We estimate nitrous oxide (N2O) emissions from Central California for the period of December 2007 through November 2009 by comparing N2O mixing ratios measured at a tall tower (Walnut Grove, WGC) with transport model predictions based on two global a priori N2O emission models (EDGAR32 and EDGAR42). Atmospheric particle trajectories and surface footprints are computed using the Weather Research and Forecasting (WRF) and Stochastic Time-Inverted Lagrangian Transport (STILT) models. Regression analyses show that the slopes of predicted on measured N2O from both emission models are low, suggesting that actual N2O emissions are significantly higher than the EDGAR inventories for all seasons. Bayesian inverse analyses of regional N2O emissions show that posterior annual N2O emissions are larger than both EDGAR inventories by factors of 2.0 ± 0.4 (EDGAR32) and 2.1 ± 0.4 (EDGAR42) with seasonal variation ranging from 1.6 ± 0.3 to 2.5 ± 0.4 for an influence region of Central California within approximately 150 km of the tower. These results suggest that if the spatial distribution of N2O emissions in California follows the EDGAR emission models, then actual emissions are 2.7 ± 0.5 times greater than the current California emission inventory, and total N2O emissions account for 8.1 ± 1.4% of total greenhouse gas emissions from California.
 Nitrous oxide (N2O) ranks as the third most important long-lived greenhouse gas (GHG) from a regulatory perspective behind CH4 and CO2 [Hofmann et al., 2006; Montzka et al., 2011] based on changes in the amount of N2O in the atmosphere since the start of the industrial revolution, its long atmospheric residence time (∼110 years), and its ability to absorb infrared radiation. Given the significance of N2O as a GHG it is important to be able to quantify changes in emissions. A recent study showed that a large portion of the increase in global atmospheric N2O can be attributed to the use of fertilizers [Park et al., 2012]. However, current process-level understanding and driving data are not sufficient to accurately predict N2O emissions from the multiple sources. Thus, there are large uncertainties in estimating N2O emissions using bottom-up models. Inversions which use concentration changes in N2O and transport to infer sources provide an effective tool for understanding N2O emissions. Correspondingly, attention has focused on inverse model assessment of global [Huang et al., 2008; Hirsch et al., 2006], and regional [Kort et al., 2008; Corazza et al., 2011] N2O sources.
 California currently emits approximately 500 Tg of CO2 equivalent (CO2eq) GHGs per year (100-year global warming potential (GWP) = 310 g CO2 eq/g N2O [IPCC, 1995]), with N2O currently estimated to contribute ∼3% of the total [California Air Resources Board (CARB), 2012]. However, regional N2O emission estimates are likely uncertain by at least 50% [National Research Council, 2010]. California has committed to an ambitious plan to reduce GHG emissions to 1990 levels by 2020 through Assembly Bill 32 (AB32). Verifying the success of emission control strategies will require quantitative accounting for current and future GHG emissions including N2O. Despite the importance of regional verification of N2O emissions, measurements have yet to constrain seasonal or regional N2O emissions from California.
 In this paper, we quantify N2O emissions from Central California using measurements of N2O from daily discrete air samples collected from December 2007 to November 2009 within a Bayesian inverse modeling framework, the first analysis of seasonal variations in N2O emissions from the mixed urban and rural area of Central California.
 In 2008 and 2009, air samples were collected nearly daily at 91 m above the surface from a tall tower near Walnut Grove (WGC), California (lat = 38.27°N, lon = 121.49°W) as part of the NOAA Global Monitoring Division, Carbon Cycle Groups' tall tower measurement program (www.esrl.noaa.gov/gmd/ccgg/towers/). The approximately 2 liter samples were each collected during a two-minute period within a few minutes of 2200 GMT (1400 local time, LT). N2O dry-air mole fractions were subsequently measured using gas chromatography with electron capture detection relative to NOAA's N2O standard scale [Hall et al., 2007] with a repeatability of 0.4 ppb (68% confidence interval). These samples were analyzed on the same analytical systems used for weekly discrete samples collected from NOAA's Global Cooperative Air Sampling network (www.esrl.noaa.gov/gmd/ccgg/flask.html).
