# Building soil to reduce climate change impacts on global crop yield

Xi Deng, Yao Huang, Wenping Yuan, Wen Zhang, Philippe Ciais, Wenjie

Dong, Pete Smith, Zhangcai Qin

► To cite this version:

Xi Deng, Yao Huang, Wenping Yuan, Wen Zhang, Philippe Ciais, et al. Building soil to reduce climate change impacts on global crop yield. Science of the Total Environment, 2023, 903, pp.166711. 10.1016/j.scitotenv.2023.166711. hal-04191432

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Building soil to reduce climate change impacts on global crop yield

2

3 Xi Deng¹, Yao Huang²,³, Wenping Yuan¹, Wen Zhang³, Philippe Ciais⁴, Wenjie Dong¹,

4 Pete Smith⁵, Zhangcai Qin¹.*

5

6 ¹School of Atmospheric Sciences, Key Laboratory of Tropical Atmosphere-Ocean

7 System (Ministry of Education), Sun Yat-Sen University, and Southern Marine Science

8 and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China

9 ²State Key Laboratory of Vegetation and Environmental Change, Institute of Botany,

10 Chinese Academy of Sciences, Beijing 100093, China

11 ³State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric

12 Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing

13 100029, China

14 ⁴Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL, CEA-CNRS-

15 UVSQ, Université Paris-Saclay, Gif-sur-Yvette 91191, France

16 ⁵Institute of Biological and Environmental Sciences, School of Biological Sciences,

17 University of Aberdeen, Aberdeen AB24 3UU, UK

18

19 Correspondence: Prof. Z. Qin; email: qinzhangcai@mail.sysu.edu.cn
## Abstract

Improving soil health and resilience is fundamental for sustainable food production, however the role of soil in maintaining or boosting crop productivity under climate change is still unclear. Here, we examined the role of soil in yield response to climate warming for four major crops (i.e., maize, wheat, rice and soybean), using global-scale datasets and machine learning techniques. We found that each °C of warming have reduced global yields of maize by 3.4%, wheat by 2.4%, rice by 0.3% and soybean by 5.0%, which are high spatial heterogeneous with positive impacts in certain regions. Soil organic carbon (SOC) would dominantly regulate negative yield responses. Improving SOC could build yield resilience to warming, avoiding an average of 3-5% °C⁻¹ of warming-induced yield loss over 60% of global planting area. The avoided loss of production in future could supply additional food for up to ~560 million people in 2050. Our findings highlight the critical role of soil in reducing warming impacts on food security, especially for developing regions, given that sustainable actions could be taken broadly.

## Main

The number of people suffering from food insecurity continues to increase, with over 700 million people in total in 2020¹. With a growing population and climate change, the global food demand in 2050 is expected to increase by 30% to 62% relative to 2010². How to feed this future population and achieve the Sustainable Development Goals (i.e., zero hunger) is a major global challenge³. Maize, wheat and rice account for 89% of global cereal production, and soybean supplies 28% of the world's vegetable oil¹. Climate change is threatening global crop production. Rising temperature has been proved to be a major cause for global yield losses⁴⁻⁶, especially in less-developed and warm areas such as sub-Saharan Africa and Latin America⁷. Recent modeling studies have also shown that, without effective adaptation, warming may also reduce yields in cooler regions⁴,⁸.

Strengthening adaptations of agricultural systems is imperative to reduce exposure and vulnerability to climate change⁹. Global assessments have mainly focused on
49 cultivar shifts and agronomic management practices to enhance adaptation<sup>10-12</sup>. A 50 combination of cultivars (e.g., higher heat tolerance) and management (e.g., soil organic 51 matter management) adaptations could reduce yield losses due to warming by ~5% in 52 the mid-21<sup>st</sup> century<sup>13</sup>. In terms of common adaptation strategies, cultivar switch and 53 irrigation contribute significantly to crop yield gains<sup>10</sup>. However, the negative effects 54 of climate change on crop production cannot be fully offset by implementing adaptation, 55 especially in lower latitudes<sup>9,13</sup>.

56 Resilient and productive soils are necessary to sustainably intensify agriculture, to 57 increase yields while minimizing environmental harm<sup>14,15</sup>. High-quality soils can buffer 58 climate variability in cropping systems and sustain yield stability<sup>16,17</sup>. Soil organic 59 carbon (SOC), in particular, has been suggested as an integrated and representative 60 indicator of soil quality, which relates to soil biological and physical properties such as 61 disease suppressiveness, heat capacity<sup>18,19</sup> and soil heath, with important functions such 62 as water retention and nutrient supply<sup>20,21</sup>. Improving SOC can help build climate 63 resilience to reduce risks to food insecurity<sup>22,23</sup>, and decrease reliance on irrigation and 64 fertilizer application<sup>24</sup>. A recent study has revealed that increasing SOC can reduce the 65 yield gaps of maize and wheat<sup>14</sup>. However, the role of soil in building crop yield 66 resilience to climate change is still missing from the crop-soil-environment system, it 67 remains difficult to quantify the complex interactions between soil, climate and 68 yield<sup>25,26</sup>.

