Fraction of nitrous oxide production in nitrification and its effect on total soil emission: A meta-analysis and global-scale sensitivity analysis using a process-based model

Nitrification in terrestrial soils is one of the major processes of emission of nitrous oxide (N2O), a potent greenhouse gas and stratospheric-ozone-depleting substance. We assessed the fraction of N2O emission associated with nitrification in soil through a meta-analysis and sensitivity analysis using a process-based model. We corrected observational values of gross nitrification and associated N2O emission rates from 71 records for various soils in the world spanning from 0.006% to 29.5%. We obtained a median value of 0.14%, and then assessed how the nitrification-associated N2O emission fraction has been considered in terrestrial nitrogen cycle models. Using a process-based biogeochemical model, we conducted a series of sensitivity analyses for the effects of different values of nitrification-associated N2O emission fraction on soil N2O emission. Using an empirical relationship between soil pH and nitrification-associated N2O emission fraction, the model well simulated global emission patterns (global total in the 2000s, 16.8 Tg N2O yr–1). Differences in the nitrification-associated N2O emission fraction caused differences in total N2O emission of as much as 2.5 Tg N2O yr–1. Therefore, to obtain reliable estimation of soil N2O emission for nitrogen and climate management, it is important to constrain the parameterization in models by ensuring extensive and accurate observations.


Introduction
Nitrous oxide (N 2 O) is the third important long-lived greenhouse gas next to carbon dioxide (CO 2 ) and methane (CH 4 ) [1] and is the most important substance depleting stratospheric ozone [2]. To reach the overarching mitigation targets of the Paris Agreement [3] we need to suppress the growth of atmospheric N 2 O concentration, to which anthropogenic emissions PLOS ONE | https://doi.org/10.1371/journal.pone.0219159 July 10, 2019 1 / 21 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 contribute at a level comparable to that from natural sources [4,5]. Also, assessment and regulation of N 2 O emission contribute to management of nitrogen cycle, which is closely related to many issues of human sustainability, such as food production and sanitation [6]. Nevertheless, there remain serious uncertainties in our understanding and predictability of N 2 O dynamics. Terrestrial soils-both natural and agricultural-are a prevailing source of N 2 O in the atmosphere [7,8], but spatial heterogeneity and temporal variability of the N 2 O flux make it difficult to quantify broad-scale budgets. Most of the N 2 O released from the soil surface is produced by two separate microbial processes, nitrification and denitrification, which differ in terms of active microbes, substrates, and environmental responsiveness [9,10]. There are still serious knowledge gaps and difficulties in using models to predict soil N 2 O emissions in a quantitative manner.
Nitrification by ammonia oxidizers is the primary process of N 2 O production in oxic (aerobic) soils and is thought to be more ubiquitous than denitrification, which occurs in anaerobic wet soils. Recent studies have revealed the contributions of different soil microbes, such as ammonia-oxidizing archaea and bacteria, to nitrification [11,12]. In nitrification, most of the oxidized ammonia is turned into nitrate (NO 3 -) via nitrite (NO 2 -), and a certain (usually small) fraction of nitrogen is released as N 2 O. The fraction of nitrification-associated N 2 O emission (fN 2 O nit ) and its regulation mechanism are important but barely understood. Although fN 2 O nit is critically important to predict soil N 2 O emission, a few studies have investigated the responses of fN 2 O nit and the corresponding nitric oxide (NO) emission fraction to soil temperature and moisture conditions [13,14]. However, observational data and knowledge are still insufficient to evaluate broad-scale emissions, including from a variety of soils. Farquharson (2016) [15] conducted a systematic analysis of fN 2 O nit from agricultural soils in Australia. He found that 0.03% to 1% of nitrogen is released as N 2 O associated with nitrification in soils and found no strong relationship with environmental factors such as soil moisture. For a broad range of natural soils, and in other regions, we have found no systematic analysis on fN 2 O nit . fN 2 O nit should be an important parameter in biogeochemical models that aim to simulate nitrogen cycles and predict N 2 O emissions from land. Many terrestrial nitrogen cycle and N 2 O emission models have been developed, from simple box-flow models (e.g., the Terrestrial Ecosystem Model [16]) to more mechanistic ones (e.g., the Denitrification Decomposition [DNDC] model [17]). In these models, fN 2 O nit or a similar parameter (i.e., the total N 2 O and NO emission fraction) has been determined in a simplified empirical manner. In the well-recognized "hole in the pipe" or "leaky pipe" concept of soil nitrogenous gas emission [18,19], fN 2 O nit represents the size of the N 2 O hole in the nitrification pipe (Fig 1). Note that the nitrification rate (as defined by pipe diameter and flow velocity) varies also with the environmental conditions, so it is possible to regard fN 2 O nit as a constant or as an independent variable that changes with environmental condition. In the latter case, empirical parameterizations have been adopted to determine the N 2 O emission fraction, using a limited amount of observational data. As a consequence, these emissions could have a considerable range of bias and error due to the uncertainty of fN 2 O nit values.
