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Impact of the atmospheric sink and vertical mixing on nitrous oxide fluxes estimated using inversion methods

2011; American Geophysical Union; Volume: 116; Issue: D17 Linguagem: Inglês

10.1029/2011jd015815

2156-2202

Rona L. Thompson, Philippe Bousquet, Frédéric Chevallier, P. J. Rayner, P. Ciais,

Atmospheric Ozone and Climate

Journal of Geophysical Research: AtmospheresVolume 116, Issue D17 Composition and ChemistryFree Access Impact of the atmospheric sink and vertical mixing on nitrous oxide fluxes estimated using inversion methods R. L. Thompson, R. L. Thompson rona.thompson@lsce.ipsl.fr Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this authorP. Bousquet, P. Bousquet Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this authorF. Chevallier, F. Chevallier Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this authorP. J. Rayner, P. J. Rayner Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, France Now at School of Earth Sciences, University of Melbourne, Melbourne, Victoria, Australia.Search for more papers by this authorP. Ciais, P. Ciais Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this author R. L. Thompson, R. L. Thompson rona.thompson@lsce.ipsl.fr Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this authorP. Bousquet, P. Bousquet Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this authorF. Chevallier, F. Chevallier Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this authorP. J. Rayner, P. J. Rayner Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, France Now at School of Earth Sciences, University of Melbourne, Melbourne, Victoria, Australia.Search for more papers by this authorP. Ciais, P. Ciais Laboratoire des Sciences du Climat et l'Environnement, Gif sur Yvette, FranceSearch for more papers by this author First published: 14 September 2011 https://doi.org/10.1029/2011JD015815Citations: 12AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract [1] This study investigates some of the principal errors arising in atmospheric inversion estimates of N2O surface fluxes. Using a synthetic data set of model-generated atmospheric N2O mixing ratio data, representative of the current observation network, we investigate the influence of errors in the stratospheric N2O sink and in vertical transport. Our inversion framework uses a variational formulation of the Bayesian problem, and atmospheric transport is modeled using the global circulation model LMDz. When only optimizing the surface fluxes (with a prescribed sink), bias errors in the sink magnitude translate into substantial bias errors in the retrieved global total surface fluxes. Conversely, we find that errors only in the temporal and horizontal distribution of the N2O sink (nonbiased magnitude) have a very small impact on tropospheric mixing ratios and thus on the retrieved surface fluxes. Bias errors in the modeled vertical transport, however, lead to notable changes in tropospheric N2O and, in particular, in the phase of the seasonal cycle. This also leads to bias errors in the spatial distribution of the derived surface fluxes, although not in the global total. Last, the simultaneous optimization of the surface fluxes and the sink magnitude was tested as a means to avoid biasing the fluxes by incorrect prior assumptions about the N2O lifetime. With this approach, a significant reduction in the error of the sink magnitude was achieved and biases in the surface fluxes were largely avoided, and this result was further enhanced when aircraft data were included in the inversion. Key Points Inversion estimates of N2O fluxes are sensitive to bias errors in the sink Simultaneous optimization of N2O surface fluxes and sink is possible Model vertical transport errors lead to errors in flux spatial distribution 1. Introduction [2] Nitrous oxide (N2O) is a trace gas of significant interest to atmospheric sciences. Atmospheric levels of N2O have been increasing steadily over the past few decades at a rate of approximately 0.3% per year [Forster et al., 2007]. This trend is of major concern as N2O is both a