Introduction

Agricultural intensification in many parts of the world has substantially increased emissions of ammonia (NH3) to the atmosphere1,2, the release of which reduces visibility and air quality through formation of secondary particulate matter3,4,5,6,7, posing risks to human health8,9. Once deposited, NH3 can harm sensitive plant species, including through its alkaline effect, contributing to a loss of biodiversity10,11. At the same time, NH3 volatilization represents a waste of valuable reactive nitrogen (Nr) resources in agriculture2. Reducing NH3 emissions can therefore benefit both the environment and agricultural sustainability.

The dominant source of NH3 emission is from agriculture12, often accounting for over 85% of the total NH3 emissions3,13. Non-agricultural sources of NH3 emissions are much smaller, typically accounting for only 5–15% of the total emissions, depending on the region14. These sources include biomass burning, transport, industry, residential and some natural sources, such as soil and ocean emissions. Volatilization of NH3 is strongly dependent on environmental conditions. For example, based on simple thermodynamics, NH3 volatilization roughly doubles every 5 °C14. Accordingly, it has been reported that measured NH3 emissions from seabird colonies increased about 3 times for an increase of 10 °C (equivalent to Q10 ~ 3; Q10 represents a relative increase in NH3 emissions for every 10 °C rise in temperature)15. However, agricultural systems are far more complex, so a generalized function that describes the temperature effect on NH3 volatilization is likely to be over-simplified for human-managed systems; the temperature sensitivity is also constrained by N-pool limitations and alternative fates of ammonium, which depend upon agricultural management decisions.

A widely applied approach for estimating NH3 emissions is the use of emission factors (EFs), which represent a unit emission rate scaled by activity statistics (such as livestock numbers or fertilizer usage). As EFs can only consider the climatic effects in a limited way, this approach is unable to provide an accurate representation of the spatial and temporal variations in emissions as climate varies from year-to-year and evolves in the longer term14. An alternative approach is the use of process-based models, which are developed based on the theoretical understanding of relevant processes that govern NH3 emissions16,17,18,19,20,21,22,23,24. Such process-based models can be applied to integrate the main effects of environmental drivers and influences of human activities when calculating NH3 emissions21,22,25,26,27,28. For global agricultural NH3 emissions in the twenty-first century, two representative process-based models quantified emissions at 35 Tg N yr−1 (CAMEO)29 and 48 Tg N yr−1 (FANv2)27, while estimates based on EFs30,31,32,33 reported varying emissions from 32 to 54 Tg N yr−1.

Global agricultural NH3 emissions have increased sharply since 197033, largely due to intensified crop and livestock production34. Meanwhile, warming further enhances NH3 volatilization, making climate change an increasingly important driver of future emissions. A recent study estimated that global NH3 emissions from three major crop production systems are projected to increase by 5–16%35 following different climate trajectories. Under scenarios of intense warming, emissions could increase by up to 40% in central to northern Europe36, by 81% in the US cropland37 and by 32% in China’s cereal production systems38. While these studies provide valuable insights into the climate-driven NH3 emissions from croplands, they largely omit livestock systems, which account for a substantial share of global agricultural NH3. More comprehensive assessments, including both crop and livestock systems, have suggested that global emissions may increase by 42% due to a 5 °C temperature rise14, or by 7–22% under alternative climate projections29. The wide range of estimates arising from different empirical and modeling approaches highlights persistent uncertainties in quantifying climate-dependent NH3 emissions and highlights the need to evaluate the effectiveness of mitigation actions in a warming climate.

In this study, we address these gaps using AMCLIM23,24, a recently developed process-based emission model that explicitly quantifies agricultural NH3 emissions in relation to Nr flows in both crop and livestock systems. AMCLIM integrates the effects of environmental factors on N processes and accounts for major sectoral differences in management practices (see “Methods”). Our simulations show how NH3 emission is co-determined by environmental factors and management practices (Fig. 1 and Supplementary Fig. 1), and how temperature sensitivity of NH3 volatilization varies strongly across climatic conditions and agricultural activities. We further make projections of warming-driven NH3 emissions for the mid-term (2041–2050) and long-term (2091–2100) under several climate scenarios, and assess how global warming alters the effectiveness of mitigation measures. Our findings show how projected warming can substantially reduce the efficacy of NH3 abatement measures, which have important implications for future air quality and N management.