Here, we focused on fN 2 O nit from the perspective of the global N 2 O budget, aiming at better predictability of emission by biogeochemical models. Our focal research questions are as follows. (1) What is the feasible range of fN 2 O nit in the terrestrial ecosystems? (2) How does fN 2 O nit vary in the field in response to environmental conditions? (3) Can we attain a better parameterization of fN 2 O nit , applicable to global scale, on the basis of present data? First, to clarify the range of variability and the broad-scale trends in these values, we conducted a metaanalysis of the observed values of fN 2 O nit for both natural and agricultural soils. Second, we surveyed how fN 2 O nit was included in current terrestrial N 2 O estimation models. Third, we used the results of the meta-analysis and model survey to conduct a series of sensitivity analyses of fN 2 O nit and N 2 O emissions by using our biogeochemical model. Finally, we discuss how we can reduce the range of estimation uncertainty in both experimental and modeling studies. Note that this study focuses on nitrification as the first step and that other important processes such as denitrification, nitrifier denitrification, and abiotic production [20] are not explicitly addressed here. We intend to address these other processes in a forthcoming study using a similar approach.

Meta-analysis
Overview. A meta-analysis was conducted to reveal the range, frequency, and tendencies of soil fN 2 O nit reported in the literature. The results were reported following the Preferred Reporting Items for Systematic Review and Meta-Analyses protocols (PRISMA) [21] protocol (S1 Table). To obtain information on the general properties of the parameter, we gathered observational values reported from a wide range of studies. By using Web of Science (Thomson Reuters, New York, NY, USA) and Google Scholar (Alphabet, Mountain View, CA, USA), we searched papers and reports that included data on nitrogenous gas exchange and soil biogeochemistry. We used combinations of three terms (each from #1 to #3) in S2 Table to search candidate papers; for example, "nitrous oxide flux" and "nitrification rate" and "soil surface". No date and time limitations were applied to harvest from the maximum extent of the literature. Also, we examined the reference lists in each paper to find additional literature that did not appear in the web searches.