Greenhouse Gas (GHG) and the primary source of stratospheric NO and NO2, which catalytically destroy ozone [Crutzen, 1970; Johnston, 1971]. Currently N2O contributes an additional global radiative forcing of 0.16 Wm−2, making it the fourth most important anthropogenic GHG after CO2, CH4 and CFC-12 [Forster et al., 2007]. Since N2O levels are very likely to continue increasing over the foreseeable future (in response to continued fertilizer production and use), while concentrations of CFC-12 are slowly declining, N2O will soon overtake CFC-12 in its contribution to global warming. Recently the importance of N2O as an ozone depleting substance (ODS) has also been recognized; emissions of N2O are now thought to be the primary ODS emissions and of greater importance than those of CFCs [Ravishankara et al., 2009], which have strongly declined as a result of the implementation of the Montreal Protocol on Substances that Deplete the Ozone Layer. [3] The growth in atmospheric N2O is predominantly due to the enhancement of N2O emissions by human activities. Most notably, the intensification and proliferation of agriculture since the mid-19th century, which has been accompanied by the increased input of reactive nitrogen to soils, has resulted in significant perturbations to the natural N cycle and emissions of N2O [Galloway et al., 2008, and references therein]. Perturbations have also occurred in the marine N cycle due to the eutrophication of coastal waters [Naqvi et al., 2000; Nevison et al., 2004; Seitzinger et al., 2000]. Emissions from other anthropogenic sources, such as industry (e.g., adipic and nitric acid production), municipal waste, and fossil fuel combustion, have also contributed to the observed trend in N2O [Olivier et al., 1998]. In total, human activities are thought to have increased the annual global N2O emission by 40 to 50% over pre-industrial levels [Denman et al., 2007]. Top-down studies estimate the contemporary emissions to be in the range of 16 to 17 TgN-N2O/yr [Corazza et al., 2010; Hirsch et al., 2006; Huang et al., 2008] while recent bottom-up estimates fall between 14 and 20.6 TgN-N2O/yr [Bouwman et al., 2002; Denman et al., 2007] including nonbiogenic emissions. The accumulation of N2O in the atmosphere is attenuated by its removal from the atmosphere via photolysis and reaction with O1D, which occur mostly in the stratosphere. The atmospheric lifetime of N2O is thought, however, to have remained stable over the past century, as would be expected from a first-order-kinetics removal process, with a mean value of 122 ± 24 years [Volk et al., 1997]. [4] Considering the importance of N2O as a GHG and its role in ozone depletion, it is imperative to monitor, and if possible, eventually curb its emissions. Emission estimates can be ascertained globally and regionally by inversion of atmospheric N2O mixing ratios with the aid of an atmospheric transport model. This 'inversion' approach has been previously employed in a number of global [Corazza et al., 2010; Hirsch et al., 2006; Huang et al., 2008; Prinn et al., 1990] and regional [Manning et al., 2003; Ryall et al., 2001; Thompson et al., 2010] studies. The global studies differ significantly in the choice of statistical error model, atmospheric transport, as well as in their temporal and spatial resolution; however, there are some important sources of uncertainty common to all of them. First, all global inversions require an estimate of the atmospheric sink of N2O in order to optimize the surface fluxes. Hitherto, this estimate has been prescribed in the setup and not optimized in the inversion (one exception to this is the early study of Prinn et al. [1990] in which the sink was optimized in conjunction with the surface fluxes using a simple global 9-box model of the atmosphere). Due to this dependency, one needs to have a handle on the sink magnitude in order to compare bottom-up with top-down estimates. The sink magnitude, derived from the total N2O atmospheric abundance and its estimated lifetime, is approximately 12.5 TgN-N2O/yr [Denman et al., 2007] and carries an uncertainty of ±2.5 TgN-N2O/yr (based on the given uncertainty of the atmospheric lifetime [Volk et al., 1997]), which is equivalent to ±15% of the estimated global annual emission. The contribution of this uncertainty to surface flux estimates is illustrated in a sensitivity test performed by Hirsch et al. [2006], which estimated global total fluxes of 20.4 and 15.2 TgN-N2O/yr for lifetimes of 98 and 146 years, respectively. Second, the uncertainty in vertical mass fluxes, calculated by the atmospheric transport model, also contributes to uncertainties in emission estimates, as has previously been pointed out for the case of CO2 [Stephens et al., 2007]. The vertical mass flux modulates the vertical gradient in N2O, the abruptness of the transition of mixing ratio across the tropopause, and the mixing ratio of N2O in the stratosphere. The impact of these uncertainties on the derived N2O emissions needs to be quantified. Regional inversion estimates, which do not directly account for N2O losses but take boundary mixing ratios from observations or models, are not sensitive to the sink uncertainty, so long as the mixing ratios from the vertical and upper horizontal boundaries match the observed N2O growth rate. [5] The goal of this study is to address the impacts of uncertainties in the N2O sink and vertical mass fluxes in a global 4D atmospheric inversion framework by first providing estimates of the impact that these uncertainties have on the retrieved emissions and second, and principally, by including the magnitude of the N2O sink in the inversion as a parameter to be optimized. The methodology for the simultaneous optimization of surface fluxes and the atmospheric sink is presented and its efficacy is tested using a global synthetic data set comprised of surface fluxes and atmospheric mixing ratios. In these tests, the utility of aircraft measurements for constraining both the surface fluxes and the sink is also assessed. For this study, we use a Bayesian inversion framework with a variational formulation, which is able to handle large numbers of variables, allowing higher temporal and spatial resolutions and thereby reducing aggregation errors in the optimized surface fluxes [Kaminski et al., 2001]. This framework has already been used in a number of global inversions for CO2 [Chevallier et al., 2005], CH4 [Pison et al., 2009], CO [Fortems-Cheiney et al., 2009], and H2 [Yver et al., 2010] and has been adapted for N2O inversion for this study. 2. Method 2.1. Inversion Framework [6] Bayesian inversions are increasingly used to optimize surface fluxes using the constraint of atmospheric observations. In this study, the Bayesian inversion is achieved using the variational framework of Chevallier et al. [2005]. This framework finds the optimal fluxes xa that fit both the observed mixing ratios y and the prior fluxes xb with their respective uncertainties. This can be written as the cost function: where the flux uncertainties are described by the error covariance matrix B, the observation uncertainties are described by the error covariance matrix R, and is an operator for atmospheric transport and chemistry. In the variational approach, the minimum of J(x) is found iteratively, in this case, using a descent algorithm based on the Lanczos version of conjugate gradient algorithm [Lanczos, 1950]. This algorithm requires several computations of the gradient of J with respect to x (where H is the linearized form of ): For very large problems (in terms of the number of variables), however, it is neither possible to directly define H nor HT owing to numerical limitations. Therefore, the elements of HT are found implicitly via the adjoint model of the atmospheric transport and chemistry [Chevallier et al., 2005; Errico, 1997]. [7] In the case of N2O, the sink in the stratosphere needs to be accounted for. Losses of N2O occur via photolysis (reaction (R1)) and reaction with O1D (reactions (R2) and (R3)), accounting for 90% and 10% of the sink, respectively [Minschwaner et al., 1993]. These reactions are included in the forward and adjoint models of the atmospheric transport: Since