Global and regional emissions estimates for N 2 O

. We present a comprehensive estimate


Introduction
Nitrous oxide (N 2 O) is a potent greenhouse gas (GHG) with a global warming potential (GWP) approximately 300 times greater than CO 2 over a 100-year time horizon (Forster et al., 2007). N 2 O is also involved in stratospheric ozone depletion (Crutzen, 1970), and although its ozone-depletion potential (ODP) is as small as 0.017, its emissions, weighted by ODP, are currently larger than those of any other ozone-depleting substances (ODSs) (Ravishankara et al., 2009). Importantly, N 2 O emissions are controlled under the Kyoto Protocol, but N 2 O production is not included in the Montreal Protocol on substances that deplete the ozone layer. N 2 O is inert in the troposphere and is only destroyed once it reaches the stratosphere by photolysis and by chemical reaction with O( 1 D). Since N 2 O is inert within the troposphere, it has a long atmospheric lifetime of 131 ± 10 years (Prather et al., 2012).
There are several known sources of N 2 O emissions and in this paper we categorize them as the following: agricultural soil, industrial (including all combustion sources), natural soil, ocean, and biomass burning. There are large uncertainties associated with estimated emissions from each of these sectors, but approximately 2/3 of the emissions have been attributed to the natural soil and ocean, with the remaining attributed to anthropogenic sources (Khalil et al., 2002;Denman et al., 2007;Nevison et al., 2007). Included in our industrial source category are major emissions from land use change, fuel combustion for energy, and waste (European Commission, Joint Research Centre (JRC)/Netherlands Environmental Assessment Agency (PBL), 2009). The increase in atmospheric N 2 O mixing ratios, since at least the 1940s, has been largely attributed to increased N 2 O emissions from agricultural soils .
Previous work has examined the source and the magnitude of these emissions with process models ("bottom-up") and with inverse methods using measurements of atmospheric mixing ratios ("top-down"). For the former, there have been efforts to quantify soil and ocean emissions. For example, Potter et al. (1996) estimated global soil N 2 O emissions using an ecosystem modeling approach. Using the "holein-the-pipe" concept established by Firestone and Davidson (1989) and simulating with an expanded version of the Carnegie-Ames-Stanford (CASA) biosphere model (Potter et al., 1993), they estimated the global N 2 O emissions from the soil to be 6.1 TgN 2 O-N yr −1 . For global soil N 2 O emissions, excluding anthropogenic nitrogen input effects, Bouwman et al. (1993) and Kreileman and Bouwman (1994) estimated emissions to be 6.6-7.0 TgN 2 O-N yr −1 . Using the DeNitrification-DeComposition (DNDC) model developed by Li et al. (1992), Saikawa et al. (2013) estimated global natural soil N 2 O emissions from 1975 to 2008 with four different available forcing data sets. Annual average estimates range from 7.4 to 11 TgN 2 O-N yr −1 . For the ocean emissions, Nevison et al. (1995) used more than 60 000 expedition measurements to estimate global annual outgassing from the ocean to be 1.2-6.8 TgN 2 O-N yr −1 . Recently, Manizza et al. (2012) used a large-scale ocean general circulation model coupled to a biogeochemical model to quantify the climatological mean emissions from the ocean to be 4.5 TgN 2 O-N yr −1 .
For the top-down approach, previous work has derived global and regional N 2 O emissions using the existing emis-sions inventories and atmospheric N 2 O measurements. Prinn et al. (1990) conducted inverse modeling of N 2 O at the global level using a 12-box model and quantified emissions from four latitudinal bands in the world. Hirsch et al. (2006) used a three-dimensional chemical transport model to estimate N 2 O emissions from global, four semi-hemispherical and six broad regions between 1998 and 2001. Two of the results combined showed that there may have been a shift in the emissions from 30 • -90 • S to 0 • -30 • N during the period 1978period -1988period to 1998period -2001period . Huang et al. (2008 estimated N 2 O emissions during the two time periods (1997-2001 and 2002-2005), using a three-dimensional chemical transport model and estimated the global N 2 O emissions to be 15.1-17.8 and 14.1-17.1 TgN 2 O-N yr −1 in the two periods, respectively. Kort et al. (2011) found that inversion results differ between including and excluding aircraft measurements and emphasized the importance of measurements covering the full tropospheric profile.
In this paper, drawing on insights from recent bottom-up estimates using four different forcing data sets for global natural soil emissions (Saikawa et al., 2013) and the climatological ocean emissions (Manizza et al., 2012), we first estimate approximate bottom-up monthly regional N 2 O emissions by source sector on a global grid during the period 1995-2008. We use these gridded emissions as an a priori estimate for an inversion to derive regional and global emission magnitudes from the atmospheric observations. For this work, we present the new observations until the end of 2008 and use them as well as previously published N 2 O atmospheric mole fraction data from several measurement networks as listed in Fig. 1 and Table 1. Although there have been papers that combined measurements from different networks for N 2 O inverse modeling (e.g., ; Corazza et al. (2011); Huang et al. (2008)), the goal of the paper was to include all available measurements (i.e., in situ, flasks, aircrafts, and ships), for the first time, from all available networks where we have reliable and consistent inter-comparison of measurements.