Fig. 1: Global annual agricultural NH3 emissions.
Fig. 1: Global annual agricultural NH3 emissions.The alternative text for this image may have been generated using AI.
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a Geographical distributions of NH3 emissions calculated from the full AMCLIM application, taking account of climate and management differences (base run for 2010, excluding mitigation measures). White areas indicate that the activity data and hence NH3 emissions are zero. b Comparison between NH3 emissions calculated from the full AMCLIM application and emissions using an Emission Factor (EF) approach for each sector combined with sector activity statistics. The values are the ratio of NH3 emissions using the full AMCLIM application divided by EF-based emissions.

Global agricultural NH3 emissions

Through application of AMCLIM, we estimate global agricultural NH3 emissions at 44.9 Tg N yr−1 in 2010, which is comparable to other studies27,28,33 (see Supplementary Note 2 and Supplementary Table 1). Taking account of climatic and management differences, our simulations show the highest agricultural emissions of NH3 to occur in South Asia, East Asia, Europe, North America and South America (Fig. 1a). To illustrate the consequences of climatic and management differences on emission patterns, we applied the AMCLIM results to establish globally averaged EFs, which were then mapped using activity statistics (see “Methods”). Figure 1b, shows that regional emissions based on the full AMCLIM modeling can be 50% larger or 40–60% smaller than the simple EF approach, highlighting the importance of incorporating spatial variability in climate and management practices. This comparison reveals that the use of simple EF estimates for NH3 would substantially overestimate emissions in many northern and other cooler regions and underestimate emissions in hotter and more continental locations. The pattern shown in Fig. 1b is complex, reflecting the combined effects of spatially varying climatic conditions and management practices.

Most NH3 emissions occur in the northern hemisphere (Fig. 1a and Supplementary Fig. 2), with largest emissions in spring and summer (Supplementary Fig. 3). Peak emissions exceeding 50 kg N ha−1 yr−1 occur in the North China Plain (NCP), northern India, Pakistan and the Netherlands (Fig. 1a); emissions over 20 kg N ha–1 yr−1 are widespread in the eastern US, India, and parts of Southern America and Europe, with the dominant source of emissions being spatially different (Supplementary Figs. 4 and 5). We estimate China, India, US, Brazil, and Pakistan to be the top five countries contributing to NH3 emissions at 8.8, 7.4, 4.5, 3.0, and 2.0 Tg N yr−1, respectively, which together account for nearly 60% of global emissions. Our simulations suggest that ~2/3 of emissions result from livestock farming (housing, manure storage/processing systems and manure applied to land), with ~1/3 of NH3 emissions from the use of synthetic fertilizer (Supplementary Fig. 6). Cattle represent the largest sector share, contributing 60% of livestock emissions and nearly 40% of total agricultural emissions (Supplementary Fig. 6).

Temperature sensitivity of NH3 emissions

Based on temperature perturbation experiments, we find that a 2 °C rise in temperature results in global annual agricultural NH3 emissions increasing by 7.0%, while NH3 emissions decline by 6.4% when temperature is reduced by 2 °C (Table 1). Going beyond this range can give non-linear responses that also differ by emission source (Supplementary Table 2). The largest absolute increase in agricultural NH3 emissions due to 2 °C additional warming occurs at 20°N–40°N (Supplementary Fig. 7a), and the highest relative increase in NH3 emissions is found in polar regions north of 60°N (Supplementary Fig. 7b).

Table 1 Results of temperature perturbation experiments. Percentage changes in global NH3 emissions and the percentage of available nitrogen volatilized (PV) due to 2 °C temperature changes
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Table 1 distinguishes the percentage changes in emissions from the percentage changes in the fraction of available N that is emitted (Pv) at each stage. For most sources, the two values are the same. However, NH3 emissions from manure storage/processing and application to land depend on previous activities, i.e., earlier stages of the processing of Nr in the system. If higher NH3 emissions originate from previous stages, less ammoniacal N in livestock excreta is available, resulting in less NH3 emissions from subsequent activities. As a result of this interaction, while the relative change in PV for manure application is 6.8%, the total NH3 emissions from this source only increase by 2.9% with a 2 °C increase (Table 1).

