Inverse modelling of European N2O emissions: assimilating observations from different networks

. We describe the setup and ﬁrst results of an inverse modelling system for atmospheric N 2 O, based on a

4DVAR inverse modelling system, thus allowing the simultaneous assimilation of observations from different networks. The N 2 O bias corrections determined in the TM5-4DVAR system agree within ∼0.1 ppb (dry-air mole fraction) with the bias derived from the measurements at monitoring stations where parallel NOAA discrete air samples are available. The N 2 O emissions derived for the northwest European and east European countries for 2006 show good agreement with the bottom-up emission inventories reported to the United Nations Framework Convention on Climate Change (UNFCCC). Moreover, the inverse model can significantly narrow the uncertainty range reported in N 2 O emission inventories for these countries, while the lack of measurements does not allow to reduce the uncertainties of emission estimates in southern Europe.
Several sensitivity experiments were performed to test the robustness of the results. It is shown that also inversions without detailed a priori spatio-temporal emission distributions are capable to reproduce major regional emission patterns within the footprint of the existing atmospheric network, demonstrating the strong constraints of the atmospheric observations on the derived emissions.

Introduction
Atmospheric mixing ratios of nitrous oxide (N 2 O) have significantly increased since preindustrial times and continue to increase by 0.2 to 0.3%/yr (IPCC, 2007). N 2 O is the fourth most important anthropogenic greenhouse gas (GHG) after CO 2 , CH 4 and CFC-12, with a global warming potential of almost 300 relative to CO 2 over a 100 yr time horizon (IPCC, 2007). Furthermore, N 2 O is considered to become the most important ozone depleting gas of the 21st century, after the drastic abatement of the chlorofluorocarbons in recent years (Ravishankara et al., 2009). A significant part of N 2 O removal in the stratosphere (∼10%) is caused by reaction with electronically excited oxygen atoms, and about half of those reactions produce nitric oxide, which is part of a catalytic cycle that destroys ozone (Crutzen, 1974;Nevison and Holland, 1997).
The current increase of atmospheric N 2 O mixing ratios of 0.73 ± 0.06 ppb/yr is equivalent to an imbalance between sources and sinks of about 3.5 TgN/yr (Hirsch et al., 2006;Hall et al., 2002). With an atmospheric lifetime of 122 ± 24 years, as derived by Volk et al. (1997) using stratospheric measurements, the global total sinks of N 2 O are estimated to be 12.5 ± 2.5 TgN/yr, and the sources from surface emissions ∼16 TgN/yr (Hirsch et al., 2006). Based on pre-industrial N 2 O mixing ratios of 265-280 ppb, Hirsch et al. (2006) estimate the preindustrial N 2 O sources to be about 11 TgN/yr.
Atmospheric measurements combined with inverse atmospheric models can provide independent "top-down" emission estimates of atmospheric trace gases. Inverse modelling has been widely applied to CO 2 and CH 4 (IPCC, 2007), while only relatively few studies are available for N 2 O. Major challenges for inverse modelling of N 2 O include (1) the very small gradients of N 2 O (and hence low signal-to-noise ratio of the measurements constraining the inversion), (2) potential biases between measurements from different laboratories, (3) the difficulty to simulate the stratospheric sink and stratosphere-troposphere exchange realistically, and (4) large spatial and temporal variability of N 2 O emissions. The first inverse analysis of the global N 2 O cycle was presented by Prinn et al. (1990) based on a 9-box model and atmospheric observations from the ALE-GAGE (Atmospheric Lifetime Experiment -Global Atmospheric Gases Experiment) network for [1978][1979][1980][1981][1982][1983][1984][1985][1986][1987][1988]. They concluded that beside the use of fertilizer and fossil fuel combustion in mid latitudes, tropical sources (probably from tropical land use change) are likely to play an important role for the global budget and the observed N 2 O increase. The more recent studies of Hirsch et al. (2006) and Huang et al. (2008), based on 3-D global inverse models, suggest an even larger contribution of the tropical sources between 0 and 30 • N to the global total (50-64% using observations from the NOAA -National Oceanic and Atmospheric Administration -network for 1998-Hirsch et al., 2006; 40-56% using the observations from the AGAGE -Advanced GAGE -network for 1997-2005-Huang et al., 2008 than estimated by Prinn et al. (1990Prinn et al. ( -32-39% for 1978Prinn et al. ( -1988) -or estimated by measurement based (bottom-up) inventories (34%; Bouwman et al., 1995).
In addition, to improve our knowledge about global GHG cycles, inverse modelling is an important tool for regional emission estimates and independent verification of international agreements on emission reductions, such as the United Nations Framework Convention on Climate Change (UN-FCCC) and the Kyoto Protocol (Bergamaschi, 2007;IPCC, 2000). First inverse modelling (top-down) estimates of European N 2 O emissions were provided by Ryall et al. (2001) and Manning et al. (2003), using N 2 O observations from Mace Head and the NAME Lagrangian particle model. Their estimates for northwest European countries agreed within ∼30% or better with emissions reported to UNFCCC. A modelindependent "top-down" approach using the 222 Rn tracer method presented by Messager et al. (2008), also agreed well with bottom-up emission estimates. It needs to be emphasized, however, that top-down approaches generally estimate total emissions, while emissions reported to UNFCCC cover only anthropogenic emissions. Hence, for quantitative comparisons, good bottom-up estimates of the natural sources are needed.
While the above European top-down emission estimates are based on one single station (Mace Head), improved emission estimates require the use of further atmospheric measurements, to provide better coverage of the European domain. Additional continuous N 2 O measurements are now available from 10 European monitoring stations, including 5 tall towers, which where setup in the framework of the European RTD (Research and Technology Development) project CHIOTTO (Continuous HIgh-precisiOn Tall Tower Observations of greenhouse gases). Despite ongoing measurement comparisons among the different laboratories, significant offsets still exist among the different networks, which are directly apparent from the comparison with flask samples from the NOAA/ESRL (Earth System Research Laboratory) network, which are available for some European monitoring stations.
Here we describe the setup of a four-dimensional variational (4DVAR) inverse modelling system for N 2 O based on the atmospheric transport zoom model TM5. The TM5-4DVAR system was originally developed and applied to CH 4 (Meirink et al., 2008;Bergamaschi et al., 2009Bergamaschi et al., , 2010. The most important update for N 2 O is the implementation of a bias correction scheme to correct for the N 2 O measurement offsets, which is a central prerequisite for the simultaneous assimilation of observations from different networks. In this paper, we present first N 2 O inversions for 2006 focussing on the European scale using continuous measurements from the various new European monitoring stations. The major objective of this paper is to demonstrate that our system can derive realistic bias corrections, assuming that the measurement offsets are constant over the inversion time period, and that after bias correction, inversions provide  (Bergamaschi et al., 2009(Bergamaschi et al., , 2010. Such "free inversions", which are largely driven by the atmospheric measurements, appear very useful in particular for N 2 O, for which the uncertainties of the bottom-up inventories are considerable and difficult to estimate (partly due the large spatial and temporal variability of emissions, especially from soils), which implies some risk that deficiencies of the a priori inventories may "guide" the inversion in a wrong direction. The development and application of the N 2 O inverse modelling system is performed within the framework of the European Integrated Project NitroEurope (http://www. nitroeurope.eu/) which is aiming on a detailed comparison of European CH 4 and N 2 O top-down estimates from various independent inverse models.

