Characterization of atmospheric nitrous oxide emissions from global agricultural soils
Nitrous oxide (N2O) is a potent greenhouse gas with an atmospheric lifetime of ~ 114 years. Agriculture activities are the main sources for N2O emission into the atmosphere by human activities. Global N2O emissions into the atmosphere are projected to increase in the coming years as demand for food, fibre and energy increases owing to increasing global population. Here, a statistical model (N2O_STAT) is developed for characterizing atmospheric N2O emissions from agricultural sources. We obtained N2O emissions and physicochemical variables (i.e. air temperature, soil temperature, soil moisture, soil pH, and N input to the soil) from published journal articles since 2000. A statistical model was developed by expressing a multiple linear regression equation between N2O emission and the physicochemical variables. The model was evaluated for 2012 N2O emissions. Results of the model are compared with other global and regional N2O models (e.g. EDGAR, EPA/USGS, and FAOSTAT). In comparison with other data sets, the model generates a lower global N2O estimate by 9–20% (N2O_STAT: 3.75 Tg N yr−1; EDGAR: 4.49 Tg N yr−1; FAO: 4.07 Tg N yr−1), but is ~ 25% higher when compared to Bouwman et al. (Glob Biogeochem Cycles 16:1–9. https://doi.org/10.1029/2001gb001812, 2002) (2.80 Tg N yr−1). We also performed a region-based analysis (USA, India, and China) using the N2O_STAT model. For the USA, our model produces an estimate that ranges from − 13 to + 32% in comparison with other published data sets. Meanwhile, the N2O_STAT model estimate for India shows N2O emissions between − 56 and + 14% when compared to other data sets. A much lower estimate is seen for China, where the model estimates N2O emissions 38–177% lower than other data sets. The N2O_STAT model provides an opportunity to predict future N2O emissions in a changing world.
KeywordsNitrous oxide Emissions Agricultural soil Statistical model
The largest human influence on climate since the end of the twentieth century is the emission of greenhouse gases to the atmosphere. In addition to carbon dioxide (CO2), nitrous oxide (N2O) is one of the most important greenhouse gases that has a global warming potential (GWP) of ~ 300 for a 100-year timescale . N2O also contributes to the destruction of ozone in the stratosphere . The lifetime of N2O in the atmosphere is ~ 114 years, indicating its long-term influence on a planetary scale .
Ciais et al.  have estimated the yearly emission of N2O to be 17.9 Tg N yr−1 for the period 2006–2011. N2O emissions from natural sources are 11.0 Tg N yr−1, which includes sources from land and oceans. Agricultural activities are the primary anthropogenic source of N2O, contributing to 5.6 Tg N yr−1 . With increasing food, fibre and energy production, along with climate change and agricultural intensification, N2O emissions from soils have increased since 1990, from 3.5 Tg N yr−1 to 4.1 Tg N yr−1 .
During the period 1961–2010, global N2O emissions from manure usage have grown from 1.17 to 2.03 Tg N yr−1 at an average rate of 1.10% yr−1 . Meanwhile during the same period, N2O emissions from synthetic fertilizers have increased from 0.14 to 1.40 Tg N yr−1 at an average rate of 3.90% yr−1 globally . This indicates that synthetic fertilizers will have a greater contribution to N2O emission than manure within less than 10 years . Besides agriculture, other sources such as fossil fuel combustion, industrial processes, and biomass burning also contribute to the total N2O emissions, but these are all relatively small sources.
Intensive fertilizer use has increased the emissions of reactive nitrogen compounds, including N2O from soils through nitrification and denitrification processes (Supplementary Figure 1S). Nitrification is the aerobic microbial oxidation of ammonium or ammonia to nitrite followed by oxidation of nitrite to nitrate. It is an important process in the nitrogen cycle in which N2O is generated as a by-product that leaks from microbial cells into soil and eventually into the atmosphere . Denitrification is a microbially facilitated process that leads to significant N losses from agricultural systems. Through denitrification, nitrate and nitrite are reduced, and a portion converted into N2O .
