2.1 Overview of the AMCLIM model

The AMmonia–CLIMate model (AMCLIM) is a dynamical emission system that quantifies climate-dependent NH₃ emissions from agriculture based on a process-level understanding. AMCLIM version 1.0, as described here, incorporates the effects of environmental conditions on the formation and transport of N compounds to simulate the temporal evolution of various N species, especially NH₃. There are three modules in AMCLIM, as shown in Fig. 1: (a) housing, (b) manure management and (c) land. The model focuses on synthetic fertilizer application (present paper) and livestock farming, simulating relevant physical, chemical and biological processes that govern the N flows in agricultural systems, while also considering agricultural management practices.

The AMCLIM model can be operated at multiple scales. It is calibrated and validated at the site scale by comparing with measurements and experimental studies and is then applied on the global scale to provide estimates of global NH₃ emissions. For site-scale simulations, the AMCLIM model explores various source sectors and can be run with different length time steps, depending on inputs given in the measurement datasets. For global simulations, the AMCLIM model covers all major agricultural sectors and aims to provide a comprehensive assessment of agricultural NH₃ emissions. Livestock sectors include pigs, poultry, cattle, sheep and goats, which together dominate the livestock NH₃ emissions. An earlier version of the model for poultry has been reported by Jiang et al. (2021). The AMCLIM model also simulates NH₃ emission from global synthetic fertilizer use on crops. In this study, the development of the land module of AMCLIM (AMCLIM–Land) is described, which was used to simulate NH₃ emissions from synthetic fertilizer use. The land module is also used elsewhere as part of AMCLIM–Manure Management, which considers emissions from the full chain of animal housing, manure storage and land application of manure.

Figure 1Components and structure of the AMCLIM model and inputs (blue arrows) used for simulations. The dashed yellow arrows represent a fraction of unmanaged N from housing that is not simulated in the manure management module (AMCLIM–MMS). Solid yellow arrows represent the N flows between modules (MMS: manure management system; Envs: environments; Techs: techniques).

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2.2 Land module of AMCLIM: AMCLIM–Land

2.2.1 Soil layering and simulated processes in AMCLIM–Land

AMCLIM–Land simulates NH₃ volatilization at the land surface and the evolution of N species in soils. AMCLIM–Land models all the crucial processes associated with fertilizer application, including NH₃ volatilization to the atmosphere, surface runoff, nitrogen diffusion and leaching into deep soil, nitrification, hydrolysis of urea, and plant N uptake, as illustrated in Fig. 2. While the main focus of the model is NH₃ emissions, these other processes are incorporated as they are relevant in determining the fate of applied nitrogen, which interacts with NH₃ emissions according to the mass balance.

Figure 2Simulated N processes in AMCLIM–Land (shown with solid black boxes). Ammonification of nitrate (or dissimilatory nitrate reduction to ammonium) and denitrification and emission of NO, N₂O and N₂ are not included in this study but are shown (as dashed arrows or outside the black boxes) to illustrate the comprehensive concept. The dotted black box indicates soil N processes. Red arrows represent physical processes, including NH₃ volatilization, surface runoff, leaching and diffusion of nitrogen to deep soils. Green arrows represent biological processes, such as plant uptake of N and decomposition of organic N. Blue arrows represent chemical transformations, including hydrolysis of urea and uric acid in animal excreta and nitrification.

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Soil layers in AMCLIM–Land

To simulate these processes, AMCLIM–Land defines four soil layers with a total depth of 28 cm, each with a specific thickness of 2, 5, 7 and 14 cm, respectively (Fig. 3a). The upper two layers (0–2, 2–7 cm) correspond to the first soil layer defined by European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ERA5) for which reanalysis data are used, while the lower two layers (7–14, 14–28 cm) correspond to the second soil layer in ERA5 (Hersbach et al., 2020). By integrating these soil layers into its model, AMCLIM–Land can simulate the soil processes related to fertilizer applications at various depths.

Figure 3Schematic view of the vertical soil layers and physical transport scheme for N species (showing TAN as an example) in AMCLIM–Land. (a) Four soil layers in the soil column from the surface (0 cm) to a depth of 28 cm (not to scale). (b) Physical transport of N species in soils and the atmosphere. Processes include (1) NH₃ volatilization, (2) surface runoff, (3) aqueous diffusion, (4) gaseous diffusion, and (5) drainage and leaching. The concentrations of aqueous TAN and gaseous NH₃ are the mean concentrations of each soil layer, represented by black dots. Soil resistances are shown between the two black dots, with the numbering representing the soil layers, i.e. R₁₂ is the soil resistance for diffusion from soil layer 1 to layer 2. Arrows represent the direction of diffusion, which can be upwards, downwards or bi-directional. Transport distances for diffusion are the distance between the midpoints of two adjacent soil layers, e.g. 3.5 cm from soil layer 1 to layer 2 and 6 cm from soil layer 2 to layer 3. The concentrations of N species in the bottom soil layer are assumed to be 0, and downward fluxes take place from the above layer 3 to this layer.

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Soil pH scheme in AMCLIM–Land

Soil pH can greatly affect NH₃ emissions from fertilizer. Urea application is found to have strong impacts on soil pH as urea hydrolysis consumes hydrogen ions (H⁺) (CO(NH₂)₂+ 2H₂O + H${}^{+}\stackrel{\mathrm{urease}}{⟶}$2NH${}_{\mathrm{4}}^{+}$ + HCO${}_{\mathrm{3}}^{-}$). Experimental studies found that soil pH increased dramatically after urea application (including urine deposition), resulting in a peak in NH₃ emissions (Chantigny et al., 2004; Curtin et al., 2020; Cabrera et al., 1991; Móring et al., 2016). Móring et al. (2016) developed a detailed chemistry scheme for soil pH dynamics in a urine patch and suggested that it is nevertheless suitable to use a fixed pH for larger-scale modelling as it is extremely difficult to explicitly simulate soil pH change on a larger scale, e.g. a global scale (Móring et al., 2017). AMCLIM–Land therefore uses an empirical relationship describing the soil pH after urea application, which is developed based on Chantigny et al. (2004) and Móring et al. (2016). As shown by Fig. 4 and Eq. (18), soil pH is assumed to reach a peak value of 8.5 within 24 to 48 h after application, and it then gradually recovers back to the original values over the next 120 h (Chantigny et al., 2004; Móring et al., 2016).

$$\begin{array}{}\text{(18)}& {\mathrm{\text{pH}}}_{\mathrm{soil}}=\left\{\begin{array}{l}\min \left({\text{pH}}_{\mathrm{initial}}+\frac{\left(\mathrm{8.5}-{\text{pH}}_{\mathrm{initial}}\right)}{\mathrm{24}\mathrm{h}}\mathrm{\Delta }{t}_{\mathrm{app}},\mathrm{8.5}\right),\\ \text{if }\mathrm{\Delta }{t}_{\mathrm{app}}\le \mathrm{48}\mathrm{h}\\ \max \left(\mathrm{8.5}-\frac{\left(\mathrm{8.5}-{\text{pH}}_{\mathrm{initial}}\right)}{\mathrm{120}\mathrm{h}}(\mathrm{\Delta }{t}_{\mathrm{app}}-\mathrm{48}\mathrm{h}),{\text{pH}}_{\mathrm{initial}}\right),\\ \text{if }\mathrm{\Delta }{t}_{\mathrm{app}}>\mathrm{48}\mathrm{h}\end{array}\right.\end{array}$$

Due to limited experimental knowledge, for soils with higher pH than 8.5, pH values are assumed to remain unchanged at the original values in AMCLIM–Land. Meanwhile, soil pH also does not change significantly for fertilizer applications other than urea, e.g. NH${}_{\mathrm{4}}^{+}$, for which a database of soil pH is used in AMCLIM–Land (see Sect. 2.3.2). Although long-term responses in soil pH can result from addition of different forms of N (including NH${}_{\mathrm{4}}^{+}$ and NO${}_{\mathrm{3}}^{-}$ salts) in relation to their ultimate fate (plant uptake, storage, nitrification, leaching), such long-term effects are not considered in AMCLIM as having a significant effect on NH₃ emission.