Observations
The European monitoring stations used in this work are listed in Table 1, while an overview of the global station distribution is given in the Supplement in Fig. S1. The backbone of the observing system used over the global domain is the NOAA global cooperative air sampling network (Dlugokencky et al., 1994;Hirsch et al., 2006), providing a globally consistent dataset. In addition, we use various new regional monitoring stations over the European domain: these include quasi-continuous measurements (with a time resolution of 1 h or better) from 5 tall towers which were setup in the framework of the European RTD project CHIOTTO (http://www.chiotto.org), the AGAGE station Mace Head, the Finnish Meteorological Institute (FMI) station Pallas, the Umweltbundesamt (UBA) station Schauinsland, and the Swiss National Air Pollution Monitoring Network (NABEL)/Global Atmosphere Watch (GAW) station Jungfraujoch. Furthermore we use flask samples from Shetland Islands (operated by the Max Planck Institute -MPI, Jena). Potential inconsistencies in the N 2 O measurements, however, prevent the direct use of the combined dataset in the inversion. At 4 of the European stations, where NOAA flask samples are measured in parallel, potential offsets in the N 2 O calibration can be determined directly. Comparing these NOAA flask samples with the corresponding continuous measurements coinciding within one hour, significant biases of up to 1.0 ppb are found for 3 of the 4 sites (see Table 2 and Fig. 1), of the same magnitude as the expected gradients of N 2 O mixing ratios. The N 2 O measurements at the different laboratories and monitoring stations are generally performed using gas chromatography (GC) with electron capture detection (ECD). However, the setup of the instruments and calibration procedures are not standardized and differ among the different laboratories.
NOAA air samples are collected from its global cooperative air sampling network in cylindrical 2.5-L borosilicate glass flasks (see Dlugokencky et al., 1994 for details). Portable sampling systems are used to flush and fill two flasks connected in series to a pressure of 1.2 to 1.5 atmospheres. N 2 O is measured by gas chromatography (GC; Hewlett-Packard 6890) with electron capture detection (ECD; anodepurged). Separation of N 2 O from other components of the sample is achieved on 5 m of HayeSep Q split into 2 columns of 2 and 3 m. The 2 m length is back-flushed to remove ECDsensitive species that elute more slowly than N 2 O. A mixture of 5% CH 4 in Ar is used as carrier gas. Samples are dried to a dew point of ≤ −70 • C. The ECD response is calibrated for N 2 O with a suite of standards (from 242.5 to 344.1 ppb on the NOAA-2006 scale) relative to reference air from a cylinder using an offline procedure that is separate from sample analysis. All samples are analyzed relative to the reference cylinder. N 2 O mole fractions are calculated from the most recent response curve and reported in units of dry-air mole fraction, nmol/mol (abbreviated ppb). Uncertainties in the highest level standards are estimated as ± 0.15% of the assigned value. Repeatability of air samples -0.4 ppb (1 σ )is estimated based on the average of the absolute values of the differences in N 2 O mole fraction between sample pair members. This is about twice the repeatability of the analytical system -∼0.2 ppb (1 σ ) estimated from repeat measurements of aliquots of natural air from a cylinder.
The methods adopted by the other laboratories differ in particular regarding the calibration procedure (see e.g. Hall et al., 2007). For instance, the CHIOTTO tall tower stations each use a set of 3-4 calibration standards based on ambient air that have been produced and of which the N 2 O mixing ratios have been determined at the central laboratory of MPI-BGC (Max-Planck-Instituts für Biogeochemie) in Jena, using a N 2 O scale different of that from NOAA. At Jungfraujoch each ambient air sample is bracketed with calibration runs, using real-air working standards with N 2 O mixing ratios determined by cross-calibration with AGAGE standards and reported on the SIO-98 scale . In general, discrepancies are mainly due to the adopted calibration method, but furthermore there are also differences in sample inlets, sample treatment, characteristics of the individual GC-ECD, or data processing. Without regular inter-comparison, no correction factors can be calculated for the scale differences, with the additional problems of the long-term drifts in the scales, so that also the relative changes between the scales need to be corrected.
An important further issue for the use of the measurements in inverse modelling is the potential influence of nearby local sources, which usually can not be realistically simulated by relatively coarse resolution atmospheric models. A very pronounced local influence is observed at the station Schauinsland (Germany), where several times per year the measured N 2 O mole fractions suddenly increase from normal values (of the order of 320 ± few ppb) to 340-380 ppb, usually associated with westerly winds. These N 2 O spikes are very likely due to a large adipic acid production facility in Chalampe, France, at about 20 km distance to Schauinsland, for which N 2 O emission of 4.96 Gg N 2 O are reported for 2006. To minimize artefacts in the inversions, we rejected all data from Schauinsland above a threshold set to 330 ppb.