Will increase N2O/NO3− ratio
Decreasing O2 concentration
Increasing H2O above field capacity
Low NH4+ concentrations
Increasing or decreasing pH
Will increase N2O/N2 ratio
[NO3−] or [NO2−]
Decreasing C availability
Low N2O reductase activity
Decreasing between 60 and 90% WFPS
Uncertainties of estimates of sources and sinks still exist in global N2O budget, especially from agricultural soils . Inadequate understanding of the mechanisms controlling N2O emission from agricultural soils may be responsible for limited attention to agriculture as a major contributor of the increasing atmospheric N2O. With increasing food and energy production, along with climate change and agricultural intensification, N2O emissions from soils and groundwater are likely to increase, indicating the need for an updated global budget for N2O that accounts for these recent changes.
The goal of this project is to develop a statistical model to predict N2O emissions from agricultural soils containing synthetic and organic fertilizers using physicochemical properties of the system from different regions. We also analyse the spatial distribution of N2O emissions from agricultural soils and compare the results with other modelled emission inventories (i.e. EDGAR v.4.3.2, EPA, and FAOSTAT).
Based on literature review, we found four variables of importance in controlling N2O emissions from soil: (1) soil moisture, (2) soil and air temperature, (3) synthetic and organic fertilizer usage, and (4) soil pH . The highest N2O emissions are usually due to high temperature and ample precipitation because increasing soil temperature stimulates microbial activities related to nitrification and denitrification. We performed a series of statistical analyses utilizing the RStudio statistical software (https://github.com/rstudio/rstudio) to examine the distribution of data and to fit an appropriate regression model with N2O as the response (dependent) variable and other variables as independent predictors. We then used Integrated Land and Water Information System (ILWIS) v.3.31 Academic (https://www.itc.nl/ilwis/download/ilwis33/), a GIS tool to prepare the global data sets and apply the statistical model to predict N2O emissions.
2.1 Data collection
Data for statistical model development
kg N ha−1 year−1
Fertilizer N content usage
kg N ha−1 year−1
Manure N content usage
kg N ha−1 year−1
Global data set used for prediction
Soil temperature; soil pH
Harmonized World Soil Database v 1.2
The Global Soil Dataset for Earth System Modeling
ERA-Interim Global Atmospheric Reanalysis
Cropland cover, fertilizer usage, manure usage
EarthStat’s Cropland and Pasture Area (with modification)
2.2 Model development
Summary of the statistical model
Table 4 summarizes the coefficients and p values of each variable. The residual standard error is 0.928, and R-squared is 0.2. The F test shows that this multivariate linear regression model is statistically significant at 90% confidence level. Based on the p value, the soil moisture, soil pH, and fertilizer type are statistically significant. Notably, the magnitude of nitrogen input does not have a significant influence on the N2O emission rate. This may seem counterintuitive, but N2O emissions are produced by nitrification and denitrification, and nitrogen concentrations may be the limiting factor for these reactions only when the levels of soil nitrogen are low. Other factors are likely to be limiting when soil nitrogen concentrations are at agronomic levels . Yu and Zhuang  corroborate these findings using their trait-based biogeochemistry model to estimate global N2O emissions that were more sensitive to temperature and precipitation and less sensitive to soil organic carbon and nitrogen contents.
2.3 Model diagnostics
After running the regression analysis, we verified that N2O_STAT works well for fitting the data and complies with the assumptions of linear regression models. A two-step model diagnostic was performed by analysing the variance and distribution of the residuals (Supplementary Figure 2S). The equal distribution with no distinct patterns of residuals around the horizontal provides a good indication of the likelihood of a linear relationship. Additionally, the residuals are well fitted on the straight line, indicating that the data are indeed normally distributed. The outliers indicated by residuals that are far from the line were excluded in further analysis.
We tested different model forms, i.e. linear form (classical emission factor approach) and exponential form (this study). The exponential form had r2 = 0.2, and residual standard error = 0.93, which are better than in the linear model (r2 = 0.14 and residual standard error = 1.02), suggesting that the exponential model is preferred in modelling the N2O emission.
2.4 Other N2O emission inventories
The Emission Database for Global Atmospheric Research compiles anthropogenic global N2O emissions and trends from 1970 to 2012 based on international statistics and emission factors . N2O emissions from fertilizer are based on the estimation from the International Fertilizer Industry Association (IFA) and the Food and Agriculture Organization Statistics Division (FAOSTAT). The N2O emission factor for direct soil emissions from the use of synthetic fertilizer and from manure and from crop residues is based on IPCC Guideline . For the comparison purposes, we use the 2012 global N2O data set for agricultural soils (subsector 4C + 4D).