Globally, we find a temperature sensitivity of NH3 volatilization that represents 3.4% relative increase in NH3 volatilization for each 1 °C increase in mean temperature, compared to the baseline results for the year 2010 (with substantial regional differences and differences between emission stage as shown in Fig. 2). We find especially high temperature sensitivity for synthetic fertilizer (Fig. 2b), with values over 10% °C−1. For manure storage (including manure processing), high temperature sensitivity frequently occurs in cold environments such as northern Europe, Siberia and Tibet (Fig. 2d). In regions with hot temperatures, such as within in the tropics, almost complete volatilization of ammoniacal N (TAN) pools limits further emission with warming, thereby reducing the temperature sensitivity. For intensive livestock housing, the effect of temperature can be smaller due to management of temperature in livestock houses16,24. Even though we have accounted for this effect, we still find substantial temperature sensitivity of NH3 emissions from livestock housing (4.9% °C−1), which is particularly seen in areas dominated by more informal livestock housing systems (i.e., partially enclosed and naturally ventilated livestock houses made with local materials like mud bricks or timber) such as in Africa (Fig. 2c).

Fig. 2: Temperature sensitivity of NH3 volatilization.
Fig. 2: Temperature sensitivity of NH3 volatilization.The alternative text for this image may have been generated using AI.
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Temperature sensitivity is expressed as percentage change in the fraction of available N volatilized as NH3 per °C compared with baseline emissions for 2010 (excluding mitigation measures). a All crop and livestock sources, b synthetic fertilizer use, c livestock housing, d manure storage (inc. manure processing), e manure application to land and f grazing.

Overall, the effect of warming on NH3 emissions estimated in this study (3.4% °C−1) is smaller than 8.4% °C−1 found by Sutton et al.14 who applied empirical relationships to estimate the temperature sensitivity. This is especially seen for manure application to land and grazing in Australia, the Middle East, and Sahel regions (Fig. 2e, f), largely because most ammoniacal N is already lost as NH3 under current conditions. In hot climates, while the volatilization potential increases substantially, in practice this can be constrained by limitation in the amount of remaining TAN available for volatilization. In extremes, once all TAN is volatilized, additional warming cannot increase emissions further. By contrast, temperature sensitivity tends to be high in regions with low NH3 volatilization because emission increases substantially when the environment gets warmer, while there is no TAN limitation to further emissions (only a small percent of the available TAN is volatilized). These cases can be particularly seen in places with low PV values for synthetic fertilizer use (Fig. 2b and Supplementary Fig. 8b).

The temperature dependence in this study is similar to the estimate of 3.0% °C−1 by Beaudor et al.29 using the CAMEO model. The similar response of AMCLIM to CAMEO29 can be considered fortuitous since their estimate is mainly associated with increased soil ammonium content, while their indoor emissions are indirectly dependent on climate through altering net primary productivity, which increased their estimated amounts of livestock feed. By contrast, the AMCLIM response focuses on the direct warming interactions of ammonia volatilization.

On the global scale, the temperature sensitivity of livestock housing (4.9% °C−1) is similar to that of manure storage emissions (5.2% °C−1). These values are both higher than the temperature dependence for synthetic fertilizer application to land (3.5% °C−1), manure application (3.5% °C−1) and grazing emissions (2.7% °C−1) (as shown in Table 2). These differences can be partly explained NH3 volatilization being the dominant N loss pathway for livestock housing and manure storage, whereas other N processes, such as nitrification and plant N uptake also deplete the TAN pool for fertilizer and manure application to land, and grazing. Since those other N processes are also temperature dependent (see Supplementary Note 5 and Supplementary Fig. 9), this affects the overall temperature dependence of NH3 volatilization for fertilizer and manure application and grazing. In this way, the difference in temperature dependence between housing/storage and land-application/grazing, gives an indication of the extent to which these other field-related factors reduce more direct temperature dependence of NH3 emissions. These effects are distinct from those that also result from the depletion of TAN through the manure management chain (from housing, to storage, to spreading). As shown in Table 1, the effect of temperature on total NH3 emissions for manure storage/processing and manure application is smaller than the corresponding effect on PV. Thus, the differences in PV reflect the mix of contributing temperature-dependent processes, while the differences in total NH3 emissions also reflect temperature-related interactions associated with the depletion of TAN through the manure management chain. The responses are further complicated by interactions with water availability, where sufficient moisture is needed to allow (temperature-dependent) urea hydrolysis as a precondition for NH3 emission, which can also be reduced in conditions of high rainfall and wet soils due to the high solubility of NH3 (Fig. 2b).