Setup of TM5 for N 2 O simulations
TM5 is an offline Eulerian transport model (Krol et al., 2005) using meteorological fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) model. It is a two-way nested zoom model, which can zoom in over the domain of interest (here Europe) at a horizontal resolution of 1 • × 1 • , embedded into the global domain, run at a resolution of 6 • × 4 • . This approach allows relatively high resolution simulations at moderate computational costs, while maintaining consistency with the global background values. In this work, the TM5 version developed for CH 4 inversions (see Bergamaschi et al., 2009Bergamaschi et al., , 2010, and references therein) has been modified for N 2 O. We use the meteorological fields from the ERA-Interim reanalysis (Dee and Uppala, 2009, and references therein), available every 6 h over sixty vertical levels. We use a subset of 25 vertical layers (extending up to 0.2 hPa, roughly corresponding to ∼60 km height), and two zoomed domains (two-way nesting) are defined over Europe (see also Fig. S1 in the Supplement). The horizontal resolution of the global model is 6 • × 4 • , while that of the two nested domains is 3 • × 2 and 1 • × 1 • respectively. For the N 2 O forward simulations, three main aspects are important to consider (i) the implementation of the chemical sink in the stratosphere (ii) the a priori inventories, and (iii) the construction of the initial field of N 2 O mixing ratios.

N 2 O chemistry
N 2 O is removed from the atmosphere mainly by two processes in the stratosphere, i.e. photolysis: and reaction with excited oxygen O( 1 D): Reactions (R1) and (R2) are responsible for roughly 90% and 10% of the removal respectively. These two processes can be described as function of N 2 O mixing ratio as follows: where [N 2 O] m,l,t represents N 2 O zonal mean mixing ratio at latitude m, level l, and time t, d dt [N 2 O] m,l,t its variation in time, and k m,l,t and j m,l,t are the first-order rate coefficients for reaction with electronically excited oxygen atoms and photolysis, respectively. We use zonal mean monthly averaged values for the reaction coefficients k m,l,t and j m,l,t , derived from the ECHAM5/MESSy1 model (Brühl et al., 2007). Both stratospheric reactions show a pronounced seasonality, as shown in Fig. S2 (Supplement).
In addition to the stratospheric sink, also small net surface sinks have been reported in some studies attributed to denitrification by bacteria (EPA, 2010;Hirsch et al., 2006, and references therein). The potential contribution to the global budget is not quantified, but assumed to be relatively small (Hirsch et al., 2006). Therefore this process is not considered in this study.

N 2 O emissions
The emission inventories applied in this study as a priori estimates for the inversion consist of 13 different source categories as detailed in Table 3. Most of the anthropogenic emissions are obtained from the Emission Database for Global Atmospheric Research (EDGAR, version V4.0). The GFEDv2 (Global Fire Emissions Database, version 2) inventory (van der Werf et al., 2004) is used to represent biomass burning emissions, and the GEIA (Global Emissions Inventory Activity) inventories are adopted for natural soil emission, enhanced soil emissions after deforestation, and ocean emissions (Bouwman et al., 1995). These emission inventories are available over the global domain at a horizontal resolution of 1 , as yearly averaged values, except biomass burning, for which monthly averaged values are reported. The total annual global emissions of our composite bottom-up inventory, equal to 13.76 Tg N 2 O-N/yr, are ∼15% smaller than the global total of ∼16 Tg N 2 O-N/yr estimated by Hirsch et al., (2006) based on simple global budget calculations (see also introduction).