Figure 4Soil pH scheme used in AMCLIM–Land. Changes in soil pH for 192 h (8 d) after urea application for soils with initial pH of six different values.

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2.3 Modelling NH₃ emissions from synthetic fertilizer use

3.1 Site simulations for NH₃ emissions from synthetic fertilizer application

Figure 5 shows the results of simulated NH₃ emissions over 10 d from the fertilized post-cutting grassland (the GRAMINAE campaign site), along with comparisons with measurements. Meteorological conditions are also given in Fig. 5, which shows that the ground temperature at the study site varied between 10 and 25 °C, with 3 particularly hot days on 9, 10 and 13 June. It is notable that ground temperature, relative humidity (RH) and friction velocity (which is dependent on wind speed and atmospheric stability) showed large diurnal variations. During the daytime, ground temperature and friction velocity were high while RH was low, with the opposite occurring at night-time. Atmospheric resistances (including aerodynamic and boundary layer resistance) are inversely related to the friction velocity, of which values were small during the day and much larger at night. A few precipitation events occurred during the study period, with the largest rainfall occurring on 10 June (Fig. 5c). Soil water content was measured every 2 d at two depths of 0.15 and 0.30 m. The grassland was watered prior to the fertilization on 15 to 17 May, and there was no irrigation between 5 and 15 June. Therefore, subsurface runoff fluxes retrieved from the ERA5 reanalysis data were used as the percolation fluxes to determine drainage and leaching, ranging from 0.60 to 0.75 mm d⁻¹ in the simulated days. The shallower layer had lower soil water content than deeper soils, and moisture levels at both depths decreased from 12 % to 10 % in the 10 d following fertilizer application. The extent to which rainfall-affected soil water content was uncertain based on the available measurements.

Ammonium nitrate fertilizer was applied on the grassland by broadcasting at 05:00–06:00 CET on 5 June 2000. Emissions of NH₃ occurred immediately after the fertilization, with maximum values of over 3000 ng m⁻² s⁻¹ observed on the same day. The measured emissions then gradually decreased over the following days but showed strong diurnal variability, peaking around the midday, when temperature and friction velocity were high, and declining to a minimum at night when these variables were low. By 7 June, the third day after fertilization, the highest emission was 1500 ng m⁻² s⁻¹, which was only half of the peak value observed on the first day. The NH₃ emissions increased substantially on 8 June relative to the previous day (7 June) and declined again. From 12 June, the measured emissions were generally less than 500 ng m⁻² s⁻¹, which was significantly lower compared with the first week.

Figure 5d demonstrates that the AMCLIM model is capable of capturing the predominant features of the measured NH₃ emissions throughout the simulated period and producing estimates for daily NH₃ emissions and sub-hourly fluctuations comparable with the measurements. However, there are some differences between modelled and measured NH₃ fluxes, particularly on the first day and during night-time simulations. Simulated emissions are higher than measurements in the afternoon and evening of the first day and night-time on 6, 7, 9 and 10 June. Meanwhile, the highest measured emissions on 8 June are over 2500 ng m⁻² s⁻¹, but AMCLIM is unable to replicate these values and underestimates the peak emissions by about 40 %. It should be noted that particularly large standard errors (shown as a shaded grey area) also exist in measured NH₃ fluxes during 8–10 June, which is likely due to instrument uncertainties (Sutton et al., 2009a). Overall, AMCLIM overestimates cumulative NH₃ emissions by 50 % from 5 June to 15 June (when there are available measurements). The modelled cumulative NH₃ flux is 0.49 g m⁻² compared with 0.32±0.07 g m⁻² from the measurements (Sutton et al., 2009a). Other diagnostic variables are shown in Sect. S9.

Figure 5Meteorological variables measured by GRAMINAE and site simulations for NH₃ emissions from a post-cutting grassland after fertilization in Braunschweig, Germany, from 5 June 2000 to 15 June 2000 by AMCLIM–Land. (a) Surface temperature and relative humidity. (b) Atmospheric resistances and friction velocity. (c) Soil volumetric water content at 0.15 m and 0.30 m depth and precipitation. (d) Modelled and measured NH₃ emissions.

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To evaluate the performance of the model against the measurements, AMCLIM–Land operated 12 runs with varying model parameters, variables and processes with different levels of complexity. In general, there were four groups of simulations, with correlation coefficients (“r” value) of each run and measurements, standard deviations normalized to measurements and normalized root-mean-square error (NRMSE) shown in Fig. 6. The base run provides the “best” fitting as the closest point to the measurement. All runs show similar correlation coefficients, ranging between 0.7 and 0.85, which demonstrates the model's robustness as over 50 % of the variability in the measured NH₃ flux can be explained by the model. Varying the thickness of the top soil layer leads to the largest changes in standard deviation and the NRMSE (circles in Fig. 6). Changing z1 to 1 cm results in much larger NRMSE than the base value of 2 cm and also overestimates the variability in the measurement. In contrast, simulations using different atmospheric NH₃ concentrations at 1 m does not show significant changes in NRMSE (triangles in Fig. 6), and the standard deviations of these simulations are close to those of the measurement. A range of tortuosity correction was tested (stars in Fig. 6). Lowering tortuosity (no tortuosity and j=6) results in large increase in NRMSE compared with the base run using j of 8.5, with an overestimation of the variations in measured fluxes. By comparison, higher tortuosity (j=10) leads to comparable NRMSE but much smaller standard deviations. AMCLIM–Land was also run by switching off several N processes, including drainage flux to the soil layer underneath, surface runoff and nitrification (“P” in Fig. 6). Excluding the drainage of N in the model results in larger NRMSE than the base run, while excluding runoff or nitrification only leads to a small change.

Based on the comparison with the GRAMINAE measurements, AMCLIM–Land provided an overall reasonable estimate for the NH₃ emission from a fertilized field and generally captured the variations in NH₃ at a high temporal resolution. The Taylor plot (Fig. 6) shows that the base model set up produces the best fitting to the measurement compared with several model runs with varying parameters. Moreover, assuming a zero background NH₃ concentration for global simulations is justified as only limited impacts were found on the overall model performance. The model performance at various temporal resolutions was tested, and an hourly time step was found to be acceptable for global simulations given the modelling results and computational costs. More details for testing the model temporal resolution are given in Sect. S10. AMCLIM–Land was then applied at the global scale, and the results are presented in the following sections.