Table 2 Global and regional NH3 emissions and mitigated emissions in reference year 2010, and projections for 2041–2050 and 2091–2100 using climate data from SSP1-2.6 and SSP5-8.5 (for scenarios, see Fig. 4, with effects of other socio-economic drivers excluded)
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Implications for future NH3 mitigation strategies at global and regional scale

Our results highlight the importance of considering NH3 emission mitigation in an integrated way, especially given the context that climate change is projected to increase emissions29,35. All source activities need to be targeted at the same time because of the close link between the sequential stages in agricultural systems39,40. Hence mitigating emissions from only housing or storage would increases emissions from manure application, unless measures are taken at all three stages. Conversely, efforts to reduce NH3 emissions from the application of manure are compromised if a large fraction of N has already been lost due to lack of measures taken to reduce N losses at earlier management stages, with the consequence that manure becomes less valuable as a N resource.

Practices to reduce agricultural NH3 emissions include: (i) optimizing N application rates to meet crop needs41,42, (ii) better application techniques such as incorporation and deep placement of fertilizers and manure40,43,44,45, (iii) limiting the emission surfaces in animal houses40, (iv) improving animal feed to decrease N surplus in excreta40,45, (v) covering manure stores40,45, and (vi) storing unmanaged manure45. By incorporating such a simple package of these six mitigation measures (see “Methods” and Supplementary Table 3), we estimate that agricultural NH3 emissions could be reduced by 31% globally (based a 2010 baseline; Table 2 and Supplementary Fig. 10). These measures are found to be generally effective across the globe, with the largest relative reductions in our simulations for East Asia and Europe (Table 2 and Supplementary Fig. 10).

However, when considering the warming effects on NH3 emissions in a changing climate, we estimate that the same package of measures would be less effective in achieving emission reductions, thereby making it harder to reach environmental policy goals. To assess this, we used a set of future climate projections based on the shared socio-economic pathways (SSPs), which describe alternative trajectories of socio-economic development and associated greenhouse gas emissions. Specifically, we chose SSP1-2.6 (a sustainability-oriented pathway with low challenges to mitigation and adaptation), SSP2-4.5 (a “middle-of-the-road” pathway with moderate challenges), SSP3-7.0 (a regional rivalry pathway characterized by high population growth, limited technological development, and high challenges to mitigation), and SSP5-8.5 (a fossil-fuel-driven development pathway with high energy demand and very high emissions)45. These scenarios span a range of radiative forcings increasing from 2.6 to 8.5 W m⁻² and were analyzed for the mid-century (2041–2050) and late-century (2091–2100) periods. Assuming the same activity data and management practices as the year 2010 (i.e., using only the temperature outputs of these scenarios), we project increases in NH3 emissions by 4.6 ± 1.4% (SSP1-2.6, where the range represents 1× standard deviation from 8 climate models for 10-year simulations), 9.9 ± 2.5% (SSP2-4.5), 15.2 ± 4.0% (SSP3-7.0) and 21.7 ± 5.3% (SSP5-8.5) in 2091–2100 (Figs. 3–4 and Table 2), as a result of warming. Under an ambitious climate mitigation scenario (SSP1-2.6), we find that global warming has small effects in increasing NH3 emissions, and the collective package of NH3 mitigation measures can still largely achieve the anticipated outcome (with globally 90% effectiveness of NH3 mitigation as the 2010 baseline of no additional warming). By contrast, under SSP5-8.5 (considering a global land temperature increase of 6.5 °C), we find that around half of the mitigation potential (of the measures package without climate warming) is offset by the warming-induced increase in NH3 emissions. Use of a full set of outputs from these scenarios (including for changed activity statistics) would imply even larger emissions than those which we examine here (see further below).

Fig. 3: Geographical distribution of projected changes in agricultural NH3 emissions.
Fig. 3: Geographical distribution of projected changes in agricultural NH3 emissions.The alternative text for this image may have been generated using AI.
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Comparisons between baseline estimates for 2010 and projections for 2091–2100 under four SSP scenarios a SSP1-2.6, b SSP2-4.5, c SSP3-7.0 and d SSP5-8.5. The focus here is on the temperature effects of these SSP scenarios; other socio-economic effects (e.g., on fertilizer use, livestock numbers) are intentionally excluded. The simulations are shown for runs without the inclusion of emission mitigation measures.