Initial N 2 O fields
The atmospheric sink is proportional to the N 2 O mixing ratios (Reaction R3) and therefore directly related to the vertical profile of N 2 O, which is almost constant in the troposphere and rapidly decreases with height above the tropopause. Due to the correspondence between the maximum values of the reaction coefficients of the stratospheric sinks and the maximum vertical gradient of the mixing ratio, small errors in the vertical N 2 O profile can lead to large errors of its removal rates. As a consequence, a good description of the vertical N 2 O profile is essential. Moreover, the lifetime of N 2 O, of the order of 120 years, would require a very long model spin-up period, unless the initial field is already very close to the true state. Therefore, we used the vertical N 2 O profile from the ECHAM5/MESSy1 model (Brühl et al., 2007). This profile, available as monthly averaged values (see Fig. S2, bottom panels, in the Supplement), is applied to a surface field constructed from the NOAA surface observations. These surface fields are constant in longitude and smoothed in latitude, using observations within a monthly time window, centred on the day chosen for the initial condition. Since this field is constructed offline without using the TM5 model, however, it might not be in a sufficiently good dynamic balance within the model. Therefore, we have run the TM5-4DVAR model at coarse resolution (6 • × 4 • ) over the period 1999 to 2006 as spin-up period, using only surface observations from the NOAA network, and the initial N 2 O field constructed as described above to initialize a first global inversion for 1999. We have then performed a series of global inversions for the following years using as initial condition the optimized N 2 O fields obtained by the previous inversion. The resulting fields from the last global inversion for 2005 are then used as initial N 2 O fields for the European zoom inversions presented in this paper (running from 1 December 2005 to 1 February 2007). An important property of this initial N 2 O field is its consistency with the surface observations of the NOAA network, which are used as reference for the bias correction.

Inverse modelling system
The 4DVAR inverse modelling system used in this work for N 2 O is derived from the TM5-4DVAR system originally developed for CH 4 (Meirink et al., 2008;Bergamaschi et al., 2009Bergamaschi et al., , 2010. We refer to these papers for a detailed description of the 4DVAR system; here we describe only briefly its main characteristics (Sect. 3.2.1), and devote particular attention to the implementation of the bias correction scheme developed for the N 2 O inversion (Sect. 3.2.2).

The TM5 4DVAR
4DVAR is a variational data assimilation technique that allows for the optimization of very large sets of parameters (described by the state vector). At the same time, very large observational datasets can be assimilated, such as satellite data or continuous surface observations. The best approximation of the true state in the space of the state vector is obtained by iteratively minimizing the cost function (3) bias correction parameters associated with different station networks, as described in detail below (Sect. 3.2.2).
To avoid negative a posteriori emissions, we apply a semiexponential description of the probability density function (as for the CH 4 inversions; Bergamaschi et al., 2009Bergamaschi et al., , 2010: where E apri0 are the a priori emissions (per grid cell, month and source group), and the optimization is performed as function of the parameter x, initially set to zero and described by a Gaussian distribution. This semi-exponential probability density function introduces a weak non-linearity in the system, while all other parts of the TM5-4DVAR system are strictly linear. For the minimization of the cost function we apply the M1QN3 algorithm (Gilbert and Lemaréchal, 1989), which also effectively minimizes weakly non-linear systems.
We optimize the emissions for 4 source groups independently: soil, ocean, biomass burning, and "remaining emissions" (see Table 3). The temporal correlation coefficients for the first 3 source groups are set to zero to give the TM5-4DVAR system enough freedom to optimize the seasonality of theses sources (especially important for soil and ocean, where the bottom-up inventories provide only annual mean values). For the categories subsumed under "remaining emissions" it is assumed that the seasonal variation is rather small, and the temporal correlation is set to 9.5 months (equivalent to a month-to-month correlation coefficient of 0.9). The a priori uncertainties chosen in the control simulation are equal to 100% per grid cell, month and source group, and the spatial correlation length is set to 200 km. As described in Sect. 3.4, different sensitivity studies for these parameters have been performed.

