Correction: From the Ground Up: Global Nitrous Oxide Sources are Constrained by Stable Isotope Values

There are errors in Table 3. The labels under the “Category” column are incorrect. Please see the corrected Table 3 here. 
 
 
 
Table 3 
 
MixSIAR model output summary.


Introduction
Since the advent of the Haber-Bosch process one century ago, humans have vastly perturbed the global nitrogen (N) cycle. Current anthropogenic activities contribute 51% of the total N fixed worldwide (210 of 413 Tg N yr −1 ) [1]. One negative consequence of this is an increase in atmospheric nitrous oxide (N 2 O) [2], a long-lived trace gas that contributes to climate warming and the destruction of stratospheric ozone [3]. The current concentration of N 2 O in the troposphere is 325 parts per billion (ppb) [4]. Future concentrations of atmospheric N 2 O are difficult to predict, yet this information is an essential input parameter for global climate change models. Further, both the prediction and mitigation of N 2 O concentrations depend on an accurate understanding of the emissions from key N 2 O sources.
Most emissions of N 2 O (natural and anthropogenic) occur from terrestrial, freshwater, and marine environments, where N compounds are processed by nitrifying and denitrifying microorganisms. These processes account for *89% of the total annual N 2 O emissions, or almost 16 Teragrams (Tg = 10 12 g) N/year [5]. However, scientists' best estimates of the N 2 O budget are still highly uncertain. The most recent Intergovernmental Panel on Climate Change Assessment Report (IPCC-AR5) reveals wide ranges in the relative uncertainty of many individual N 2 O sources. In addition, the uncertainty on the annual cumulative emissions of N 2 O for 2006 from natural soils, oceans, rivers, estuaries, coastal zones, and agriculture combined ranged between 6.9-26.1 Tg N [5].
The clear separation and accounting of individual N 2 O sources remains challenging, but is essential if we are to make meaningful reductions in emissions. Measurements of stable isotope ratios (δ 15 N-N 2 O and δ 18 O-N 2 O) and the intramolecular site preference (SP) of 15 N are one way to track sources if they are isotopically distinct. Several accounts of the global N 2 O budget have used 'top-down' isotope mass-balance models to estimate the strength and isotopic composition of anthropogenic and natural N 2 O sources [2,[6][7][8][9][10][11]. In this approach, changes in atmospheric N 2 O over time are modelled by comparing our modern-day atmosphere (a mixture of post-industrial, anthropogenic N 2 O and natural N 2 O) to relic air trapped in glacial firn and ice. All these studies have assumed that soils are the main source of post-industrial N 2 O because its calculated isotopic composition was most similar to a limited body of published soil N 2 O measurements. Yet we do not have a clear synthesis of the isotopic character of individual N 2 O sources. For example, freshwaters and estuaries may contribute up to 25% of anthropogenic N 2 O emissions [5], but prior to 2009 there was only one publication reporting freshwater δ 15 N-N 2 O and δ 18 O-N 2 O values [12] (S1 Dataset). In reality, there is extreme variation in the measured values of δ 15 N-N 2 O and δ 18 O-N 2 O (Fig. 1), and no systematic examination of individual sources has occurred.
In this paper, we use a 'bottom-up' approach to define key N 2 O sources and demonstrate that their global average δ 15 N and δ 18 O values are isotopically unique. Further we use these in situ N 2 O isotope data to substantiate what 'top-down' global atmospheric models have predicted; soils, and not marine or freshwater ecosystems, are the main source of rising atmospheric N 2 O levels.