Fig. 4: Projected NH3 emissions in 2100 under four future climate scenarios and emission reductions estimated to be achieved applying a package of six agricultural management measures.
Fig. 4: Projected NH3 emissions in 2100 under four future climate scenarios and emission reductions estimated to be achieved applying a package of six agricultural management measures.The alternative text for this image may have been generated using AI.
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a Global and regional increases in NH3 emissions under the four SSP scenarios compared with 2010 (assuming the same activity level and considering climate effects only). b Effectiveness (dimensionless) of future NH3 emissions mitigation under climate warming, being the ratio of emission reduction for each future scenario relative to the reduction achieved for 2010 (see Table 2), for a package of six mitigation measures applied equally in all the climate scenarios. A negative value of effectiveness means that the increase in emissions due to warming exceeds mitigation. The SSP climate scenarios are based on the Shared Socioeconomic Pathways approach, with radiative forcing increasing by 2.6 (least warming), 4.5, 7.0, or 8.5 W m−2 (greatest warming), denoted as SSP1–2.6, SSP2-4.5, SSP3-7.0, and SSP5–8.5, respectively. As with Fig. 3, the focus is on climate warming interactions, and the effects of other socio-economic drivers are deliberately excluded. The boxplots show the mean (black dots), median (horizontal lines), 25th–75th percentile (boxes) and 5th–95th percentile (whiskers) of the estimated changes for global and regional emissions from 2091 to 2100 relative to the baseline year 2010. The region boundaries are shown in Supplementary Fig. 11.

Based on our analysis, the largest effect of warming is estimated for South America, which is associated with only 0.03 effectiveness of the standard abatement package (i.e., mitigation is almost entirely offset by the warming-induced increase in emissions) compared with mitigation in the absence of climate warming (Fig. 4b). This can be attributed to both a lower mitigation potential of the measures package compared with other regions (Table 2) and a rather high sensitivity to temperature increase (Fig. 4a), which in turn reflects a high share of grazing and fertilizers to total emissions (Supplementary Figs. 4 and 5).

Our results show that additional abatement measures would be needed in a warmer climate to achieve the same level of NH3 emission reduction than achieved in the present climate. It emphasizes the need for substantial action to reduce NH3 emissions, especially considering that the anthropogenic Nr inputs in the future may increase due to increasing food demand46, amplifying the tendency to globally increasing NH3 emissions.

High-latitudes are projected to experience more warming than mid- and low-latitudes47. Given that the higher temperature sensitivity under cold conditions, there is a substantially greater risk of larger NH3 emissions increases in high-latitude regions than elsewhere (Figs. 3 and 4a), with implications for increased pollution, adverse environmental effects and reduced nutrient use efficiency.

We expect that the temperature sensitivity estimated by our approach is probably conservative since we do not include the impacts of higher temperature on soil moisture change. Hence, the warming effect could be amplified by further dryness, which can cause more NH3 emissions under certain circumstances48,49,50, given that NH3 emissions are also regulated by water availability. Similarly, our simulations do not include the effect of leaf-surface interactions on bi-directional NH3 fluxes, which are expected to increase temperature dependence for field-based emissions19,23. Conversely, if a region were to become both hotter and wetter, the temperature effect could be offset while increasing the share of Nr that is lost as leaching or runoff23. We should emphasize that our projections focus specifically on the effect of global warming on NH3 emissions. The SSP scenarios and variants (e.g., Kanter et al.51) also provide outputs related to socio-economic development with corresponding agricultural practices embedded in the SSPs, including dietary change. For example, a SSP scenario that represents substantial future agricultural intensification along with high animal protein intake diets and resource-intensive production would require higher demand of N inputs through fertilizer application and expanded livestock production and further increase NH3 emissions compared with the effects considered here focusing specifically on temperature. Consideration of such wider socio-economic interactions can be considered as multiplicative to the AMCLIM estimates we present here, and could be explored further in future research. Other drivers that are worth investigating in future research include the N interactions with emission and deposition of nitrogen oxides and changes in land use under contrasting SSPs.

In this study, we highlight the importance of integrating future climate warming into global and regional NH3 reduction policies. Whereas a simple package of six measures can reduce NH3 emission substantially, in a warmer world, further and more ambitious measures will be needed to achieve the same level of emission reduction. It is also important to see NH3 mitigation in the context of actions to “halve the global waste of Nr resources”52,53. Based on a typical present fertilizer value of US$1.30 per kg N, the 2010 estimate of global NH3 emissions represents an annual waste of US$58 billion. Together with other forms of wasted Nr and the wider costs for human health, ecosystems and climate change, it presents a strong case for adopting cost-effective methods to reduce agricultural NH3 emissions, as part of a wider package of actions towards more efficient management of the N cycle.

