# Reducing soil nitrogen losses from fertilizer use in global maize and wheat production

Chao Wang, Yun Shen, Xiantao Fang, Shuqi Xiao, Genyuan Liu, Ligang Wang, Baojing Gu, Feng Zhou, Deli Chen, Hanqin Tian, et al.

► To cite this version:

Chao Wang, Yun Shen, Xiantao Fang, Shuqi Xiao, Genyuan Liu, et al. Reducing soil nitrogen losses from fertilizer use in global maize and wheat production. Nature Geoscience, 2024, 10.1038/s41561-024-01542-x. hal-04711541

HAL Id: hal-04711541

https://hal.science/hal-04711541v1

Submitted on 3 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Reducing soil nitrogen losses from fertilizer use in global maize and wheat production

Received: 29 November 2023

Accepted: 22 August 2024

Published online: 17 September 2024

<figure><img src="image_2.png" /></figure>

Check for updates

Chao Wang<sup>1,2</sup>, Yun Shen<sup>1,2</sup>, Xiantao Fang<sup>1,2</sup>, Shuqi Xiao<sup>1,2</sup>, Genyuan Liu<sup>1,2</sup>, Ligang Wang<sup>3</sup>, Baojing Gu<sup>1,4</sup>, Feng Zhou<sup>1,5</sup>, Deli Chen<sup>1,6</sup>, Hanqin Tian<sup>1,7</sup>, Philippe Ciais<sup>1,8</sup>, Jianwen Zou<sup>1,12</sup> & Shuwei Liu<sup>1,12</sup>

Maize and wheat are two major staple foods that collectively contribute two-thirds of the world's grain supply. The extensive use of nitrogen (N) fertilizers during the cultivation of both crops leads to significant losses of reactive nitrogen (Nr) into the environment. Here, using machine learning algorithms, we generate high-resolution maps of crop-specific soil Nr losses based on global field measurements. We estimate that global annual soil Nr losses from the use of synthetic N fertilizer in 2020, including direct emissions of nitrous oxide (N₂O), nitric oxide (NO), ammonia (NH₃), N leaching and run-off, amount to 0.18, 1.62, 0.09, 1.47 and 1.10 million tonnes N for maize, and 0.12, 1.33, 0.07, 1.21 and 0.95 million tonnes N for wheat, respectively. The annual indirect N₂O emissions induced by synthetic N fertilizer use from these soil Nr losses are estimated to be 45,000 and 37,000 tonnes for maize and wheat, respectively, with hydrologic pathways playing a predominant role. Enhancing N use efficiency up to 60% for regions below this value can achieve a total soil Nr loss mitigation potential of 4.00 million tonnes per year for the two crops, thereby reducing indirect N₂O emissions by 49%. Our results contribute to constrain global N budgets from the use of fertilizer in agriculture, which then can help to improve projections of nitrogen cycle-climate feedbacks using modelling approaches.

Nitrogen (N) is an essential nutrient element for crop growth as well as human existence, mainly supplied by the application of N fertilizer in agriculture<fnref n="1" />. Maize and wheat are crucial for guaranteeing world food security, and rank as the first and second largest global N fertilizer consumers among all crops, respectively². Unfortunately, over half of fertilizer N is not absorbed by crops or immobilized into soils but lost to the environment³. The two crops consume approximately 38% of total N fertilizer applied to all crops globally⁴, contributing significantly to

soil reactive N (Nr) losses caused by fertilization. Soil Nr losses lead to unintended adverse impacts on human health and environment, including air pollution caused by nitrogen oxides (NOₓ) and ammonia (NH₃) emissions, freshwater and coastal eutrophication attributable to N leaching and run-off, nitrous oxide (N₂O)-associated climate change and biodiversity decrease⁵,⁶.

It is widely believed that soil Nr losses from fertilized soils generally increase with the amount of applied N (refs. 7,8). The proportion of

<footnote n="1">¹Key Laboratory of Low-Carbon and Green Agriculture in Southeastern China, Ministry of Agriculture and Rural Affairs, College of Resources and Environmental Sciences, Nanjing Agricultural University, Nanjing, China. ²Jiangsu Key Laboratory of Low Carbon Agriculture and GHGs Mitigation, College of Resources and Environmental Sciences, Nanjing Agricultural University, Nanjing, China. ³Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing, China. ⁴College of Environmental and Resource Sciences, Zhejiang University, Zhejiang, China. ⁵Institute of Carbon Neutrality, Laboratory for Earth Surface Processes, College of Urban and Environmental Sciences, Peking University, Beijing, China. ⁶School of Agriculture, Food and Ecosystem Sciences, The University of Melbourne, Parkville, Victoria, Australia. ⁷Earth and Environmental Sciences Department, Boston College, Boston, MA, USA. ⁸Laboratoire des Sciences du Climat et de l'Environnement, UVSQ, CEA CNRS, Gif-sur-Yvette, France. ✉e-mail: jwzou21@njau.edu.cn; swliu@njau.edu.cn</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1** | Global soil N loss factors for maize and wheat fields at a 5 arcmin resolution in 2020 derived from RF models. **a–e**, Global maps of soil N loss factors of direct N₂O emissions (**a**), NH₃ volatilization (**b**), NO emissions (**c**), N leaching (**d**) and run-off (**e**) for maize. **f–j**, Global maps of soil N loss factors of direct N₂O emissions (**f**), NH₃ volatilization (**g**), NO emissions (**h**), N leaching</figcaption></figure>

(i) and run-off (j) for wheat. The global mean soil N loss factors using the total N inputs of grid cells (that is, N input rate multiplied by the harvest area) as weights, and 95% CIs were estimated by the Monte Carlo approach with 10,000 simulations.

applied N lost to the environment as Nr through a particular pathway is defined as the soil N loss factor (F-Nr, %) according to the Intergovernmental Panel on Climate Change (IPCC)⁹. Soil N loss factors from bottom-up approaches are generally used to estimate global or regional soil N losses from N fertilizer input, which are calculated as the F-Nr multiplied by the amount of fertilizer N applied¹⁰⁻¹². However, the quantification of F-Nr and soil Nr losses remains highly uncertain due to spatiotemporal variations¹³, especially for N run-off. Particularly, soil

N₂O is emitted directly from N fertilizer input, and also indirectly from the deposition of NH₃ and NOₓ following their emissions and hydrologic N sources⁹,¹⁴. Thus, a full accounting of soil N losses and a linkage of soil direct N losses to indirect N₂O emissions are urgently needed to bridge our knowledge gap on the global N budget.

A variety of agricultural management practices have been used to mitigate soil N losses and improve crop N use efficiency (NUE)¹⁵⁻¹⁷. However, options targeted at mitigating the loss of a given N component
<figure><img src="image_4.png" /><figcaption>**Fig. 2 |** Spatial patterns of dominant drivers regulating variation in soil Nr loss factors. **a–e**, Soil Nr loss factors of direct N₂O emissions (F-N₂O) (**a**), NH₃ volatilization (F-NH₃) (**b**), NO emissions (F-NO) (**c**), N leaching (F-Nleaching) (**d**) and run-off (F-Nrun-off) (**e**) for maize. **f–j**, Soil Nr loss factors of direct N₂O emissions (F-N₂O) (**f**), NH₃ volatilization (F-NH₃) (**g**), NO emissions (F-NO) (**h**), N leaching (F-Nleaching) (**i**) and run-off (F-Nrun-off) (**j**) for wheat. The dominant</figcaption></figure>

driver is defined as the factor with the maximum absolute value of the partial
correlation coefficient in each grid, which has been done for a 3.75° × 3.75°
moving window. Only significant correlations (P < 0.05) are shown. The inset
doughnut charts indicate the percentage of grids for which soil Nr loss factors
variation is regulated by the dominant drivers.