The paper is organized as follows: Sect. 2 describes the atmospheric measurements. Section 3 explains the inverse modeling methodology. Section 4 examines results from our inversion to analyze regional emissions by source sector. We present a summary of our results and suggestions for future research in Sect. 5.

Archived and ambient measurements
In this study, we use measurements of atmospheric N 2 O from six networks: (1) in situ measurements from the Advanced Global Atmospheric Gases Experiment (AGAGE) network; (2) the Global Monitoring Division of NOAA's Earth System Research Laboratory (NOAA/ESRL) Carbon Cycle Greenhouse Gases (CCGG) group global cooperative air sampling flask network; (3) the NOAA/ESRL Halocarbons and other   at five sites since 1978. In this study, we use measurements of the air sampled at the following AGAGE sites: Cape Grim, Tasmania; Trinidad Head, California, USA; Mace Head, Ireland; Ragged Point, Barbados; and Cape Matatula, American Samoa (see Fig. 1 and Table 1). Stations that previously existed at Cape Meares, Oregon (1979Oregon ( -1989 and at Adrigole, Ireland (1978-1983 were replaced by Trinidad Head and Mace Head, respectively. All AGAGE in situ measurements are calibrated using the SIO-98 absolute calibration scale. The estimate of all the errors involved in the calibration scale such as reagent purity, possible analytical interferences, statistics of primary standard preparation, and propagation is approximately 0.5 %. At NOAA/ESRL, discrete air samples have been collected at remote locations and analyzed for N 2 O since 1997 as part of the CCGG global cooperative air sampling network (Dlugokencky et al., 1994). Samples of air are collected regularly in paired glass flasks (2-3 L) and pressurized to 0.20 MPa, and analyzed on one of two GC/ECD instruments in Boulder, Colorado. In this study, we use measurements from 72 sites ( Fig. 1 and Table 1). Repeatability of the analytical system is 0.2 ppb (1σ ), and the total uncertainty including reagent purity, interferences, etc. is 1.0 ppb (0.3 %).
In situ and flask measurements are also collected by the NOAA HATS program over the globe. The NOAA RITS in situ program started at the following four stations in 1987: Barrow, AK, USA; Mauna Loa, HI, USA; Cape Matatula, American Samoa; and South Pole, as well as in Niwot Ridge, CO, USA in 1990. The CATS program started using new in situ gas chromatographs at all of the above-mentioned five sites, and also added Summit, Greenland in 2007. The OTTO program has also collected flasks at weekly to monthly intervals from the above six stations as well as at the seven following sites: Alert, Canada; Cape Kumukahi, HI, USA; Cape Grim, Australia; Palmer Station, Antarctica; Mace Head, Ireland; Trinidad Head, CA, USA; and Tierra del Fuego, Argentina. All NOAA measurements are on the NOAA-2006A N 2 O scale (Hall et al., 2007), and the estimate of all the errors for the OTTO, RITS, and CATS programs is less than 0.4 ppb (0.1 %) (Hall et al., 2007).
We also use flask measurements from the CSIRO network (Francey et al., 1996(Francey et al., , 2003. There are 11 measurement sites including the one at Cape Rama, India ( Fig. 1 and Table 1). The flasks have been collected at weekly to monthly intervals at these sites and are analyzed by GC/ECD at CSIRO. The measurements are referenced to the NOAA-2006A N 2 O scale (Hall et al., 2007). Repeatability of the analytical system is 0.3 ppb (1σ ), and the estimate of the error in accuracy is less than 0.1 % for the majority of the samples. NIES has been measuring N 2 O at two field sites (Hateruma Island and Cape Ochiishi, see Fig. 1 and Table 1). These N 2 O measurements are calibrated using the NIES-96 scale (Tohjima et al., 2000). The precision of the measurement system is approximately 0.3 ppb (1 σ ) and the estimate of the error in accuracy is approximately 0.4 ppb (0.1 %).
Monthly aircraft measurements have been made near the city of Surgut, Russia since July 1993, using a chartered aircraft as described in Ishijima et al. (2010). Outside air is collected at 0.5, 1, 1.5, 2, 3, 4, 5.5, and 7 km above the surface in glass flasks, pressurized and then analyzed by an GC/ECD instrument in NIES. The NIES-96 N 2 O scale is used for calibration, and the repeatability of the analytical system is 0.3 ppb. The estimate of the error in accuracy is approximately 0.4 ppb (0.1 %).