Bias correction
4DVAR is a variational method that assumes unbiased observations described by a normal distribution. Since, as described above, stations belonging to different networks may exhibit non-negligible calibration offsets, it is not possible to use the available measurements without a major modification to the scheme. This problem has been faced in the past years in numerical weather modeling, for instance at NCEP (National Centers for Environmental Prediction) by Derber and Wu (1998) and at ECMWF by Dee (2005). In the framework of inverse modeling, Bergamaschi et al. (2009) modified the same 4DVAR system used in this work to account for biases in SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric CHartographY) satellite retrievals.
Here we follow their method, adapted for the surface observational networks.
The 4DVAR state vector, x in Eq.
(1), can be modified to include new parameters β i describing the station biases. The modified state vector can be therefore written asx = (x,β 1 ,...,β n ), where n is the number of bias-correction parameters used. The modification of the state vector requires the observation operator H and the background error covariance matrix B to be changed accordingly, so that H (x) =H (x, β) and B →B. Equation (1) can therefore be written as follows: and the minimization performed in function of the new state vector. As stated above, stations belonging to NOAA network are considered to be the unbiased reference, assuming that no bias exists among the NOAA sites. This assumption is reasonable, since all NOAA samples are analyzed in the same laboratory using the same calibration standards.
For the other networks we have chosen independent bias parameters for each station. The major general assumption is that measurement offsets are constant in time, i.e. potential trends in the calibration offset are not considered in this study. The a priori estimates for β i have been set to 0 for every station, and their uncertainties to 1 ppb.

Inversion set-up
The representation of the errors associated with the observations is composed of two parts, i.e. the estimate of the error associated with the observation itself and the estimate of the uncertainty related to the capability of the model to represent the observed mixing ratios at the scales simulated by the model, the so called model representative error. We apply the same scheme as used for the CH 4 inversions (Bergamaschi et al., 2010), decomposing the total error y tot associated with the observations as follows: where y BL is the estimate of the uncertainty due to the subgrid variability of emissions, applied only for stations in the boundary layer, y 3-D is the estimate of the potential model errors due to large gradients of the mixing ratios, y t is the largest standard deviation for observed or modeled mixing ratios within the 3 h time window used by the model, and y OBS is the observational error. In this study we assume an observational error of 0.3 ppb for all observations. As in Bergamaschi et al. (2010), in case of continuous observations only one value per day is assimilated, to avoid giving too much weight to these observations (since consecutive hourly measurements are usually correlated). After applying this "data thinning", time correlations in the observation error covariance matrix R are neglected, and R is therefore represented as a diagonal operator. In case of boundary layer stations, daytime samples are assimilated (in the window 12:00-15:00 LT) to maximize representativeness of the Table 4. List of the experiments described in this work. L corr denotes the spatial correlation length applied for the emissions.

Inversion
L corr Description S1 200 km Reference inversion S2 300 km As S1, but spatial correlation length 300 km S3 100 km As S1, but spatial correlation length 100 km S4 200 km As S1, without using the parallel NOAA measurements at 4 European stations S5 50 km As S1, but homogeneous a priori emissions (two different values over land and over ocean, respectively). Spatial correlation length 50 km, and uncertainty of emissions set to 500%. Only total emissions optimized.
observations and to minimize errors related to subgrid scale effects. For mountain stations located above the boundary layer data are assimilated during night (00:00-03:00 LT) to minimize errors related to local thermal wind circulations.

Simulations
The reference inversion S1 is run as described above, using a spatial correlation coefficient for the a priori emission inventories of 200 km. In addition, various sensitivity inversions were performed to analyze the robustness of the retrieved emissions, as described in Table 4. The first two sensitivity experiments (S2 and S3 in Table 4) test the impact of different correlation lengths for the a priori emission datasets, using 300 km and 100 km values respectively. Sensitivity experiment S4 is performed to check the consistency and reliability of the bias correction system. The reference inversion includes NOAA measurements from discrete flask samples collected in parallel with the continuous measurements at 4 European sites (Table 2), resulting in very strong constraints for the bias parameters for these stations. To test the capability of the new bias scheme to satisfactorily correct measurement offsets of these stations independently from the parallel flask measurements, we run an experiment (S4) with the same configuration as S1, but without using the NOAA measurements at these four locations. Finally, in S5 we investigate the impact of the a priori emission inventory used, by replacing the standard a priori inventory by the assumption of constant, homogeneous emissions over land, and small homogeneous emissions over the ocean. Two constant emission values for land and ocean have been set with the total amounts over land and ocean equal to those of the control simulation S1. In contrast to all the other simulations only to-tal emissions are optimized in this inversion. The uncertainty and the correlation length are set to 500% and 50 km respectively in S5 to give the system enough freedom to obtain large increments capable to relax to the information coming from the observing system.

Global background
Although the main focus of this work is on the European scale, we discuss briefly also the results obtained for the global domain, mainly to assess the capability of the inverse modelling system to provide realistic boundary conditions to the nested European domains. Figure S3 (Supplement) shows several global NOAA background sites, illustrating that the a posteriori simulations reproduce in general the measurements rather well. However, at the high latitude sites ALT and BRW the model simulations show some systematic bias towards higher values than observations, while at ZEP a rather good agreement is achieved. This discrepancy could point to some inconsistencies in the simulations of the stratospheric-tropospheric exchange, or in the emissions, and needs to be further clarified in subsequent studies. The overall relatively good agreement with observations is achieved by significant inversion increments of the emissions. As expected, the annual global total emissions increase significantly from the apriori value of 13.76 Tg N 2 O-N/yr to 16.06 Tg N 2 O-N/yr (Fig. S4 in the Supplement), consistent with the estimate of ∼16 Tg N 2 O-N/yr by Hirsch et al. (2006) for the global total emissions. We compute an atmospheric N 2 O lifetime of ∼127 yr (total atmospheric burden/total sinks). This is in good agreement with the estimate of 122 ± 24 years derived by Volk et al. (1997), indicating that the stratospheric sink is realistically simulated in the model. The inversion increments are largely located in the tropics, consistent with the results of Hirsch et al. (2006) and Huang et al. (2008).
The natural sources represent about 62% of the global total emissions in our inversion, mainly distributed over oceans and tropical lands, broadly consistent with the estimates of Hirsch et al. (2006) (between 66% and 71%) and EPA (2010) (64%). We emphasize, however, that our estimate of natural sources largely depends on the information coming from the chosen bottom-up inventories.