69 This study provides a soil-focused perspective to address escalating climate 70 challenges on global agriculture, and to look for opportunities in soils for future food 71 security. Here, we firstly determined the response of maize, wheat, rice and soybean 72 yields to warming temperature at grid scale, i.e., temperature response index 73 (TRI, % °C<sup>-1</sup>). Then, we identified the role of soil properties (including SOC) in 74 explaining spatially heterogeneous responses of crop yield to warming, by using a 75 machine learning approach. With outcomes from these processes, we finally proposed 76 soil related strategies for securing food production under future climate change 77 scenarios, and further explored the potential impacts on food security. 78
78 **Results**

79 **Climate change impacts on global crop yield**

80 We defined the temperature response index (TRI) as partial yield percentage changes
81 for each degree Celsius (°C⁻¹) increase. By isolating effects of temperate, it can show
82 crop yield response to climate warming, and indicate yield resilience to future warming
83 by crop and location. TRI was computed for maize, wheat, rice and soybean at the grid
84 level (0.5°×0.5°), using global time series datasets. In general, warming has caused
85 global-scale yield loss, with crop-specific and spatially heterogeneous responses at finer
86 scales (Fig. 1). Globally, the estimates for all four crops show negative TRIs, suggesting
87 an average yield loss of -3.4% °C⁻¹ (-32.0 to -19.1% °C⁻¹, 95% distribution interval),
88 -2.4% °C⁻¹ (-21.2 to -15.0% °C⁻¹), -0.3% °C⁻¹ (-22.8 to -17.4% °C⁻¹), and -5.0% °C⁻¹
89 (-25.2 to -14.3% °C⁻¹) for maize, wheat, rice, and soybean, respectively. However,
90 crop- and location-specific TRIs vary significantly.

91 In particular, the TRIs for maize are consistently negative across five continents,
92 ranking from high to low: Africa (-6.6% °C⁻¹), South America (-6.3% °C⁻¹), North
93 America (-3.4% °C⁻¹), Oceania (-2.8% °C⁻¹) and Europe (-2.2% °C⁻¹). While on
94 average, maize in Asia is less negatively affected by warming, yield loss is still observed
95 in regions including Southeast Asia, Central Asia and Northwest China (Fig. 1a). For
96 wheat, Africa is the most vulnerable continent, with a TRI of -15.5% °C⁻¹, followed by
97 South America (-7.3% °C⁻¹) and Asia (-1.1% °C⁻¹) (Fig. 1b). Rice is least affected by
98 rising temperatures in many regions, with continental scale TRIs closing to zero (Fig.
99 1c). The highest yield loss for soybean occurred in South America (-9.8% °C⁻¹), the
100 largest soybean producer, followed by Africa (-8.7% °C⁻¹). The lowest yield loss (-
101 1.4% °C⁻¹) appeared in North America (Fig. 1d). In general, crop production in Africa
102 and South America is more susceptible to warming.
103

103
<figure><img src="image_2.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>(c)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(d)</figcaption></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

Temperature response index (% °C⁻¹)
**Fig. 1.** Global temperature response indices (TRIs, % °C⁻¹) of four crops. (a) Maize (n=14134), (b) wheat (n=8406), (c) rice (n=9048) and (d) soybean (n=5996). TRI values show yield changes per °C of temperature increase, with positive and negative values indicating yield gain and loss, respectively. The black marks in the grids represent the significant influence of warming. The box chart reflects the interquartile range and the middle line in the box represents the median. The boxes from left to right represent Africa, South America, North America, Oceania, Asia and Europe, and the blank indicates insufficient data in Oceania (b-d).

**The role of soil in reducing climate impacts on yield**

The spatially heterogeneous response of crop yield to warming can largely be explained by soil heterogeneity in terms of soil properties, including SOC, total nitrogen (NT), clay and sand content, pH and cation exchange capacity (CEC). A random forest technique, based on the concept of bagging sampling and regression decision trees²⁷, was used to detect soil and spatial TRI relationship (Methods). After training and testing, the random forest model can replicate the crop-specific yields to soil with the coefficient of determination (R²) of 0.46 to 0.66 (Supplementary Fig. 1), and the relationships can be visualized by centered individual conditional expectation (c-ICE) plot (Fig. 2). c-ICE plot can highlight the average change (colored curves) and variation range (corresponding shadows) of TRI along with soil properties (Fig. 2a–f), and also identify where, and to what extent, heterogeneities might exist²⁸. Among six soil properties that potentially affect crop growth, SOC is identified as the most important predictor to TRI, followed by TN, considering the variable importance metric (Fig. 2g). Other soil properties do not affect TRI consistently across the whole range (Fig. 2c-g). This implies that, with increased SOC or TN (except maize) in locations where their current levels are relatively low, TRI could be improved, suggesting increased yield resilience to warming (e.g., Fig. 2a-b). In particular, with increasing SOC, the TRI of four crops would increase until reaching a “plateau” (Fig. 2a). When the SOC is lower than about 2.0%, increasing SOC can considerably reduce TRI, indicating improved yield resilience to warming. Considering current low levels of SOC (Supplementary Fig. 2), global soils have great potential to increase carbon content before reaching the TRI
“plateau” level. Current soil TN content, however, has already reached the “plateau”
level in most of the planting regions (Supplementary Fig. 3), leaving limited room for
improving TRI via TN change. Therefore, in this study, we further quantify spatial TRIs
after soil improvement, specifically SOC increase, with associated TN change to
maintain soil C:N (Methods).