may stimulate the release of another and even increase emissions of
other greenhouse gases, resulting in pollution transfer or even com-
promising yields¹⁸,¹⁹. The NUE has been proposed as a robust index
for predicting soil Nr losses, and to improve it is also considered as an
effective approach to mitigate soil Nr losses and boost crop yields²⁰,
which can benefit soil carbon sequestration¹⁹. However, the interac-
tions and trade-offs between NUE and soil Nr losses in maize and wheat

cultivation at the global scale remain unclear²⁰, especially the extent to
which enhanced NUE will contribute to reduce soil Nr losses is not well
quantified. The NUE generally showed a trend to decline with increas-
ing N input rates, which in turn resulted in an increase in surplus N in
fields responsible for enhanced soil Nr losses. Generally, the applica-
tion of enhanced-efficiency N fertilizers (EEFs) can serve as a better
option to achieve synchrony of fertilizer N supply with crop demand
<figure><img src="image_5.png" /><figcaption>b</figcaption></figure>

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

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

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>d</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>e</figcaption></figure>

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

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

**Fig. 3 | Synthetic N fertilizer-induced soil Nr losses and mitigation potentials of different scenarios for maize.** The central map shows the synthetic N fertilizer-induced soil Nr losses from maize field in 2020. **a–g.** Each stacked bar charts shows the mean value of Nr losses under different scenarios for maize

globally and across six continents: North America (**a**), Europe (**b**), Asia (**c**), South America (**d**), Africa (**e**) and Oceania (**f**) and globally (**g**). The error bars indicate 95% CIs estimated by the Monte Carlo approach with 10,000 simulations. The definitions of different scenarios can be found in Methods.

by controlling the physicochemical release process of nutrients from fertilizers and biological N transformations in soils²¹.

Here, using random forest (RF) algorithms, we created global maps of F-Nr for maize and wheat fields at a resolution of 5 arcmin for 2020, by incorporating the effects of climate, soil and fertilization. Further, we presented a global estimate of soil Nr losses through major pathways due to maize and wheat fertilization, including direct and indirect N₂O emissions, NH₃ volatilization, NO emissions, N leaching and run-off. Finally, we defined optimized scenarios to assess soil Nr loss mitigation potentials through EEFs substitution and NUE improvement.

## Direct soil Nr loss factors and dominant drivers

High-resolution (0.083° spatial resolution) global maps of F-Nr of synthetic N fertilizer for maize and wheat fields were generated using RF models for 2020. Both crops showed similar patterns, but striking spatial heterogeneity regardless of Nr loss pathways, driven collectively by climate, soil property and fertilization (Fig. 1). Global mean F-N₂O, F-NH₃, F-NO, F-Nleaching and F-Nrun-off values of synthetic N fertilizer were estimated to be 0.88% (95% confidence interval (CI) 0.53–1.24%), 8.11% (95% CI 4.77–11.77%), 0.44% (95% CI 0.26–0.65%), 7.36% (95% CI

4.21–10.93%) and 5.52% (95% CI 3.20–8.06%) for maize, respectively, which were slightly greater than those estimates for wheat (Fig. 1). Soil Nr loss factors diverged by more than one order of magnitude globally, and there is an urgent need to disentangle the source of variation influencing F-Nr from global maize and wheat fertilization. F-Nr varied across crops, environments and management practices (Supplementary Tables 1–5). Here, we revealed the dominant drivers shaping F-Nr at the grid scale (Fig. 2). It showed between-crop consistency but varied across Nr loss pathways and regions. Overall, soil property played a crucial role in controlling soil F-Nr. For instance, for maize, the spatial variation in F-N₂O was positively associated with soil organic carbon content (SOC) in 28% of grids, yet was negatively correlated with pH in a quarter of the regions (Fig. 2a). This result agrees well with the role of labile carbon substrates for denitrification and confirms the fact that acidic soil conditions may promote higher N₂O/N₂ ratios by hindering N₂O reductase activities during denitrification²²,²³. Similarly, SOC was the dominant factor for the spatial variation of F-Nleaching in a third of the regions for both maize and wheat (Fig. 2d,i). Besides soil property, climate also regulates soil Nr losses. Particularly, mean annual temperature (MAT) was the primary driver shaping F-NH₃ in 19% of grids
<figure><img src="image_13.png" /><figcaption>**Fig. 4** | Synthetic N fertilizer-induced soil Nr losses and mitigation potentials of different scenarios for wheat. The central map shows the synthetic N fertilizer-induced soil Nr losses from wheat field in 2020. **a–g.** Each stacked bar charts shows the mean value of Nr losses under different scenarios for wheat</figcaption></figure>

globally and across six continents: North America (a), Europe (b), Asia (c), South America (d), Africa (e) and Oceania (f) and globally (g). The error bars indicate 95% CIs estimated by the Monte Carlo approach with 10,000 simulations. The definitions of different scenarios can be found in Methods.

for maize and 23% for wheat (Fig. 2b,g), concentrated in tropical and subtropical areas. In line with ref. 24, these findings highlight the influence of global warming on NH₃ emissions from croplands, although regional differences existed in the degree of response to warming. As previously emphasized, the N input rate is essential in regulating F-N₂O and F-NO, with more N input usually generating higher F-Nr (refs. 7,25). This is particularly evident for F-NO in regions with higher N input rates, such as in the North China Plain, Western Europe and eastern and central United States (Fig. 2c,h). Our study further emphasizes the importance of better N management for soil Nr loss abatement.

## Soil direct Nr losses and indirect N₂O emissions

Using high-resolution soil F-Nr, combining with N input data, we generated spatially explicit and crop-specific soil direct Nr losses from synthetic N fertilization in global maize and wheat fields for 2020. Higher soil Nr loss regions showed similar spatial patterns with more N fertilizer input at both the grid (Extended Data Fig. 1 and Supplementary Fig. 1) and country (Extended Data Fig. 2 and Supplementary Fig. 2) scales, and generally overlapped with the distribution of higher F-Nr (Fig. 1), indicating synthetic N fertilization was the dominant factor

shaping the loss of soil Nr. Specially, for maize, Asia (1.62 TgN yr⁻¹) and North America (1.35 TgN yr⁻¹) stood out as the hotspots of soil Nr losses, together contributing approximately two-thirds of total soil Nr losses (Fig. 3), of which, China (1.07 TgN yr⁻¹) and the United States (1.05 TgN yr⁻¹), together accounted for 48% of global soil Nr losses (Extended Data Fig. 2f). In contrast, Asia had the highest soil Nr losses at 1.96 TgN yr⁻¹ for wheat, greater than the sum of all other continents, including Europe (0.89 TgN yr⁻¹) and North America (0.45 TgN yr⁻¹) (Fig. 4). India, China and Pakistan together contributed 45% of the total loss of soil Nr (Extended Data Fig. 2i), due to vast harvest areas and extensive N fertilizer input (Supplementary Fig. 2).