Methods

AMCLIM model

We used the AMCLIM version 1.0 model to estimate agricultural NH3 emissions from livestock farming and synthetic fertilizer use. AMCLIM is a dynamical process-based model that incorporates the effects of environmental drivers on the formation and transport of N compounds to simulate the temporal evolution of various N species, with a focus on NH3 volatilization. Three modules are specially designed to simulate relevant physical, chemical, and biological processes that govern the N flows in agricultural systems while also considering management practices: (a) livestock housing, (b) manure storage (including processing) and (c) application of manure to land. Pools of N compounds are determined by a mass balance approach at every time step, with flows between the N pools calculated. Simulated fluxes depend on the context. Details of simulated physical transport, chemical transformation and plant N uptake are presented in refs. 23,24.

Here, we focus on describing the volatilization of NH3, which is a physiochemical process that typically takes place from wet or drying surfaces. Gaseous NH3 is in dynamic equilibrium with aqueous ammonium depending on the substrate pH and temperature, which can be calculated by the following equations that represent the combined effects of gas solubility (Henry’s Law) and aqueous phase dissociation:

$${{{\rm{\chi }}}}\,=\,\frac{161500}{T}\exp \left(\frac{-10378}{T}\right)\Gamma$$
(1)
$${\Gamma }\,=\frac{[{{{{\rm{NH}}}}}_{4}^{+}]}{[{{{{\rm{H}}}}}^{+}]}=\frac{[{{{\rm{TAN}}}}]}{{K}_{{{{{\rm{NH}}}}}_{4}^{+}}+[{{{{\rm{H}}}}}^{+}]}$$
(2)

where KNH4+ is the dissociation constant of ammonium (NH4+), and Γ is the NH3 emission potential defined as the ratio of [NH4+]/[H+] in refs. 18,54. TAN is total ammoniacal nitrogen that is an aggregated N species (TAN = NH3 + NH4+).

The concentration difference of NH3 between the surface and the atmosphere, along with the atmospheric resistances, determine the volatilization of NH3 (\({F}_{{{{{\rm{NH}}}}}_{3}}\), gN m−2 s−1) from surface to the atmosphere, which is calculated as:

$${F}_{{{{{\rm{NH}}}}}_{3}}=\frac{{[{{{{\rm{NH}}}}}_{3}({{{\rm{g}}}})]}_{{{{\rm{srf}}}}}-{\chi }_{{{{\rm{atm}}}}}}{{R}_{{{{\rm{a}}}}}+{R}_{{{{\rm{b}}}}}}$$
(3)

where \({[{{{{\rm{NH}}}}}_{3}({{{\rm{g}}}})]}_{{{{\rm{srf}}}}}\) and \({\chi }_{{{{\rm{atm}}}}}\) are NH3 concentrations at the surface and atmospheric NH3 concentration at a reference height consistent with atmospheric resistances. The atmospheric NH3 concentration was set to zero in all AMCLIM simulations presented here. Ra and Rb are aerodynamic and boundary layer resistance, respectively. AMCLIM simulates NH3 volatilization as a unidirectional process, i.e., emission only, and deposition is not simulated. For the sources considered here (fertilizer, manure, urine patches), \({[{{{{\rm{NH}}}}}_{3}({{{\rm{g}}}})]}_{{{{\rm{srf}}}}}\) is much larger than \({\chi }_{{{{\rm{atm}}}}}\), so that inclusion of \({\chi }_{{{{\rm{atm}}}}}\) has negligible effect. There is no interaction with surface vegetation, so that surface resistance is excluded in Eq. (3). Therefore, the quantified emissions should be considered as net gross emissions. Conversely, for simulation of bi-directional exchange fluxes with vegetation (not the focus of the present study) the value of \({{{{\rm{\chi }}}}}_{{{{\rm{atm}}}}}\) would need to be included14.

Model input data

There are three major types of geospatial inputs to AMCLIM: meteorological inputs, soil properties and activity data. The AMCLIM model is driven by hourly ERA5 reanalysis meteorology55, including air temperature, relative humidity (derived from dew point temperature), wind speed, rainfall, soil temperature, and water content at two depth levels (0–7, 7–28 cm), and surface and sub-surface runoff fluxes.

Soil properties required by AMCLIM include soil pH, soil texture (sand, clay, and silt fraction) and soil organic matter content. These data are from Harmonized World Soil Database (HWSD) v1.256.