Methods
We mined 1920 data points from 52 studies that measured in situ δ 15 N-N 2 O and δ 18 O-N 2 O in atmospheric, terrestrial and marine systems from 1987 to present [2,. If the published data was not tabulated, we used the software 'g3data' (http://www.frantz.fi/software/g3data. php) to extract data from figures [61]. The accuracy of our method was tested by plotting a subset of data from Well et al. [51], re-extracting it, and then comparing it to the original values. The mean (min/max) difference (‰) was 0.06 (0.00/0.13) for δ 15 N and 0.02 (0.00/0.07) for δ 18 O. This represents a worst-case accuracy of our ability to extract data from figures because the test data had an unusually wide range (−80 to +120‰ for δ 15 [19]. Twenty-seven studies also measured the intramolecular distribution of 15 N in the linear NNO molecule (780 data points) and these data are provided in the supplementary datasets (S1 Dataset and S2 Dataset). This difference between the central (δ 15 N α ) and terminal (δ 15 N β ) 15 N enrichment is often expressed as the site preference (SP). This parameter is thought to be a unique indicator of the microbial pathway that produces N 2 O and not to be affected by variations in the isotopic ratios of substrates. Recently, this idea has been called into question by Yang et al. [62], who showed that SP can vary depending on the growth conditions of microbial cultures. Regardless, if the SP of different global sources is unique it can be used in conjunction with traditional measures of δ 15 N-N 2 O and δ 18 O-N 2 O values to separate sources in three-dimensional isotope space.
To this compendium of published data we added 1367 new in situ δ 15 N-N 2 O and δ 18 O-N 2 O data from 16 sites across Ontario and New Brunswick, Canada (S1 Dataset). Soil pore gas and static flux chambers were sampled at four Ontario sites. Urban wastewater treatment plants, streams, rivers, and agricultural drainage tile outlets were sampled across four watersheds in Ontario and New Brunswick. Groundwaters were sampled from numerous domestic Global N 2 O isotope measurements from atmospheric, marine, and terrestrial samples. All the data compiled in this study that fit within the axis ranges shown are plotted here. Each point represents one measurement, or in a few cases a reported average value, and is two-thirds transparent to allow the density of data to be displayed. Standard ellipses encompass *40% of the data (Fig. 2) and are shown for the six non-atmospheric categories. Most data fall to the left of the current tropospheric value. Stratospheric data falls along a line (δ 18 O = 0.89 × δ 15 N + 38.4) (R 2 = 0.999) that originates from the tropospheric value, and is caused by isotopic fractionation during N 2 O destruction [13]. and monitoring wells (some multi-level) distributed across nine research sites in Ontario and New Brunswick.
Liquid samples were stripped of N 2 O using an off-line purge-and-trap system described in Baulch et al. [35]. With the exception of samples from one location (ERS) that were analyzed at UC Davis-SIF, all analyses occurred at the University of Waterloo on an IsoPrime isotope ratio mass spectrometer (IRMS) with a TraceGas pre-concentrator with an analytical precision of 0.2‰ (δ 15 N-N 2 O) and 0.4‰ (δ 18 O-N 2 O). All samples were analyzed alongside an internal N 2 O isotope standard that was previously calibrated at the University of Waterloo against local tropospheric air (assumed to be equal to 6.72‰ for δ 15 N and 44.62‰ for δ 18 O [17]). This internal standard gas was also submitted to UC Davis-SIF for isotopic analysis, and the standard deviation of 8 replicates (at varying concentrations including ambient) was 0.34‰ (for δ 15 N) and 0.77‰ (for δ 18 O). The absolute difference in the assigned value of this internal standard gas (blind inter-lab comparison) was 0.29‰ (for δ 15 N) and 0.81‰ (for δ 18 O). Given there are no internationally-recognized standardization methods or materials for N 2 O isotope analysis, these inter-laboratory results are in good agreement with one another. All values are reported here in units of per mill (‰) relative to air-N 2 and VSMOW for δ 15 N and δ 18 O, respectively.
All data were categorized as either Antarctic, freshwater, groundwater, marine, soil, stratosphere, troposphere, or urban wastewater, and a bivariate ellipse-based metric [63] was used to analyze and describe individual N 2 O reservoirs (Table 1). This circular statistical analysis is an improvement over other techniques that qualitatively summarize isotope data with a polygon or a freeform shape e.g., [6,15,46,47]. There is often a high degree of covariance between δ 15 N-N 2 O and δ 18 O-N 2 O and this statistical technique provides an accurate description of the central tendency of the data. By definition, the standard ellipse contains *40% of the data, is centered on the mean and has standard deviations of the bivariate data as semi-axes ( Fig. 2) [63,64]. The data and an R file that contains the code to perform the statistical analyses and create the figures shown here are found at https://github.com/jjvenky/Global-N2O-Ellipses.