From a global perspective, in 2020, 19.99 TgN yr⁻¹ and 18.96 TgN yr⁻¹ synthetic N fertilizer was supplied to maize and wheat, respectively, of which 42.2% and 42.8% was absorbed by maize and wheat crops for growth (Fig. 5a). Meanwhile, roughly 4.46 TgN yr⁻¹ (95% CI 3.41–5.58 TgN yr⁻¹) and 3.69 TgN yr⁻¹ (95% CI 2.84–4.64 TgN yr⁻¹) was lost to the environment in the form of multiple Nr forms, accounting for 22.3% and 19.5% of synthetic fertilizer N input for maize and wheat, respectively. Global soil Nr losses through direct N₂O emissions, NH₃ volatilization, NO emissions, N leaching and run-off due to synthetic N
<figure><img src="image_14.png" /><figcaption>**Fig. 5 |** Global budgets of synthetic N fertilizer-induced soil Nr losses from maize and wheat cultivation. **a,** The coloured arrows represent synthetic N fertilizer input and soil Nr losses from synthetic N fertilization in global maize (right) and wheat fields (left). The numbers in parentheses represent 95% CIs.</figcaption></figure>

**b,** The mean value of total soil Nr losses from maize and wheat fertilization partitioned by gaseous and hydrologic pathways. The error bars indicate 95% CIs estimated by the Monte Carlo approach with 10,000 simulations.

fertilization were estimated to be 0.18, 1.62, 0.09, 1.47 and 1.10 TgN yr⁻¹, respectively, for maize, slightly greater than those of 0.12, 1.33, 0.07, 1.21, 0.95 TgN yr⁻¹ for wheat (Fig. 5a). Overall, the F-Nr for NH₃, N leaching and run-off were approximately an order of magnitude greater than those of N₂O and NO (Fig. 1). As a result, soil Nr losses through NH₃ volatilization and hydrologic pathways predominated total soil Nr losses from fertilizer N (ref. 25), which together contributed over 94% of the total.

Relative to direct soil Nr losses, 'off-site' indirect N₂O emissions induced by soil N volatilization, leaching and run-off contributed significantly to global total N₂O emissions, comprising 20.2% and 23.1% total N₂O emissions from maize and wheat fertilization, respectively (Extended Data Figs. 3 and 4), which play an integral role in the global N₂O budget²⁶, but have previously received less attention²⁷. When taking into account indirect N₂O emissions, total N₂O emissions were estimated at 220.31 GgN yr⁻¹ and 160.40 GgN yr⁻¹ from maize and wheat fertilization, accounting for 5.8% and 4.2% of total emissions from N additions in agriculture, respectively¹⁴. According to our estimates, approximately three-fifths of soil Nr was lost to the water environment through leaching and run-off for both crops (Fig. 5b), comparable to an earlier estimate using a crop growth model²⁸. Generally, indirect N₂O emissions from soil hydrologic Nr losses contributed more than those from gaseous N deposition. This finding challenges our efforts to reduce hydrologic Nr losses in the context of future climate change, since increasing extreme rainfall events are projected to occur as climate change intensifies, especially in the spring and early summer²⁹, which will lead to hydrologic Nr losses being exacerbated in the future.

## Mitigation potential

The mitigation of soil Nr losses from cropland soils has received extensive attention, mainly through EEFs substitution and NUE

improvement³⁰. Among field management practices, the use of EEFs has the largest potential to mitigate soil Nr losses while sustaining crop yields (Supplementary Figs. 3 and 4), indicating a synchrony of fertilizer N supply with crop demand by controlling fertilizers nutrient release and biological N transformations in soils²¹,³⁰,³¹. However, most of suggested mitigation options have limited benefits in reducing soil Nr losses and even lead to trade-offs among soil Nr loss pathways, potentially complicating our mitigation efforts¹⁸,³². Here, we took the lead to evaluate the mitigation potential of EEF application on five soil Nr loss pathways at a high spatial resolution with the assistance of artificial intelligence (Figs. 3 and 4). The effect of EEFs on improving NUE showed striking spatial heterogeneity across global maize and wheat fields (Supplementary Fig. 5), implying that environmental conditions and field management practices should be considered when applying EEFs³¹. To the largest extent possible, when synthetic N fertilizers were fully substituted by EEFs in regions where EEFs substitution was effective to enhance NUE, our RF model predicted a global reduction in N input of 1.25 TgN yr⁻¹ for maize and 1.31 TgN yr⁻¹ for wheat, while keeping the current level of agricultural management and technology constant. This remarkable N input reduction combined with lower F-Nr of EEFs could reduce global total soil Nr losses to 3.33 TgN yr⁻¹ and 2.61 TgN yr⁻¹, accounting for 74.7% and 70.7% of the loss under the business as usual (BAU) scenario for maize and wheat, respectively (Figs. 3 and 4).

Besides EEFs application, enhancing the NUE of synthetic N fertilizer is another alternative to reduce soil Nr losses from maize and wheat production. Numerous studies have proposed to mitigate soil Nr losses via enhancing NUE in croplands³³,³⁴. Across the three cereal crops, improving NUE to 50% could save a total of 6.6 Tg synthetic N fertilizer per year in China, representing 41% of the total synthetic N input, showing great potential to mitigate direct N₂O emissions from croplands³³. Our results showed that the NUE exhibited a consistent
trade-off relationship with soil F-Nr, suggesting high NUE would decrease soil N losses for a given rate of N fertilizer (Supplementary Fig. 6). However, the random effects (study site) in our linear mixed-effects models explained more variance in F-Nr than the fixed effects, implying that NUE interacts with the local environment to shape F-Nr. If NUE increased up to 50% for regions below this value, relatively easy to achieve, global total soil Nr losses can be reduced by 26.5% (1.18 TgN yr⁻¹) and 24.7% (0.91 TgN yr⁻¹) from maize and wheat fertilization, respectively (Figs. 3 and 4). The ambitious option to assume that NUE can be increased up to 60% would mitigate 49.7% and 48.4% of total soil Nr losses from maize and wheat fertilization, respectively.

In addition, we associated direct soil Nr losses with indirect N₂O emissions to quantify the mitigation potential of indirect N₂O emissions by EEFs replacement and the increase of NUE, which can be achieved by decreasing hydrologic Nr losses to a greater extent (Extended Data Figs. 3 and 4). The combined option of 50% EEFs substitution and NUE increased up to 50%, as a realistic goal, could effectively mitigate total soil Nr losses (1.51 TgN yr⁻¹ for maize and 1.24 TgN yr⁻¹ for wheat; Figs. 3 and 4), and contribute to a total reduction of N₂O emissions by 33.7% for maize and 33.8% for wheat (Extended Data Figs. 3 and 4). As an ambitious goal, if NUE can be increased up to 60%, indirect N₂O emissions would be reduced by 49.7% for wheat and 48.4% for maize production (Extended Data Figs. 3 and 4).

Our results emphasize that the enhancement of NUE by improving agricultural management has great potential to mitigate soil Nr losses from global maize and wheat fields. According to a recent prediction³⁵, the current global cropland mean NUE can be increased by 30% through optimizing field management. Therefore, the present relatively low global averaged NUE (42.2% and 42.8% for maize and wheat, respectively; Extended Data Fig. 5) has a large potential for improvement and, in turn, for soil Nr loss mitigation. Combining the spatially explicit NUE map with N input data allowed us to identify the regions with the largest potential for soil Nr loss mitigation (that is, regions with high N input but low NUE). Maize and wheat exhibited similar spatial distribution patterns of these regions, mainly located in central North America, southeast South America, East Asia, Western Asia and Eastern Europe (Extended Data Fig. 6). The use of EEFs is a promising option for increasing NUE, but it may not be applicable to all regions. For instance, EEF substitution had no effects on NUE in North China Plain, Turkey and Spain for maize (Supplementary Fig. 5). It is also noteworthy that regions with low NUE do not always have high NUE enhancement potential (Supplementary Fig. 7), which is the joint result of N input and environmental factors²¹,³¹. As a result, the regions that are suitable for EEF substitution do not overlap completely with the hotspots of soil Nr losses (Extended Data Fig. 7). Thus, to reduce future environmental impacts of N pollution, the priority should be given to develop tailored management practice combinations that match site-specific conditions to better synchronize crop N demand with fertilizer N supply³⁵,³⁶. For regions characterized by high N inputs, the optimization of N application strategy is urgent, as N input rate was the primary driver in regulating NUE (Extended Data Fig. 8). Evidence also confirmed that downward adjusting of N input rates through optimizing N management is promising to achieve soil Nr loss abatement³⁷. However, for regions with moderate or low N inputs but where higher yields are desired, despite marginal returns for additional N inputs, applying more N fertilizer usually leads to a decrease in NUE³⁸. Hence, enhancing NUE to sustain yields requires a suit of tailored new practices towards improving the yield response to N application strategies. These strategies include, but are not limited to, fertigation, deep/band placement of fertilizers, modification of fertilizer structure, fertilizer split application and the cultivation of high-yielding varieties⁵,¹⁰,³⁹⁻⁴¹.