Figure 6A Taylor plot of correlation of simulated and measured NH₃ emissions by GRAMINAE and normalized standard deviation of the model and measurements for four groups of model runs. Circles show the base run (red), with a top soil layer thickness of z1=1 cm (orange) and z1=3 cm (green). Triangles show atmospheric NH₃ concentration set to 0 (red), 2.0× the measured NH₃ concentration (orange) and 0.5× the measured NH₃ concentration (green). Stars show no soil tortuosity correction for diffusion (red), with a tortuosity correction factor j=1.0 (orange) and j=0.65 (green). P1–P3 represent simulations without drainage, surface runoff and nitrification, respectively. The blue contours represent the root-mean-square error normalized by measurements (NRMSE).

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3.2 Global NH₃ emissions from synthetic fertilizer use

According to simulations using AMCLIM–Land, the global NH₃ emissions from synthetic fertilizer use are 15.0 Tg N yr⁻¹ in 2010 and 16.8 Tg N yr⁻¹ in 2018. The use of synthetic fertilizer increases from 102.3 to 120.5 Tg N yr⁻¹ during this period. The overall volatilization rates, which represent the percentage of applied N in ammonium and urea fertilizer that volatilizes as NH₃, are 17.2 % in 2010 and 16.7 % in 2018, respectively. Additional details about the use of three types of fertilizer are summarized in Table 1.

Table 1Use of three types of synthetic fertilizers, corresponding NH₃ emissions and percentage of volatilization (P_V) simulated by AMCLIM–Land in 2010 and 2018. Data for synthetic fertilizer use are derived from GGCMI3 and IFA.

^a Nitrate fertilizer is assumed to not contribute to NH₃ emissions in AMCLIM–Land. ^b Percentage of volatilization when not including nitrate fertilizers. ^c Percentage of volatilization when including nitrate fertilizers. ^d Percentage of volatilization from ammonium input (rather than of total N applied).

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The geographical distributions of NH₃ emissions and the volatilization rates for 2010 and 2018 are shown in Figs. 7 and A2 (see Appendix A). The spatial patterns are similar for both years, with the highest emissions occurring in some parts of South Asia (mainly India and Pakistan), the North China Plain (NCP) and northeastern China, and the central US and southern Canada. Regions including Europe, the Middle East and South America also had high emissions in some countries, such as France, Spain, Türkiye and Argentina.

For the volatilization rates (P_V), the highest rates are found in eastern Africa (e.g. Kenya, Ethiopia and Somalia), southern Africa (e.g. Namibia) and part of East Asia (e.g. Mongolia and northern China) exceeding 50 %. High P_V values are also found in several regions in the western US, the southern part of South America, the Sahel region, Ukraine, southwestern Russia and western Australia. It should be noted that regions with high volatilization rates do not always coincide with high emissions. Countries with high emissions often have moderate P_V rates. In particular, the NCP and northeastern China show P_V values of around 20 %, with high-volatilization hot spots. The estimated volatilization rates of India are approximately 24 %, while some regions in central and southern India show higher P_V values. In most parts of Europe, estimated P_V rates range from low to moderate (6 % to 18 %). However, both relatively high emissions and high volatilization rates are observed in Argentina and the central US.

Figure 7Simulated (a) annual global NH₃ emissions (Gg N yr⁻¹ per grid) from synthetic fertilizer use in 2010. The colour bar represents the 5th, 15th, 25th, 35th, 50th, 65th, 75th, 85th, 95th and 99th percentiles of NH₃ emissions from synthetic fertilizer application in 2010. (b) Percentage of applied N in synthetic fertilizers (urea and ammonium fertilizers) that volatilizes (P_V) as NH₃ in 2010. The resolution is 0.5° × 0.5°. Maps of global fertilizer use in 2010 are shown in Fig. S1 (see Sect. S8 in the Supplement).

Figures 8 and A3 show the NH₃ emission from ammonium and urea fertilizer and the corresponding volatilization rates. In both 2010 and 2018, urea application results in more emissions than ammonium application due to its widespread use, although the emissions from each type of fertilizer are comparable. In 2010, about 40 % of emissions are from the use of ammonium and 60 % are from urea, and the relative contribution of ammonium to NH₃ emissions increases to 43 % in 2018. The volatilization rates of both fertilizers are similar, with ammonium application resulting in slightly higher volatilization rates. The overall volatilization rate from ammonium application decreases from 19.3 % in 2010 to 18.1 % in 2018, while the rate for urea also decreases from 16.1 % in 2010 to 15.7 % in 2018. These differences are directly linked to meteorological differences between these years.

As shown in Fig. 8, ammonium application in 2010 shows higher volatilization rates than urea application in most of the regions, especially in Argentina, the central US, the Middle East (Iran and Türkiye) and South Asia (Pakistan, although note that there was no urea application in Pakistan in 2010 according to IFA), while urea application shows higher volatilization than ammonium in northern China, Mongolia and Ukraine (Fig. 8b and d). In 2018, the spatial variations in the volatilization rates for both fertilizers are very similar (Fig. A3b and d).

Figure 8Simulated NH₃ emissions (Gg N yr⁻¹) from two main types of fertilizers (global maps on the left) and the corresponding volatilization rates (P_V) in 2010 (global maps on the right). Ammonia emissions from (a) ammonium application and (c) urea application. Percentage of applied N that volatilizes as NH₃ from (b) ammonium application and (d) urea.

Simulated NH₃ emissions from individual crops are shown in Figs. A7 and A8 (see Appendix A). Among the 16 major crops, wheat, maize and rice are the top three emitter crops. The NH₃ emissions associated with wheat are the largest, with NH₃ increasing from 4.6 Tg N yr⁻¹ in 2010 to 5.3 Tg N yr⁻¹ in 2018. Maize contributes 2.9 and 3.2 Tg N yr⁻¹ in 2010 and 2018, respectively, and emissions from rice increase from 2.4 Tg N yr⁻¹ in 2010 to 2.5 Tg N yr⁻¹ in 2018. For the other crops, emissions range from 41.9 (rye) to 843.4 Gg N yr⁻¹ (cotton) in 2010, and from 45.4 (rye) to 1116.3 Gg N yr⁻¹ (cotton) in 2018.

The total global NH₃ emissions from synthetic fertilizer use in 2018 are generally higher than 2010 as a result of increasing synthetic fertilizer, and most of crops have higher emissions in 2018 compared to 2010. Cotton and groundnut in particular have a 32 % increase in NH₃ emissions, which is the topmost increase over time among these crops. By comparison, rapeseed is the only crop for which emissions decreased, with around 3 % less NH₃ emitted in 2018 than in 2010.

Figures A9 and A10 show the component NH₃ emissions from fertilization by different techniques for the 2 years. Broadcasting is responsible for more than 90 % of the estimated NH₃ emission, whereas incorporation and deep placement together contribute less than 10 % of the estimated global emissions (see Table A1 for assumptions). The geographical distributions of the volatilization rates for broadcasting are consistent with the global totals, given that broadcasting is the primary method used in fertilizer applications (Riddick et al., 2016). By comparison, incorporation and deep placement result in lower volatilization rates. Specifically, incorporation reduces simulated emissions by more than 50 % based on the P_V rates, while deep placement could potentially reduce emissions by almost 98 % (Figs. A9 and A10), although this reduction needs to be further investigated as it may be an overestimation. Regions with high volatilization rates for broadcasting also have high rates even when fertilizers were assumed to be incorporated into the soils in the simulations, such as Argentina, northern China, Mongolia, Namibia and the central US (Figs. A9b and d, A10b and d).

