, wheat, c, rice. Climate zones were divided
based on IPCC criteria
43
. N
treat
is the number of treatments rather than the number
of field trials in each climate zones. The distributions of maize, wheat and rice
producing regions were obtained from EarthStat
44
. The shaded regions are the
global producing regions for the three studied crops. Climate zones where only
few field trials distribute are excluded from the map including maize tropical dry
zone (N
treat
= 10), rice tropical dry zone (N
treat
= 15) and rice cool temperate dry
zone (N
treat
= 15). Basemap reproduced from ArcGIS/Esri.
Page 19
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0.5
1
2
4
8
...10
20
40
80
160
320
640
0.5
1
2
4
8
≤ 0.25
≤ 0.25
≥
≤
≥
(a) Yield increases as a proportion of current annual crop production
under technical potential of SOC increases
(b) Yield increases as a proportion of current annual crop production
under unconstrained SOC increases
(c) Absolute yield increases under technical potential of SOC increases
(d) Absolute yield increases under unconstrained SOC increases
(e) Yield increases as a proportion of annual crop production at best
management under technical potential of SOC increases
(f) Yield increases as a proportion of annual crop production at best
management under unconstrained SOC increases
Yield increases by increasing SOC as a proportion of current annual maize, wheat and rice production in each country (%)
Yield increases by increasing SOC as a proportion of annual maize, wheat and rice production at best management in each country (%)
Yield increases of the sum of maize, wheat and rice per unit harvested area by increasing SOC in each country (kg ha
-1
)
Extended Data Fig. 8 | Global yield increases of maize, wheat and rice by
increasing soil organic carbon (SOC) in each country. Yield increases of the
three crops by increasing SOC in each country was normalized to total yield
increases of the three crops from SOC relative to annual current crop production
of the three crops (
a, b), to the yield increases of the three crops from SOC per
unit harvest area (
c, d), and to the total yield increases of the three crops from
SOC relative to annual crop production of the three crops at best management
(
e, f). Total yield increase relative to annual current crop production was
calculated by using yield increases of the three crops by increasing SOC in each
country under technical potential and unconstrained increase in SOC divided
by its current annual crop production of the three crops in each country. Yield
increases of the three crops per unit harvested area was calculated by using
the yield increase of the three crops by increasing SOC in each country under
the technical potential and unconstrained SOC increase divided by the total
harvested area of the three crops in each country. Total yield increases relative
to annual crop production at best management was calculated by using yield
increases of the three crops by increasing SOC in each country under technical
potential and unconstrained increase in SOC divided by annual crop production
of the three crops at best management in each country.
Page 20
Nature Geoscience
Article
https://doi.org/10.1038/s41561-023-01302-3
0
100
200
300
400
500
2.5
5
10
20
40
0
10 20 30 40 50 60 70 80 90 100
0
10 20 30 40 50 60 70 80 90 100
0
10 20 30 40 50 60 70 80 90 100
0
10 20 30 40 50 60 70 80 90 100
SOC1234 (kg)
≤
≥
≥
≥
≥
(a) Depth of food deficit
(b) Prevalence of undernourishment
(c) Technical potential to address food deficit in countries with weak
and moderate food security environment
(d) Unconstrained to address food deficit in countries with weak and
moderate food security environment
(e) Technical potential to address food deficit in countries with good
and very good food security environment
(f) Unconstrained to address food deficit in countries with good and
very good food security environment
Calorie deficit (kcal undernourished
person
-1
day
-1
)
Undernourished population as a
proportion of total population (%)
Proportion of food deficit addressed (%)
Proportion of food deficit addressed (%)
Proportion of food deficit addressed (%)
Proportion of food deficit addressed (%)
Extended Data Fig. 9 | Depth of food deficit, prevalence of undernourishment
and the proportions of food deficit addressed by improving SOC under the
technical potential or unconstrained SOC increases. Depth of food deficit (a)
is the average calorie deficiency per capita per day below the minimum dietary
daily energy requirement in each country. Prevalence of undernourishment
(
b) is the ratio of total undernourished population to the total population in
each country that experiences national food deficits. Proportions of food
deficit addressed were estimated by using the kilocalories provided by a daily
increase of maize, wheat and rice per undernourished person resulting from a
SOC increase under either the technical potential (
c,e) or unconstrained SOC
increases (
d,f) for each country divided by the daily food deficit in kilocalories
per undernourished person (Supplementary Table 6). The countries (
c-f) were
grouped based on the Global Food Security Index
50
and classified as ‘weak and
moderate food security environment’ or ‘good and very good food security
environment’ (Supplementary Table 6). The technical potential represented
yield gains when SOC increased to levels that are achieved using a combination
of high organic matter inputs and zero tillage; an unconstrained increase in SOC
represented yield gains when SOC increased to optimum levels.
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