## Limitations of this study and future perspectives

This study provides us a full accounting of fertilizer-induced soil Nr losses from global maize and wheat cultivation, and takes the lead

to associate direct soil Nr losses with potentially caused indirect N₂O emissions. However, our estimates involve some limitations and uncertainties stemming from data sampling and modelling (Extended Data Figs. 9 and 10 and Supplementary Figs. 8–10). More details about the limitations of this study are provided in Supplementary Information. For a refined estimation of soil Nr losses from croplands and their mitigation potentials, our study emphasizes the need to (1) explore the interannual variations of soil Nr losses using long-term measurement data²⁵, (2) incorporate soil Nr losses during the fallow cropping seasons into the total N budget due to fertilization⁴²⁻⁴⁴, (3) develop biogeochemical models to constrain the current estimates of global soil Nr losses from croplands using machine learning methods¹⁰ and (4) seek tailored management practices to mitigate soil Nr losses induced by N fertilizer input given the trade-off relationship between F-Nr and NUE among cereal crops. Particularly, for the mitigation of soil Nr losses, we should also pay attention to the challenges when using EEFs. Improved N application strategies should be simultaneously considered when applying EEFs¹⁸,³¹. Moreover, new EEFs with low cost and less potential environmental risks should be developed to minimize soil Nr losses from agriculture²¹. In summary, this study improves our understanding of the contribution of gaseous and hydrologic pathways to total cropland soil Nr losses from global maize and wheat fertilization, which highlights the importance of integrating indirect N₂O emissions caused by direct soil Nr losses resulting from N fertilization into the global N budget.

## Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41561-024-01542-x.

## References

1. Chen, X. et al. Producing more grain with lower environmental costs. *Nature* **514**, 486–489 (2014).

2. *Fertilizer Use by Crop and Country for the 2017–2018 Period* (International Fertilizer Association, 2022).

3. Foley, J. A. et al. Solutions for a cultivated planet. *Nature* **478**, 337–342 (2011).

4. *Consumption* (International Fertilizer Association, 2022); https://www.ifastat.org/databases/plant-nutrition

5. Liu, W. et al. Achieving high crop yields with low nitrogen emissions in global agricultural input intensification. *Environ. Sci. Technol.* **52**, 13782–13791 (2018).

6. Compton, J. E. et al. Ecosystem services altered by human changes in the nitrogen cycle: a new perspective for US decision making. *Ecol. Lett.* **14**, 804–815 (2011).

7. Shcherbak, I., Millar, N. & Robertson, G. P. Global metaanalysis of the nonlinear response of soil nitrous oxide (N₂O) emissions to fertilizer nitrogen. *Proc. Natl Acad. Sci. USA* **111**, 9199–9204 (2014).

8. Hickman, J. E. et al. Nonlinear response of nitric oxide fluxes to fertilizer inputs and the impacts of agricultural intensification on tropospheric ozone pollution in Kenya. *Glob. Chang. Biol.* **23**, 3193–3204 (2017).

9. IPCC 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories (eds Calvo Buendia, E. et al.) (IPCC Switzerland, 2019).

10. Ma, R. et al. Data-driven estimates of fertilizer-induced soil NH₃, NO and N₂O emissions from croplands in China and their climate change impacts. *Glob. Chang. Biol.* **28**, 1008–1022 (2022).

11. Ma, R. et al. Global soil-derived ammonia emissions from agricultural nitrogen fertilizer application: a refinement based on regional and crop-specific emission factors. *Glob. Chang. Biol.* **27**, 855–867 (2021).
12. Xu, P. et al. Role of organic and conservation agriculture in ammonia emissions and crop productivity in China. *Environ. Sci. Technol.* **56**, 2977-2989 (2022).

13. Zhan, X. et al. Improved estimates of ammonia emissions from global croplands. *Environ. Sci. Technol.* **55**, 1329-1338 (2021).

14. Tian, H. et al. A comprehensive quantification of global nitrous oxide sources and sinks. *Nature* **586**, 248–256 (2020).

15. Bouwman, L. et al. Exploring global changes in nitrogen and phosphorus cycles in agriculture induced by livestock production over the 1900–2050 period. *Proc. Natl Acad. Sci. USA* **110**, 20882–20887 (2013).

16. Yin, Y. et al. A steady-state N balance approach for sustainable smallholder farming. *Proc. Natl Acad. Sci. USA* **118**, e2106576118 (2021).

17. Yu, X., Keitel, C., Zhang, Y., Wangeci, A. N. & Dijkstra, F. A. Global meta-analysis of nitrogen fertilizer use efficiency in rice, wheat and maize. *Agric. Ecosyst. Environ.* **338**, 108089 (2022).

18. Zhang, C. et al. Using nitrification inhibitors and deep placement to tackle the trade-offs between NH₃ and N₂O emissions in global croplands. *Glob. Chang. Biol.* **28**, 4409–4422 (2022).

19. Xia, L. et al. Trade-offs between soil carbon sequestration and reactive nitrogen losses under straw return in global agroecosystems. *Glob. Chang. Biol.* **24**, 5919–5932 (2018).

20. Omonode, R. A., Halvorson, A. D., Gagnon, B. & Vyn, T. J. Achieving lower nitrogen balance and higher nitrogen recovery efficiency reduces nitrous oxide emissions in North America's maize cropping systems. *Front. Plant Sci.* **8**, 1080 (2017).

21. Lam, S. K. et al. Next-generation enhanced-efficiency fertilizers for sustained food security. *Nat. Food* **3**, 575–580 (2022).

22. Liu, S. et al. A meta-analysis of fertilizer-induced soil NO and combined NO+N₂O emissions. *Glob. Chang. Biol.* **23**, 2520–2532 (2017).

23. Wang, Y. et al. Soil pH as the chief modifier for regional nitrous oxide emissions: new evidence and implications for global estimates and mitigation. *Glob. Chang. Biol.* **24**, e617–e626 (2017).

24. Xu, P. et al. Fertilizer management for global ammonia emission reduction. *Nature* **626**, 792–798 (2024).

25. Huddell, A. M. et al. Meta-analysis on the potential for increasing nitrogen losses from intensifying tropical agriculture. *Glob. Chang. Biol.* **26**, 1668–1680 (2020).

26. Yao, Y. et al. Increased global nitrous oxide emissions from streams and rivers in the Anthropocene. *Nat. Clim. Change* **10**, 138–142 (2019).

27. Del Grosso, S. J. et al. Global scale DAYCENT model analysis of greenhouse gas emissions and mitigation strategies for cropped soils. *Glob. Planet. Change* **67**, 44–50 (2009).

28. Liu, W. et al. Global assessment of nitrogen losses and trade-offs with yields from major crop cultivations. *Sci. Total Environ.* **572**, 526–537 (2016).

29. Feng, Z. et al. More frequent intense and long-lived storms dominate the springtime trend in central US rainfall. *Nat. Commun.* **7**, 13429 (2016).