139

<figure><img src="image_7.png" /></figure>

140

Fig. 2. The temperature response indices (TRIs) vary with soil properties. a–f, centered individual conditional expectation (c-ICE) plot of TRI by six soil properties. Red, blue, green and purple lines represent the averaged TRI changes of maize, wheat, rice and soybean, respectively, with shadow indicating the distribution of all individual instances, relative to the starting point fixed at zero. g, the importance of soil properties, sorted from high to low according to the model outputs.

147

Our analysis shows that improving soil can generally lead to less negative or more
positive TRIs (Fig. 3), relative to those with existing soil conditions (Fig. 1). SOC can
be sequestered in croplands, depending on biomass and manure inputs, and other
management practices, but with an upper limit<sup>29,30</sup>. By considering a “medium”
sequestration scenario that SOC increase rate would achieve 26% of the “4p1000”
target<sup>31,32</sup>, the SOC level can be increased by an average of 1.3% in the study areas
(Supplementary Fig. 2). The considerable SOC increase would mostly occur in Europe (2.6%), North America (2.4%) and Asia (1.6%), where soil carbon loss hotspots are located³³. With the increase of SOC, the warming-induced yield losses could be significantly reduced (Fig. 3). From a global perspective, the TRIs for maize, wheat, rice and soybean would be 0.1% °C⁻¹ (−10.4 to 18.8% °C⁻¹), 2.7% °C⁻¹ (−4.5 to 15.0% °C⁻¹), 3.4% °C⁻¹ (−6.7 to 17.4% °C⁻¹) and −0.6% °C⁻¹ (−11.2 to 14.2% °C⁻¹), respectively. With improved yield resilience owing to soil improvement, about 3.3%-5.1% °C⁻¹ of yield loss can be avoided relative to the scenarios without soil improvement.

For maize, in the United States, the largest maize producer, the average TRI would change from −3.7% °C⁻¹ to −1.5% °C⁻¹, about 60% of warming-induced yield loss could be avoided (Fig. 3a). In West Africa and East Africa, where yield has reduced by more than 30% °C⁻¹ in some areas (Fig. 1a), most of the loss decreased to less than −10% °C⁻¹ after improving SOC (Fig. 3a). As for wheat, in both China and India, two of the largest producers, the yield has suffered from different degree of loss due to warming, about −0.1% °C⁻¹ and −7.0% °C⁻¹, respectively. With improved soil, the TRIs turns positive in both countries (3.9% °C⁻¹ in China, and 1.1% °C⁻¹ in India), suggesting potential yield benefit with warming regardless of possible effects from other factors. It is not unexpected that rice is less affected by warming as an irrigated crop, it also benefits from SOC improvement. In particular, for China and India, the top two rice producers, the average TRIs would increase from 1.0% °C⁻¹ and 0.3% °C⁻¹ to 3.5% °C⁻¹ and 4.7% °C⁻¹, respectively, showing even stronger yield resilience to warming. For soybean, its high vulnerability to warming would also be significantly reduced, especially in the main producing countries, Brazil, Argentina and India (Fig. 3d). The SOC strategy would reduce soybean yield loss by 6.4% °C⁻¹ in South America (Fig. 3d).

Globally, 53.2%, 67.8%, 51.8% and 71.6% of planting area for maize, wheat, rice and soybean, respectively, could benefit from improved crop resilience due to increased SOC, covering 60.0% of global total planting area (Fig. 1, 3 and Supplementary Fig. 4). Among these area, 77.1%, 95.9%, 90.2% and 88.3% of maize, wheat, rice and soybean, respectively, have experienced yield loss due to warming (i.e., TRI<0). For most of the
184 cropland that have already benefited from warming, i.e., with original TRI>0, SOC

185 improvement has only minimum effect on yield resilience, especially for wheat and rice.
<figure><img src="image_8.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(c)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(d)</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

Temperature response index (% °C⁻¹)
Fig. 3. The estimated global TRIs (% °C⁻¹) of four crops with SOC improvement. (a) maize, (b) wheat, (c) rice and (d) soybean. The box plots and the curve on the left show the frequency distribution of TRI at global scale. Orange and green boxes represent the overall results without and with SOC improvement, respectively. Green boxes at the bottom show the frequency distribution of TRI of six continents, Africa, South America, North America, Oceania, Asia and Europe, and the blank indicates insufficient data in Oceania (b-d).