The Tohoku University group has been measuring N 2 O at multiple locations using aircraft and ships since 1991 (Ishijima et al., 2001(Ishijima et al., , 2009(Ishijima et al., , 2010. Collected air samples are analyzed using the GC/ECD at Tohoku University. The data between 2003 and 2009 are new and cover a wide latitude range from the north of Japan to the Oceania region (see We compare atmospheric N 2 O measurements collected from each group, as they are based on different absolute calibration scales (Table 2) and differences exist among measurement networks. Because the global average mole fraction of N 2 O increases at approximately 0.2-0.3 % per year (see Fig. 2), the calibration ratio of 0.9975 corresponds to a one year's rise in mole fraction, and thus a calibration difference as small as 0.6 % can be significant. Hence, it is very important for us to adjust all of the measurements into a single scale referenced to that of AGAGE, even though calibration scales appear to be close to one another. Shifts in the differences between co-located measurements result from uncertainty in propagating the scale to in situ measurement sites, and those shifts result from various factors, but the standard calibration scales do not change over time. We include generous uncertainties to account for these shifts in the differences over time, and this divergence is small compared to other uncertainties.
First, the comparisons between AGAGE and NOAA are conducted using measurements collected at the same site at approximately the same time. NOAA CCGG flask samples collected at the four AGAGE sites (CGO, SMO, RPB, and MHD) between 1997and at THD between 2002 and 2012 were compared with AGAGE GC-ECD in situ measurements at those sites. Data from the two networks agree well in general for N 2 O with a mean ratio (CCGG/AGAGE) of 0.9994 and a standard deviation of 0.0005 for the matching mixing ratios. In addition, NOAA CATS in situ samples collected at SMO from 2000 to 2012 were compared with AGAGE GC-ECD in situ measurements at the same site. The data also agree well with a mean ratio (CATS/AGAGE) of 1.0009 and a standard deviation of 0.0010. RITS measurements compare well with CATS, and thus we use the same factor for both. We therefore adjust the NOAA measurements to the SIO-98 scale by applying 1.0006 for CCGG flask and 0.9991 for OTTO, RITS, and CATS in our inversions. We also apply an offset factor for the measurements taken in the OTTO network as a difference from the CATS measurements at the same site. The adjustment is 1.3 ppb at American Samoa and 0.6 ppb elsewhere.
Second, the comparisons between the AGAGE and CSIRO networks are conducted at the CGO site, where the average difference is 0.35 ppb (AGAGE-CSIRO), which is equivalent to the ratio (CSIRO/AGAGE) of 0.9989. Therefore, we adjust the CSIRO flask network measurements by applying a factor of 1.0011 in our inversions.
Third, the comparisons between NOAA CATS and Tohoku University, as well as between NIES and Tohoku University, are conducted at the same site at approximately the same time. On average, Tohoku University measurements are 0.2 ppb and 0.8 ppb higher than NOAA and NIES measurements, respectively. These values translate into the mean ratios (Tohoku/CATS and Tohoku/NIES) of about 1.0006 and 1.0025. These two comparisons also allow us to quantify the constant offset values between CATS and NIES measurements (CATS-NIES) of 0.6 ppb with a ratio (CATS/NIES) of approximately 1.0019. Based on these comparisons, the ratios (Tohoku/AGAGE and NIES/AGAGE) are approximately 1.0015 and 0.9990. Therefore, we apply 0.9985 and 1.0011 to convert Tohoku and NIES measurements into the SIO-98 scale.

Emissions inversion method
Using reasonable prior estimates of annual regional N 2 O emissions by source sector and the three-dimensional chemical transport model, Model for Ozone and Related Chemical Tracers version 4 (MOZART v4), we apply an inverse method to estimate annual regional emissions by source sector using the measurements of N 2 O atmospheric mole fractions discussed above. In this section, we outline our inverse modeling methodology.

Prior emission estimates
For conducting inversions, we created a priori emission estimates by combining the existing emissions inventory for the three sectors (i.e., industrial, agricultural soil, and biomass burning) with new estimates from two process models for the ocean and natural soil. For industrial and agricultural soil emissions, we used the EDGAR v4.1 emissions with a spatial resolution of 1  , 2010). GFED v3 provides monthly emissions between 1997 and 2008, so we extrapolated for years between 1990 and 1996 by applying the average annual growth rate between 1997 and 2008. Manizza et al. (2012) estimated climatological monthly air-sea N 2 O fluxes using a bottom-up process modeling approach. Their model includes both denitrification and nitrification process-induced fluxes at a spatial resolution of 2.8 • latitude × 2.8 • longitude. They adopted the parameterization of Suntharalingam and Sarmiento (2000) for the production of N 2 O in the water column. A more detailed description of their physical and biogeochemical model can be found in Manizza et al. (2012).