A wide range of activity data have been extensively used by AMCLIM. For livestock farming, livestock and storage and other manure management systems (MMS) data are obtained from FAO Global Livestock Environmental Assessment Model (GLEAM, https://www.fao.org/gleam/en/). The livestock data contain information on the geographical distribution at a resolution of 1 × 1 km2 of livestock population, average live-weight, and total N excretion rates, which are categorized by livestock category, species, and production system. The global livestock populations and their geospatial distributions were based on FAOSTAT data for 2010 and the Gridded Livestock of the World (GLW) model57.

For synthetic fertilizer use, the Global Gridded Crop Model Intercomparison Phase 3 (GGCMI3) dataset provides N application data for 16 major crops, including N application rates and total N applied to crops58,59. The areas of croplands are then derived from GGCMI3, which have incorporated the harvested area from the Farming the Planet 2 (FTP2) dataset60.

We use the crop calendars from the GGCMI3 dataset in AMCLIM simulations, which distinguish the planting and harvesting seasons of crops between rain-fed and irrigated systems. The crop calendars are static, based on a climatology, and are used to determine the timing of fertilizer application. The Global Rainfed, Irrigated and Paddy Croplands (GRIPC) dataset is used to classify cropland into rain-fed and irrigated systems and to determine the irrigation events and corresponding crop calendars.

Model simulations

Simulations for livestock farming include the following sectors: cattle (including buffaloes), pigs, chicken, sheep, and goats. All three modules in AMCLIM are operated for representing the activities and different practices of the livestock sectors, from animal housing to manure storage/management and then to the ultimate land application. Ruminant (cattle, sheep, and goat) grazing is also specifically modeled to differentiate the processes from land application of fertilizers.

We categorize three N types for synthetic fertilizer use: urea, ammonium and nitrate. Combining the GGCMI3 N application data with IFA country-level synthetic fertilizer consumption statistical data, we split the application rates into fractions of these three groups of applied N. The area of cropland that uses a specific type of fertilizer is proportional to the fraction of the fertilizer used.

The AMCLIM model has been applied at the site scale and has been intensively evaluated by a series of detailed comparison of time series between measured and modeled fluxes for agricultural activities23,24. Global simulations were conducted for the reference year 2010 on a longitude-latitude grid at a resolution of 0.5° × 0.5° (equivalent to 39 × 55 km2 at 45° latitude) and were performed at an hourly time step. All model inputs were resampled to the model resolution if necessary. AMCLIM was set up to use a one-year spin-up in order to keep an annual cycle of simulation period for each grid. Detailed descriptions of the global application of AMCLIM can be found in refs. 23,24.

We use the percentage of N that is lost via NH3 emissions, PV, as an indicator of NH3 volatilization, which is expressed as follows:

$${P}_{{{{\rm{V}}}}}=\frac{{F}_{{{{{\rm{NH}}}}}_{3}({{{\rm{annual\; total}}}})}}{{N}_{{{{\rm{activity}}}}}}\times 100$$
(4)

where Nactivity refers to excreted flux of N in livestock houses for housing, stored or managed N from livestock excreta for manure management, excreted N on pastures by ruminants for grazing, applied N from manure and synthetic fertilizer for land application of manure and synthetic fertilizer, respectively. \({F}_{{{{{\rm{NH}}}}}_{3}({{{\rm{annual\; total}}}})}\) is the annual total NH3 emission from the corresponding activity. The PV was also used to derive a set of generalized EFs for synthetic fertilizer use and livestock systems from the baseline simulations. We calculated global average EFs (expressed in the same way as PV) for synthetic fertilizer application (16% for urea and 13% for non-urea fertilizer such as ammonium nitrate), and for each type of livestock with all management stages included (see Supplementary Table 4). These global average EFs varied across each activity source were then used to generate a comparison map that shows spatial differences between the baseline results and EF-derived emissions (Fig. 1b).