The fate of applied N in fertilizers for 2010 and 2018 is shown in Fig. 9. For both years, N uptake by crops is the largest among all processes, equivalent to 46.6 % (40.6 Tg N yr⁻¹) and 45.1 % (45.6 Tg N yr⁻¹) of fertilizer N applied in 2010 and 2018, respectively. Surface runoff is responsible for the smallest estimated N loss, which is only 3.6 % (3.1 Tg N yr⁻¹) in 2010 and 2.4 % (2.4 Tg N yr⁻¹) in 2018. The amounts of N losses (in the form of ammonium and urea) due to volatilization and nitrification and dissolved in soils through diffusion and leaching are comparable. In 2010, around 16.8 % (14.6 Tg N yr⁻¹) of N is estimated to undergo nitrification, with 14.5 % (12.6 Tg N yr⁻¹) transferred to deeper soils. Nitrification is estimated at 16.2 Tg N yr⁻¹ in 2018, accounting for 16.2 % of the total pathways, which is similar to 2010. The diffusive fluxes and leaching in 2018 are approximately 50 % higher than the 2010 values (12.6 Tg N yr⁻¹), which together account for 11.0 % (18.5 Tg N yr⁻¹) of the N in applied synthetic fertilizers.

Figure 9The fate of N of ammonium and urea application in 2010 and 2018 simulated by AMCLIM–Land. Note that the runoff only includes surface runoff of TAN and urea, while nitrate runoff is excluded. “Uptake” refers to plant uptake of N.

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3.3 Seasonal and regional NH₃ emissions from synthetic fertilizer use

As NH₃ emissions are greatly influenced by climatic conditions and local management, NH₃ emissions exhibit strong seasonality that varies across the globe. Figures 10 and A4 (see Appendix A) show the seasonal NH₃ emissions from fertilizer applications for 2010 and 2018, respectively. The seasonal emissions in both years are similar, with over 50 % of NH₃ occurring in the Northern Hemisphere (NH) summer months and about 25 % in March–April–May (MAM). September–October–November (SON) and December–January–February (DJF) both contribute slightly over 10 % of the annual emissions. In the NH, more than 70 % of annual emissions are from June–July–August (JJA), while emissions in SON and DJF are significant in the Southern Hemisphere (SH). For example, Brazil and central African countries have predominantly SON emissions, while Argentina and southern Africa have emissions that largely occurred in JJA. Countries with high annual NH₃ emissions such as China, India and the US generally show similar seasonal patterns, with the highest emissions occurring in JJA and lower emissions in other months.

Figure 10Seasonal NH₃ emissions (Gg N per grid) from ammonium and urea fertilizer application (global maps on the left) and the relative fraction of annual emissions that are from the corresponding season (f_season) in 2010 simulated by AMCLIM–Land (global maps on the right). Ammonia emissions in (a) March, April, and May (MAM); (c) June, July, and August (JJA); (e) September, October, and November (SON); and (g) December, January and February (DJF). Percentage of annual emissions in the season of (b) MAM, (d) JJA, (f) SON and (h) DJF.

Global monthly emissions of NH₃ from synthetic fertilizer use categorized between the 16 crops are shown in Figs. 11 and A5 (see Appendix A). The seasonal trends for both 2010 and 2018 are generally the same. The highest emission of around 4.0 Tg N per month occurs in July, with August showing the second highest emission of around 2.5 Tg N per month. Large emissions take place in between April and August. The first emission peak is in May, which is the first month of the year when NH₃ emissions reach 2.0 Tg N per month in both years. Emissions slightly decrease in June but then reach the maximum in July. Wheat-related emissions are seen throughout the year and are the most significant emissions in most months, except for August, September and October, in which rice contributes to the largest estimated emissions. Maize is also one of the most important crops that result in NH₃ emissions from May to August.

Figure 11Global monthly NH₃ emissions (Gg N per month) from ammonium and urea fertilizer applications for 16 major crops in 2010 simulated by AMCLIM–Land.

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The seasonality of NH₃ emissions differs between regions across the globe. Figures 12 and A6 present monthly NH₃ emissions from 12 different geographical regions and the percentage of global monthly emissions that each region contributes. The map of the geographical regions defined in AMCLIM is given by Fig. A11. The highest emissions are from South Asia and East Asia, with both regions responsible for roughly a quarter of global emissions. North America has the third-highest emissions, accounting for over 17 % of global emissions. Southern Africa has the lowest emissions and only accounts for about 1 % of the global total. In terms of country-level statistics, China results in the largest emissions of 3.7 Tg N yr⁻¹ in 2010 and 4.1 Tg N yr⁻¹ in 2018, followed by India, which contributes to 3.4 Tg N yr⁻¹ and 3.5 Tg N yr⁻¹ in 2010 and 2018, respectively. The US creates third-largest amount of national emissions, with emissions of 1.9 Tg N yr⁻¹ in 2010 and 2.0 Tg N yr⁻¹ in 2018.

Regions in the NH, including East Asia, South Asia, north and central Asia, northern Europe and the Mediterranean, North America, and the Middle East, generally show high emissions in JJA and MAM, as shown in Figs. 12 and A6. In particular, East Asia, northern Europe and North America exhibit very similar monthly variations. Northern and central Asia and South Asia also show similar monthly trends. The NH₃ emissions in the Mediterranean region are high for spring and summer emissions but much lower in autumn and winter. By contrast, South America and southern Africa show higher winter emissions and lower emissions in other seasons. Oceania has distinct seasonal emission patterns. The emissions in Oceania peak in May and are high in August and September. Figures 12 and A6 show that different regions dominate NH₃ emissions in different seasons, with East Asia and South Asia being the largest contributors to spring and summer emissions, while South Asia and South America dominate autumn and winter emissions. North America also contributes significantly to summer emissions.

Figure 12Monthly NH₃ emissions from ammonium and urea fertilizer application in different regions of the world and the relative fraction of the global monthly emissions that are from the corresponding regions (f_region). Annual total NH₃ emissions of the region are given at the top-right corner of each plot with the percentage of emissions from each region. The figure is for 2010.

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Table 2 provides a summary of the regional volatilization rates from the use of synthetic fertilizers in both 2010 and 2018. The data show that ammonium application generally results in higher estimated volatilization rates than urea application according to the AMCLIM model, noting that the values would be half those shown if ammonia volatilization is referenced to total N input where ammonium nitrate is used. Africa and Oceania have the highest volatilization rates for both 2010 and 2018, with over 23 % to 25 % of N in ammonium and urea application volatilized as NH₃, while South America shows the lowest volatilization rates with less than 13 %. In the listed regions, the volatilization rates of both ammonium and urea application for 2018 are higher than 2010, except for Europe, North America and South Asia.

Table 2Volatilization rates of synthetic fertilizer use in different regions for the years 2010 and 2018 (percentage values). Values in the parentheses are volatilization rates when including nitrate application.

* Volatilization rates are half the specified figure if referenced against total N input when applying ammonium nitrate.