2.2. Footprint Simulations
 Predicted contributions to N2O mixing ratios from emissions within the modeling domain are calculated as FE, where F is the footprint, which represents the sensitivity of the receptor to surface influences, and E is the a prioriemissions. Footprints are calculated using the Stochastic Time-Inverted Lagrangian Transport (STILT) model [Lin et al., 2003]. In this study, 500 particles are released from the WGC tower at the time of each air sample and transported backward in time 5–7 days to insure a majority of the particles reach positions representative of the background conditions relative to the California region. The meteorology used to drive this transport model is simulated by the Weather Research and Forecasting (WRF2.2) model [Skamarock et al., 2005], which has been slightly modified to be coupled with STILT [Nehrkorn et al., 2010] (see the auxiliary material).
2.3. A Priori Emissions
 We use EDGAR 32FT2000 (henceforth EDGAR32) [Olivier et al., 2005] and EDGAR version 4.2 (EDGAR42) (European Commission Joint Research Centre (JRC) and Netherlands Environmental Assessment Agency, Emission Database for Global Atmospheric Research (EDGAR), release version 4.2, 2011, http://edgar.jrc.ec.europa.eu) a priori emission maps (see the auxiliary material) to represent surface emission sources and sinks for N2O at different spatial resolutions (1.0° and 0.1°, respectively). The EDGAR inventory includes all anthropogenic sources of N2O; emissions are constant in time, without seasonality. The annual total emission for California from EDGAR32 and EDGAR42 is 21.6 and 20.0 Tg CO2 eq, respectively. Both EDGAR inventories list emissions that are higher than the current CARB inventory (16 Tg CO2 eq) [CARB, 2012]. In terms of spatial distribution at the sub-regional scale, annual emission sums for Regions 6, 7 and 8 near the WGC tower (see theauxiliary material for region classification) from EDGAR32 are 1.6, 2.8, 1.4 Tg CO2 eq, which are similar to those of EDGAR42: 1.3, 2.7, and 1.4 Tg CO2 eq. As in Kort et al. , we assume that N2O emissions from unfertilized natural soils are small (see details in the auxiliary material) compared to emissions from agricultural soils and other anthropogenic sources in California. In this regard, N2O emissions from fertilized forest soils are included in EDGAR42.
2.4. Inverse Method
 We apply a scaling factor Bayesian inverse (SFBI) method to estimate N2O emissions from Central California using N2O measured at WGC. The local measured mixing ratios, c, are calculated by subtracting a boundary condition mixing ratio, representing the estimated mixing ratio of air entering the domain (see the auxiliary material). As described in Gerbig et al. , Zhao et al.  and Jeong et al. , c can be modeled as
with an analytical solution for λ as
where K = FE, λ is a state vector for scaling factors, vis a vector representing the model-measurement mismatch with a covariance matrixR, λprior is the a priori estimate for λ, and Qλ is the error covariance associated with λprior. The posterior error covariance for λ, Vpost, is (KTR−1K + Qλ−1)−1. We apply the SFBI method at the monthly scale (λ = 13 × 1 vector for each month) to resolve seasonal variations. Data for the same month from 2008 and 2009 are combined, yielding 30–60 data points depending on the availability of flask measurements. National Research Council  reported that N2O emission estimate uncertainties for agricultural soils and manure management range from 10% to more than 100%. Because the Central California region includes large N2O emission sources such as agriculture fertilizers and livestock [Park et al., 2012], we use 100% uncertainty in our a priori emission models.
 Following Bergamaschi et al.  and Jeong et al. , outliers are removed after the initial inversion to avoid biases that might be introduced by the outliers. The second (final) inversion uses data that are accepted by applying the selection criteria |ci − (Kλ)i|2 < αRi, where α is a fixed value within each month. As in the first inversion, the final inversion is performed using the original a priori emission maps. The value of αfor each month is chosen such that the chi-square values from the final inversion are close to unity [Tarantola, 1987] and ranges between 1.7 and 3 in this study.