For natural soil emissions, we use another newly developed process model (CLMCN-N 2 O) that is able to reproduce the seasonality and inter-annual variability of global emissions at some sites (e.g., Amazon) but not at others (e.g., North America) (Saikawa et al., 2013). This model is an addition to the Community Land Model with coupled Carbon and Nitrogen cycles version 3.5 (CLM-CN v3.5) (Thornton et al., 2007;Thornton et al., 2009;Randerson et al., 2009). CLMCN-N 2 O includes the DeNitrification-DeComposition (DNDC) Biogeochemistry Model (Li et al., 1992), and similarly to the ocean process model, it captures both the nitrification and denitrification processes that are important producers of N 2 O in soil. The four forcing data sets used are Global Meteorological Forcing Dataset (GMFD) by Sheffield et al. (2006); NCEP Corrected by CRU (NCC) by Ngo-Duc et al. (2005); Climate Analysis Section (CAS) by Qian et al. (2006); and Global Offline Land-Surface Dataset (GOLD) by Dirmeyer and Tan (2001) and Betts et al. (2006). For our regional inversion, we assume 40 % uncertainty for our prior values for the emissions from all sources, sectors, and regions. This range, decided empirically based on previous studies (i.e., Hirsch et al. (2006); Huang et al. (2008)), is justifiable as there have been high uncertainties in N 2 O emissions, especially in recent years after an increased agricultural nitrogen fertilizer use in developing countries. We also note that although we separate the emissions from different sectors, in reality nitrogen fertilizer applied to agricultural soil, for example, can be leached into rivers and thus on to the ocean, where it can be emitted as N 2 O. But the effect of these transfers on emissions have significant uncertainty in existing inventories and process models so the aim of our inversions is to improve the existing emissions inventories and the process model results using atmospheric observations.

Global chemical transport model
The global three-dimensional chemical transport model, MOZART v4 (Emmons et al., 2010) is used to simulate the three-dimensional N 2 O atmospheric mole fractions between 1995 and 2008. MOZART v4 is a model for the troposphere, has updates over the previous MOZART version 2, and is built on the framework of the Model of Atmospheric Transport and Chemistry (MATCH) (Rasch et al., 1997). Previous studies have found too strong net downward transport from the stratosphere in the model using the reanalysis meteorology (Holloway et al., 2000;van Noije et al., 2004;Xiao et al., 2010) resulting, for example, in errors in the tropospheric ozone budget as well as in the ozone mixing ratios in the upper troposphere (Emmons et al., 2010). Because this can lead to a potentially large bias in our analysis, we restricted ourselves to estimating regional annual and not monthly emissions by source sector. This, however, provides new annual estimates for 14 years at the regional level and by the source sector globally, which is an advancement from past studies (i.e., Hirsch et al. (2006); Huang et al. (2008); Thompson et al. (2011);Corazza et al. (2011)). The horizontal resolution of MOZART v4 is 1.9 • latitude × 2.5 • longitude, including 56 vertical levels from the surface to approximately 2 hPa. Chemical and transport processes are driven by the annually varying Modern Era Retrospective-analysis for Research and Applications (MERRA) meteorological fields (Rienecker et al., 2011).
We assume that N 2 O is inert in the troposphere and chemical loss is by photolysis and reaction with O( 1 D) in the stratosphere. The spatial and temporal pattern of the inter-annually changing photolysis field is calculated for the three wavelength-ranges 200-217 nm, 217-230 nm and 230-278 nm, and it includes the temperature dependency of the absorption cross sections, similarly to Ishijima et al. (2010). For the wavelength band 178-200 nm, Minschwaner et al. (1993) is used. The annually repeating O( 1 D) field is estimated using the LMDZ4-INCA2 global climate model (Hourdin et al., 2006). Both of these fields are interpolated to match our horizontal and vertical resolutions, conserving the mass. The spinup was done for 10 years starting with a uniform latitudinal mixing ratio and with vertical distributions based on observations. We then compared surface mixing ratios to available observations in 1995 to start the simulation. The lifetime of N 2 O, calculated by the ratio of the annual total global burden to the loss rate calculated in the chemical transport model is 116 ± 5 yr, which is slightly lower than the current estimate of 131 ± 10 yr by Prather et al. (2012) but is in alignment of 114 years with Montzka et al. (2011).
We estimate emissions from seven land regions and six ocean regions for 5 source sectors between 1995 and 2008 incorporating all the measurements in Table 1, including all data without pollution event filtering. The MERRA meteorological reanalyses were used at 6-hourly intervals, and the model was run with a 15-minute time step. When there were measurements from multiple different networks, we first generated monthly averages for each network at each site, and then combined the data sets to create monthly averages and standard deviations at a site using the number of measurement-weighted averages, accounting for the different measurement frequency (e.g., flask versus in situ sampling) at each station in the various networks.

Sensitivity estimates and inverse method
To conduct inverse modeling, we follow the methodology in Saikawa et al. (2012). We quantify the atmospheric mole fractions response to an increase in emissions for each sector and region at each measurement site (which we herein call the "sensitivity") using the global chemical transport model MOZART v4. We incorporate these sensitivity values into a matrix H and estimate emissions by deriving a Bayesian weighted least-squares solution. This technique provides an optimal estimate by minimizing the following cost function with respect to x: where y is the vector of the difference between measurements and modeled mole fractions, x is the vector of the difference between the prior and the optimized emissions, W is the measurement uncertainty covariance matrix, and S is the prior uncertainty covariance matrix. W and S are both diagonal matrices.