Study selection. We carefully selected source data of fN 2 O nit for the meta-analysis, particularly taking into account the consistency between N 2 O emission and nitrification rates. First, we removed papers that addressed non-soil N 2 O emissions (i.e., from ponds, landfills, animal slurry, etc.). For quantitative consistency, we selected papers including data on gross nitrification (i.e., NH 4 + consumption) and associated N 2 O emission. Therefore, several papers that reported only net nitrification (i.e., NO 3 production) rates, potential emission rates, and data under oxygen-free condition, were carefully removed from the meta-analysis. Also, we focused on daily or longer phenomena, so that rates of N 2 O emission from the soil surface to the atmosphere could be adequately approximated to N 2 O production rates within the soil (i.e., the vertical diffusion time lag was negligible). As a result, papers reporting only instantaneous (i.e., for seconds to minutes) measurements were excluded; in general, these instantaneous measurement data show extremely wide ranges of variability, making a robust analysis difficult. Finally, we selected the source papers by measurement method used in each study, because several methods could give biased values under certain conditions (e.g., DMPP inhibition slows greatly at >25˚C [22]). We confirmed that the method-based selection had a small impact on the analysis results. The paper selection was made by two authors and discrepancies were resolved by discussion. Data extraction. Data on fN 2 O nit values and associated properties were extracted: soil pH, solvent of pH, soil temperature, soil moisture content with units, soil texture, clay / silt / sand composition, latitude, longitude, land-cover type, and soil-type classification. Few papers provide values of fN 2 O nit directly, and therefore, if applicable, we calculated the values from gross nitrification and associated N 2 O emission rates measured under the same condition.
Data analyses. A statistical software R [23] was used to calculate the statistical metrics for the records: i.e., mean, median, maximum, minimum, standard deviation [σ], kurtosis, skewness, and quartiles. A few extreme values can, in most cases harmfully, affect the results of statistical metrics. To assess the influences of outliers, these statistical metrics were also calculated after removing top and bottom outliers (10% from all the records). Note that we used both datasets with and without outlier values in the following analyses and model simulations. Furthermore, to reduce the size effect of different sample numbers (i.e., weights) among papers, these metrics were also calculated using the mean values for each paper.

Parameterization of fN 2 O nit in other models
We then assessed how fN 2 O nit has been parameterized in other terrestrial nitrogen models and evaluated the influence on N 2 O emission estimation. According to a review by Frolking et al. (1998) [24], former models have adopted different constant fN 2 O nit values, namely 0.5% in the ExpertN model and 2% in the CENTURY model. These values were examined in the sensitivity simulations mentioned below. In later models, fN 2 O nit was parameterized as a function of environmental conditions in different manners. The modified DNDC model [25] (their Table 3, Eq 8) adopted the following parameterization: Ft ¼ ½ð60 À TsÞ=25:78� 3:503 exp½3:503ðTs À 34:22Þ=25:78�; ð2Þ where Ft is a scholar function of soil temperature (Ts,˚C) and WFPS is water-filled pore space (fraction). This parameterization gives a peak value, about 0.06%, at about 35˚C under saturated soil water conditions (Fig 2A). The Dynamic Land Ecosystem Model [26] (DLEM) parameterizes fN 2 O nit as a function of WFPS (%): In this parameterization, the fN 2 O nit value increases with increasing soil water content ( Fig  2B) and does not exceed 0.1%. The Community Land Model [27] and O-CN model [28] adopted a version of the DNDC parameterization. In the recent paper on N 2 O model intercomparison [29], an elaborate table summarizes how nitrification and N 2 O emission are formulated in contemporary land nitrogen models.

Description of the N 2 O simulation model
To assess the range of estimations associated with variations in fN 2 O nit , we conducted a series of simulations using a process-based model, namely, Vegetation Integrative SImulator for Trace gases (VISIT [30,31]). This model was selected, because it has an intermediate complexity among the global N 2 O models and gave moderate results in the model intercomparison project [29]. Also, the model was used for a regional evaluation of soil N 2 O emission in East Asia, one of the highly human-influenced regions, demonstrating the credibility for broadscale applications [32]. Briefly, the model consists of water, carbon, and nitrogen cycling schemes for terrestrial ecosystems and is aimed at assessing atmosphere-ecosystem exchange of greenhouse gases and trace gases. The nitrogen cycle is fully included, from inputs (atmospheric deposition, biological fixation, and fertilizer input) to outputs (leaching, ammonia volatilization, and nitrogenous gas emissions through nitrification and denitrification). Intraecosystem dynamics of nitrogen among plant, soil, and microbe is simulated in an explicit manner. The model was validated by comparing various biogeochemical aspects with observational data [33][34][35]. In the VISIT model, fN 2 O nit is assumed to be a universal, constant value (1% of gross nitrification).