2.5. Uncertainty Analysis
 Along with Qλ, the model-measurement mismatch covarianceR controls the relative weighting of the prior flux estimates and the data in the inversion. In our study that uses daily air samples, the temporal correlation is expected to be weak as Lin and Gerbig  showed that the correlation timescale for wind errors is less than 3 hours. Therefore, following Gerbig et al. , Zhao et al. , Göckede et al. , and Jeong et al.  the diagonal elements of R(off-diagonal elements equal to zero) are estimated from the linear sum of contributing uncertainties as
 Details for error sources are explained in the auxiliary material, and we describe them briefly below.
 The background uncertainty (Sbkgd) is estimated by comparing two marine boundary layer background data sets available for 2008: (1) latitudinally averaged marine boundary layer N2O background (a 2-dimensional look-up table), and (2) latitudinally averaged 3-dimensional N2O curtain for eight different vertical levels (see the auxiliary material for details). Uncertainty estimates in background N2O are 0.38, 0.46, 0.24, and 0.28 ppb (henceforth, all errors reported at 68% confidence) for spring, summer, fall, and winter, respectively. Uncertainty in predicted N2O signals due to errors in modeled planetary boundary layer (PBL) height (StransPBL) is estimated by comparing PBL heights (Zi) from WRF with measured Zi at wind profiler stations near the WGC tower as in Zhao et al.  and Jeong et al. . We estimate uncertainties of 0.05, 0.03, 0.27, and 0.49 ppb for spring, summer, fall and winter, respectively. Uncertainty in modeled N2O signals due to errors in modeled winds (StransWIND) is estimated using modeled and measured winds for the 127 m height on the WGC tower. Following the experiment with CH4 signals [Jeong et al., 2012], we adopt 10% of the mean signal level for the wind uncertainty. For the uncertainties due to the particle number (Spart) and aggregation error (Saggr), we use 5% and 11% of the mean signal level respectively, following Jeong et al. . Finally, the uncertainties were combined in quadrature to yield total model-data mismatch estimates of 0.40, 0.48, 0.41, and 0.63 ppb for spring, summer, fall and winter, respectively. Seasonally estimated model-data mismatch uncertainties are used for all the months belonging to the given season.
Figure 1shows the average footprints for spring, summer, fall, and winter in 2008–2009. The footprints for each season were averaged during the afternoon hours when measurements were available, mostly at 1400 LT. There is a clear seasonal pattern for the distribution of footprints, which is important to attribute signals to different emission sources for each season. The summer footprints are strongest from the San Francisco Bay area to the west of the WGC tower due to the dominance of land-ocean winds. In the transition seasons of spring and fall, footprints are also strong in the North Central Valley due to a shift toward north-south winds. The winter footprints are strongest in the Central Valley, while reaching the northern San Joaquin Valley. The spatial distribution of footprints for the four seasons shows that tower measurements are sensitive to Regions 6, 7, and 8, and our inverse analysis focuses on these three regions where a large reduction in posterior uncertainties is obtained.
3.2. Linear Regression Analysis
 We compare predicted and measured local N2O signals at WGC using a chi-squared (fitexy) linear regression analysis [Press et al., 1992] that considers uncertainties in parameters of both axes. Table 1 summarizes the results obtained from regression analyses for each month between December 2007 and November 2009. The slopes of predicted on measured N2O from both emission models are generally less than 1, while showing some seasonal variation. The low slopes suggest that actual N2O emissions are significantly higher than the EDGAR inventory. The linear analysis result also suggests that there is no significant difference between EDGAR32 and EDGAR42 as one might expect from the regional N2O sums and their spatial distribution (see Section 2.3). A linear analysis based on continuous N2O measurements at WGC during April 2010 showed a similar result with a slope of 0.34 ± 0.05 (see the auxiliary material).