only the loss of N2O (and not the products of the reactions) is of interest here, these 3 equations can be combined into a single statement to update the mixing ratio c of N2O for photolysis and chemistry in every grid cell of the forward model over the model time step t: where si = (k1 + k2)[O1D]i + σi is the total sink term, σ is the reaction cross section for photolysis (or equivalently the actinic flux), and λ is a scalar for the magnitude of the total sink. The number density of O1D and the reaction cross-section σ are defined for each grid cell and time step and are taken from prior simulations of the global circulation and atmospheric chemistry model LMDZ-INCA [Hauglustaine et al., 2004] with the same transport fields as used in the inversion. The tangent linear and adjoint statements for the N2O mixing ratio c and for the sink scalar λ are derived from the following equation: In this adaptation of the variational scheme, λ is included as a variable for optimization in the state vector x and has a prior value assigned in xb. One scalar λ is used to scale the sink term s for the vertical column in each of the latitudinal bands: 90°N–30°N, 30°N–0°, 0°–30°S, and 30°S–90°S, thus in total there are 4 sink scalars included in the state vector at each resolved time step. We refrained from using a higher resolution for the sink scalar optimization since very little is known about the spatial distribution of the errors of λ and how independent they would be. [8] The flux and sink scalar variables in x are resolved in 4-weekly intervals. The choice of temporal resolution for the fluxes is a compromise between the time coverage of the available observations to constrain the fluxes, the number of state variables (which strongly determines the computational memory load) and the risk of temporal aggregation errors. Here the temporal resolution is consistent with that currently being used for global N2O inversions [e.g., Corazza et al., 2010]. Furthermore, the decision to temporally resolve the sink scalars (in this case at the same temporal resolution as the fluxes) was made to reduce the accumulation of rounding errors for each of the λ variables in the optimization algorithm, which would otherwise be considerable as each λ applies to all grid cells, horizontally and vertically, in its respective latitudinal band (i.e., for this model framework, in the order of 3 × 104 grid cells). Conversely, the spatial resolution of the fluxes was chosen to be at the highest possible horizontal resolution, that is, that of the transport model grid (3.75° × 2.5° longitude-latitude grid), in order to give the inversion scheme sufficient freedom to adjust small-scale flux patterns. 2.2. Atmospheric Transport Model [9] The described inversion framework relies on an off-line version of the LMDz general circulation model [Hourdin and Armengaud, 1999; Hourdin et al., 2006]. This version computes the evolution of atmospheric compounds, in this case N2O, using archived fields of winds, convection mass fluxes, and planetary boundary layer (PBL) exchange coefficients that have been built from prior integrations of the complete general circulation model, which was nudged to ECMWF winds [Uppala et al., 2005]. The LMDz model is on a 3D Eulerian grid consisting of 96 zonal columns and 73 meridional rows and 19 hybrid pressure levels in the vertical. The daytime PBL is resolved by 4–5 levels, the first of which corresponds to 70 m, and are spaced between 300 to 500 m apart from there upwards. Above the PBL the mean resolution is 2 km up to a height of 20 km, above which there are 4 levels with the uppermost level at 3 hPa. Tracer transport is calculated in LMDz using a second-order finite-volume method of Van Leer [1977] and is described for LMDz by Hourdin and Armengaud [1999]. Turbulent mixing in the PBL is parameterized using the scheme of Mellor and Yamada [1982] and thermal convection is parameterized according to the scheme of Tiedtke [1989]. LMDz was run with a physical time step of 30 min. [10] For the calculation of the J and its gradient ∇J (equations (1) and (2)), the tangent linear H and adjoint HT operators were coded from the off-line LMDz version [Chevallier et al., 2005]. 