A brief description of the method used to estimate fN 2 O nit is given below. In the VISIT model, soil N 2 O production through the nitrogen cycle is conceptualized by using the "hole in the pipe" scheme (see Fig 1). Gross nitrification (R nit ) and associated N 2 O emission (N 2 O nit ) are related as follows: Nitrification rate and its environmental dependencies were derived from the NGAS scheme developed by Parton et al. (1996) [36], as follows: where p WFPS-nit , p pH , and p Ts denote the environmental scalar functions derived from observations (see ref. [36]) of water-filled pore space (WFPS), soil pH, and soil temperature (Ts), respectively. K denotes the coefficient of N turnover, taking values from 3.5 of natural soils to 12.0 of agricultural soils. F max is the maximum nitrification-associated gas flux coefficient and NH 4 + is the soil ammonium content. WFPS and NH 4 + were simulated by VISIT and so varies temporally and spatially. Global simulations by using the VISIT model were conducted with the common protocol and initial and boundary conditions. Namely, they were conducted at a spatial resolution of 0.5˚x 0.5˚for latitude and longitude, during the period from January 1901 to December 2016. Historical climate data from CRU TS3.25 [37] (temperature, precipitation, vapor pressure, and cloudiness) and land-use data [38] were used to drive the model. Historical changes in atmospheric nitrogen deposition were derived from Galloway et al. (2004) [39], and in croplands, input of nitrogen fertilizer was determined on a country-basis by using FAOSTAT (http:// www.fao.org/faostat). The amount of national fertilizer use was divided by total cropland area and allocated to each grid cell. For each grid, a spin-up calculation was conducted for 300 to 2000 years, depending on case, under stationary conditions until a stable-state carbon budget was reached, before starting the historical experiment.

Sensitivity simulations
All sensitivity simulations were conducted by VISIT using the common forcing dataset and protocols; only the fN 2 O nit value was changed. First, to simply assess the sensitivity of N 2 O emission estimation to fN 2 O nit , we halved (i.e., 0.5%) and doubled (2%) the parameter value (originally 1% in VISIT) and compared the results. We then changed the fN 2 O nit values to those obtained by the meta-analysis mentioned above, that is, mean and median values for all data and several subsets. In these simulations, constant fN 2 O nit values were applied to all grids. Second, the fN 2 O nit value was replaced by those of DNDC and DLEM described above, using the same temperature and moisture conditions. Third, finally, we derived an empirical relationship between soil pH and fN 2 O nit value from the meta-analysis data. Such a relationship was shown in laboratory studies [40] and previous meta-analysis [15], but has not been examined by models at the global scale. Here, we used the global soil pH map (S1 Fig) produced by the Global Soil Data Task of the International Geosphere-Biosphere Programme [41].

Results and discussion
We obtained 71 records from 13 studies in the published literature (Table 1; Fig 3), covering a wide range of different ecosystems and soil texture types; see S3 Table for the data extracted. Although no date and time limitation were applied, the data were obtained from 1985 to 2013.
Although a large number of papers addressed the nitrification and N 2 O emission (2184 papers), we found that only a small number of papers (35 papers) contain the data on gross nitrification rate for a sufficiently long period. Other 2149 papers were rejected, although they contained partial data on nitrification-associated N 2 O emission. Furthermore, many of the measurements (22 out of 35) were made using problematic methods or conditions and so removed. As a result of data selection, measurements in the literature used in this study were made mainly by using two methods of soil incubation: the inhibitor (C 2 H 2 , N-serve, and NaClO 3 ) treatment and the stable carbon isotope ( 15 N labelling) method [10,42]. Most of the measurements were conducted in the laboratory: only one study was done in the field. The record number is not so abundant, but the dataset covers a wide variety of ecosystems and soils such as forest, grassland, and cropland. Therefore, we used this dataset for following analyses and model assessments.