30. Gu, B. et al. Cost-effective mitigation of nitrogen pollution from global croplands. *Nature* **613**, 77–84 (2023).

31. Li, T. et al. Enhanced-efficiency fertilizers are not a panacea for resolving the nitrogen problem. *Glob. Chang. Biol.* **24**, e511–e521 (2018).

32. Venterea, R. T. et al. Challenges and opportunities for mitigating nitrous oxide emissions from fertilized cropping systems. *Front. Ecol. Environ.* **10**, 562–570 (2012).

33. Huang, Y. A. O. & Tang, Y. An estimate of greenhouse gas (N₂O and CO₂) mitigation potential under various scenarios of nitrogen use efficiency in Chinese croplands. *Glob. Chang. Biol.* **16**, 2958–2970 (2010).

34. Gao, Y. & Cabrera Serrenho, A. Greenhouse gas emissions from nitrogen fertilizers could be reduced by up to one-fifth of current levels by 2050 with combined interventions. *Nat. Food* **4**, 170–178 (2023).

35. You, L. et al. Global mean nitrogen recovery efficiency in croplands can be enhanced by optimal nutrient, crop and soil management practices. *Nat. Commun.* **14**, 5747 (2023).

36. Chatzimpiros, P. & Harchaoui, S. Sevenfold variation in global feeding capacity depends on diets, land use and nitrogen management. *Nat. Food* **4**, 372–383 (2023).

37. Cui, Z. et al. Pursuing sustainable productivity with millions of smallholder farmers. *Nature* **555**, 363–366 (2018).

38. Mueller, N. D. et al. Declining spatial efficiency of global cropland nitrogen allocation. *Global Biogeochem. Cycles* **31**, 245–257 (2017).

39. Zhang, X. et al. Managing nitrogen for sustainable development. *Nature* **528**, 51–59 (2015).

40. Xia, L. et al. Can knowledge-based N management produce more staple grain with lower greenhouse gas emission and reactive nitrogen pollution? A meta-analysis. *Glob. Chang. Biol.* **23**, 1917–1925 (2017).

41. Senapati, N. et al. Global wheat production could benefit from closing the genetic yield gap. *Nat. Food* **3**, 532–541 (2022).

42. Shang, Z. et al. Measurement of N₂O emissions over the whole year is necessary for estimating reliable emission factors. *Environ. Pollut.* **259**, 113864 (2020).

43. Cui, X. et al. Global mapping of crop-specific emission factors highlights hotspots of nitrous oxide mitigation. *Nat. Food* **2**, 886–893 (2021).

44. Wang, Y., Yao, Z., Zheng, X., Subramaniam, L. & Butterbach-Bahl, K. A synthesis of nitric oxide emissions across global fertilized croplands from crop-specific emission factors. *Glob. Chang. Biol.* **28**, 4395–4408 (2022).

**Publisher's note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

© The Author(s), under exclusive licence to Springer Nature Limited 2024
# Methods

## Literature search and data extraction

A comprehensive database was compiled by collecting data from peer-reviewed publications retrieved from the Web of Science, Google Scholar and the China Knowledge Integrated Database published between January 2000 and May 2022, with search topics related to soil Nr losses ($NH_3$ volatilization, $N_2O$ and NO emissions, N leaching and run-off) from global maize and wheat croplands. The keyword combinations include: 'maize' or 'corn' or 'wheat' AND '$N_2O$' or 'nitrous oxide' AND '$NH_3$' or 'ammonia' AND '$NO_3^-$' or 'NO' or 'nitric oxide' or 'nitrogen oxide' AND '$NO_3^-$' or 'N leaching' or 'N runoff' AND 'reactive N' or 'Nr' or 'N loss'. To avoid bias in screening literature, studies were selected using the following criteria: only field-based or undisturbed lysimeter experiments were selected, whereas laboratory or pot experimental data, as well as soil column-based or modelling-simulated results were excluded; at least one soil Nr component was reported and continuously measured throughout an entire growing season (from sowing to harvesting); information on fertilizer regime and the number of experimental replications should be clearly reported; soil $NH_3$ volatilization had to be measured using the micrometeorological method or the German wind tunnel method with low uncertainties³⁷,⁴⁵; and soil N leaching had to be measured using the suction cups, lysimeters or tile drainage methods to allow for comparisons⁴⁶.

In total, we obtained a global dataset derived from 560 peer-reviewed publications, consisting of 4,000 flux observations of $N_2O$, 1,259 flux observations of $NH_3$, 339 flux observations of NO, 1,532 flux observations of N leaching and 185 flux observations of N run-off (Extended Data Fig. 10). Measurements from different sites and different treatments within a single study were considered as independent in data collection. From each publication, the seasonal cumulative soil Nr losses (kgN ha⁻¹) along with s.d. and the number of replicates were simultaneously extracted. If studies reported only the variation of soil Nr fluxes, the cumulative losses were estimated by summarizing daily Nr fluxes obtained using the linear interpolation method. For N leaching and run-off, if only the seasonal temporal volume and N concentration of leaching/run-off water were reported, we calculated the seasonal cumulative Nr losses by calculating the product of the two seasonal means. For literature data sources where the s.e.m. rather than s.d. was reported, the s.d. was determined as follows:

$$s.d. = s.e.m. \times \sqrt{n}, \qquad (1)$$

where n is the number of replications. In the absence of either s.d. or s.e.m., we contacted the corresponding author and asked for information. Otherwise, s.d. values were estimated using the averaged coefficient of variation (c.v.) (that is, the ratio of s.d. to the mean value) for the known data⁴⁷.

In addition, the following information was also collected from the literature: the geographical coordinates (latitude and longitude), crop type, tillage method, irrigation regime, residue management, fertilizer rate/source/placement/splitting frequency, experimental duration, MAT, mean annual precipitation (MAP), mean annual potential evapotranspiration, soil texture (sand, silt and clay content), pH, soil bulk density (BD), SOC, soil total N content, soil C/N ratio and crop yield as well as crop N uptake. All soil data measured once (0–20 cm) were collected from the control plots without N fertilizer input before the experiment, representing the seasonal background values to allow for comparisons. For the dynamic soil Nr loss data, we calculated the seasonal means by distinguishing the data with and without N fertilizer input. Note that due to extremely limited or insufficient literature information on the previous management of control and treatment plots, no legacy effects were considered in this analysis. Data presented only in graphs were digitized using Get Data Graph Digitizer (http://www.getdata-graph-digitizer.com/). In selected studies, gravimetric/volumetric soil water content was more frequently reported rather than

soil water-filled pore space (WFPS). Given this case, reported data were unified to the WFPS as follows:

$$WFPS\% = [VWC/(BD/2.68)] \times 100\%, \qquad (2)$$

$$VWC = GWC \times BD, \qquad (3)$$

where VWC and GWC represent soil volumetric water content and gravimetric water content, respectively.