Bias correction
Test inversions without bias correction clearly demonstrate that, despite large inversion increments, no satisfactory agreement between model simulations and observations can be achieved (results not shown). The bias correction scheme described in Sect. 3.2.2 corrects for these measurement offsets. The scheme yields very satisfactory results, reproducing the biases determined at 4 European monitoring stations from the parallel NOAA flask measurements within 0.1 ppb (Table 2). These results give us confidence that the offsets computed for the other stations are also reliable. In fact, we derive for most stations, with the exception of Mace Head and Cabauw, a non-negligible bias correction with respect to the reference NOAA network, further confirming that a bias correction scheme is a prerequisite for jointly using measurements made by independent laboratories. Very similar results were also obtained for 2007 (not shown), with the exception of the Ochsenkopf tall tower, for which a much smaller bias of 0.2 ± 0.7 ppb (n = 11) was derived from the parallel NOAA measurements, but which has also been well captured by the bias correction in an analogous inversion for 2007 (derived bias correction equal to 0.3 ppb).
This case illustrates that our assumption of constant biases might not be valid over longer time periods. The approach of using a constant bias correction (in contrast to a function of time), however, has the advantage of avoiding any potential interference with the signal from emissions (i.e. the risk to partially attribute an emission signal to the bias correction).
The robustness of our bias correction scheme is also confirmed by the results of the sensitivity experiments, discussed in Sect. 4.3.

Temporal variability of N 2 O mixing ratios at monitoring stations
The inversion significantly improves the agreement of model simulations with observations, as illustrated in Fig. 2  Synoptic-scale variations are simulated well at most stations, e.g. Mace Head, a station which usually represents background mixing ratios, but occasionally also samples air from Ireland, UK and continental Europe. Also at more continental stations, such as Bialystok (bottom panel in Fig. 2), synoptic-scale variability is generally simulated well. However, we observe at several of these regional continental stations slightly poorer agreement between observed and simulated high-frequency variability compared to CH 4 (Bergamaschi et al., 2010), probably due to much larger variability of N 2 O emissions. In particular N 2 O emissions from soils may exhibit pronounced spatial and temporal variations following changes in soil water content (rainfall), while the a priori emission inventories are constant throughout the year. Also the inversion is not capable to derive high-frequency variations of emissions, since only monthly mean values are optimized in the current system. The measurements shown in Fig. 2 are corrected with our calculated offset obtained using the bias correction scheme in the inversion (see Sects. 3.2.2. and 4.2.1), which is essential to achieve the overall good agreement with model simulations.

Derived emissions
Also at the European domain we see a general increase of N 2 O emissions compared to a priori inventories (Fig. 3). Exceptions are UK and western Poland, where a small decrease is calculated. Total emissions over the European zoom domain increase from 1.05 TgN/yr to 1.19 TgN/yr for the control simulation. In contrast to the global emissions the percentage of emissions attributed to natural sources is much smaller, typically of the order of 10%, reaching values up to 20% in some countries of eastern Europe, and being close to zero in densely populated areas like, for instance, Benelux.
For further interpretation of results it is important to evaluate the sensitivity of the derived emissions to the available observations. For this purpose, we analyze the uncertainty reduction determined by the inverse modeling system, i.e. the ratio between a posteriori and a priori uncertainties (Fig. 4), based on an additional simulation using a conjugate gradient algorithm and the linear TM5-4DVAR system (for details see Bergamaschi et al., 2010;Meirink et al., 2008). The figure illustrates that the largest uncertainty reductions are achieved for northwest European countries and some east European countries, while hardly any uncertainty reduction is achieved for south Europe.
Therefore, we restrict in the following the discussions to countries for which the observational constraints are strongest.
In Fig. 5 and Table 5 we show the total annual emissions derived for these countries in our inversion and compare with the emissions reported to UNFCCC (National Inventory Reports, Submission 2009, http://unfccc.int/) Since the latter cover only anthropogenic emissions we separate the estimated small contribution of natural sources from the total emissions derived in the inversion. For discussion of emissions on the European scales we use the unit Tg N 2 O/yr to facilitate the comparisons with other studies on the European scale (e.g. Manning et al., 2003), while for the global studies usually the unit TgN/yr is used. In general, the derived total anthropogenic emissions agree very well with the emissions reported to UNFCCC for most countries: While for UK and Ireland our top-down estimate is about 30% lower than UN-FCCC emissions, the agreement is generally better than 30% for all other countries.
This very good agreement is indeed rather surprising, since very large uncertainties are reported for the UNFCCC N 2 O inventories, in general much larger than 100% (as compiled in Table 6 for north western European countries; not