The observational fN 2 O nit values (n = 71) were distributed widely from 0.006% to 29.4%, with a mean of 1.92% and a median of 0.19% (first column of Table 2). The high mean value was likely attributable to the presence of a few anomalous values in the dataset. A histogram of the observed fN 2 O nit values (Fig 4) showed a concentrated and skewed distribution with a clear peak around the median value. Additionally, with removal of 10% outliers (top 4 and bottom 3 records, second column of Table 2) the mean (0.43%) and median (0.14%) values became lower. Notably, standard deviation narrowed greatly after the removal of outliers, and both the maximum value and minimum value were obtained when the C 2 H 2 inhibition method was used. When publication-based data (i.e., the means of the values reported in each paper) were used, the mean and median value became higher (5.17% and 0.57%, respectively; third column of Table 2). In comparison with the study of Australian agricultural soils by Farquharson (2016), typical values of fN 2 O nit obtained by our meta-analysis seem comparable. That study found that fN 2 O nit values varied from 0.03% to 1%, with a typical value of 0.2%, that falls between the mean and median values obtained in the present study for all data. When removing outlier values, our results of mean and median became even closer to the result of Farquharson (2016). Namely, we examined anomalous values removed from the present meta-analysis, such as zero to negative and extremely high, 100% values. Several these values were obtained by Ambus (1998) [53] in the only study that conducted C 2 H 2 treatment in the field; this probably led to a larger fluctuation in values than in the laboratory studies. Negative values of fN 2 O nit are attributable to net N 2 O uptakes, which are sometimes observed but are usually small [54]. The fN 2 O nit values used by emission models assuming a constant N 2 O emission fraction (0.5% to 2.0%) fell within the range of observed values. For example, the constant fN 2 O nit value used in the original VISIT model, 1%, did not differ significantly from the mean value of the observed dataset (Student's t-test, t = 1.36, p = 0.177). However, it should be noted that the median observed value (0.19%) was much lower than the model-assumed value.
The fN 2 O nit values used in the DNDC and DLEM models including the environmental variability of the N 2 O emission fraction were generally lower than those used in the models assuming constant values. As shown in Fig 2, these models assume the maximum fN 2 O nit values of 0.06 to 0.1%. However, these fN 2 O nit values were still within the range of observed values. We examined the spatial distribution of mean fN 2 O nit values estimated by the DNDC ( Fig  5A) and DLEM (Fig 5B). When the DNDC parameterization was used, higher fN 2 O nit values were estimated mainly in the humid tropics. In contrast, when the DLEM parameterization was used, higher fN 2 O nit values were obtained in humid temperate to boreal regions such as Europe, eastern and western North America, and the Tibetan Plateau. Note again that a common soil temperature and moisture (after the VISIT simulation) were used in this comparison, and the differences among the results were caused exclusively by differences in the fN 2 O nit parameterizations. The difference of fN 2 O nit indicated here may account for a part of outcomes of the N 2 O model intercomparison project [29]. The project showed that the existing models differ in global soil N 2 O emission by about 20%, and our study implies that fN 2 O nit is one of the key parameters to reduce the estimation uncertainty.