Results and Discussion
The data are highly non-uniform within and between categories (Figs. 1 and 3), and even within individual field sites (S1 Dataset). Historically, this has made it challenging to define an 'isotopic signature' for a given environment. Multiple factors cause this variability: (1) N 2 O is produced by nitrification and denitrification, and the isotopic composition of N and oxygen (O) endmembers can vary widely [26,31,32,54]; (2) the apparent fractionation of 15 [26,51]. An initial analysis of all the data compiled in this study shows there is no clear separation of sources because each is described by an ellipse that overlaps at least one other source category ( Figs. 1 and 3).
A similar comparison of all the published SP data (excluding Antarctic and groundwater categories) shows poor isotopic separation of sources (Fig. 4). It is difficult to determine how much of this variability is real, and how much is due to standardization issues and differences  [65], and this study (n = 83) are summarized here with a standard ellipse. The centre of the ellipse is located at the sample mean (x, ȳ), where the semi-major (a) and semiminor (b) axes intersect. The major axis is inclined versus the positive x axis by the angle θ. The tangent lines parallel to the x and y axes are related to the standard deviations (σ x , σ y ) and the correlation coefficient (r). The two regression lines shown intersect the ellipse at the points of tangency [64]. in measurement techniques. A recent inter-laboratory assessment of the methods used to determine nitrogen isotopomers revealed poor SP reproducibility [69]. Eleven laboratories employing either IRMS or laser spectroscopy techniques analyzed a single N 2 O target gas and the resulting standard deviation for SP was 4.24‰. Further, the inter-lab variation in the mean SP value was high, spanning a range of 11.62‰ [69]. This may help explain why there are two distinct groupings of SP data in each of the troposphere [2,17] and the stratosphere [29,45,58]  The colour of each point is two-thirds transparent to allow the density of data to be displayed. Although the ellipses are the same as in Fig. 1, the scales of the axes are narrowed to better show the data relative to current atmospheric values.
doi:10.1371/journal.pone.0118954.g003 (Fig. 4). Reaching an international consensus on standardization methods for the measurement and reporting of nitrogen isotopomers should vastly improve the utility of this data in sourceapportionment studies at all scales. Finally, we note the reproducibility of δ 15 N-N 2 O and δ 18 O-N 2 O measurements in this recent round-robin test was much better than for SP, which gives us confidence in our ability to use these data here to make useful comparisons. The standard deviation (and range) of the N 2 O target gas in the inter-lab comparison was 1.37‰ (1.89‰) for δ 15 N-N 2 O and 1.00‰ (3.47‰) for δ 18 O-N 2 O [69].
Much of the low concentration data from soils and surface waters are highly influenced by mixing with tropospheric N 2 O. This is evident by the high density of soil, freshwater and marine data that lies near the tropospheric N 2 O value (Fig. 3). In contrast, groundwater N 2 O, which does not mix with the atmosphere following recharge, is unaffected by this mixing process. Other processes such as substrate enrichment and N 2 O consumption control the isotopic composition of groundwater N 2 O, which displays extreme variability even within the same location ( Fig. 1) [50,51]. Only 15 studies reported flux-weighted average δ 15 N-N 2 O, SP, and/or δ 18 O-N 2 O values, or provided enough information for us to calculate these values (2 freshwater studies, 2 marine studies, 10 soil studies, and 1 urban wastewater study; Fig. 5; S2 Dataset). The available flux-weighted data from soil and freshwater environments shows much overlap among this combined continental source, but the flux-weighted marine source appears to be unique. Importantly, there are very few flux-weighted data from all sources so robust conclusions cannot be made at this time. Additionally, these data were not weighted equally across studies so conclusions drawn from this analysis can be misleading. Only some of the values are time-weighted, and the sample size used to calculate the flux-weighted average varies from 3 to *50 (S2 Dataset). Emissions of N 2 O from soils (and potentially freshwaters and oceans) are inherently episodic, so future estimates of the flux-weighted average should attempt to include multiple measurements made over long timescales (months to years and encompassing seasonal differences) whenever possible.