Fig. 2.
Time series (days) of observed and simulated N 2 O mixing ratios at 5 of the available European stations: Pallas, Mace Head, Bialystok, Cabauw, and Schauinsland. One year of data, from 1 January to 31 December 2006, is split into two 6-month panels for each station. Blue lines represent a priori simulations and red lines are a posteriori simulations for the reference inversion S1. Shaded areas represent estimated uncertainties of the model simulations. Measurements are shown as black dots. The calculated bias corrections (offset) are given on the right of each panel and have been subtracted from the measurements. Units are ppb.   shown in Fig. 5 due to the large magnitude of these uncertainties). The overall model uncertainties are estimated to be on the order of 40% (2 σ ), based on the calculated uncertainties (using the conjugate gradient algorithm) and taking into account potential additional model errors estimated from a preliminary model comparison performed within the NitroEurope IP project (see Table 7). Compared to CH 4 , where estimated uncertainties of bottom-up and top-down emission estimates are in the same order of magnitude, the uncertainties of the N 2 O top-down estimates are obviously significantly lower than uncertainties of N 2 O bottom-up inventories, demonstrating that inverse modeling can narrow down the overall uncertainties significantly. We also notice that the relatively good agreement between our derived emissions and the bottom-up inventories is consistent with the recent study of error statistics of bottom-up inventories by Leip (2010), suggesting that the present uncertainty estimates of N 2 O bottom-up emission inventories are likely overestimated.  Table 5). The filled colored circles represent the annual total emissions from the 5 inversions and open circles are the applied a priori emissions. The small natural emissions have been subtracted for S1-S4 (while this is not possible for S5, which does not use any detailed a priori knowledge). Emissions reported to UNFCCC are shown by the black solid line (uncertainties of the order of 150% are not shown here, but compiled in Table 6). North-western Europe represents the sum for Germany, France, Benelux, United Kingdom and Ireland, while Eastern Europe represents the sum of Poland, Czech Republic, Slovakia, and Hungary. Finally North-central Europe represents the sum of all considered countries. Colored solid lines represent the seasonal variation of anthropogenic emissions derived in the inversions (3 month running mean), while the colored dash-dotted lines show the small contribution from natural sources.
The a posteriori emissions show a remarkable seasonal variation (solid lines in Fig. 5), with a peak emission during spring that could be due to agricultural soil emissions affected by the use of fertilizers. The only exception to this is the Benelux area, where we observe only a secondary peak during spring, with the maximum during autumn. We emphasize, however, that the seasonal cycle of the emissions needs to be analyzed in more detail in future work, in particular considering the important role that vertical transport and Stratospheric-Tropospheric exchange can play in forcing it. The removal of N 2 O associated with the sinks has a marked seasonal cycle and the relative importance of this processes with respect to the seasonality of surface mixing ratios needs more detailed research.

Spatial correlation length (S2 and S3)
In a first set of sensitivity experiments we explore the impact of the assumed spatial correlation length (Meirink et al., 2008), which was set to 200 km in the reference inversion. Increasing the correlation length to 300 km (S2) or decreasing it to 100 km (S3) has an overall only very small impact on the increments at small scales, but leads to some changes on larger scales with respect to our reference inversion S1 (Fig. S5 in the Supplement). The latter can be explained by the fact that increasing the correlation length also increases the aggregated uncertainty of the a priori emission over larger regions (since we did not modify the grid-scale uncertainty), thus allowing for a larger correction towards the observational data. The impact on the country totals, however, remains very small (Fig. 5), generally much smaller than the assumed overall uncertainty of about 40%. Furthermore, the calculated bias corrections remain very stable for these sensitivity experiments (Table 2).

Use of parallel NOAA flask samples at continuous monitoring stations (S4)
We generally include the parallel NOAA flask measurements at all continuous monitoring stations for which these flask measurements are available (4 stations). This clearly leads to very strong constraints of the calculated bias correction, since two simultaneous data sets are used for these stations.
In experiment S4 we examine the robustness of the derived bias correction, when omitting the parallel flask measurements at these 4 sites. The results show derived bias corrections very close (within 0.1 ppb) to those of our reference inversion S1 (Table 2). Apparently the different stations are linked to each other via atmospheric transport, allowing rather consistent estimates of the bias correction, even if no parallel flask measurements are available at these stations.  6. A posteriori emissions for S5 (top panel) and difference to reference inversion S1 (mid panel of Fig. 3).
This gives some confidence that also the derived bias correction at other stations (where a direct experimental comparison is not available) can be considered reliable. Furthermore, S4 provides a posteriori emissions very similar to the reference inversion S1, with only minor local differences (see Fig. S6 in the Supplement).