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4.1 Comparison with other studies

The GRAMINAE dataset proved especially useful for testing the model in detail given that a robust set of ammonia flux data are available (based on comparison of several instruments) together with extensive supporting data that allow AMCLIM to be applied at a high time resolution (15 min resolution). However, many published ammonia flux datasets do not have comparable detail to the GRAMINAE dataset. This highlights the importance of providing sufficient information on micrometeorological conditions, soil data and management information to allow detailed model simulations.

Nevertheless, it is possible to make a simpler overall comparison between the results of the global simulations of AMCLIM and the average volatilization rate of other published studies according to the latitude and longitude of each study. In a simple way, this takes into account the effects of environment and climate and soil and management conditions as they are estimated in AMCLIM. By doing this, the simulated volatilization rates from synthetic fertilizer use by AMCLIM were compared with measurements, focusing on experimental studies that measured cumulative NH₃ emissions from urea and ammonium fertilizer application to agricultural land (Fig. 13; detailed information can be found in Table A2). Modelled volatilization rates were extracted from the global simulations and compared with the reported volatilization rates from these experimental studies that were conducted in different regions across the globe. These experimental studies used for comparisons were from 17 sites in seven countries (as shown in Fig. A13). The sites included show a reasonable spatial distribution from various climatic conditions (represented by average temperature from 8.5 to 31.7 °C during measurements) and soil conditions (represented by soil pH between a range from 5.7 to 8.5), with five major crops being examined.

As shown in Fig. 13a, AMCLIM can either overestimate the volatilization rates of urea application compared with measured estimates (e.g. studies “E”, “K”, “M”, “N”, “P”, “Q” and “R”) or underestimate them (e.g. study “A”). For ammonium fertilizer application (Fig. 13b), AMCLIM overestimated the volatilization rates, which has been also shown in the GRAMINAE simulations (Fig. 5d). The differences between the observed and modelled P_V rates could be due to the diffusion and infiltration processes as irrigation was usually done in the experimental studies and the complex soil pH dynamics after urea application. It is also worth noting that the results from global simulations are largely dependent on the timing of fertilization (crop calendar), which might not be reflected in or not consistent with the experimental studies. The limitations of such comparisons emphasize the urgent need for well-documented and good-quality measurements to improve the development and performance of models.

Figure 13Modelled percentage volatilization rates (P_V, %) compared with experimental studies (Hayashi et al., 2008; Sanz-Cobena et al., 2008; Yang et al., 2011; Datta et al., 2012; Jantalia et al., 2012; Turner et al., 2012; Ni et al., 2014; Schwenke et al., 2014; Huo et al., 2015; Li et al., 2015; Tian et al., 2015; Thapa et al., 2015; Engel et al., 2017; Liu et al., 2017; Cowan et al., 2021; Zhang et al., 2022; Bhatia et al., 2023). Measurement data were from literature that studied NH₃ volatilization from (a) urea application and (b) ammonium fertilizer application to fields. The dashed black line is the 1:1 line, and the dotted grey lines indicate the values within a factor of 2. AS stands for ammonium sulfate, and CAN stands for calcium ammonium nitrate.

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As shown in Fig. 14a and b, both measured and modelled P_V tend to be larger as soil pH increases, with modelled P_V having a stronger response. Results of ammonium fertilizer application more obviously illustrate positive correlation between volatilization rates and soil pH compared with urea application, although this could be due to the studies having fewer data points. The general trend is consistent with the fact that more alkaline soils can result in higher NH₃ volatilization. The soil pH used in AMCLIM for global simulations are sometimes lower than the measured values, and this indicates that the simulated volatilization rates would have been even larger if using higher pH. The difference in pH could be partly due to the model still not having high enough resolution to deal with the heterogeneity of soil characteristics. Overall, the comparisons reflect that AMCLIM is likely to overestimate NH₃ emissions from fertilizer application as compared with the reported measurement results.

The comparatively high volatilization rates of ammonium fertilizers estimated by AMCLIM are possibly due to the following reasons.

1. AMCLIM does not simulate the dissolving process of ammonium fertilizers and instead assumes that ammonium “pellets” instantly dissolves in soil moisture according to the soil pH specified in the global soil database, which results in large initial emission potential and might cause an overestimation of NH₃ emissions (Fig. 5d shows that the majority of overestimation by AMCLIM occurs in the first day).

2. The drainage and diffusion in AMCLIM might be underestimated, meaning that more N in the ammonium fertilizer is available for volatilization than may be the case in actuality.

3. The present version of AMCLIM does not include the potential for NH₃ recapture by an overlying plant canopy. This may be particularly relevant for tall canopies and those with small soil ammonia emissions in wet environments.

4. Measurements also have uncertainties, especially when using enclosure methods to measure NH₃ emissions (Kamp et al., 2024), which can significantly underestimate emissions. For example, companion studies at the GRAMINAE site suggested that NH₃ fluxes measured by a cuvette system were only about a quarter of the net canopy fluxes estimated using micro-meteorological techniques, e.g. AGM and REA (David et al., 2009; Milford et al., 2009; Sutton et al., 2009a). Low levels of turbulent mixing and absorption to surfaces (especially if condensation occurs) are possible reasons for such underestimation of measured fluxes by chamber systems.

Each of these points indicates the need for further experimentation and comparison of published studies on the dependence of ammonia emission on dissolution processes, soil properties, canopy structure and alternative fates of the added nitrogen (see Fig. 9), with the prospect of improved simulation of these interactions. For example, future development of AMCLIM is planned to include assessment of interactions with the overlaying plant canopy.

Figure 14Measured percentage volatilization rates (P_V, %) vs. measured soil pH (a). Modelled P_V vs. soil pH used in AMCLIM (b). Soil pH used in AMCLIM compared with measured soil pH (c), with the dashed black line representing the 1:1 line.

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Table 3 compares the simulated NH₃ emissions from synthetic fertilizer use by AMCLIM–Land with those estimated by other studies, including models and inventories, on global, continental and national scales. Table 3 also includes volatilization rates, where available. Among all studies for comparisons, DLEM and FAN are both processed-based models (see Table 3 for references for all model descriptions and studies), while the other studies are inventories that mainly use EF methods. DLEM incorporates a bi-directional exchange scheme for NH₃, and FAN is interactively coupled to an Earth system model.

Table 3 shows AMCLIM–Land compared with DLEM and FAN at several spatial scales. Among models, estimated global NH₃ emissions by AMCLIM are the second largest, which are in close agreement with DLEM. For the year 2010, AMCLIM and DLEM estimate 15.0 and 16.7 Tg N yr⁻¹ of NH₃ emissions, respectively. By comparison, the FAN model provides lower estimates of 12 Tg N yr⁻¹ for 2000 by FANv1 and 11 Tg N yr⁻¹ for 2010–2015 by FANv2. The lower NH₃ emission value suggested by FAN is partially due to less total N application in FANv2, which is 79–87 Tg N yr⁻¹ compared to 102 Tg N yr⁻¹ in AMCLIM and DLEM. The volatilization rates estimated by the three models are comparable, ranging between 13 % and 16 %. For different types of fertilizers, it is estimated that about 16 % of N in urea fertilizers is lost as NH₃ compared to 19 % by FANv2, and NH₃ emissions from ammonium and nitrate fertilizer application account for 12 % to 13 %, which is higher than 7 % estimated by FANv2, while DLEM does not specifically report NH₃ emissions from urea or ammonium fertilizers.