For studies that only soil organic matter was provided, we converted soil organic matter to SOC using a Bemmelen index value of 0.58 (ref. 22). If the latitude and longitude were missing in the original studies, we extracted relevant data from http://www.google.cn/maps according to the study sites provided in the literature. If climate information is missing, we obtained the data from http://www.worldclim.org/. The aridity index was calculated as the ratio of MAP to mean annual potential evapotranspiration. Missing soil properties were derived from the Harmonized World Soil Database version 2.0 (https://data.isric.org/geonetwork/srv/api/records/54aebf11-ec73-4ff8-bf6c-ecff4b0725ea). If studies only reported data on particle size distribution (sand, silt and clay content) of soil, we obtained soil texture information based on the International Classification System of Soil Texture. In addition, to allow for comparisons, the soil pH values measured with $CaCl_2$ were transformed with the formula $pH_{[H_2O]} = 1.65 + 0.86 \times pH_{[CaCl_2]}$ (ref. 48). We further calculated fertilizer-induced soil Nr loss factors (F-Nr) and crop NUE using the equations as follows:

$$F - Nr(\%) = \frac{L_f - L_c}{N_{\text{rate}}} \times 100\%, \qquad (4)$$

$$\text{NUE}(\%) = \frac{U_f - U_c}{N_{\text{rate}}} \times 100\%, \qquad (5)$$

where $L_f$ and $L_c$ represent cumulative soil Nr losses (kgN ha⁻¹) with and without N fertilizer input, respectively; $U_f$ and $U_c$ represent cumulative crop N uptake (kgN ha⁻¹) by biomass with and without N fertilizer application, respectively; and $N_{\text{rate}}$ refers to N fertilizer applied rate (kgN ha⁻¹). The resulting database comprised 2,329, 714, 238, 744 and 81 loss factors of $N_2O$ emissions (F-$N_2O$), $NH_3$ volatilization (F-$NH_3$), NO emissions (F-NO), N leaching (F-$N_{\text{leaching}}$) and run-off (F-$N_{\text{run-off}}$), respectively, in addition to 1,273 NUE observations (Supplementary Fig. 11).

## Meta-analysis and statistics

Before analysis, the outliers were removed based on the Z-score outlier test (that is, the values exceeding ±3 s.d. from the population mean). We performed a standard pair-wise meta-analysis to calculate the weighted means of F-Nr (Supplementary Tables 1–5). As the s.d. of F-Nr was rarely reported, the variance of F-Nr ($V_{F-Nr}$) was calculated from the s.d. of soil cumulative Nr losses and the number of replicates⁴⁹ following equation (6)

$$V_{F-Nr} = \left( \frac{100}{N_{\text{input}}} \right)^2 \times \left( \frac{s.d._f^2}{n_f} + \frac{s.d._c^2}{n_c} \right), \qquad (6)$$

where $N_{\text{input}}$ is the seasonal total amount of N applied in the fertilized plots, s.d., and s.d., are the s.d. of soil cumulative Nr losses from the fertilized and control plots, respectively, and $n_f$ and $n_c$ are the number of replicates of the fertilized and control plots, respectively. The weighted means of F-Nr were calculated using the escalc function from the R package metafor version 2.4.0 (ref. 50). The potential non-independence of studies within the same site was examined by including 'study site' as a random effect. We used a non-parametric function for weighting based on the inverse of coefficient of variation per observation, instead of the inverse of the variance due to its
significant correlation with the F-Nr, which could bias the results by giving more weight to studies with small soil Nr loss rates⁵¹. Mean F-Nrs among different subgroups were significant if the 95% CI values did not overlap. For each category, between-group heterogeneity ($Q_b$) tests were used to examine whether the F-Nr showed significant differences among crop types, management practices, climatic conditions and soil properties. The Rosenthal's fail-safe number ($N_{fs}$) was calculated to examine the possibility of publication bias⁵². If the $N_{fs}$ was higher than $5n + 10$ (where n is the number of observations), we considered our results robust in this analysis (Supplementary Table 6).

Moreover, to assess the impact of different management practices (Supplementary Table 7) on soil Nr losses and crop productivity, we also performed a pair-wise meta-analysis to examine the differences in soil Nr losses, NUE, N uptake and crop yields as affected by management practices relative to the control (Supplementary Figs. 3 and 4) using the following equation⁵³:

$$RR = \ln\left(\frac{x_t}{x_c}\right) = \ln(x_t) - \ln(x_c), \quad (7)$$

where RR is the log-transformed response ratio and $x_t$ and $x_c$ are the means of soil Nr losses, NUE, N uptake and crop yields for the treated and control groups, respectively. The variance ($\nu$) is estimated as follows⁵³:

$$\nu = \frac{s_t^2}{n_t \times x_t^2} + \frac{s_c^2}{n_c \times x_c^2}, \quad (8)$$

where $s_t$ and $s_c$ are the standard deviations for the treatment and control, respectively, and $n_t$ and $n_c$ are the corresponding number of replications, respectively. Multi-level meta-analytic models were used to assess the significance of mean effect size (RR++) with 95% CIs using 'study site' as a random effect. Effect sizes from individual studies were weighted by the inverse of the variance. The effects were considered significant if the 95% CI values of the mean effect size did not overlap with 0. To improve understanding, all results were back-transformed and reported as percentage change calculated by the formula ($(e^{RR++} - 1) \times 100\%$). The meta-analysis procedures was performed using rma.mv function from the R package metafor⁵⁰.

Linear mixed-effects models of F-Nr = $\beta \times (1 \text{ NUE}) + \pi_{\text{Study site}} + \varepsilon$ were employed to evaluate how fertilizer-induced F-Nr changed in response to the increase of crop NUE (Supplementary Fig. 6). Where $\beta$ is the coefficient of (1 NUE), $\pi_{\text{Study site}}$ is the random effect of 'study site' to explicitly account for the autocorrelation among observations within each study site and $\varepsilon$ is the sampling error. We conducted these analyses using the maximum likelihood estimation with the lme4 package in R, and used R packages ggplot2 and ggeffects for visualization.

## Scaling-up estimation

We employed machine learning models to generate global maps of crop-specific soil F-Nr and NUE in 2020. The RF model was selected for its better performance on predicting soil Nr losses and agro-nomic performance by considering complex non-linear effects and interactions²⁴,⁵⁴,⁵⁵. Crop type (maize and wheat), climate (MAP, MAT and aridity index), soil properties (BD, SOC, soil C/N ratio, pH, sand/ clay content), N input rate and fertilizer type (synthetic, organic and EEFs) were incorporated into RF models as predictors. Note that spatial locations were not incorporated into our models for scaling up. Before modelling, the outliers of dependent variables were filtered based on the Z-score outlier test. To test the fit of the model, we split the total observations into a training dataset and a test dataset using a 70/30 random split, stratified by both the crop type and fertilizer type. We determined the best parameter combination of models with minimized root mean squared prediction error, based on tenfold clustered cross-validation on the training dataset. That is, for parameter

tuning, the models were trained with 90% samples of the training dataset for each fold and validated on the remaining 10%. Then, we retrained models by setting the optimized parameter combination on training dataset, and assessed predictive ability of the models using the test dataset according to root mean squared prediction error and the $R^2$ (Supplementary Fig. 10). We used the R package randomForest to train the RF models.

For global upscaling considering limited data, we combined the training and test datasets and retrained the final RF model using the same hyperparameter combinations determined by tenfold clustered cross-validation. The global gridded dataset included crop harvest areas, N input, climate and soil properties. Crop-specific harvest areas and N input data for 2020 were derived from Adalibieke et al.⁵⁶ at 5 arcmin resolution, which was the latest high-resolution data currently available. Annual climate data were obtained from the Climate Research Unit Time Series version 4.07 at 0.5° resolution (https://crudata.uea.ac.uk/cru/data/hrg/cru_ts_4.07/). We averaged climate data over the years 2018–2022 to reduce uncertainties. Spatial topsoil (0–20 cm) properties were derived from the Harmonized World Soil Database version 2.0 with 1 km resolution. For global prediction, all data were resampled at 0.083° resolution.

According to the updated spatially explicit and crop-specific F-Nr of synthetic N fertilizer established in this study, we scaled up our results to develop the global inventory of different soil Nr losses from maize and wheat fertilization. The global total soil Nr losses for each Nr loss pathway were estimated as:

$$N_{\text{loss},r} = \sum_{i}^{i} (N_{\text{rate},i} \times \text{Area}_i \times F - N_{\text{r},i}), \quad (9)$$

where $N_{\text{loss},r}$ is the global fertilizer-induced soil Nr losses including direct $N_2O$ emissions. $NH_3$ volatilization, NO emissions, N leaching and run-off; $N_{\text{rate},i}$ is the N input rate for ith grid (kgN ha⁻¹); $\text{Area}_i$ is each grid's harvested area (ha) and F-Nr, indicates soil Nr loss factors (%) for each grid. Additionally, we calculated global mean F-Nr using the total N inputs of grid cells as weights.