The results of our analyses shown in Figs. 1 and 3 are not flux-weighted, nor are all the categories important atmospheric sources. For example, the most recent IPCC assessment reports that human excreta (all forms of treated/untreated sewage) contributes between 0.1-0.3 Tg N yr −1 as N 2 O, or only *1.1% of all natural and anthropogenic sources [5]. Of this, N 2 O emissions from urban wastewater treatment plants constitutes a very small fraction. To address this, we analyzed subsets of the data from important atmospheric sources (freshwaters, oceans, and soils) that were not strongly influenced by mixing with tropospheric N 2 O, and thereby make an important contribution to the flux-weighted average source value (Table 2; Fig. 6). To do this we filtered the data to include: (i) all reports of emitted N 2 O, regardless of the strength of the flux (two freshwater studies [13,46], two marine studies [16,43] and several soil studies) (see S2 Dataset); (ii) isotope data in the soil profile that had concentrations of N 2 O >650 ppb v/v (or 200% ambient); and (iii) isotope data in freshwater and near-surface marine environments (depths >100 m) with dissolved N 2 O concentrations >200% saturation with respect to atmospheric N 2 O [70].
Most of the freshwater and soil data were retained (71% and 90%, respectively), and the ellipses of these data subsets are similar to the ellipses for all data in these categories (Table 1). Although the median δ 15 N and δ 18 O values of freshwater and soil N 2 O are significantly different (p < 0.001, Mann-Whitney test), their ellipses intersect one another at the 1σ level ( Fig. 6top panel), and we conclude that these sources are not isotopically distinct at the global scale.
In order to further delineate freshwater and soil N 2 O more stable isotope measurements from freshwaters are needed; especially from non-temperate environments because the current data coverage from these systems is lacking. Measurements of SP may prove to be a useful means of separating these sources because the ellipses that describe SP vs. δ 15 N bulk for freshwater and soils do not overlap (Fig. 6-middle panel).
Of the 495 published marine values compiled here, only 62 originated from the top 100 m of the ocean and were >200% saturation. Relative to continental N 2 O sources, the δ 15 N and δ 18 O values of near-surface oceanic N 2 O sources are poorly constrained. We found no reports of N 2 O isotope values from estuaries, which could represent an important fraction of the marine source but should be similar to marine or freshwater values. Tropical systems including reservoirs are also poorly studied. Future campaigns to more fully characterize δ 15 N and δ 18 O values of N 2 O emissions from aquatic environments, especially those impacted by anthropogenic N sources, are needed.
Although N 2 O generated from fossil fuel and biomass combustion may contribute *8% of the total source (or *20% of the anthropogenic source [5]), its isotopic composition is largely unknown. A lab-scale investigation of coal combustion revealed δ 15 N-N 2 O and δ 18 O-N 2 O values that were both enriched (unstaged combustion) and slightly depleted (air-staged combustion) relative to tropospheric N 2 O [71], indicating coal-derived N 2 O isotope values might be similar to marine sources but are dependent upon combustion conditions. A controlled study of gasoline-powered automobile exhaust concluded the average δ 15 N-N 2 O and δ 18 O-N 2 O values are similar to freshwater sources (−4.9 ±8.2‰ and +43.5 ± 13.9‰, respectively) [72]. Finally, N 2 O derived from biomass burning appears to closely resemble the δ 15 N and δ 18 O values of its endmembers; biomass-N and atmospheric O 2 , respectively [73]. We recognize the need to further investigate these potentially important sources and evaluate how they might affect the global N 2 O isotope budget.