2.3. Synthetic Data [11] Although the tests presented are performed using synthetic data, the data and their errors were chosen to best represent the magnitude and distribution of N2O fluxes according to the current state of knowledge, and are commensurate with those used in the NitroEurope project [Corazza et al., 2010]. Fields of monthly N2O fluxes were compiled from anthropogenic (EDGAR-4.0), terrestrial biosphere (L. Bouwman, personal communication, 2008), and ocean [Bouwman et al., 1995] fluxes. Anthropogenic emissions included those from agriculture, livestock, biomass burning, deforestation, agricultural waste burning, industry, and fossil and biofuel combustion. The fluxes were provided at 1° × 1° resolution and were interpolated to match the horizontal grid of the transport model. In total, the estimate of the global annual emission is 13.8 TgN-N2O/yr, which is significantly lower than recent estimates of between 16 and 20 TgN-N2O/yr [Corazza et al., 2010; Denman et al., 2007; Hirsch et al., 2006; Huang et al., 2008], therefore, the emissions were scaled up uniformly to give a global annual emission of 19 TgN-N2O/yr, which resulted in an atmospheric growth rate close to that of the observed growth rate. These resulting fields are hereinafter referred to as the true fluxes as they were used in the generation of the synthetic observations (as described below). [12] Since knowledge of the uncertainty of N2O flux estimates is still limited, we calculated the uncertainty for each surface grid cell as 100% of the maximum flux for the year found in the 8 surrounding grid cells plus the cell of interest. This was done to allow more freedom in the inversion to correct the small-scale spatial pattern of the fluxes. (In some tests 50% of the maximum flux was used, as indicated in section 2.4). Correlations of surface flux errors were also incorporated into the definition of B and were calculated as an exponential decay with distance and time using correlation scale lengths of 500 km over land and 1000 km over ocean, and 8 weeks, respectively. The correlation scale length of the errors in land fluxes depends strongly on the source; here we chose 500 km as an educated guess to represent the correlation of the errors in the spatially diffuse soil emission, which is the dominant source and is modulated by land use, soil type, moisture and temperature, as well as by the amount of nitrogen input. For the inversions that include the optimization of the sink magnitude, B also contains error estimates for λ (of 50%, which equates to between 2.5 and 4 TgN-N2O/yr). These were assumed to have no spatial correlation but a temporal correlation of 12 months. [13] Pseudo-observations were generated for use in the inversion tests (i.e., S1 to Sref and O1 to O3) and were consistent with a lifetime of 122 years [Volk et al., 1997]. The pseudo-observations were produced for the years 2005 to 2008 by coupling the true fluxes (established above) to the forward LMDz model using the archived fields of winds, convection mass fluxes, and PBL exchange coefficients. The desired sink strength (and consequently the lifetime) was achieved by changing the value of λ, which scales the sink rate (one value of λ was used throughout the entire atmosphere and period of the simulation). The new λ for a lifetime τ is found from a reference lifetime τ0, its corresponding λ0, the atmospheric N2O abundance A and the initial concentration ci, according to equation (5) (derived from equation (3)) and was tested in forward model simulations. For these LMDz simulations, starting mixing ratios were taken from a previous run of LMDz (of 8 years) that had reached quasi-steady state. In the generation of the mixing ratios, atmospheric loss of N2O was calculated according to equation (3) using precalculated fields of σ and O1D. Pseudo-observations were extracted from the 4-D fields of mixing ratios to best represent the actual current sampling network available (see Figure 1). We used the time stamps