193

## Building SOC to secure future food production

Under future climate change, temperature will continue to increase and crop yields are expected to decrease. Over the growing seasons, the average temperature can increase by 0.18-0.21°C, and 1.18-1.44°C in 2050 under RCP 2.6 and RCP 8.5, respectively (Table 1 and Supplementary Fig. 5). Without any improvement to the SOC level, a total of about 15.0 million tonnes of the four crops would be lost in 2050 under RCP 2.6 due to warming (Table 1), leaving 60.0 million people suffering from food insecurity. The loss of production would mainly occur in South America (4.7 million tonnes) and Africa (4.8 million tonnes). The total production loss and the food insecure population would be tripled under RCP 8.5. The largest loss of production can be seen for maize, mainly due to yield loss and relatively large production area (Table 1).

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<table><caption>Table 1. Changes in temperature (°C) and warming-induced crop production (million tonnes) in 2050 relative to 2020 level under two climate scenarios.</caption><thead><tr><th rowspan="2">Crops</th><th colspan="2">Temperature increase</th><th colspan="2">Production change without SOC improvement</th><th colspan="2">Production change with SOC improvement</th></tr><tr><th>RCP 2.6</th><th>RCP 8.5</th><th>RCP 2.6</th><th>RCP 8.5</th><th>RCP 2.6</th><th>RCP 8.5</th></tr></thead><tbody><tr><td>Maize</td><td>0.19 (±0.12)</td><td>1.42 (±0.31)</td><td>-7.5 (±4.6)</td><td>-45.7 (±10.1)</td><td>-1.4 (±0.9)</td><td>1.3 (±0.3)</td></tr><tr><td>Wheat</td><td>0.21 (±0.06)</td><td>1.44 (±0.17)</td><td>-3.5 (±1.1)</td><td>-13.9 (±1.6)</td><td>3.2 (±1.0)</td><td>31.7 (±3.7)</td></tr><tr><td>Rice</td><td>0.18 (±0.04)</td><td>1.18 (±0.24)</td><td>-0.2 (±0.0)</td><td>-2.9 (±0.6)</td><td>5.0 (±1.0)</td><td>30.3 (±6.2)</td></tr><tr><td>Soybean</td><td>0.20 (±0.12)</td><td>1.39 (±0.27)</td><td>-3.8 (±2.3)</td><td>-26.7 (±5.1)</td><td>-0.5 (±0.3)</td><td>-2.9 (±0.6)</td></tr><tr><td>Total</td><td>0.20 (±0.06)</td><td>1.36 (±0.20)</td><td>-15.0 (±4.8)</td><td>-89.3 (±13.2)</td><td>6.4 (±2.0)</td><td>60.4 (±8.9)</td></tr></tbody></table>
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However, our analysis showed that with improved yield resilience due to SOC improvement, the warming-induced yield loss can be largely minimized or even reversed. Compared with current SOC levels, improving soil could increase total production of maize, wheat, rice and soybean by 0.6%-1.0% under RCP 2.6, and 4.3%-6.7% under RCP 8.5 in 2050, which would significantly reduce yield loss for maize and soybean, and lead to a global net yield gain for wheat and rice, relative to the reference scenario without SOC improvement. The global production of these four crops would increase by 6.4-60.4 million tonnes, depending on the climate scenario (Table 1). With global efforts to enrich soil carbon, food systems are predicted to provide additional 49.9, 99.7 and 149.6 million tonnes of food that would otherwise lost due to warming, which would be enough to feed an additional 187.9, 375.8, and 563.7 million people in 2030, 2040 and 2050 under RCP 8.5, respectively (Fig. 4). Asia would benefit the most from SOC improvement. An additional 78.5, 157.0 and 235.5 million people could be fed in 2030, 2040 and 2050 under RCP8.5, respectively (Fig. 4). Among the four crops in Asia, wheat and rice contribute more than 90% to the increase of food production. In Africa, an additional 21.2, 42.4 and 63.6 million people are expected to avoid hunger in 2030, 2040 and 2050 under RCP8.5, respectively, mainly due to the contribution of maize (Fig. 4). Other areas would also benefit from improved yield resilience owing to increased soil carbon content (Fig. 4).
<figure><img src="image_13.png" /><figcaption>**Fig. 4. Increased food secure population (people) with improved soil.** The results are aggregated by continents. A pair of pies in each continent correspond to RCP 8.5 (left) and RCP 2.6 (right) climate scenarios. Pies from the inside out indicate the results in 2030, 2040 and 2050, and the area of the pie represents the predicted size of increased food secure population. The background map shows the number of people undernourished in 2020¹. The undernourished people consume calories below the minimum energy requirement for an active and healthy life, and food secure population indicates that an individual's dietary calorie requirements are fully met.</figcaption></figure>