Global estimates of emissions from other studies vary significantly, ranging from 5.9 to 28.6 Tg N yr⁻¹. MASSAGE_NH₃ and NH₃_stat both suggest that annual global NH₃ emissions are less than 10 Tg N yr⁻¹ for 2008 and 2012. The NH₃_stat model estimates much lower emissions of 5.9 Tg N yr⁻¹, which is only about 35 % of AMCLIM's result. In contrast, estimated emissions by Yang et al. (2023) are the highest (28.6 Tg N yr⁻¹) for the 2010s. The large differences among the studies can be partly explained by the different agricultural activities included and different input data used in each study.

For NH₃ emissions from major continents and emitters (China, India and the US), AMCLIM provides consistent estimates as compared with DLEM for regions including Africa, Asia, Europe and China but higher emissions than FANv2. However, the volatilization rates of AMCLIM and FANv2 agree with each other in Africa, Asia, Oceania, China and India, indicating that the different NH₃ emissions can be partly explained by the different inputs of N fertilizer to the models. As shown in Table 3, AMCLIM has similar estimates for NH₃ emissions to other studies for most of regions except for North America, US and India. For the US, emissions estimated by AMCLIM are higher than EPA by 60 % and NH₃_stat and MASSAGE_NH₃ by 2 to 4 times. Meanwhile, NH₃ emissions from India are also higher in AMCLIM, approximately 10 % to 20 % higher than other models and inventories. Only Yang et al. (2023) suggested even higher NH₃ emissions from India than AMCLIM. However, the volatilization rate for India estimated by AMCLIM is similar to FANv2. The slightly lower values of AMCLIM than FANv2 indicate that the difference mainly results from different input data used. For example, the total N application in India is 16 Tg N yr⁻¹ in AMCLIM compared to 10 Tg N yr⁻¹ in FANv2.

Table 3Comparisons of global, continental and national NH₃ emissions from fertilizer (Tg N yr⁻¹) and corresponding volatilization rates (%) between AMCLIM and other inventories, models and studies.

^a Xu et al. (2019). ^b Xu et al. (2018). ^c Riddick et al. (2016). ^d Vira et al. (2020). ^e Beusen et al. (2008). ^f Yang et al. (2023). ^g Kurokawa et al. (2013); Kang et al. (2016); and Zhang et al. (2017, 2018). ^h Aneja et al. (2012) and Kurokawa et al. (2013). ⁱ EPA (2011). ^j Paulot et al. (2014). ^k Aneja et al. (2020). ^l Values are calculated based on the results in the literature.

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Key features of several models are summarized and listed in Table 4. Compared with existing models, AMCLIM is a dynamical emission model with an emphasis on the NH₃ volatilization. AMCLIM shows adequate levels of complexity in terms of soil layering construction, simulations for N processes in soils, NH₃ volatilization simulation and soil pH dynamics. AMCLIM has relatively high temporal resolution, which provides implications for the temporal variations in NH₃ fluxes. The highly resolved outputs can be used by atmospheric transport and chemistry models. It is worth noting that AMCLIM is considered a comprehensive emission model rather than a biogeochemical model.

Table 4Comparisons of model features between AMCLIM and other models for NH₃ emission simulations.

^a Based on Gurung et al. (2021), who developed a new NH₃ volatilization scheme for urea application in DayCent. ^b Based on a model version DLEM-Bi-NH₃ (Xu et al., 2018).
Letters indicate the following processes: A is mass balance calculation of N pools; B is NH₃/NH${}_{\mathrm{4}}^{+}$equilibrium; C is urea hydrolysis; D is TAN partition; E is surface runoff; F is leaching; G is diffusion in soils; H is nitrification; I is plant N uptake; J is microbial N uptake; K is mechanical N loss; M1 is fluxes that are concentration gradient driven and constrained by resistances derived from well-established micrometeorological theory; and M2 is empirically derived mass transfer coefficient.

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For modelling global-scale NH₃ emissions, calibrations were not explicitly done at site scale for models such as FANv2 (Vira et al., 2020), CAMEO (Beaudor et al., 2023), DNDC (Yang et al., 2022) and DLEM (Xu et al., 2019). This is possibly because global models tend to provide general representation and try to avoid over calibration. In contrast, DayCent is widely used for simulating N₂O emissions rather than NH₃ emissions and is intensively calibrated using N₂O measurements from fields. The parameters can be quite different between simulations for different places, e.g. North America vs. Europe. However, there are limited studies that apply DayCent at a global scale, and little evidence was found that explicit model calibration was done in the global application of DayCent (e.g. Del Grosso et al., 2009).

In this study, the AMCLIM model was firstly applied to simulate the NH₃ emission from fertilized grassland at the GRAMINAE site and was intensively evaluated by a detailed comparison of time series between measured and modelled fluxes. AMCLIM was then applied at the global scale to simulate NH₃ emissions from 16 major crops. Admittedly, there is a gap resulting from using model settings for fertilized grassland to represent croplands. The development of AMCLIM was based on understanding at a process level. The management practices at the GRAMINAE site were not complicated, which provides a good test situation for the numerical representations of the physical and chemical processes. The model results show close agreement with the GRAMINAE measurements (Fig. 5). The multi-site comparison demonstrates that the model provides reasonable estimates for various crops under different climatic and soil conditions (Fig. 13), and the global estimates by AMCLIM are broadly consistent with existing models (as shown in Table 2). On the other hand, it has been found that the critical factor that affects NH₃ emissions is the timing of fertilization and amount of fertilizer applied under current model settings (see Sect. 4.3 and Figs. A14 and A15). Therefore, considering the model structure and complexity, the processes included in AMCLIM are believed to be robust and representative of simulations for synthetic fertilizer use.

Table 5 summarizes the crop-specific NH₃ emissions from synthetic fertilizer applications estimated by AMCLIM–Land and other studies. Although there are limited data available for NH₃ emissions from individual crops, the results from each study are generally consistent in magnitude. Zhan et al. (2021) focuses on year 2000, and their values are the smallest. The results from Yang et al. (2023) are average values for the period from 2010 to 2018 and are generally higher. All studies agree that wheat, rice and maize are the top three crops that dominate the NH₃ emissions. AMCLIM has similar estimates for maize but much higher wheat emissions and lower soybean emissions compared with DLEM. The emissions related to rice estimated by AMCLIM are nearly 50 % lower than estimates by DLEM, which might be partly due to the fact that AMCLIM does not include a flooded paddy scheme for rice simulations. Urea hydrolysis can be faster in a flooded rice paddy, which can result in higher NH₃ emissions depending on floodwater pH. There are no data for fertilization of this type of rice systems in the GGCMI3 dataset that was used in AMCLIM. However, the simplification is considered reasonable for global application of the current model version as the comparisons (as shown in Fig. 13) indicate the simplification provides estimates that are accurate within an order of magnitude (mostly within a factor of 2). The differences in crop-specific NH₃ emissions highlight the need for further research to improve the understanding of NH₃ emissions from different crops and fertilizer management practices. Future work should include addressing of individual cropping systems in more detail.