After analyzing the filtered δ 15 N-N 2 O and δ 18 O-N 2 O data, the 'bottom-up' global N 2 O sources defined here were compared to estimates derived from 'top-down' atmospheric models (Fig. 7). Modelled estimates of the average anthropogenic and natural source fall within (or very close to) the soil ellipse and along a mixing line between soil and tropospheric N 2 O. All but two of the modelled estimates fall outside the freshwater ellipse, indicating the bulk of the combined anthropogenic and natural sources are not from freshwaters. If freshwaters were a major source of atmospheric N 2 O, a mixing line between freshwater and tropospheric N 2 O would be much closer to the anthropogenic and natural source values. It is not, and therefore Table 2. Summary statistics of filtered δ 15 N-N 2 O and δ 18 O-N 2 O data. These values show a subset of data that were not strongly influenced by mixing with tropospheric N 2 O, and thereby make an important contribution to the flux-weighted average source value (see Fig. 6). we confirm what 'top-down' approaches have previously inferred: soil is the main source of N 2 O to the atmosphere. We used the newly constrained δ 15 N-N 2 O and δ 18 O-N 2 O values for freshwater and soil (the combined continental source) and the ocean source to model their relative contributions to the total annual flux of N 2 O. We began with a box-model approach similar to that presented in [8,9,11,29]. We adapted the following isotope mass-balance equation for atmospheric N 2 O from Park et al. [29]: where,Burden = Present-day burden of N 2 O in the troposphere [1553 (± 21.742) Tg N] as reported by Stocker et al. [5]. This estimate is for year 2011, and is updated from data provided in Prather et al. [74], who report an uncertainty of 1.4% for year 2010.  Table 1). " = Apparent enrichment factor (‰) for N 2 O destruction processes in the stratosphere. These values are taken from Table 3 in Park et al. [29], and are −14.9‰ (± 0.5) for 15 N and −13.5‰ (± 0.5) for 18  L = Photochemical loss rate of N 2 O in the stratosphere (14.3 Tg N yr −1 ) [5]. Following [29], we applied an uncertainty of 25% in our calculations.
The term (− " × L) is a very close approximation of the 'Net Isotope Flux' (‰ Tg N yr −1 ) as defined in [29], and is the net annual flux of N 2 O isotopologues from the stratosphere to the troposphere. Equation 1 can be rearranged to solve for δ Sources (Eq. 2), and all the known quantities provided above can be substituted into Eq. 2 to derive a flux-weighted, average modern source value (δ Sources ) for δ 15 N-N 2 O and δ 18 O-N 2 O (‰).
Accordingly, we derive an average modern source value (± propagated standard deviation) for δ 15 N-N 2 O and δ 18 O-N 2 O of −8.4‰ (± 4.0) and +31.7‰ (± 13.9), respectively. If we were to assume that all N 2 O fluxes (F) originate only from marine and continental sources, then: X Sources % F Ocean þ F Cont % 17:9 Tg N yr À1 ð3Þ and the flux-weighted modern source value is approximated by: where the δ value of the continental and ocean sources are given in Table 2.
Combining Eq. 2 with Eq. 4 yields: Given the assumption that F Cont ≈ ∑ Sources − F Ocean (Eq. 3), we can approximate F ocean by: Accordingly, using N isotope ratios we derive a value for F ocean of *4.6 (± 12.6) Tg N yr −1 , which is *26% of all sources (17.9 Tg N yr −1 ) [5]. The F Cont is found by difference, and is approximately equal to 13.3 (± 13.4) Tg N yr −1 , or 74% of all natural and anthropogenic N 2 O sources. The largest source of uncertainty in the N isotope mass-balance lies in the δ 15 N value of the continental source (1σ = 11.5‰), followed by ∑ Sources and L, which have a relative uncertainty of 25% in our model.
The most recent N 2 O budget estimates the combined soil, freshwater, and ocean flux to be *15.7 Tg N yr −1 , or 87.7% of the total source [5]. Our approach assumes the ∑ Sources = 17.9 Tg N yr −1 (as reported in IPCC-AR5) because other terms in the mass-balance (e.g., N 2 O burden and loss rate) are based on a budget that includes all known sources. As such, we ignore the contributions from smaller sources such as human sewage, fossil fuels, industry, biomass combustion, and chemical production processes in the atmosphere, which have a combined annual flux of *2.2 Tg N yr −1 [5]. Despite this, our result for F ocean is similar to the estimate provided in IPCC-AR5, which shows oceans contribute 21% of the annual N 2 O budget [5].