## Discussion

This study specifically investigated partial crop yield response to warming by excluding other factors (e.g., precipitation, crop variety, management), showing relatively comparable findings with other relevant studies. Globally, rising temperature caused maize, wheat and soybean yield losses on average, but with spatial divergence (Fig. 1). For instance, crop in high-latitude regions would benefit from climate warming due to the relief of chilling³⁴. Rice yield was less affected by rising temperature compared with the other three major crops, consisted with previous meta-analyses and statistical modeling⁵,¹³. More irrigated area of rice in the main producing country may bridge the water deficit associated with warming³⁵. Note that the yield loss per °C of
global average warming for maize and wheat was smaller than that found in previous studies<sup>5,6</sup>. A major reason is that we further isolated the effects of nitrogen and phosphate fertilizer application. Fertilizer additions can meet higher nutrient requirements of crops under climate change<sup>36,37</sup>. With SOC improvement, the yield losses due to warming are predicted to be reduced or even reversed, and therefore the food demands of tens to hundreds of millions of people worldwide would be met.

While there have been studies investigating the relationships between crop yield and climate factors, there has been a lack of field evidence to isolate the role of soil in building yield resilience to climate warming<sup>16</sup>. However, some existing understanding and evidence can still imply the importance of soil system. A recent report from on-farm trials in China suggests that high-quality soils can reduce the sensitivity of crop yield to climate variability and stabilize crop yield<sup>16</sup>. Compared with soils of low quality, high-quality soils are proven to improve yield under climate change by an average of 1.7%<sup>16</sup>. This study provides field evidence to our findings at the global scale that soil improvement can increase resilience of the soil-crop system to climate change (i.e., soil resilience, crop resilience and resilience of the integrated system) and help secure future crop production. Globally, the benefits of increased SOC are particularly pronounced in wheat cropping systems (Table 1), and this negative-to-positive effects of improved soil on yield also appeared in regional cases<sup>16</sup>. More importantly, our study indicates that for regions that are more susceptible to warming, increasing SOC would lead to greater yield resilience. For instance, in Africa that has the highest prevalence of undernourishment (19% in 2018-2020)<sup>1</sup>, the TRI of maize and soybean can be increased by ~7% °C<sup>-1</sup> with SOC improvement, doubling the global average. In these warmer and less irrigated areas, increasing SOC would prominently alleviate the heat stress on crops (Supplementary Fig. 4, 6). However, SOC above 2% would not result in additional benefits to crop yields (Fig. 2). The threshold effects of SOC was also detected in field experiments<sup>24</sup>. Currently, SOC content is below 1.5% in two-thirds of planting grids (Supplementary Fig. 2), which leaves great potential to stabilize crop yield under warming by improving SOC.

Notably, the mechanisms by which improved soil reduces the climate impact on
crops are not fully known. Soil health management by increasing SOC can increase crop resilience under extreme climate stress<sup>22,26,38</sup>, which is likely to ensure food security under climate change at regional and global scales. Specifically, SOC underpins soil structure, soil formation, water cycling and nutrient cycling<sup>20</sup>. Poor soil structure (e.g., soil compaction) lowers root biomass. Increasing SOC concentration could therefore increase the porosity across different soil textures<sup>39</sup>, which promotes root growth, and nutrient and water uptake of crops under climate change<sup>40</sup>. Increased organic matter can increase soil water holding capacity, thereby alleviating the damage of heat and drought and increasing resilience of maize<sup>41</sup>. The crop is less sensitive to heat in medium- and fine- textured and carbon rich soils, partially due to restricted water loss through evapotranspiration<sup>42</sup>. In this study, compared with wheat and soybean, maize and rice would benefit less from improving SOC, probably because maize as C4 plant has smaller stomatal conductance to concentrate CO<sub>2</sub><sup>43,44</sup>, and rice are often irrigated and less water-stressed. Field experiment showed that rice could benefit from a higher temperature when soil nutrients keep up with the demand<sup>36</sup>. Given that higher crop biomass returns more C into soil<sup>45</sup>, the interaction between yield and SOC increase presents a positive feedback<sup>24</sup>. SOC and TN losses, which were pre-simulated by the process-based model under a 3°C warming, would reduce wheat yield by 13% and maize yield by 19%<sup>46</sup>. However, few studies have achieved timely feedback on the interaction between crop yield resilience and soil properties, primarily because multiple factors and complex processes are involved, and the role of soil cannot easily be isolated in the overall yield resilience observation. It is expected that the relationship between TRI and soil might be revealed if paired warming experiments could include diverse crop-soil-environment conditions.