Temperature perturbation experiments were performed with temperatures (both air and ground) increased and decreased by 2 °C, while other conditions were kept the same as the baseline simulations (the soil water content was not simulated explicitly in these experiments). The temperature sensitivity kT at present state is derived from the relative change in PV due to ±2 °C normalized by temperature change, using following equation:

$${k}_{{{{\rm{T}}}}}=\frac{{{dP}}_{{{{\rm{V}}}}}}{{P}_{{{{\rm{V}}}}}d{T}_{{{{\rm{air}}}}}}$$
(5)

We examined a simple package of six linked mitigation measures for NH3 emission abatement. By a “simple package” we mean: (a) a short list of measures that are widely available and cost-effective (as informed by the UNECE Ammonia Guidance Document40), (b) a combined package that fits simply and logically together, where the selected measures complement each other, as outlined in Chapter 7 of the UNECE Guidance Document on Integrated Sustainable Nitrogen Management39, and which (c) draw on simple principles of Sustainable Nitrogen Management as outlined in Chapter 2 of the same UNECE nitrogen guidance document39. By cost-effective, we mean measures that with basic investment can typically pay for themselves considering fertilizer N and other benefits to farmers, for which see Sutton et al.61. The simulated package of six measures consisted of:

A1: decreasing application rates of synthetic N fertilizer by 20% (matching to N savings accomplished by measures A2, B2, C1, and C2, in accordance with UNECE Principle 639, that reductions in N losses should be matched by reductions in N inputs to avoid pollution swapping).

A2: incorporation, deep placement or injection of 25% of fertilizers and manure applied to field, which reduces exposure of these N resources to the atmosphere. We selected this modest ambition of 25% (rather than 100%) to emphasize that the approach be focused in the most cost-effective situations (e.g., largest farms or where sufficient labor available); a more ambitious strategies could assume a higher share.

B1: reducing livestock N excretion by 10% through improved animal feed. This operates on the UNECE principle39, that reducing N inputs by improved diets (e.g., avoiding excess crude protein intake) leads to reduced excretion and hence reduced NH3 emissions.

B2: decreasing emitting surface area in houses by 20%. This measure applies the simple UNECE principle39 that reducing the area of manure exposed to the atmosphere tends to reduce NH3 emissions.

C1 and C2: covering storage tanks holding of liquid manure (C1) and properly storing solid manure in covered storage units (C2). This simple measures applies the same UNECE principle39 as B2. Covering manure stores also avoids odor and helps retain valuable fertilizer value of manures.

As compared with the full list of 74 measures identified by the UNECE Nitrogen Guidance Document39, this short list of six basic and widely cost-effective measures can thus be considered as a simple package. The selection is informed by comparison of cost-effectiveness, noting that some measures (not selected here), such as scrubbing of exhaust air of animal houses, tend to be more expensive61. Cost-effectiveness will vary regionally (e.g., in relation to labor and capital costs and detailed mode of implementation), but the underlying principles are common to all regions.

We first quantify the effect of each measure on NH3 abatement individually and then applied all six mitigation practices as a package to evaluate the integrated reduction. Details are given in Supplementary Note 4 and Supplementary Table 3.

Estimated NH3 emissions under climate scenarios

We estimate future NH3 emissions under four Shared Socioeconomic Pathways (SSPs): SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5, respectively62. These pathways represent climate change scenarios for different levels of radiative forcing resulting from greenhouse gas emissions. We focus on investigating the effects of temperature changes on NH3 emissions. We use near-surface air temperature from eight Earth Systems Models (ESMs) in the context of Coupled Model Intercomparison Project Phase 6 (CMIP6).

These ESMs include CanESM5, CESM2, CIESM, GFDL-ESM4, IPSL-CM6A-LR, MPI-ESM1-2-LR, MRI-ESM2-0, and UKESM1-0-LL, which together form a range of plausible climate projections. We applied AMCLIM to simulate global agricultural NH3 emissions for the year 2010, which is then set as the baseline simulation to derive the baseline volatilization percentage, PV. Subsequently, we performed four rounds of temperature perturbation experiments with near-surface air temperature (at 2 m) changed by −2, +2, +5 and +10 °C. The PV of these four groups of experiments was calculated, which was then used to perform linear interpolation. By doing this, we are able to find the relative changes in PV due to temperature change. We projected annual mean volatilization rates using future temperature data provided by the ensemble mean of eight climate models under the four SSP scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5). Subsequently, the projected NH3 emissions are calculated from the following equation:

$${F}_{{{{{\rm{NH}}}}}_{3}}=\sum {P}_{{{{\rm{V}}}},{{{\rm{activity}}}}}{F}_{{{{\rm{N}}}},{{{\rm{activity}}}}}$$
(6)

where FN,activity is the annual total N input from agricultural sectors, assuming the same activity data as the reference year 2010. Since it is difficult to determine the amount of N from manure storage and application to land (as this is related to previous stages), an aggregated temperature sensitivity is calculated for the overall volatilization from housing, manure storage/processing, and land-application together.