Measurement-model uncertainty estimation
Five types of uncertainty were considered for total measurement uncertainty: errors in the measurements themselves (precision), scale propagation error, sampling frequency error, model-data mismatch (representation) error, and model transport and aggregation error. The total variance is therefore calculated by combining the five types as follows, assuming that they are uncorrelated (e.g., Chen and Prinn (2006) and Rigby et al. (2010)): Here the measurement error σ measurement is the estimated total uncertainty due to the repeatability of each measurement (precision) at each site. The instrumental precision of N 2 O is approximately 0.1 % for AGAGE, NOAA CCGG, NIES, and CSIRO, 0.2 % for NOAA OTTO, RITS, and CATS, and 0.3 % before 2002 and 0.1 % since 2002 for Tohoku University, and thus these values are included as our instrumental precision errors in this study. The error σ scale propagation arises in the chain that links the primary standards to ambient air measurements. For N 2 O, the mean assumed scale propagation error was approximately 0.006-0.012 % for all the SIO, 0.07 % for NOAA CCGG and OTTO, RITS, and CATS, 0.016 % for CSIRO, and 0.015-0.03 % for NIES and Tohoku University scales, respectively. We therefore include 0.012 %, 0.07 %, 0.016 %, and 0.03 % for all the data that come from AGAGE, for NOAA, for CSIRO, and for NIES and Tohoku University, respectively. The error σ sampling frequency accounts for the number of samples measured in a month to create a monthly mean for each measurement site (Chen and Prinn, 2006). Because of the difference in the number of measurements in a month between high-frequency observations (every 2 h) and weekly flask measurements, this error is approximately 3 to 10 times lower for high-frequency observations, compared with the error associated with NOAA and AGAGE measurements at the same site. Even when we assume a 10-hour serial correlation for the AGAGE in situ measurements (resulting in approximately 70 uncorrelated measurements in a month), it does not affect the results in any substantial way (the largest difference being less than 0.5 % change in optimized emissions). The error σ mismatch describes the difference between a point measurement and a model-simulated observation that represents a large volume of air Chen and Prinn, 2006). As in Saikawa et al. (2012), we calculate it from the following equation:

Atmos
where y i is the atmospheric mole fraction in a grid box surrounding the measurement site location i, and y is the mole fraction in the grid cell at the measurement site. Similarly to the sampling frequency error, the mismatch error also varies by month at each site, taking into account the monthly changes in transport in the model. Finally, σ model is the error associated with the global chemical transport model, which we choose to interpret as an additional measurement error. One contribution to this error is transport error that in the model inter-comparison study of  implies that there is approximately a 0.2 ppb difference among various chemical transport models, which translates into 0.06 % uncertainty. A significant "aggregation" error is also possible when solving for aggregated regions as we do here, because we assume that the spatial distribution in the prior emissions is correct (e.g., Kaminski et al. (2001); Engelen et al. (2002); Meirink et al. (2008)).
This "aggregation" error is also incorporated in our model error, with a value of 0.8 % in our inversion, as Kaminski et al. (2001) find the highest aggregation error of 3 ppm out of 370 ppm in CO 2 in summer at Cape Grim, Tasmania. Summing the two errors in quadrature gives a total model error of 0.8 %.

Regional emissions by source sector between 1995 and 2008
In this section, we present results from our inversion to derive regional N 2 O emissions by source sector for the 13 regions using all available data from AGAGE, NOAA CCGG, NOAA OTTO, RITS, and CATS, CSIRO, NIES, and Tohoku University networks ( Fig. 1 and Table 1), as well as MOZART v4. We seek to determine the locations and magnitudes of these emissions, and if we see any change in the recent years from a specific region or sector.
We created the regions based on their proximity to the measurement sites, and with the intention of separating emissions based on large ocean groups. For those areas very distant from these sites the regions are entire continents, and if there are sufficient measurements, we divided the continent         into multiple regions. The closer a given region is to a measurement site, the larger the sensitivity to emission perturbations in that region we would expect. The seven land regions in this study are (1) Africa and Middle East; (2) Central and South America; (3) Northern Asia; (4) Southern Asia; (5) Europe; (6) North America; and (7) Oceania (see Fig. 3). Asia is divided into two, because there are multiple measurement stations in the region. This division within Asia is also of interest, because there is a high uncertainty in the winter soil emissions under snow and thawing conditions in the higher latitude regions (e.g., Groffman et al. (2006)) that apply to Russia, covered under "Northern Asia". China under "Southern Asia" is by far the largest consumer of nitrogen fertilizer between 1995 and 2008, as shown in Fig. 4 (International Fertilizer Industry Association, 2013). Its total nitrogen consumption is more than twice that of India, the second largest consumer since 2004 before the United States, and also under "Southern Asia". The six ocean regions in this study are (1) North Pacific; (2) South Pacific; (3) Northern Ocean; (4) Atlantic; (5) Southern Ocean; and (6) Indian Ocean (see Fig. 3). We conduct regional inversions using four sets of a priori emissions for 1995 through 2008. The four sets differ only in natural soil emissions due to the different estimates that come from the four different forcing data sets used in the bottomup estimates for this sector, and there is no difference in other sectors. We conduct an inversion using all measurements available, including AGAGE, NOAA, CSIRO, NIES, and Tohoku University networks. We find that by emission sector, the largest uncertainty reduction is for natural soil and, by region, it is for Northern Asia. We achieve these results because natural soil has the largest emissions among all sources and because we have the largest number of long-standing stations close to our Northern Asia region (see Fig. 1) that have high sensitivities. Figure 3 provides the prior and posterior emissions with uncertainty bars for all the sectors and regions quantified from this inversion, and Table 3 provides prior and posterior emissions with uncertainties for global total, global land, and total emissions by source sector. Table 4 lists prior and optimized emissions with uncertainties for each region, and Tables 5-9 provide prior and optimized emissions derived from this inversion for each sector and region using all the measurements. Some regional emissions by source sector can be constrained well, with a substantial reduction in posterior emissions uncertainty by using the measurements from different network stations between 1995 and 2008. However, Atmos. Chem. Phys., 14, 4617-4641       in other regions, especially for biomass burning emissions we see little uncertainty reduction due to the lack of observational data to constrain emissions at the sector and regional levels.