It should also be noted that the ability of building SOC to improve yield resilience may be limited in certain regions (Supplementary Fig. 4), and management practices should be well examined. Due to the increase of soil water retention, the negative effects of increasing SOC on maize, wheat and soybean may occur in wet regions with poorer drainage<sup>42</sup>. The increase of SOC significantly increases the specific heat capacity of the soil<sup>47</sup>, which causes soil to warm slowly during the wheat rejuvenation period<sup>42</sup>. The
areas with greater benefits after improving SOC could be given higher priority in regional or national planning (Fig. 1, 3 and Supplementary Fig. 4). For areas with higher poverty and undernourishment, smallholders may not be able to afford costly measures<sup>48</sup>, so effective economic and policy incentives would need to be in place<sup>25,49</sup>. Food security and other benefits, including ecosystem service and negative emissions<sup>50,51</sup>, can further justify government investment. Fast and effective action is required globally<sup>52,53</sup>.

Soil management should also well reflect the level of confidence in both science and practice. The potential SOC in our study considered the management scenario with cover cropping, manure application and conservation tillage, it would be higher than the potential based on the meta-analysis with applicable constraints<sup>54</sup>. Compared with “4p1000” initiative, potential SOC was simulated with a relatively conservative sequestration rate, reaching only 26% of the “4p1000” target<sup>31</sup>. SOC losses due to warming was not specifically considered in this estimation. Regarding the regional sequestration potential, long-standing cropping regions in Europe, North America and Asia show higher rate (Supplementary Fig. 2), which is associated with large carbon losses due to intensive land use, leaving more room for carbon accumulation<sup>33,55</sup>. From a technical perspective, increasing organic inputs (e.g., crop residue, cover crop and manure) is considered as the most effective measure to accumulate SOC in cropland<sup>56,57</sup>. Crop residue return is a feasible and efficient way to increase SOC density by 0.69 Mg C ha<sup>-1</sup> yr<sup>-1</sup> under a high retention rate<sup>45</sup>. Irrigation of arid and semiarid regions may increase SOC through increase biomass production<sup>58</sup>. Optimal agricultural management in China is estimated to sequester 2.4 Pg C into cropland before 2050, with higher potential for paddy soil (26.1 Mg C ha<sup>-1</sup>)<sup>29,59</sup>. Notably, soil N<sub>2</sub>O and CH<sub>4</sub> emissions may change as a result of management improvement, which should be further studied and well balanced in estimating crop yield and climate benefits<sup>60,61</sup>.

Future work is urgently required to further improve yield resilience and future yield estimation, and investigate potential unintended consequences. Modeling uncertainties may arise from data limitation, choice of GHG emission scenarios, climate model projections and understanding of mechanisms. For instance, although precipitation
change was included in our modeling analysis, no significant trends were detected. The lack of irrigation in the model, due to data limitation, may have partially missed the water impacts. If crop-specific irrigation data with high spatio-temporal resolution become available, the cooling and water supply effects of irrigation could be better modeled<sup>62,63</sup>. Spatially referenced and crop-specific data on fertilization, if become available, could also help improve model simulations. Additionally, since TRI is a simplification of the actual response of crop to temperature change, future studies could further include biophysical processes to better understand crop-soil-environment interactions<sup>20</sup>. Furthermore, socioeconomic drivers of food supply and demand besides domestic production of crops, e.g. trade<sup>64</sup>, are important to assess the hunger and food secure population. Finally, acting on soil may lead to other unintended negative environmental (e.g., water, nutrients input), social (e.g., competitive use of resources) and even economic outcomes (e.g., shift of investment), and these should be avoided to the greatest extent possible<sup>65-67</sup>. Given the multiple benefits of building SOC, the priority should be given to take efficient management steps considering the integrated crop-soil-environment system to close the yield gap and ensure the security of food supply.
356 **Methods**

357 **Yield response to temperature.** On the basis of historical data reflecting crop yields, 358 climate and management, the yield models (Eq. 1) were developed for individual crops 359 (i.e., maize, wheat, rice, and soybean), and then used to identify yield's partial response 360 to temperature (i.e., TRIs or temperature response indices, Eq. 2). Historical yields 361 (1981–2010) of main crops, maize (major), wheat (winter), rice (major) and soybean 362 with the spatial resolution of 0.5°, were derived from GDHY v1.3, a global dataset of 363 historical yields of major crops with a data combination of agricultural census, satellite 364 and model⁶⁸. Historical daily weather data were sourced from the AgMERRA, a 365 post-processing dataset of the NASA Modern-Era Retrospective Analysis for Research 366 and Applications (MERRA) for agricultural modeling⁶⁹. Average temperature (T), total 367 precipitation (P) and solar radiation (R) of crop growing season were extracted 368 according to phenology of each crop⁷⁰. Both linear and quadratic forms of temperature 369 and precipitation were characterized in the model to account for the non-linear response 370 of crop yields to climate (Eq. 1). The model has been widely applied in the studies of 371 yield-climate relationship⁵,⁷¹,⁷², and fully verified⁷³,⁷⁴. Nitrogen (Nfer) and phosphorus 372 (Pfer) fertilizers⁷⁵ were further included to better estimate the impacts of management 373 on crop yields. The input datasets with higher resolution were integrated to 0.5°, to be 374 consistent with the resolution of yields (Supplementary Table 1). The model structure 375 is shown as:

$$
\begin{align}
\ln(Y_{i,t}) = \beta_{0,i} &+ \beta_{1,i} t + \beta_{2,i} T_{i,t} + \beta_{3,i} T_{i,t}^2 + \beta_{4,i} P_{i,t} + \beta_{5,i} P_{i,t}^2 + \beta_{6,i} R_{i,t} + \nonumber \\
& \beta_{7,i} Nfer_{i,t} + \beta_{8,i} Pfer_{i,t} + \varepsilon_{i,t} \tag{1}
\end{align}
$$

378 where ln(Yᵢ,t) represents the logarithm of crop yields. Models of four crops were 379 developed for grid cell i (0.5°×0.5°). The time term (t) was used to simulate the 380 possible impact of other factors on crop yields (Supplementary Fig. 7), e.g. cultivar 381 shifts. As showed in this study (Supplementary Fig. 8) and elsewhere⁵,⁷⁶, including the 382 quadratic form (e.g., T²) can better simulate the nonlinear responses of the crop to 383 warming. The response of crop yield to temperature was measured by the partial
384 derivative of equation (1)⁷⁶:

$$385 \qquad \partial\ln(Y_i)/\partial T_i = \partial Y_i/(Y_i \times \partial T_i) = \beta_{2,i} + 2\beta_{3,i}T_i \qquad (2)$$

386 where $\partial Y_i/\partial T_i$ represents the proportion of yield change in grid cell i. Temperature response index (TRI) was defined as the yield change (%) per °C of temperature change, 387 which can be measured as⁷⁷:

$$389 \qquad TRI_i \approx (\beta_{2,i} + 2\beta_{3,i}\bar{T}_i) \times 100\% \qquad (3)$$

390 where $\bar{T}_i$ is the average temperature of the crop growing season during 1981–2010. 391 The parameters $\beta_{2,i}$ and $\beta_{3,i}$ represent the location-specific response of yield to 392 temperature change. TRI varies spatially, with values determined by grid level 393 parameters and local climate. The TRI at the continental and global scales was 394 calculated on the basis of the area-weighted average, considering geographic 395 distribution of crop harvest area derived from a gridded dataset⁷⁸. Modeling and 396 analysis were batched in Python version 3.6. 397

398 **Estimation of the role of soils.** Soil plays a crucial role in providing nutrients, 399 maintaining relatively stable environment, and supporting crop growth as a whole²⁴,²⁶. 400 We hypothesized that the spatial heterogeneity of TRI correlates to the differences of 401 soil properties across space. The machine learning approach, random forest²⁷, was 402 employed to estimate the correlation between TRI and soil properties due to its efficient 403 modeling performance. WISE30sec dataset⁷⁹ was selected for its comprehensive soil 404 properties and data sources. Six key soil properties (0–30 cm), SOC (%), total nitrogen 405 (TN, %), cation exchange capacity (CEC, cmol kg⁻¹), clay content (%), sand content 406 (%), and pH were extracted by depth-weighted method and resampled to 0.5° resolution. 407 Random forest models were built for individual crops, maize (n=13935), wheat 408 (n=8303), rice (n=8925) and soybean (n=5935). Model training and testing were 409 implemented with the Scikit-learn Library in the Python. Three key parameters needed 410 to be adjusted for training the models, the number of trees in the forest (n_estimators), 411 the maximum depth of the tree (max_depth) and the number of soil variables in the
random subset at each node (*max_features*), for the trade-off between over-fitting and high bias of the model. When training, all decision trees in the forest were formed by the method of bagging sampling with replacement. In each training set, about one third of samples were left out as out-of-bag data, which were then used to estimate the generalization error.

The key soil properties were determined by the importance and the interaction between *TRI* and each soil variable. The former was measured by calculating the increase of prediction error after randomly permuting the target soil variables in the random forest model. The greater the increase in error, the more important the variable is. The latter was visualized by centered individual conditional expectation (c-ICE) plot<sup>28</sup>. The curve in the plot showed how the *TRI* changes when a soil variable changed after considering the average effects of other variables. All individual samples were centered at a certain point in the plot, which was helpful in examining the cumulative effect of the selected feature. Besides, the c-ICE plot visualized the condition of each individual sample (shaded areas on both sides of the curve, Fig. 2).