Table 1. Linear Analysis Results Before and After Inverse Optimization
 Posterior predicted N2O mixing ratios using EDGAR emissions were compared with measurements, and the results are also summarized in Table 1. Compared with the results before inverse optimization, the fitting slopes from the final inversion are closer to unity for most of the months, and the RMS errors are reduced significantly. For March, the posterior fitting slopes from both EDGAR emission models are relatively low compared to those of the other months but do not limit our ability to interpret seasonal N2O emissions. As will be discussed later, monthly inversion results are not different from those of seasonal inversions where posterior slopes for all seasons are near unity.
 In the final inversion, outlier points were removed following Bergamaschi et al. . The outlier removals vary with month, excluding 6–20% (mean removal rate = 11.1%) and 4–22% (mean = 13.6%) of the data used in the first inversion for the EDGAR32 and EDGAR42 models, respectively. These removal rates are comparable to the 12–14% rate in Bergamaschi et al. . In the final inversion, to solve for 9 × 13 unknowns (13 regions for each month) we used 313 and 304 observations for the EDGAR32 and EDGAR42 cases, respectively.
 Inferred N2O emissions are reported by season and as a regional sum over Regions 6, 7 and 8 where reduction in the posterior uncertainty is significant (Figure 2). The annual posterior N2O emission summed over the three regions is 11.5 ± 2.1 and 11. 6 ± 1.9 Tg CO2 eq from the EDGAR32 and EDGAR42 emission models, respectively. Although the two emission maps have different spatial resolutions, the estimated regional emissions are consistent. As a sensitivity analysis, we performed inversions using 200% and 300% uncertainties in the a priori emission models in addition to the baseline prior uncertainty (100%). For EDGAR42, the annual posterior N2O emissions for the three regions were 13.2 ± 2.7 and 13.1 ± 3.0 Tg CO2 eq for the 200% and 300% uncertainties in the a priori emissions, respectively. The EDGAR32 case also showed a similar result with no significant difference in posterior N2O emissions. Averaging over seasons, annual mean scaling factors from EDGAR32 are 2.4 ± 0.5, 2.1 ± 0.6, and 1.3 ± 0.8 for Regions 6, 7, and 8, respectively, consistent with those obtained with EDGAR42: 2.6 ± 0.6, 2.3 ± 0.5, 1.4 ± 0.7. Note that these scaling factors are obtained by comparing posterior emissions from each EDGAR model with the corresponding prior sum. This result suggests that estimated emissions are considerably greater than the EDGAR emission maps in Region 7 containing San Francisco Bay and surrounding urban areas. Estimated emissions are also significantly higher than the EDGAR emission maps in Region 6 containing the southern end of the Sacramento Valley, where a large fraction of N2O emissions is expected from agriculture. While posterior uncertainties are reduced significantly in Regions 6 and 7 for all seasons, the uncertainty reduction in Region 8 is relatively small except for the winter period when footprints extend significantly to the south of the tower (see Figure 1). This suggests additional measurement stations are needed to constrain emissions in Region 8, which is likely an important sub-region in inferring emissions for livestock and crop agriculture.
 The posterior scaling factors show clear evidence of seasonal variation in N2O emissions that is not captured in the EDGAR a priori models. Summing over Regions 6, 7 and 8, posterior seasonal emissions are 14.1 ± 2.4, 11.1 ± 2.2, 9.1 ± 1.8, 11.8 ± 2.1 Tg CO2 eq yr−1 for spring, summer, fall, and winter, respectively, which are comparable to those of EDGAR42: 13.8 ± 2.3, 12.2 ± 2.0, 8.9 ± 1.5, and 11.4 ± 1.9 Tg CO2 eq yr−1. We compare this final inversion result from EDGAR32 with that of the first inversion, which yielded 17.1 ± 2.4, 12.0 ± 2.1, 9.6 ± 1.8, 13.0 ± 1.9 Tg CO2 eq yr−1 for spring, summer, fall, and winter, respectively. There is no significant difference between the two inversions, and we found the same result for the EDGAR42 case. As a sensitivity analysis on the temporal scale, we used a seasonal temporal scale for inversion instead of the monthly scale used in our inversion. We found that the seasonal inversion with EDGAR32 was not significantly different from the monthly inversion, yielding posterior emission estimates of 13.6 ± 2.0, 13.2 ± 3.2, 8.5 ± 1.0, and 11.7 ± 1.0 Tg CO2 eq yr−1. The sensitivity analysis using a fixed value of 2 for α and EDGAR32 also showed no significant change in posterior emissions, yielding 14.3 ± 2.5, 11.3 ± 2.1, 10.0 ± 2.1 and 11.0 ± 2.2 Tg CO2 eq yr−1. These combined results indicate that posterior N2O emissions for all seasons are significantly higher, compared to the annual EDGAR32 total (5.8 Tg CO2 eq) or EDGAR42 total (5.4 Tg CO2 eq) for Regions 6, 7 and 8.