Emissions trend by source sector and region
We find a significant increase in global agricultural soil emissions (see Fig. 3a), and Southern Asia -the region that includes China and India -shows the most visible signal (see Fig. 3c and Table5). The 4-year mean agricultural soil emissions between 2005 and 2008 (1.49 ± 0.14 TgN 2 O-N yr −1 ) is 54 % greater than that from 1995 to 1998 (0.97 ± 0.12 TgN 2 O-N yr −1 ) for Southern Asia. We realize that there are anti-correlations contained and derived in statevector error covariance matrix (W) in some of the estimates we find due to the nature of our inversion methodology. To find out how well observations could constrain emissions by sector and by region in our inversion, we calculated the average correlations (R) between optimized emissions (see Table S2 in the Supplement). High negative correlations indicate that these emissions are not well constrained, and we expect some neighboring regions and specific sectors to have emissions fall under this category due to the lack of nearby measurements in the current networks. Between Southern Asia's agricultural and natural soil emissions, the average correlation value is −0.36, showing some anti-correlation. This illustrates that we are unable to differentiate between the two source emissions (natural vs. agricultural), but given that this increasing trend still holds when we combine the agricultural and natural soil together in the region (see Fig. 3f Table 9. Prior and optimized regional biomass burning N 2 O emissions with uncertainties using the GMFD forcing data sets for natural soil (GgN 2 O-N yr −1 ).  Figure 3a also illustrates that the optimized emissions using the GOLD forcing data set still produces substantially different results up to 1997 for global total, global land, and global natural soil, illustrating that the uncertainty is under-estimated for the earlier time periods, and that the emissions are not very well constrained. However in later years, the optimized natural soil emissions converge in North America, Central/South America, Africa/Middle East, Northern  Asia, and Southern Asia, giving us some confidence in the inversion results. At the same time, we also see some impact of El Niño-Southern Oscillation (ENSO) events on soil emissions. Some of the inter-annual variability we find in soil emissions (see Fig. 3f) is qualitatively correlated with ENSO events. Specifically, decreased emissions are found in El Niño years in Northern Asia, Southern Asia, and North America, whereas the opposite is true for La Niña years. The effect of ENSO on sources and sinks of these emissions is complex (Davidson et al., 2004) and is beyond the scope of this paper. A detailed discussion of ENSO effects on natural soil emissions can be found in Saikawa et al. (2013).
We do not find much inter-annual variability in other sector emissions including industrial and biomass burning. The main reason is because those emissions are smaller, which lead to sensitivities also being equally small. Therefore, we do not obtain a large uncertainty reduction from our inversion as seen in Fig. 3d and h. The only exception where we find a decreased emissions trend is in Southern Asia's biomass burning, where the emissions in recent years are much smaller than during the 1990s. However, this is simply due to the prior emissions estimates and is not due to our inversion, as can be seen by the small uncertainty reduction.