Through these analysis, SOC content was determined to be the most important soil factor affecting crop response to temperature change, followed by TN. For global soil, a linear relationship was observed between SOC and TN (R<sup>2</sup>=0.91), and this was further built into the equation to estimate future TRI with improved SOC. In other words, the improved yield resilience would be realized by feeding in SOC potential and associated TN change. Specifically, SOC potential was based on the field-supported assumption that best management could help soil carbon accumulation and reach a relatively high and stable SOC level<sup>54</sup>. In this analysis, SOC data from Zomer, et al.<sup>31</sup> was used for its global-scale availability and accuracy. The medium scenario was considered here with the sequestration rate of 0.56 t C ha<sup>-1</sup> yr<sup>-1</sup> (0.9 Pg C yr<sup>-1</sup> globally) lasting at least 20 years<sup>31</sup>, by implementing practices including cover cropping, manure application, and reduced tillage. The unit (%) and resolution (0.5°) of SOC data were converted and integrated to match the random forest model. The average TN content modeled through the linear model was 0.19% (0.07-0.49%, 95% percentile).
442 **Crop yields under future climate.** With the changing temperature in the future, crop
443 yield would respond differently among crops following individual TRI pattern. The
444 highest and lowest additional radiative forcing scenarios (RCP2.6 and RCP8.5), 2.6 and
445 8.5 W m⁻², respectively, were considered for future climate scenarios⁸⁰,⁸¹. The monthly
446 temperatures of two scenarios were obtained from the outputs of Global climate models
447 (GCMs) in CMIP6. According to the latest comparison of the equilibrium climate
448 sensitivity (ECS)⁸², we chose three GCMs with lowest ECS from different institutes,
449 including INM-CM5-0, CAMS-CSM1-0 and NorESM2-MM. In order to be spatially
450 consistent with other data, we aggregated the temperature data of above GCMs to a 0.5°
451 resolution. We averaged all model outputs for a relatively stable and accurate
452 temperature projection. According to the phenology data of maize, wheat, rice and
453 soybean, we extracted growing season temperature between planting and harvest date.
454 Warming trends of crops in growing season were detected by linearly fitting the
455 temperature from 2015 to 2100 in each grid. Then, we calculated the warming level in
456 2030, 2040 and 2050 relative to 2020 by using the above parameter of trends. The future
457 crop yield changes as a result of yield response and future warming.
458

459 **Estimation of increased feed.** Future production under changing climate varies with
460 SOC strategies (i.e., with vs. without SOC improvement), which would lead to different
461 estimates of food secure population (FSP) that could be met with full dietary calorie
462 requirements. The production was determined by yield depending on crop-specific TRI,
463 and harvest area simulated under future climate⁸³. The FSP was calculated as follows:

$$
464 \qquad FSP_{c,j,t} = TRI_{c,j} \times \Delta T_{c,j,t} \times Y_{c,j} \times H_{c,j} \times CC_j / PC_{c,t} \quad (4)
$$

465 where TRIc,j,t indicates the temperature response index of continent c, crop j and year t.
466 Δ Tc,j,t is the temperature change of the crop growing season under two climate
467 scenarios compared to current level. Yc,j and Hc,j represent the yield and harvest area⁸³,
468 which were assumed to be constant. Using four variables described above, we
469 calculated the production change due to future warming. CCj is the calorie content per
470 unit of crop j⁸⁴. PCc,t is the calorie need per capita per year⁸³, which was simulated
471 under two scenarios, business-as-usual (BAU) and towards sustainability (TSS)
472 scenarios, corresponding to RCP8.5 and RCP2.6, respectively, to be consistent with
473 future climate scenarios. $PC_{c,t}$ of two scenarios was estimated based on the different
474 forward-looking assumptions, e.g., economic growth and policy<sup>83</sup>. The $FSP_{c,j,t}$ with and
475 without SOC strategy was estimated with their corresponding $TRI_{i,j,t}$. The $FSP$, and
476 increased food secure population ($\Delta FSP$, difference between $FSP$ with and without
477 SOC strategy) were estimated for year $t$ (i.e., 2030, 2040 and 2050).
478

479 **Data availability**

480 All the source data of this study are freely available online and referenced within the
481 paper. The summary of the dataset is included in the Supplementary Information.
482

483 **Code availability**

484 The code used to perform analyses in this study is generated in Python36 and is
485 available upon reasonable request.
486

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675

676 Acknowledgements

677 This work was supported by the National Natural Science Foundation of China
678 (41975113, 42141020), the Guangdong Provincial Department of Science and Technology (2019ZT08G090), and China Postdoctoral Science Foundation (2021M693583).

681

682 **Author contributions**

683 Z. Q. and Y. H. conceived and designed the research. X. D. and Z. Q. developed data-model simulations and analyzed results, with key inputs from Y. H., W. Y. and W. Z. on model improvement. P. C., W. D. and P. S. helped with interpretation of the results and discussion. X. D., Y. H. and Z. Q. wrote the manuscript with contributions from all authors.

688

689 **Competing interests**

690 The authors declare no competing interests.