Table 5Crop-specific NH₃ emissions (Tg N yr⁻¹) from synthetic fertilizer use simulated by AMCLIM and comparisons with other studies.

^a Xu et al. (2019); ^b Yang et al. (2023); ^c Zhan et al. (2021)

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4.2 Spatial and temporal variations in NH₃ emissions

The NH₃ emissions from synthetic fertilizer use are primarily determined by the amount of N applied and are strongly influenced by both environmental conditions and local management practices. Regions with high NH₃ emissions are typically found in countries with intensive agricultural activities, such as China, India, Pakistan and the US, where a large amount of synthetic fertilizer N has been used. The P_V rate is an important indicator that shows the percentage of applied N volatilizes as NH₃. The regional pattern of the P_V rate does not always match the distribution of NH₃ emissions due to the combined effect of environmental factors and management practices. Since AMCLIM was applied in this study using the management practices that do not vary significantly for 2010 and 2018, this means that differences in P_V between these years are mainly due to environmental differences between these years, as shown in Figs. 7 and A2.

When considering the environmental effects on NH₃ emissions, there are several factors that can cause volatilization rates to vary, including soil pH, soil temperature and moisture, and wind speed. Alkaline soils tend to cause higher estimated NH₃ emissions in AMCLIM, meaning that regions with high soil pH, such as the western US, Argentina, the Middle East, Namibia, Mongolia and part of northern China show high volatilization rates (soil map as shown in Fig. A12). Since the base soil pH distribution is fixed in AMCLIM–Land according to HWSD v1.2 (FAO/IIASA/ISRIC/ISS-CAS/JRC, 2012; Wieder et al., 2014) and does not vary over time, the similar geographical patterns of the volatilization rates in the 2 simulated years of 2010 and 2018 indicate clear climatic dependences (due to temperature, water and wind conditions) featured in NH₃ volatilization.

High temperature leads to faster rates and quicker processes, which can result in larger emissions. Soil moisture influences the concentrations of N species in soils. When the soil is dry, soil TAN concentrations can be high, which may result in a greater emission potential at the soil surface, especially under alkaline soil conditions. This effect could be further amplified for ammonium fertilizer application as AMCLIM does not simulate the initial dissolving of fertilizer pellets. Dry regions, such as Mongolia, Namibia, the western US and the Middle East show high volatilization rates. It is worth noting that these regions also have alkaline soils with high pH values, suggesting that the high volatilization may be due to a combined effects of soil dryness and alkalinity. Moreover, when the soil is dry and the subsurface percolation flux is small, there may be a lack of infiltration or drainage, which prevents N from moving from the surface to deeper soil layers. Instead, more N will volatilize as NH₃ from the surface. It is notable that the estimated N fluxes to run off are lower in 2018, but the NH₃ volatilization rate is higher in 2018 than in 2010 (Fig. 9). Wind speed is also a critical factor that impacts NH₃ volatilization since it influences the turbulence, which affects the atmospheric resistances. Emissions are higher under windy conditions because atmospheric resistances are smaller. Simulations for the GRAMINAE site indicate that the sub-hourly NH₃ emissions vary with temperature and the friction velocity (which is related to wind speed and atmospheric resistances; Fig. 5) and show strong diurnal cycles. Rainfall can also affect the NH₃ emission, mostly causing a reduction. Similarly, nitrogen species are washed off from the land surface during heavy rainfall event. Although the effects of rainfall are not explicitly included in AMCLIM, they are reflected implicitly by the runoff fluxes, and the magnitude of scavenged NH₃ is small compared with the emission flux. The above meteorological factors can interactively affect the NH₃ emission.

Management plays another key role in affecting the NH₃ emissions in the agricultural activities, specifically through the timing of fertilizer application during planting seasons, the type of fertilizer used and the application techniques. The temporal variations in NH₃ emissions are largely related to the timing of fertilizer application, since volatilization usually takes place soon after the fertilizers are applied. The regional monthly emissions are closely linked to the planting seasons, with large emissions being found in a few months throughout the year. On the global scale, NH₃ emissions are the highest in MAM and JJA, with the first peak of emissions in May and the largest emissions in July, corresponding to the typical planting seasons for crops in the NH.

The second factor is the type of fertilizer used. According to simulations using AMCLIM–Land, application of ammonium and urea have similar volatilization rates on the global scale. The comparable volatilization rates of the two fertilizer types are possibly because of the following reasons. Ammonium is a direct input to soil TAN pool, which is readily volatilized as NH₃, while urea must be hydrolysed before it is converted to TAN. The hydrolysis process is limited by water availability. If the soil is very dry, the amount of urea that hydrolyses is reduced (Rodríguez et al., 2005). Furthermore, hydrolysis of urea can cause soil pH to increase, leading to more NH₃ emissions. As a result, NH₃ volatilization from urea application is controlled by two processes with opposite effects. When including both ammonium and nitrate fertilizers (e.g. ammonium nitrate, where the N content doubles but the volatilization rate of NH₃ halves because the nitrate part does not contribute to NH₃ emissions), urea application is found to result in higher NH₃ emission due to the elevated soil pH by hydrolysis.

The third critical factor is the application techniques. How fertilizers are applied on land can have huge impacts. Broadcasting is the most commonly used method and contributes to the largest fraction of NH₃ emissions, while both immediate incorporation and deep placement of fertilizers are effective methods that can reduce NH₃ emissions to a large extent. According to the assumptions specified in Table A1, only a small fraction of fertilizer was incorporated according to the development level of each region (WB, 2022). In practice the adoption of increased use of incorporation and deep placement could substantially reduce NH₃ emissions as compared with the present estimates. The availability of national statistics on such practices is therefore a priority for improving estimates of the model and demonstrating the benefits of improved fertilizer placement practices.

Based on current estimates, less than 50 % of applied N is taken up by crops, which may be partly due to the very simple application techniques used. In addition to the three factors discussed above, irrigation can also influence NH₃ emissions as it has been found in literature that less NH₃ emissions occur after irrigation (Dawar et al., 2011; Yang et al., 2022; Zhang et al., 2022), although AMCLIM is not evaluated against observations for this effect because of insufficient input data. Irrigation leads to an increase in the soil moisture and reduction in emissions by diluting concentrations of N species and transporting them to deeper soil layers. Proper management practices, such as timely and precise application of fertilizers and adequate application techniques, can help reduce NH₃ emissions and improve crop uptake of N.

4.3 Uncertainty and limitations

In general, uncertainty in NH₃ emissions arises from two main aspects: input data and model parameters. Input data uncertainty includes the N application rates, the crop calendars that determine the application dates and the soil characteristics. The crop calendars used in AMCLIM are static. Emissions could be influenced if using different crop calendars as the environmental conditions may also change. AMCLIM assumes that fertilizers are applied twice during the growing season, which is a moderate value used as a representation for fertilization. This value mostly varies between one and three or four applications across the globe. For example, there can be two to four fertilizer applications in North America or zero to three applications in South America (Xu et al., 2019). Additional rounds of simulations were performed to test the following three possible scenarios: (1) 100 % of fertilizer N applied at the beginning of the planting season; (2) 75 % of N applied at the beginning of the planting season and 25 % midway through the growing season; and (3) 40 % of N applied at the beginning of the planting season, 30 % at one-third through the growing season, and 30 % at two-thirds through the growing season. The global NH₃ emissions from synthetic fertilizer use based on the different scenarios were 10.8, 12.9 and 15.8 Tg N yr⁻¹, respectively, as compared with the base assumption of 15.0 Tg N yr⁻¹ (when applied at 50 % : 50 %). In general, this shows that in AMCLIM adding a larger share of fertilizer later in the growing season is associated with increased emission, which can be linked to warmer temperatures as the growing season progresses. However, it should be noted that further testing of this effect would be warranted given the possible effect of tall crop canopies in reducing emissions, which is not addressed in the present version of AMCLIM reported in this study. The differences in spatial distribution and seasonal variation between different fertilization scenarios are shown by Figs. A14 and A15.