Besides, we also estimated the indirect $N_2O$ emissions from N fertilizer input in global maize and wheat cultivation to create a linkage. According to the IPCC 2019 refinement to the 2006 IPCC guidelines⁹, the indirect $N_2O$ emissions resulting from anthropogenic N inputs following gaseous N ($NH_3$ + N + $NO_x$ + N) deposition were calculated by multiplying the amount of gaseous Nr losses by $EF_4$ (0.010) (emission factor (EF) represents the proportion of gaseous N loss to total anthropogenic N input). Similarly, indirect $N_2O$ emissions due to N leaching and run-off were estimated by multiplying the amount of hydrologic Nr losses by $EF_5$ (0.011). To gain a full perspective on soil Nr losses from maize and wheat cultivation, we depicted a global budget of soil Nr losses from the two crops due to the use of synthetic N fertilizer (Fig. 5).

## Relative importance assessment

We used the percent increase in the mean square error to assess the feature importance for the RF models (Supplementary Fig. 12). Furthermore, a partial correlation analysis was employed to explore the dominant drivers of variation in soil F-Nr and NUE at the grid scale (Fig. 2 and Extended Data Fig. 8). This analysis was performed with $3.75° \times 3.75°$ moving windows¹³. As the resolution of the grid data is $5' \times 5'$, the surrounding 2,025 pixels were used. Initially, we calculated the coefficient and significance of the partial correlation for each pixel. Drivers with non-significant correlations ($P > 0.05$) were dropped. We then defined the dominant driver as the one with maximum absolute value of the correlation coefficient.

## Mitigation potential assessment

We explored the mitigation potential of synthetic N fertilizer-induced soil Nr losses and the relevant indirect $N_2O$ emissions due to global maize
and wheat fertilization. To test the effects of mitigation options, the BAU scenario was defined as the baseline. We assumed that the current N fertilizer application strategy remained unchanged, that is, the same as latest available in 2020. Five mitigation scenarios based on the degree of EEF substitution and NUE improvement of synthetic N fertilizer were defined as follows: (1) the EEFs 50% scenario, that is, half of synthetic N fertilizer was substituted by EEFs for each grid; (2) the EEFs 100% scenario, that is, full substitution of synthetic N fertilizer with EEFs; (3) the NUE 50% scenario, we assumed to enhance NUE of synthetic N fertilizer up to 50% for regions below this value, through optimizing technologies and management practices (such as optimizing nutrient management and crop genetic improvements); (4) the NUE 60% scenario, is similar to the NUE 50% scenario, but assumed to improve NUE up to 60% for regions below this value; and (5) a combined scenario, that is, half of synthetic N fertilizer was substituted by EEFs together with enhancing NUE up to 50% by combining other optimal management practices. For the above five scenarios, we assumed that the N demand for each crop remained consistent with the BAU scenario, that is, N input rates would decrease due to the increase of NUE. For the two EEF substitution scenarios, we obtained downward-adjusted N input rates through multiple iteration runs. We excluded a few areas that are unsuitable for EEF substitution, where EEF substitution exhibited no effect on NUE. For three mitigation measures related to NUE improvement (including the combined scenario), we calculated the target N input rates and corrected F-Nr for each grid using the following equations³⁷:

$$N_{t,i} = \frac{\text{NUE}_{u,i}}{\text{NUE}_{t,i}} \times \text{N}_{u,i}, \qquad (10)$$

$$F - \text{Nr}_{c,i} = \frac{1 - \text{NUE}_{t,i}}{1 - \text{NUE}_{u,i}} \times \text{FNr}_{u,i}, \qquad (11)$$

where Nt,i and Nui,i represent the target and regular N input rates for each grid (kgN ha⁻¹), respectively; NUEt,i and NUEu,i indicate the target and regular NUE (%), respectively; F-Nr,c,i indicates corrected soil Nr loss factors (%) due to NUE improvement and F-Nr,u,i represents uncorrected soil Nr loss factors (%) for each grid.

## Uncertainty analysis and the extent of extrapolation

To evaluate uncertainty related to modelling, we first generated 100 independent bootstrapped samples by bootstrapping the total observations, stratified on both the crop type and fertilizer type. We then trained separate RF models on each of the 100 bootstrapped samples (each with different random seed values) using the best parameter combinations²⁴,⁵⁸. Our final model is the ensemble of the 100 RF models, where the final model prediction (F-Nr and NUE) is the average of the predictions from the 100 RF models. We then calculated the coefficient of variation of the predicted values for each grid cell based on 100 model outputs to identify where larger uncertainty existed (Extended Data Figs. 5 and 9). We further used the Monte Carlo approach with 10,000 runs to estimate 95% CIs of global direct soil Nr losses and indirect N₂O emissions based on the variations in F-Nr and N input data following normal distribution. We assumed that the coefficient of variation for N input data for each grid was 20%. For EF₄ and EF₅, 10,000 random values were simulated by the normal distribution based on their means and uncertainty ranges reported by the IPCC 2019 refinement to the 2006 IPCC guidelines⁹.

We further assessed the degree of extrapolation in predicting the global F-Nr and NUE, by considering ten global layers (environmental variables and N input rate)⁵⁸. We first derived the minimum and maximum values of the ten variables from our site-based database. We then evaluated whether the values of the ten variables for each cropland pixel were within the scope of respective database ranges. Finally, we mapped the crop-specific relative proportions of interpolation and extrapolation for each pixel (Supplementary Figs. 8 and 9).

## Data availability

The dataset supporting our results and maps generated during this study are available via figshare data at https://doi.org/10.6084/m9 figshare.25546771 (ref. 59). The base maps used in this study were sourced from Natural Earth as provided at http://www.naturalearth-data.com/downloads/.

## Code availability

The source code used for this study has been deposited in the figshare data repository at https://doi.org/10.6084/m9 figshare.25546771 (ref. 59).

## References

45. Cui, Z. et al. Closing the yield gap could reduce projected greenhouse gas emissions: a case study of maize production in China. *Glob. Chang. Biol.* **19**, 2467–2477 (2013).

46. Tamagno, S. et al. Quantifying N leaching losses as a function of N balance: a path to sustainable food supply chains. *Agric. Ecosyst. Environ.* **324**, 107714 (2022).

47. Wang, Y. et al. Potential benefits of liming to acid soils on climate change mitigation and food security. *Glob. Chang. Biol.* **27**, 2807–2821 (2021).

48. Biederman, L. A. & Harpole, W. S. Biochar and its effects on plant productivity and nutrient cycling: a meta-analysis. *Glob. Change Biol. Bioenergy* **5**, 202–214 (2013).

49. Charles, A. et al. Global nitrous oxide emission factors from agricultural soils after addition of organic amendments: a meta-analysis. *Agric. Ecosyst. Environ.* **236**, 88–98 (2017).

50. Viechtbauer, W. Conducting meta-analyses in R with the metafor package. *J. Stat. Softw.* **36**, 1–48 (2010).

51. Cayuela, M. L. et al. Direct nitrous oxide emissions in Mediterranean climate cropping systems: emission factors based on a meta-analysis of available measurement data. *Agric. Ecosyst. Environ.* **238**, 25–35 (2017).

52. Rosenberg, M. S. The file-drawer problem revisited: a general weighted method for calculating fail-safe numbers in meta-analysis. *Evolution* **59**, 464 (2005).