and locations of all the observations made available for use in the NitroEurope project [Corazza et al., 2010] to extract the pseudo-observations from the synthetic data (see Table 1). For the continuous measurement sites at low elevation, only afternoon data were selected, while for mountain sites, only nighttime data were selected. In both cases, the selected data were assimilated hourly. In the real data, there are fewer surface observations in 2008; specifically only 2 of the European in situ sites had data in this year. Therefore, there are also fewer pseudo-observations for this year relative to 2006 and 2007. Additionally, we created pseudo aircraft observations using the flight tracks of the START and HIPPO campaigns (S. Wofsy, personal communication, 2010), as well as the CARIBIC passenger aircraft long range regular transects [Brenninkmeijer et al., 2007] and NOAA (C. Sweeney, personal communication, 2010) routine flights, which were not included in the NitroEurope data set. The CARIBIC, START and HIPPO flight data include sampling locations up to 14 km, while the NOAA flight data extend up to 7 km. Of these data, approximately 35% were stratospheric samples while the remaining 65% were tropospheric samples. The pseudo aircraft data were subsampled so that only one data point was assimilated in the inversion per grid cell and time step of the model and where more than one observation was available, the mean was used. This was done in order to avoid assimilating highly correlated data, since correlations between observational errors were not accounted for (see below). Figure 1Open in figure viewerPowerPoint Map showing all sites where pseudo-observations were generated. In situ sites are in blue, flask-sampling sites are in red, and locations of regular aircraft measurements are in green. Flight paths for aircraft campaign measurements are shown by the black dashed lines. Table 1. Station Locations Where Pseudo-observations Were Generatedaa Not including flight campaigns, i.e., CARIBIC and Harvard University flights. Station Coordinates ALT, Alert, Canada 82.5°N, 62.5°W, 200 m KZM, Kazakhstan 43.3°N, 77.9°E, 2519 m ASC, Ascension Isl. 7.9°S, 14.4°W, 54 m MHD, Mace Head, Ireland 53.3°N, 9.9°W, 25 m ASK, Assekrem, Algeria 23.2°N, 5.4°E, 2728 m MID, Midway, USA 28.2°N, 177.4°W, 4 m AZR, Terceira Isl., Azores 38.8°N, 27.4°W, 40 m MLO, Mauna Loa, Hawaii 19.5°N, 155.6°W, 3397 m BAL, Baltic Sea, Poland 55.4°N, 17.2°E, 3 m NWR, Niwot Ridge, USA 40.1°N, 105.6°W, 3523 m BIK, Bialystok, Poland 52.3°N, 22.8°E, 460 m OXK, Ochsenkopf, Germany 50.1°N, 11.8°E, 1185 m BME, Bermuda 32.4°N, 64.7°W, 30 m PAL, Pallas, Finland 67.97°N, 24.1°E, 560 m BMW, Bermuda 32.3°N, 64.9°W, 30 m PFA, Poker Flat, Alaska, Flights 65.1°N, 147.3°W BRW, Barrow, Alaska 71.3°N, 156.6°W, 11 m PSA, Palmer Station, Antarctica 64.9°S, 64.0°W, 10 m BSC, Black Sea, Romania 44.2°N 28.7°E, 3 m RPB, Ragged Point, Barbados 13.2°N, 59.4°W, 45 m CBW, Cabauw, Netherlands 52.0°N, 4.9°E, 198 m RTA, Raratonga Flights 21.3°S, 159.8°W CBA, Cold Bay, Alaska 55.2°N, 162.7°W, 21 m SEY, Mahe Isl., Seychelles 4.7°S, 55.2°E, 3 m CHR, Christmas Isl. 1.7°N, 157.2°W, 3 m SHM, Shemya Isl., Alaska 52.7°N, 174.1°E, 40 m CRZ, Crozet Isl. 46.5°S, 51.9°E, 120 m SIL, Schauinsland, Germany 47.9°N, 7.9°E, 1205 m EIC, Easter Isl. 27.2°S, 109.5°E, 50 m SMO, Samoa 14.3°S, 170.6°W, 42 m GMI, Mariana Isl. 13.4°N, 144.8°E, 1 m SPO, South Pole 89.98°S, 24.8°W, 2810 m HAA, Hawaii, Flights 21.2°N, 159.0°W STM, Norway 66.0°N, 2.0°E, 0 m HBA, Halley Station 75.6°S, 26.5°W, 30 m SUM, Summit, Greenland 72.6°N, 38.5°W, 3238 m HPB, Hohenpreißenberg Germany 47.8°N, 11.01°E, 985 m SYO, Antarctica 69.0°S, 39.6°E, 11 m HUN, Hegyhatsal, Hungary 47.0°N, 16.7°E, 248 m TDF, Tierra del Fuego, Argentina 54.87°S, 68.5°W, 20 m ICE, Iceland 63.4°N, 20.3°W, 118 m TT1, Angus, Scotland 56.6°N, 3.0°W, 535 m IZO, Tenerife, Canary Isl. 28.3°N, 16.5°W, 2360m ULB, Ulaanbaatar Mongolia, Flights 47.4°N, 106.0°E JFJ, Jungfraujoch, Switzerland 46.6°N, 8.0°E, 3580 m UUM, Ulaan Uul, Mongolia 44.5°N, 111.1°E, 914 m KUM, Kumukahi, Hawaii 19.5°N, 154.8°W, 3 m WIS, Israel 