Figure 2 shows the seasonality in N2O emissions in each sub-region. N2O emissions from Region 6 based on both EDGAR emission models vary seasonally, showing largest emissions in spring and summer. Posterior emissions for Region 7 show seasonal variation where spring and summer emissions are higher than the other seasons. The EDGAR42 case also shows that summer and spring emissions are higher than the other seasons. For Region 8, seasonal variation in N2O emissions is undetermined because of high posterior uncertainties although winter posterior emissions are significantly higher than EDGAR.
 The N2O emissions estimated in this study can be compared with those from other work for the Continental U.S. Spatially averaged N2O emissions from Regions 6, 7 and 8 during late spring and early summer are 2.5 ± 0.4 times the EDGAR32 inventory. This is essentially consistent with results described in Kort et al. , where N2O emissions over a larger area of the U.S. and southern Canada were larger than the EDGAR32 inventory by a factor of 2.6 ± 0.5 for the May – June, 2003 period.
 Beyond the comparison for spring and summer, seasonal dynamics of N2O emissions appear important for the mixture of urban, agricultural, and natural landscapes. Emissions for Central California in fall differ from EDGAR32 and EDGAR42 inventories by factors of 1.6 ± 0.3 and 1.6 ± 0.3, respectively, indicating that N2O emissions vary by nearly 30% throughout the seasonal cycle.
 While it would be desirable to spatially resolve emissions, the footprints obtained for the single tower limit our ability to separate emissions from different sub-regions. This can be judged by the magnitude of cross-correlations between posterior emission estimates between different sub-regions [e.g.,Bergamaschi et al., 2005]. For our study, cross-correlations derived from the posterior covariance matrix were negative between Regions 6 and 7 (−0.6 to −0.1), with smaller anti-correlations between those regions and Region 8. This suggests that the large emissions in Region 7 in spring and summer can be traded off against emissions from Region 6 in a manner that cannot be uniquely resolved from the inversion system driven by data from a single tower [Tarantola, 1987].
 Putting our results in the context of California's total N2O emissions requires an assumption about the spatial distribution of N2O emissions. If the spatial distribution of EDGAR is applied across California using the mean estimated scaling factor from Regions 6, 7, and 8, then total N2O emissions would be larger than the current state emission inventory by a factor of 2.7 ± 0.5, constituting 8.1 ± 1.4% of California's total estimated GHG emissions [CARB, 2012]. While there is no current evidence to suggest that the spatial distribution of N2O emissions is incorrect, analysis of long-term measurements with footprints covering more of California is needed to improve the estimate of state total annual N2O emissions.
 We thank the NOAA-ESRL staff for technical assistance, Los Gatos Research for loan of the in-situ N2O instrument, John Lin, Steve Wofsy, Janusz Eluszkiewicz and Thomas Nehrkorn for generously sharing the STILT code, and two anonymous reviewers for valuable comments. We acknowledge NOAA Air Resources Laboratory (ARL) for the use of HYSPLIT underlying STILT, and NCEP for the provision of the NARR meteorology. This study was supported by the Public Interest Environmental Research Program of the California Energy Commission and Laboratory Directed Research and Development support from the Lawrence Berkeley National Laboratory under U.S. Department of Energy contract DE-AC02-05CH11231. The findings, views, and opinions presented in this paper do not represent the views and opinions of the California Energy Commission or the State of California.
 The Editor thanks two anonymous reviewers for assisting in the evaluation of this paper.