53. Hedges, L. V., Gurevitch, J. & Curtis, P. S. The meta-analysis of response ratios in experimental ecology. *Ecology* **80**, 1150–1156 (1999).

54. Xu, X. et al. Climate change may interact with nitrogen fertilizer management leading to different ammonia loss in China’s croplands. *Glob. Chang. Biol.* **27**, 6525–6535 (2021).

55. Guilpart, N., lizumi, T. & Makowski, D. Data-driven projections suggest large opportunities to improve Europe’s soybean self-sufficiency under climate change. *Nat. Food* **3**, 255–265 (2022).

56. Adalibieke, W., Cui, X., Cai, H., You, L. & Zhou, F. Global crop-specific nitrogen fertilization dataset in 1961–2020. *Sci. Data* **10**, 617 (2023).

57. Chang, J. et al. Reconciling regional nitrogen boundaries with global food security. *Nat. Food* **2**, 700–711 (2021).

58. van den Hoogen, J. et al. Soil nematode abundance and functional group composition at a global scale. *Nature* **572**, 194–198 (2019).

59. Wang, C. et al. Data and codes for 'Reducing soil nitrogen losses from fertilizer use in global maize and wheat production'. figshare https://doi.org/10.6084/m9 figshare.25546771 (2024).

## Acknowledgements

This work was supported by the National Key Research and Development Program of China (grant no. 2022YFD1901600 to S.L.), the Technology Innovation Special Fund of Jiangsu Province for Carbon Dioxide Emission Peaking and Carbon Neutrality (grant nos. BE2023398 and BE2022423 to S.L. and J.Z.) and the Fundamental Research Funds for the Central Universities (grant nos. KYT2023001, KYTZ2023017 and KJJQ2024018 to S.L. and C.W.).
**Author contributions**

S.L., J.Z. and C.W. designed the investigation. C.W., Y.S. and S.X. established the dataset. C.W., G.L., S.X., X.F. and Y.S. performed the statistical analyses, created the figures and wrote the paper. L.W., B.G., F.Z., D.C., H.T. and P.C. participated in relevant scientific discussions and commented on the paper. All authors contributed to improving and finalizing the paper.

**Competing interests**

The authors declare no competing interests.

**Additional information**

**Extended data** is available for this paper at
https://doi.org/10.1038/s41561-024-01542-x.

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41561-024-01542-x.

**Correspondence and requests for materials** should be addressed to Jianwen Zou or Shuwei Liu.

**Peer review information** *Nature Geoscience* thanks Alex Huddell, Phillip Agredazywczuk 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.
<figure><img src="image_15.png" /><figcaption>**Extended Data Fig. 1** | Spatial patterns of synthetic N fertilizer-induced soil N losses for global maize and wheat fields in 2020. a-e, Global maps of direct soil N₂O emissions, NH₃ volatilization, NO emissions, N leaching and</figcaption></figure>

runoff per hectare of maize, respectively. f-j, Mapping of direct N₂O emissions, NH₃ volatilization, NO emissions, N leaching and runoff per hectare of wheat, respectively.
<figure><img src="image_16.png" /></figure>

**Extended Data Fig. 2** | Global synthetic N fertilizer-induced soil Nr losses for maize and wheat fields by country in 2020. Global maps of direct soil N₂O emissions (a, g), NH₃ volatilization (b, h), NO emissions (c, i), N leaching (d, j), N runoff (e, k) and total Nr losses (f, l) by country for maize (a–f) and wheat (g–l), respectively.
<figure><img src="image_17.png" /><figcaption>**Extended Data Fig. 3** | Synthetic N fertilizer-induced total N₂O emissions and mitigation potentials of different scenarios for maize. The central map shows the synthetic N fertilizer-induced total N₂O emissions from maize field in 2020. Each stacked bar charts (a-g) shows the mean value of total N₂O emissions</figcaption></figure>

under different scenarios for maize globally and across 6 continents. Error bars indicate 95% confidence intervals (CIs) estimated by the Monte Carlo approach with 10,000 simulations. The definitions of different scenarios can be found in Methods section.
<figure><img src="image_18.png" /></figure>

**Extended Data Fig. 4** | Synthetic N fertilizer-induced total N₂O emissions and mitigation potentials of different scenarios for wheat. The central map shows the synthetic N fertilizer-induced total N₂O emissions from wheat field in 2020. Each stacked bar charts (a-g) shows the mean value of total N₂O emissions

under different scenarios for wheat globally and across 6 continents. Error bars indicate 95% confidence intervals (CIs) estimated by the Monte Carlo approach with 10,000 simulations. The definitions of different scenarios can be found in Methods section.
<figure><img src="image_19.png" /><figcaption>**Extended Data Fig. 5** | Spatial patterns of N use efficiency (NUE) and their coefficient of variation (c.v.) for global maize and wheat fields. The mean values (a, b) and bootstrapped (100 iterations) coefficient of variation (standard deviation divided by the mean predicted value) (c, d) of NUE are calculated across the 100 model runs (see Methods) for each grid cell.</figcaption></figure>
a

<figure><img src="image_20.png" /></figure>

b

<figure><img src="image_21.png" /></figure>

**Extended Data Fig. 6** | Spatial patterns of hotspots for soil N loss mitigation from maize and wheat cultivation. Bivariate maps comparing the N input of grid cells (that is, N input rate multiply by harvest area) with N use efficiency (NUE) for maize (a) and wheat (b). The status groups were allocated using equal distributions. Regions with high N input but low NUE are regarded as hotspots for soil N loss mitigation.
a

<figure><img src="image_22.png" /></figure>

b

<figure><img src="image_23.png" /></figure>

**Extended Data Fig. 7** | Spatial patterns of hotspots for soil N loss mitigation by enhanced-efficiency N fertilizers (EEFs) substitution. Bivariate maps comparing the N input of grid cells (that is, N input rate multiply by harvest area) with NUE enhancement by EEFs substitution for maize (a) and wheat (b).

The status groups were allocated using equal distributions. Regions with high N input and high NUE improving potential are regarded as hotspots for soil N loss mitigation by EEFs substitution.
<figure><img src="image_24.png" /></figure>

**Extended Data Fig. 8** | Spatial patterns of dominant drivers regulating variation in NUE. Maize (a) and wheat (b). The dominant driver is defined as the factor with the maximum absolute value of the partial correlation coefficient in each grid after applying a moving 3.75° by 3.75° window. Only significant

correlations (*P* < 0.05) are shown. The inset donut charts indicate the percentage of NUE variations regulated by the dominant drivers. MAP, mean annual precipitation; MAT, mean annual air temperature; SOC, soil organic carbon content.
<figure><img src="image_25.png" /><figcaption>Extended Data Fig. 9 | The coefficient of variation (c.v.) of fertilizer-induced soil Nr losses for maize and wheat fields in 2020 derived from random forest models. The coefficient of variation of soil Nr loss factors of direct N₂O emissions (a, f), NH₃ volatilization (b, g), NO emissions (c, h), N leaching (d, i) and runoff</figcaption></figure>

(e, j) for maize (a-e) and wheat (f-j) cultivation, respectively. The bootstrapped (100 iterations) coefficient of variation (standard deviation divided by the mean predicted value) are calculated across the 100 model runs for each grid cell (see Methods for details).
<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /><figcaption>**Extended Data Fig. 10 | Geographical distribution of study sites of soil Nr losses.** Geographical distribution of study sites for maize (a) and wheat (b). Different colors of dots indicate different soil Nr loss pathways. The point size</figcaption></figure>

indicates the number of observations from that site. (c) Distribution and the number of observations (the numbers in parentheses) for soil Nr losses from maize and wheat fields.

<figure><img src="image_28.png" /></figure>