31.1°N, 34.9°E, 400 m KZD, Kazakhstan 44.1°N, 76.9°E, 601 m WLG, Mt Waliguan, China 36.3°N, 100.9°E, 3810 m LU1, Lutjewad, Netherlands 53.4°N, 6.4°E, 60 m ZEP, Svalbard, Sweden 78.9°N, 11.9°E, 475 m a Not including flight campaigns, i.e., CARIBIC and Harvard University flights. [14] Random Gaussian-distributed noise with a mean of 0 and SD of 0.2 ppb was added to the pseudo-observations to represent the errors in the measurements. These measurement errors were accounted for in the error covariance matrix R, which was defined as diagonal (there are no correlated errors in the observations). We chose to use an error of 0.2 ppb, instead of a larger error that would arguably be closer to the real value of the representation and measurement errors, so that the impact of bias errors in the transport and chemistry (photolysis and reaction with O1D) model could be highlighted. The inversion tests (see section 2.4) isolate the impacts of these errors on the retrieved surface fluxes. [15] Additionally, we used the forward LMDz model to perform a number of sensitivity tests for the impact of the sink strength and sink temporal and spatial distribution, as well as for vertical transport errors. The pseudo-observations, generated in these forward model runs, and the results from these tests are discussed in the supplementary material. Note that the pseudo data set P1, in the supplementary material, was also used as the observations in the following inversion tests. 2.4. Inversion Tests [16] All inversion tests were performed for the years 2006 to 2008 and a summary of the tests is given in Table 2. Table 2. Summary of Inversion Tests Testaa S, static sink (i.e., the sink was not optimized in the inversion); O, optimized sink (i.e., both surface fluxes and sink are optimized). Optimize Sink Number of Iterations τprior Prior Surface Fluxes Prior Flux Uncertainty Flight Data O1D and σ Fields Vertical Mass Fluxes S1 no 20 122 equal to true 100% no flat realistic S2 no 20 122 equal to true 100% no realistic recycled Sref no 30 98 Perturbed 50% no realistic realistic O1 yes 30 122 Perturbed 50% no realistic realistic O2 yes 30 98 Perturbed 50% no realistic realistic O3 yes 30 98 Perturbed 50% yes realistic realistic a S, static sink (i.e., the sink was not optimized in the inversion); O, optimized sink (i.e., both surface fluxes and sink are optimized). [17] Two inversion tests were designed to examine the impacts that incorrect assumptions in the spatial and temporal sink distribution and the vertical mass fluxes have on the retrieved N2O surface fluxes (tests S1 and S2, respectively). In these two tests, the sink term is not optimized in the inversion, i.e., the sink scalar is static and the magnitude of the sink was equal to that used in the generation of the pseudo-observations (i.e., τ = 122 years). For both tests, the prior surface fluxes were equal to those of the true fluxes but with a prior uncertainty of 100%, to allow freedom in the inversion to adjust the surface fluxes according to the model–pseudo-observation mismatch induced by errors in either the atmospheric sink or the transport model. [18] In test S1, errors were created in the temporal and spatial distribution of the atmospheric sink by replacing the true fields of actinic flux σ and O1D (used in the tangent linear and adjoint calculations) with fields that had no temporal or horizontal variation. In this study, we decided not to test the impact of changing the vertical distribution of the stratospheric sink, even though this would have a strong impact on the magnitude of N2O lost, as its impact is strongly dependent on the vertical resolution of the transport model used. In test S2, the vertical mass fluxes were perturbed by recycling the convective and advective mass fluxes from March 2006 for other every month, while the realistic fields of σ and O1D were used. [19] A reference inversion, Sref, which also has a static sink (i.e., not optimized) was included to determine the impact of an incorrect assumption about the sink magnitude on the surface fluxes and forms a basis against which the follo