The O isotope mass-balance fails to derive a positive ocean flux (F ocean = −4.5 ± 19.9 Tg N yr −1 ). This is because the δ 18 O separation between the troposphere and the continental source is smaller than it is for δ 15 N, and the term ∑ Sources (δ Trop − δ Cont ) is too small to make the numerator in Eq. 6 a net positive number. However, decreasing the loss rate (L) by 4 Tg N yr −1 and increasing ∑ Sources by the same amount yields a positive ocean flux = 4.6 Tg N yr −1 . Therefore, if the uncertainty of these parameters is reduced in the future we may find that the O isotope budget balances. Finally, we used a stable isotope Bayesian mixing model (MixSIAR) [75] to determine the proportions of soil, freshwater, and marine N 2 O that best predicted the average modern source (anthropogenic plus natural) (Eq. 7).
where, F Soil + F Freshwater + F Ocean = 1. MixSIAR, which is a front-end interface of the model SIAR (Stable Isotope Analysis in R) [76], is an ecological mixing model traditionally used to describe food web and predator-prey relationships. Values of δ 15 N bulk -N 2 O, δ 15 N α -N 2 O, δ 15 N β -N 2 O, and δ 18 O-N 2 O for the average modern source (the mixture) were taken from Röckmann et al. [9]. These estimates are almost identical to the ones calculated in our 2-box-model (above), and Röckmann et al. [9] provided 15 N isotopomers, which allowed us to use 3 variables in our model runs (δ 15 N bulk , δ 18 O, and SP). A series of Markov Chain Monte Carlo simulations, using values for soil, freshwater, and marine N 2 O (filtered, raw data compiled in this study), were done to find mixing solutions that best fit the average modern source (Table 3). Gelman-Rubin and Geweke diagnostic tests indicated a chain length of 300,000, burn in of 200,000, thinning of 50 (2-isotope) or 100 (3-isotope), and 3 chains were appropriate.
Model runs using only the δ 15 N-N 2 O and δ 18 O-N 2 O data (2-isotope mixing model, n = 1383 data pairs) produced results very similar to the model runs that also included SP data (3isotope mixing model, n = 235 data triads). Overall, this Bayesian modeling exercise predicted the soil, freshwater, and ocean contributions (± 1σ) to the average modern N 2 O source were 0.43 (0.20), 0.34 (0.22), and 0.24 (0.16), respectively (Table 3). Unlike the box-model, this approach does not place a priori bounds on the data, and is not constrained by terms such as the stratospheric N 2 O loss rate (L), which have large uncertainty. However, this method also ignores the contributions of several small sources, which have a combined contribution of *12.3% to the total budget presented in IPCC-AR5 [5].
Both SIAR and the box-model predict the ocean flux to be 24% and 26% of the total, respectively, which closely confirms the scientific community's best estimate of the ocean flux as presented in IPCC-AR5 (21% of the total source). Further, the SIAR model output shows that freshwaters may contribute much more N 2 O than previously thought. The current N 2 O budget estimates the combined flux from rivers, estuaries, and coastal zones is 0.6 Tg N yr −1 , or just 3% of the total source. While we acknowledge that there is δ 15 N-δ 18 O overlap in the soil and freshwater source (Fig. 6-top and bottom panels), these sources appear to be unique in δ 15 N-SP space (Fig. 6-middle panel). Therefore, we suggest there is a great need to quantify N 2 O fluxes from freshwaters, estuaries, and coastal zones, which have received considerably less attention than soil and off-shore marine environments.
Supporting Information S1 Dataset. A comma-delimited text file with all the data collected and analyzed in this study. In addition to δ 15 N-N 2 O, SP and δ 18 O-N 2 O values, we provide a reference citation, the category, a brief site description, and the criteria used to filter the data subsets (S1_Dataset. csv).