2.4.2 EPA greenhouse gas inventory report and USGS county-level data sets
We calculated N2O emission from agriculture soils over the continental USA based on subsectors described in the EPA report . The subsector emissions are taken from the county-level information compiled by USGS from the 2012 census of agriculture [19, 20]. The county-level information consists of fertilizer usage, manure applications, and crop residue. Then we calculated the emissions which are interpolated to generate a spatial distribution of the emission for the USA.
2.4.3 FAOSTAT (http://www.fao.org/faostat/en/)
Food and Agriculture Organization of the United Nations develops methods and standards for food and agriculture statistics, provides technical assistance services, and disseminates data for global monitoring. It provides the N2O global emissions from synthetic fertilizers, manure applied to soils, manure left on pasture, and crop residues in 2012.
Figure 3b shows spatial distribution of global N2O emission from agricultural soil based on EDGAR. Total annual global N2O emissions from N2O_STAT and EDGAR are 3.75 Tg N yr−1 and 4.49 Tg N yr−1, respectively. It is encouraging to see that, in general, the model captures the global spatial pattern in N2O emissions well. Figure 3c shows the absolute difference between N2O_STAT and EDGAR. In comparison with EDGAR, N2O_STAT gives lower N2O emission values in North America, South America, India, and China, while higher values in Eastern Europe and mid-Africa.
3.2 Continental USA, India, and China
Summary of N2O emission from different inventories
N2O (Tg N yr−1)
Bouwman et al. 
Aneja et al. 
Garg et al. 
Sharma et al. 
Gao et al. 
Zhou et al. 
Meanwhile for China, our estimate using N2O_STAT is 2.3–2.8 times lower than those estimated by EDGAR and FAO. Our N2O emission estimate, however, is in good agreement with Gao et al.  and Zhou et al.  being 2% higher and 38% lower, respectively. These two studies employ different methods in estimating N2O emission from Chinese agricultural soils. Gao et al.  studied N2O direct emissions from croplands by using localized emission factors, while Zhou et al. , in addition to using regional emission factors, utilized high-resolution activity data and localized parameters.
We have developed a novel way to approach global nitrous oxide emissions from agricultural soils (N2O_STAT). We have also used three case studies (USA, India, and China) to strengthen our model development. Unlike all previous N2O emission studies, our approach relies on global emission measurements rather than emission factors and activity data.
Table 5 summarizes the data comparison between N2O_STAT, EDGAR, EPA/USGS, and FAOSTAT for N2O emission from agricultural soils for the USA, India, China, and globally. The FAOSTAT, EDGAR, and EPA estimates are slightly different, although consistent given the large uncertainties in the IPCC default methodologies . Tubiello et al.  compared N2O emission from four databases. The results show that the EPA 2006 and EPA 2011 provided the highest values, while FAOSTAT gave the lowest, consistent with our study.
In developing N2O_STAT, we collected data for published N2O emissions that correspond to the use of fertilizer and manure on particular soils (Supplementary Table 1S). N2O_STAT, however, does not include ancillary emissions from leaching and surface runoff, as such information is not often available. As a result, our estimate is only driven by the direct N2O emissions from agricultural soils. This may represent a fundamental difference when comparing the results across different data sets. EDGAR and FAOSTAT incorporate both direct and indirect N2O emissions in estimating the global emissions. Additionally, the agricultural sources from which the emissions are tabulated for our model are different from other data sets. For example, EDGAR includes rice cultivation and crop residue in its estimate . Another key difference between N2O_STAT and other models lies in the methodology of collecting the model inputs. The N2O_STAT model uses the measured N2O emissions reported from field experiments, whereas the other approaches derive their emissions by using intermediate data sets (e.g. fertilizer production, livestock counts) and apply emission factors to the corresponding data sets. The N2O_STAT model only considers physicochemical variables of the emissions, excluding the soil management practices that might contribute to the emissions. In addition, the methods used to measure N2O emissions in the field were different from one study to another; these differences are not taken into consideration in developing N2O_STAT.