Impact of a priori emission inventory (S5)
As expected, the inversion starting from homogeneous emissions (S5) shows larger differences compared to the reference inversion S1 (Fig. 6). The smoother pattern is explained by the fact that the a priori emission pattern is flat and the corrections can not entirely reproduce the smaller-scale patterns guided by more realistic a priori information. Setting a larger background error for emissions and a smaller correlation length compared to the reference inversion plays an important role to give the system enough degrees of freedom to retrieve regional scale emission patterns as well as possible. Overall this "free inversion" can derive emission patterns of larger regions similar to those of the other simulations within the area that is sufficiently constrained by the observational network. However the emission hotspots (attributed to industrial N 2 O emissions) are not retrieved. Despite the latter shortcoming, the derived country totals are very close to the reference inversion (Fig. 5). Furthermore, the bias correction calculated in S5 is close to that obtained by the other simulations for most stations. One exception is Cabauw, for which the bias correction is significantly higher compared to all other simulations (0.6 ppb instead of 0.2 ppb). This difference is probably due to its location in the Netherlands, for which somewhat smaller emissions are derived in S5 compared to the reference inversion. This is likely due to the very high emission peak in this region that requires a very large increment when starting from the homogeneous emissions. While S5 probably slightly underestimates the Benelux emission, the system may "use" the bias correction scheme to partly compensate for this systematic error and to improve in this way the agreement with observations.

Conclusions
We have presented a further development of the TM5 4DVAR inverse modeling system for atmospheric N 2 O. The main objective of the present study is the application of this system on the European domain, utilizing a new comprehensive data set of continuous measurements from various European monitoring stations. An important prerequisite for assimilating the data from this heterogeneous network, however, is the correction of potential measurement biases, which are directly evident from comparison with parallel NOAA measurements, available at 4 of the European stations. We demonstrated that our new bias correction scheme is capable of reproducing this experimentally derived bias within 0.1 ppb. Furthermore, we showed that virtually identical bias corrections (and emissions) are retrieved, when omitting the parallel flask measurements at these 4 sites. This demonstrates that the monitoring stations are strongly linked via atmospheric transport, especially during synoptic situations with higher wind speeds (when emissions have a smaller impact on the mixing ratios, and the mixing ratios are close to the baselines of the stations). During the inversion period (14 months) many different synoptic situations are encountered (e.g. situations where air masses are transported from station A to B, but also from B to A). This apparently allows the inversion system to differentiate between differences of mixing ratios (station B-station A) arising from emissions between the stations (which depend on the wind direction) and differences arising from the calibration offset (which are independent of the wind direction / synoptic situation). The use of bias correction implies that the inversion system cannot derive any information from the spatial gradient between the stations (for those stations which have independent bias corrections). Instead, the system utilizes the information within the footprint of each station independently, while the bias correction allows to make the measurements consistent with each other. However, the global NOAA flask sampling network is essential for the realistic simulations of the global emissions, and as reference which can be assumed to be un-biased. We emphasize that the very encouraging bias corrections do not replace systematic comparisons of standards and measurements, which are crucial to improve the consistency of the measurements from different sites and independent laboratories. In this study we made the simple assumption that the measurement bias is constant in time and can be described by a constant offset. While this approach seems to be able to correct for a significant part of the measurement biases, the systematic errors may have in reality a more complex structure. Eg., the measurement bias may have additional components varying in time, which are difficult to be quantified by the inverse modelling system in the absence of additional information about the underlying processes leading to the biases. In addition, the biases may also depend on the N 2 O mixing ratios (given the non-linear response function of the currently used ECD detectors). Hence, further improvement of the measurements is indispensable to improve the top-down emission estimates in the future.
Total anthropogenic emissions derived by the TM5-4DVAR system for the northwest European and several east European countries agree well with bottom-up inventories reported to UNFCCC, with much smaller differences than the very large uncertainties of the UNFCCC estimates. Furthermore, the estimated model uncertainties (of the order of 40%) are much smaller than the uncertainties of the UN-FCCC estimates, currently estimated to be larger than 100% for most European countries. This illustrates that atmospheric observations combined with inverse modeling can significantly decrease the uncertainties of N 2 O emissions.
Finally, we demonstrated that our "free inversion" (sensitivity experiment S5 starting from homogenous emissions), yields larger scale regional emission patterns very similar to the reference inversion (guided by detailed a priori emission inventories) within the area constrained by the network. An exception, however, is the pronounced emission peaks related to industrial N 2 O emissions (adipic acid production), which are typically smeared out over much larger regions in inversion S5. The country totals derived in S5, however, are generally very close to the reference inversion, illustrating the potential of completely independent top down verification of bottom up emission inventories, avoiding the use of detailed a priori information. This is considered very important especially for N 2 O, for which bottom-up inventories have still considerable uncertainties, hence bearing the risk that using these inventories may guide the inversion in a wrong direction in some cases.
Further improved top-down emission estimates are expected from the ongoing detailed model intercomparison performed within the NitroEurope project, involving 5 independent inverse models. In addition, this intercomparison will provide more realistic estimates of overall uncertainties of top-down emission estimates.