Sensitivity of N 2 O flux to fN 2 O nit
The default VISIT model with a constant fN 2 O nit of 1% estimated total N 2 O emission from terrestrial soils as 15.47 ± 0.52, 16.32 ± 0.98, and 17.03 ± 0.73 Tg N 2 O yr -1 (average ± s.d. of interannual variability) in the 1980s, 1990s, and 2000s, respectively (Fig 6). When converted into nitrogen weight (multiplied by 28/44), these values correspond to 9.85 to 10.84 Tg N yr -1 . These estimates are close to previous estimations: e.g., 11.1 Tg N yr -1 by IPCC (2013) [1] and 11.4 Tg N yr -1 by Syakila and Kroeze (2011) [55] for emissions from natural vegetation, agriculture, and deposition on land. In the 2000s simulation, 16.5% of total N 2 O emission was   2016 as a result of the increase of fertilizer and deposition inputs. See our resent study [32] on the temporal change and its driver of the regional N 2 O emissions. The sensitivity analysis using different values of fN 2 O nit (constant) indicated that the simulated total N 2 O emission was sensitive to the assumed emission fraction. When fN 2 O nit = 0.5% was used, the total nitrification-associated N 2 O emission was reduced to 1.59 Tg N 2 O yr -1 (-43% in comparison with fN 2 O nit = 1% case) in the 2000s. Because of the smaller nitrogen loss by nitrification in these cases, N 2 O emission from denitrification increased slightly because of the use of excess inorganic nitrogen in the soils. As a result of compensation, total N 2 O emission was only slightly affected (-4.3%) by the halved fN 2 O nit value. When fN 2 O nit = 2% was used, total nitrification-associated N 2 O emission increased to 4.4 Tg N 2 O yr -1 (+56.6%). The asymmetric sensitivity of nitrification-associated N 2 O emission to the change in fN 2 O nit value is attributable to alteration of the nitrogen stock in the soils and the non-linear response of N 2 O emission to nitrogen availability [36]. Finally, when using the parameterizations of DNDC and DLEM models, lower total N 2 O emissions were estimated (15.0 Tg N 2 O yr -1 ) with lower contribution of nitrification-associated emission due to the generally low value of fN 2 Onit (data not shown).
When the median fN 2 O nit value of the meta-analysis (0.14%) was used in the VISIT simulation, the total N 2 O emission was estimated as 15.4 Tg N 2 O yr -1 in the 2000s; nitrification-associated N 2 O emission was largely reduced to 0.50 Tg N 2 O yr -1 . In contrast, when the mean value of all data (fN 2 O nit = 1.92%) was used, higher rates of total and nitrification-associated N 2 O emission (17.5 and 4.3 Tg N 2 O yr -1 ) were estimated. Therefore, selection of representative fN 2 O nit value can affect the simulation result by as much as 2.1 Tg N 2 O yr -1 at the global scale. When including the difference in model parameterizations, the uncertainty becomes even larger to 2.5 Tg N 2 O yr -1 .
These results confirmed that the estimated N 2 O emission was sensitive to the assumed fN 2 O nit value, which was poorly constrained in the present models and varied with selection of the metric from the observational data. Although observations implied that the fN 2 O nit can be variable in response to environmental conditions such as temperature and moisture, the scarcity of observational evidence has prevented us to use a standard parameterization and permitted us to assume constant values. Apparently, additional constraints and new parameterizations are required to obtain a reliable N 2 O budget and its flow components. Observational data and insights are accumulating with support of technical developments such as isotopic tracers, but it would take decades to obtain a comprehensive dataset with enough coverage. Next, we made an attempt to develop a new parameterization of fN 2 O nit applicable at the global scale.

Application of pH-based parameterization
In 54 records of the meta-analysis data, soil pH condition was included, allowing us to relate with fN 2 O nit (Fig 7A). It was found that fN 2 O nit takes higher values at acidic soil conditions with pH below 5 and lower values under neutral to alkaline soil conditions. We obtained a regression curve using exponential function, which gives slightly higher fN 2 O nit values in comparison with the equation of Martikainen (1985) [40]. Using the soil pH map and the regression curve, global distribution of pH-based fN 2 O nit was obtained ( Fig 7B). As expected from the pH pattern, boreal conifer forest soils and humid tropical soils show higher fN 2 O nit values. High fN 2 O nit in humid tropics estimated by the present study is consistent with those by DNDC and DLEM parameterizations, while the three maps differ largely in temperate regions. When using the pH-based parameterization, total N 2 O emission in the 2000s was estimated as 16.8 Tg N 2 O yr -1 (25.2% by nitrification and 74.8% by denitrification). Global distribution of soil N 2 O emission was reasonably simulated (Fig 8; see S2 Fig for seasonal change), in comparison with those obtained by atmospheric inversion studies [56]. For example, high emissions from temperate croplands and tropical forests were well captured.