Here and in all subsequent discussions, the uncertainties we list are one standard deviation. Miller et al. (2012) analyzed tall tower observations in 2004 and 2008 using a Lagrangian model and found peak emissions in June over the central United States. Jeong et al. (2012) have looked at emissions from central California from December 2007 through November 2009, using measurements from a tall tower (Walnut Grove), and they also found posterior emissions to be twice the EDGAR emission inventory estimates. Similarly, Kort et al. (2008), using measurements from the CO 2 Budget and Regional Airborne-North America (COBRA-NA) campaign in May-June 2003 and a Lagrangian model, estimated annual N 2 O emissions from North America to be 2.7 TgN 2 O-N yr −1 . As Miller et al. (2012) indicate, extrapolating these values to the US and Canada results in this region accounting for 12-15 % of the total N 2 O source and 32-39 % of the global anthropogenic source in 2007. Our estimate suggests that North America is 6.1-8.4 % of the total N 2 O source and 20.9-27.0 % of the global anthropogenic source, and they differ from these previous estimates. The discrepancies may be due to these regional inversion results being based on short-term data and from selected sites, whereas our study uses data from six measurement networks with extensive spatial coverage to constrain the global budget. Short-term and regional inversion results might not be appropriate to constrain annual N 2 O emissions. At the same time, there is a significant difference in the Lagrangian and Eulerian models that are worth investigating. However, our estimates agree with other studies conducted in Europe. For example, Corazza et al. (2011) used NOAA/ESRL and other quasi-continuous measurements and a four-dimensional variational (4DVAR) technique with an atmospheric transport zoom model to estimate European emissions in 2006 and quantified annual European N 2 O emissions to be 0.78 TgN 2 O-N yr −1 , and this value is in alignment with ours (0.93 ± 0.12 TgN 2 O-N yr −1 ). Manning et al. (2003) derived annual EU N 2 O emissions between 1995 and 2000 using the Numerical Atmospheric Dispersion Modeling Environment (NAME) driven by three-dimensional synoptic meteorology from the Unified Model. Their estimated range, 0.84-0.88 TgN 2 O-N yr −1 , also agrees with our estimate of 0.83 ± 0.19 TgN 2 O-N yr −1 for the same period. Our result is also in alignment with Thompson et al. (2011), who used observations from a tower site at Ochsenkopf, Germany and a Lagrangian model to estimate western and central European emissions at a weekly time step in 2007, and found emissions peaked during August and September.
For Asia, Yan et al. (2003), using a bottom-up approach, estimated agricultural emissions from Asian countries (including China, India, Pakistan, Indonesia, Thailand, Philippines, Bangladesh, Myanmar, Viet Nam, Japan, and others) for 1995 to be 1.19 TgN 2 O-N yr −1 . Our result for agricultural soil from the same region in 1995 is 0.79 ± 0.22 TgN 2 O-N yr −1 , which is slightly smaller, but this may be due to the difference in the countries included in our estimates.
For North America, Europe, and Oceania, we also compared our posterior emission estimates including agricultural, industrial, and biomass burning emissions using the GMFD forcing data set for natural soil with United Nations Framework Convention on Climate Change (UNFCCC) estimates (United Nations Framework Convention on Climate Change, 2013) (Fig. 5). For North America and Europe, our estimates are lower than the UNFCCC estimates for anthropogenic N 2 O emissions. For both of these regions, however, our posterior emission estimates in 2008 are closer to the UNFCCC estimates than in 1995. This is due to our deduced 1995-2008 increase in agricultural soil emissions in North America, and the 1995-2008 decrease in UNFCCC anthropogenic emission estimates in Europe. For Oceania, our estimates are higher than those of UNFCCC, mainly due to our prior estimates being higher than theirs. It is worth noting that there is little uncertainty reduction in Oceania due to the calculated low sensitivities of the measurement sites to emissions from this region (Fig. 3).
The global total that we find from this study is consistent with results from past studies. Our results for the two time periods (1997-2001 and 2002-2005) are 16.8 ± 0.64 and 18.1 ± 0.60 TgN 2 O-N yr −1 , respectively, and they align with the ranges estimated by Huang et al. (2008) for the same period (15.1-17.8 and 14.1-17.1 TgN 2 O-N yr −1 , respectively). Our results for 1998-2001 (17.0 ± 0.62 TgN 2 O-N yr −1 ) also compare well with those by Hirsch et al. (2006) (15.2-20.4 TgN 2 O-N yr −1 ). Furthermore, quantifying the ODPweighted emissions, which provide an estimate of the impact N 2 O has on global stratospheric ozone depletion in relative terms, results in 0.47 Mt CFC-11-equivalent in 2008, and this is larger than the sum of the ODS emissions of those controlled by the Montreal Protocol (approximately 0.45 Mt CFC-11-equivalent) (Daniel et al., 2011).
Our results also indicate that the ratio of anthropogenic (including agricultural soil, industrial, and biomass burning) to natural (natural soil and ocean) emissions has increased in recent years in Southern Asia and in Central/South America. In addition to Southern Asia, Central and South America shows a 49 % increase in nitrogen fertilizer consumption between 1995 and 2008 (International Fertilizer Industry Association, 2013). Indeed, the 5 years' mean of the percentage of regional anthropogenic emissions shifts from 69.4 % between 1995 and 1999 to 77.4 % between 2004 and 2008 in Southern Asia, and similarly from 42.6 % to 45.8 % in Central/South America. Our inversion results indicate, however, that the natural soil and ocean emissions still share approximately two-thirds of the global total N 2 O emissions, as has been discussed in the past (Werner et al., 2007).