In AMCLIM, only NH₃ emissions from grazed grassland were simulated, which will be described by the second part of the model in a forthcoming paper (for the livestock sector). Fertilized grasslands (with synthetic fertilizers) were not included and simulated because there are no data specified for this type of vegetation in the GGCMI3 dataset used. This addresses the need for future work to use a more complete compilation of statistical data and model input data. It is worth noting that the majority of synthetic fertilizer used globally was for croplands rather than grasslands (although in Europe and some other locations grasslands can receive significant amounts of fertilizers). The total applied N from synthetic fertilizer was 102.3 Tg N yr⁻¹ in AMCLIM, which is comparable to the 99.6 Tg N yr⁻¹ of consumed fertilizer suggested by the International Fertilizer Association.

The heterogeneity of the land during fertilization can also contribute to uncertainty in the overall estimates. In intensive farming countries like China and India, where fertilization can take up to a week or more, the assumption of fertilization being completed within a day in AMCLIM introduces uncertainty. Soil characteristics including soil pH, bulk density, soil constituents and organic matter content are assumed to remain constant in AMCLIM–Land, which can affect the chemical equilibrium and variables dependent on these data.

Uncertainty is also introduced from various parameters used in the AMCLIM model. First, the representation of soil pH evolution after urea application relies on an empirical relationship due to the complexity of simulating soil pH dynamics. Soil pH is assumed in AMCLIM to reach a maximum of 8.5 after urea application and will eventually decline to the original value. The duration of such perturbed soil pH is assumed to be around 1 week. In addition, long-term trends of soil pH changes, i.e. soil acidification due to fertilization, are not included in AMCLIM. Instead, simulations for different years used the same base soil pH. Potentially the most important uncertainty is the extent of variations in soil pH between microsites, as this can substantially affect simulated ammonia emissions, for example if dissolving fertilizer particles are not well coupled to soil pH.

Second, AMCLIM assumes the atmospheric concentrations of NH₃ to be zero rather than a positive value for the background NH₃, which may cause some overestimation of emissions, although this is expected to be small (Fig. 6). Third, the model uses linear relationships to calculate the diffusive and drainage pathways, including irrigation-related drainage, which is difficult to simulate accurately. The overestimation of night-time NH₃ at the GRAMINAE site by approximately a factor of 2 suggests that the diffusive fluxes were not well represented.

Fourth, the relative fraction of techniques used in fertilizer application worldwide are assumed to be dependent on country income level, as shown in Table A1. Wealthy countries are assumed to have better application techniques that result in less NH₃ emissions compared to less developed countries that tend to use simpler application methods. Such an assumption is based on expert judgement due to the lack of statistical data and thus can introduce uncertainty. There are also sub-national-level variations in techniques used, which can affect the weighted sum and lead to different estimates. Application of a urease inhibitor was also not included in the current version of AMCLIM due to insufficient statistical data, which may result in an overestimation of NH₃ emissions from urea application. However, this impact is limited because very few countries have regulations on the use of urease inhibitors. Future work on incorporating existing regulations will be possible once there are sufficient data.

A systematic calculation of uncertainty associated with a process-based model can be very complicated. Instead, considering all the factors discussed above, a simple analysis for estimating the uncertainty in AMCLIM was performed. For ammonium fertilizer, the estimated uncertainty is suggested to be 33 %, which was derived from the simulation of GRAMINAE. For urea application, the uncertainty was estimated to be 20 % based on the multi-site comparison (as shown in Fig. 13). As a result, the overall expected uncertainty in emissions from synthetic fertilizer use is 3.9 Tg N yr⁻¹ in 2010 and 4.3 Tg N yr⁻¹ in 2018, which accounts for 26 % of the emissions in each year. It is worth noting that readers should only interpret the estimates and the uncertainty within the context of modelling.

The AMCLIM model only simulates NH₃ volatilization and does not include a bi-directional exchange scheme for NH₃, which may overestimate the NH₃ flux when there is enhanced deposition, especially for areas close to agricultural and semi-agricultural land. Another limitation of AMCLIM is the N uptake scheme. The current scheme for N uptake by crops has limited interactions with the carbon cycle, and the crop dynamics are represented by fixed empirical parameters that only account for temperature effects. There is no consideration of water stress constraining the uptake. Microbial N uptake is also not included in AMCLIM. However, these points are considered beyond the scope of this study due to the complexity involved in simulating the relevant processes.

It must be acknowledged that the detailed evaluation of AMCLIM focused on the GRAMINAE dataset, where all needed inputs and parameters were available, as well as clearly quantified uncertainties in the measured fluxes. Other possible evaluation datasets that were accessible to the authors had either key gaps in data following fertilizer application or major measurement uncertainties. For this reason, the wider evaluation took an approach of comparing with multiple studies where average flux estimates are available but the datasets are not sufficient for a detailed, hourly comparison with the model. This emphasizes the need to establish more high-quality and accessible ammonia flux datasets following fertilizer application that can be used for model development and evaluation. Considering the needs for detailed model testing, such measurements should meet the following requirements.

1. They should contain information about the field site (coordinates, basic climatic and soil conditions).

2. They should include meteorological variables that are measured at high frequency and reported with high temporal resolution (ideally sub-hourly, e.g. 15 min), including air temperature and wind speed at a reference height, atmospheric pressure, precipitation, and humidity. Radiation and heat flux measurements are also very useful, especially to establish canopy temperature, humidity and wetness.

3. They should include soil temperature and soil moisture measured at a specified depth (better to have measurements at multiple depths) with the same measured frequency as the meteorological variables.

4. They should include soil textures, bulk density and pH. If possible, the soil pH should be measured continuously or periodically following urea application.

5. They should include above-canopy fluxes of ammonia and atmospheric concentration of NH₃ at a reference height above the canopy (e.g. 1 m), together with a report of the uncertainties involved (especially where uncertainties vary over time), with clear information provided about the NH₃, measurement method and the flux method used, including any assumptions.

6. They should include a description of the field site, including estimates of surface displacement height, roughness height and single-sided leaf area index (LAI, if vegetation is present).

7. They should include a record of human management practices, such as fertilization information (date, time, amount and technique) and irrigation.

8. If possible, information about the temporal changes in atmospheric concentrations of other air pollutants, especially acidic compounds such as sulfur dioxide and nitric acid, should also be included.

9. Optionally, hydraulic conductivity and cation exchange capacity would be a useful addition.

10. It is critical that the measurements avoid large gaps in measurement data, especially at key periods (such as immediately after fertilization events), if measurement data are to be used for detailed comparison with a model application.