Impacts on global N 2 O budget
The simulated N 2 O emission account for important features of the global budget. For example, interannual variability in the total N 2 O emission was comparable with the atmospheric growth rate especially after 1990, i.e. the period when ample observational data became available (Fig  9). The decline after the Mt. Pinatubo eruption in 1991 and following increase were well captured, implying the major impact of soil emission on the atmospheric N 2 O variability in recent decades. As clearly shown in the relationship between nitrogen input and N 2 O emission ( Fig  10A), the historical increase of N 2 O emission in recent decades is mainly attributable to increased land N inputs by atmospheric deposition and fertilizer use. The slope, so-called emission factor, was estimated as 1.75%. This is a bit higher than the typical emission factor value of IPCC guideline [57], 1%, but note that the present estimate includes the effects of climate and land-use changes. In the model simulation, N 2 O emissions from nitrification and  denitrification increased in parallel, as shown by the linear relationship between the two emissions (Fig 10B). Validating the N 2 O production scheme at broad scales is difficult even by comparing with inversion studies. In forthcoming studies, appropriate observations of N 2 O isotopomers may provide supporting evidences [58,59].  [60] and a global synthesis [55]). Because the global nitrogen cycle would be further perturbed by human activities and climate change [5], the uncertainty in the present models can be a critical limiting factor for environmental management. Although global N 2 O budget may be constrained by using atmospheric observational data to some extent, in-depth understanding of flow components and their environmental regulations is essential to conduct effective nitrogen and climate managements.

Concluding remarks
To our knowledge, this is the first study to have focused on fN 2 O nit in a comprehensive manner. We should pay attention to the fact that this study used a limited number of observational data and extrapolated them to the global scale. Nevertheless, the dataset covering a variety of ecosystems and soils and the process-based model assessment gave us clues to better understanding of N 2 O cycle. Our findings gives an explanation for the results of the N 2 O model intercomparison project, which shows 20% of global soil N 2 O emission difference among terrestrial models [61]. In our analysis, selection of fN 2 O nit affected the estimation of global N 2 O emission by about 15% (2.5/16 Tg N 2 O yr -1 ). Because of the scarcity of reliable observational data, our meta-analysis did not give a conclusive value or equation for fN 2 O nit . Most of observed values were low (<1%) but neglecting high values may result in underestimation of nitrification-associated N 2 O emission at broad scales. We found a potential and representative range of fN 2 O nit values and a useful pH-based empirical model covering both natural and agricultural soils. This result should encourage extensive observations of nitrification-associated N 2 O emission and fN 2 O nit by using a standardized protocol especially in the field. Although the present meta-analysis showed that the majority of empirical data were obtained by the C 2 H 2 inhibition or isotopic tracer methods, further discussions on effective measurement strategy (e.g., spatial and temporal coverage and representativeness) are required for field and model researchers to improve model accuracy. Because of extreme complexity of the soil biogeochemical processes, it is inevitable to use simplified schemes like the 'hole-in-apipe' concept and bulk parameters like fN 2 O nit to conduct simulations at broad scales. Because N 2 O has a high global warming potential, a small difference in estimated N 2 O emission can considerably influence the total greenhouse gas budget, as shown by our sensitivity simulations. To develop a better parameterization of fN 2 O nit and other, related properties, further observations-especially in the field-and process studies of the nitrogen cycle and greenhouse gas emissions are critically important.
Supporting information S1 Table.