Inversions using different measurements
In addition to using all measurements, we conducted separate inversions as follows: (1) only including the in situ measurements (AGAGE, NIES, and NOAA RITS & CATS); (2) only including the flask measurements (Surgut aircraft, NOAA CCGG & OTTO, Tohoku University, and CSIRO); and (3) only including AGAGE and NOAA CCGG measurements. We chose these three options because of several reasons. First, by selecting only the in situ and the flask measurements, these comparisons allow us to determine the importance of spatial and temporal resolutions of the measurements in estimating regional emissions by source sector. Second, we excluded measurements that had significant calibration difference to understand how calibration differences could impact the inversion results. For example, AGAGE and NOAA CCGG are on very similar standard scales as shown by frequent comparisons of all measurements, whereas all others have gone through some minor adjustment. Fig. 6 shows the uncertainty reduction for natural soil emissions in seven regions for each inversion. We find that in all regions except for North America, inversions using all measurements provide the largest uncertainty reduction for natural soil emission estimates most of the time (see Fig. 6). In North America, we achieve the largest uncertainty reductions when including only flask data. The reason the largest uncertainty reduction is not achieved when using all available measurements in this region is due to the differences in measured values at several sites. There are several, such as BRW, MHD, and NWR, where more than three different measurement networks are co-located, and although we do apply ratios to minimize these differences (as explained in Sect. 2), Fig. 6 illustrates that these scale differences still limit our ability to constrain regional emissions. This highlights the need for unification of standard scales and more ongoing measurement comparisons among networks.
In all cases, only including in situ measurements results in the smallest uncertainty reduction due to the spatial sparsity of the data after 1997, when a significant number of NOAA CCGG measurements start. Fig. 6 also illustrates that consistency and wide coverage of the measurements are both very important, especially for analyzing regional emissions by source sector. However, it is important to point out the differences between in situ and flask measurements. In situ measurements are high-frequency measurements that are able to collect a random subset of total N 2 O data at a particular site, whereas flask data are for representing the background air at a site. In our coarse-resolution modeling, it is often not possible to make the best use of high-frequency in situ measurements. Such differences between the two measurement networks are especially visible in Europe and Oceania, where the regional coverage is small.
There are several ways we could improve the accuracy of N 2 O emissions inferred from inverse modeling in the future. First, expanding measurements in data-sparse regions such as Africa, the Middle East, Eastern Europe, South Asia, Central/South America, Oceania, Atlantic Ocean, Indian Ocean, and Northern and Southern oceans would allow us to better constrain emissions from these regions, which in turn would also improve the global emission estimate. Second, the use of finer-resolution chemical transport models and meteorology data would also allow us to disaggregate regions further and detect sensitivities to atmospheric mole fractions due to increases in emissions more accurately, as shown by the work of Corazza et al. (2011) focusing on Europe. In the future, we could potentially combine a global Eulerian model with a Lagrangian model to focus on a specific region of interest (Rigby et al., 2011). Third, including the whole stratosphere (e.g., using the Whole Atmosphere Community Climate Model) and better implementation of the stratospheric sink may improve the simulation of stratosphere-troposphere interactions, which could result in a better representation of the monthly variability that we observe in the measurements.

Conclusions
We utilized published and new atmospheric mole fraction measurements of N 2 O between 1995-2008 from six measurement networks (AGAGE, NOAA CCGG, NOAA OTTO, RITS, and CATS, CSIRO, NIES, and Tohoku University), comprised of archived air samples, flask measurements at a daily, weekly, and monthly frequency (surface, towers, aircrafts, and ships), and high-frequency in situ observations to derive regional emission estimates by source sector. Recently,  used an extensive network similar to ours for estimating N 2 O emissions. Here we included two additional networks in our analysis: NOAA RITS and NOAA OTTO. This is the first time that an almost allinclusive comprehensive data set has been utilized for an inverse study of N 2 O. We estimated regional (seven land and six ocean) emissions of N 2 O by source sector (agricultural soil, industrial, natural soil, ocean, and biomass burning) from 1995 to 2008 using these measurements and the global three-dimensional chemical transport model MOZART v4 with a Bayesian inverse methodology. Our estimated emissions generally agree with previously published estimates, although there are major discrepancies in North America between our results and those of Miller et al. (2012), Jeong et al. (2012), and Kort et al. (2008) using a Lagrangian model.
Our regional inversion results indicate no significant emissions increase or reduction in all sectors except in agricultural soil, and we find inter-annual variability in soil emissions. Global total emissions have been increasing in recent years, and we find a significant increasing trend in agricultural soil emissions from Southern Asia, which includes China and India, mostly due to the rise in nitrogen fertilizers in these developing economies, as suggested in the past studies (Davidson, 2009;Park et al., 2012). In addition, we find that the anthropogenic emissions are increasing in Southern Asia and in Central/South America, most likely due to the increase in these agricultural soil emissions.
We do not necessarily obtain the largest uncertainty reduction for our optimized emissions by utilizing all available data. Our inversion results using different combinations of measurements illustrate the importance of unifying measurement scales, as well as broad spatial coverage for regional emissions estimates by source sector. More research is essential to accurately assess regional emissions at a finer scale, especially to investigate the impact of different models used in the study, but we show that soil is the largest source of N 2 O emissions and that our optimized N 2 O emissions estimate results in ODP-weighted emissions larger than the sum of the ODS emissions of those controlled by the Montreal Protocol.