The region-based analysis (USA, India, and China) indicates that our model gives lower estimates than other modelling efforts. The global N2O agricultural soil emission from N2O_STAT estimate is 9–20% lower than EDGAR and FAOSTAT. The major differences, as observed in Fig. 3c, are most prominent in India and China. In India, negative differences are depicted in Fig. 6c in the northern and central regions, while the positives are mainly to the west and south of the subcontinent. However, the finely resolved agricultural emissions of N2O in India , as well as from EDGAR and FAOSTAT, agree well with N2O_STAT (< 20% differences). It is to be noted that the estimate from Aneja et al.  was calculated for 2003. Despite this difference, there are similarities between these data sets with respect to the areas from which high emissions are estimated. Such similarities are not observed when we compared our model estimate with EDGAR.
Our approach is subject to uncertainty. In particular, our statistical analysis was restricted to parameters which were available in the measurement literature and in global databases. Thus, the analysis did not include parameters such as soil composition and porosity, which could also influence N2O emissions. We also do not take into account short-term changes in moisture and temperature which may result in enhanced N2O emissions. Further, data were not available to systematically incorporate differences in agricultural practices, such as the cultivation of more than one crop per year, or the use of multiple fertilizer applications in a year. This may account for some of the difference between our estimates and other estimates for China, where two crops are grown per year in many places.
Nevertheless, previous N2O emissions inventory approaches are also subject to large uncertainties. Our literature survey identified N2O emission factors from less than 0.1 to almost 10 kg N2O–N kg−1 N applied [29, 30]. This demonstrates the difficulty of using an emission factor approach to compute N2O emissions. In fact, diagnostic tests for our model indicated that N2O emissions are a nonlinear function of N input . N2O_STAT can be used to estimate a median value for the N2O emission factor by calculating the ratio between N2O emission and applied N fertilizer in every grid cell of the map. We calculated the N2O emission factor for USA. In our calculation, we distinguished the two sources of N2O emissions, i.e. synthetic fertilizer and organic fertilizer, and determined emission factors for each of these sources. Our results suggest that for the USA, the median values for the emission factor for synthetic fertilizer and organic fertilizer are 1.03% and 1.52%, respectively, based on the N input from the fertilizer. The emission factor for synthetic fertilizer is comparable to those from Stehfest and Bouwman  (0.9%) and De Klein et al.  (1.0%).
N2O_STAT is a statistical model developed for characterizing atmospheric N2O emissions from agricultural soils. We obtained N2O emissions and physicochemical variables (i.e. air temperature, soil temperature, soil moisture, soil pH, and N input to the soil) from published journal articles since 2000. In comparison with other data sets, the model generates a lower global N2O estimate by 9–20% (N2O_STAT: 3.75 Tg N yr−1; EDGAR: 4.49 Tg N yr−1; FAO: 4.07 Tg N yr−1), but is ~ 25% higher when compared to Bouwman et al.  (2.80 Tg N yr−1). A region-based analysis (USA, India, and China) using the N2O_STAT model produces an estimate for the USA that ranges from − 13 to + 32% in comparison with other published data sets. Meanwhile, the N2O_STAT model estimate for India shows N2O emissions between − 56 and + 14% when compared to other data sets. A much lower estimate is seen for China, where the model estimates for N2O emissions are 38–177% lower than other data sets.
The N2O_STAT uses measured values for N2O emissions including N content in the fertilizer to develop the model. The correlations between N2O emissions and most physicochemical variables are at a high significance level (90%), suggesting that these variables are likely affecting the emissions despite excluding other variables. Moreover, the N2O_STAT model provides an opportunity to predict future N2O emissions in a changing world. This statistical model provides an innovative and relatively simple way to estimate global N2O emission from agricultural soils.
The underestimation of N2O emissions in comparison with other data sets and the fact that N2O_STAT may be still missing some key N inputs to its variables should be taken into account in future work. Parameterization of soil biological activity would more fully represent the processes governing the N2O emissions.
Support for this work was provided by U.S. GFDL-NOAA project NOAA CPO AC4. We thank Dr. Larry Horowitz and Dr. Fabien Paulot for their ongoing discussions on the project. We also thank Dr. Francesco Tubiello, UN Food and Agriculture Organization, for discussions of our results.
The five co-authors contributed equally to the work; however, VPA and WHS jointly supervised the work. AN prepared the global emission maps. All authors reviewed the manuscript. QL and AN performed the statistical analysis related to the modelling framework.
Compliance with ethical standards
Conflict of interest
The authors declare no competing interests.
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