Description of the N2O inversion production chain

Last modified on Jan 08, 2025 14:53

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1. Introduction

The CAMS N₂O fluxes are estimated using the atmospheric inversion framework, PyVAR-N₂O. Atmospheric inversions use observations of atmospheric mixing ratios, in this case, of N₂O, and provide the fluxes that best explain the observations while at the same time being guided by a prior estimate of the fluxes. In other words, the fluxes are optimized to fit the observations within the limits of the prior and observation uncertainties. To produce the optimized (a posteriori) fluxes a number of steps are involved: first, the observations are pre-processed (described in section 2), second, a prior flux estimate is prepared (described in section 3), third mixing ratios are simulated using the prior fluxes and are used to estimate the model representation error (described in sections 4 and 5), and fourth, the inversion is performed (described in section 6).

2. Atmospheric observations

2.1. Atmospheric measurements and locations

Figure 1: Map of the observation network 

Table 1. List of sites and campaigns. The symbol “V” means various locations. The measurement types are: FM = flask measurement (ground-based), AM = aircraft measurement, SM = ship or ocean mooring, CM = continuous measurement (ground-based).

In total 110 ground-based sites, ship transects and aircraft profiles are included in the inversion (see Table 1 and Fig. 1). The term “site” refers to locations where there is a long-term record of observations from ground-based measurements, both from discrete samples (or “flasks”) and quasi-continuous sampling by in-situ instruments. N₂O concentrations are measured using Gas Chromatographs equipped with an Electron Capture Detector (GC-ECD). Of the ground-based sites, 15 are in-situ sites with approximately hourly data and 77 are flask sampling sites with approximately one sample per week. The aircraft data are from flask samples taken from vertical profiles at 18 sites flown approximately monthly. Other data include approximately weekly flask samples from ship transects in the Drake Passage and approximately monthly flask samples from ocean moorings in the Pacific Ocean.

Up to now, satellite observations of N₂O have been neither accurate nor precise enough to be used for estimating fluxes, with bias errors of ~7 ppb (parts-per billion) and precisions of ~1% (~3 ppb) (Xiong et al. 2014), compared to the <0.3 ppb achieved by ground-based observations.

Observations of N₂O with sufficient accuracy for inverse modelling are available from the mid-1990s and the most recent year fully covered by observations is 2022, thus the period covered by this inversion is from 1996 to 2022. The data density over time is shown in Fig. 2.

Figure 2: Availability of ground-based data over time by site and laboratory (number of observations per month). Shown are the tower and flask sampling sites (top) and aircraft profile data (bottom).

2.2. Processing of observations

Owing to the small signal to noise ratio of N₂O observations, it is critical to pre-process the observations to remove outliers and to correct for calibration differences between laboratories. Outliers are determined as observations outside 2-σ standard deviations of the running mean calculated over time window of 90 days, for flask observations, 0.5 days for continuous and aircraft observations, and 60 days for ship observations. The removal of outliers is performed iteratively until no more data are removed. Using this method, in the order of 2% of all observations are classified as outliers.

Calibration differences are determined relative to the NOAA-2006A scale maintained by NOAA ESRL GMD (Hall et al. 2007). A number of other laboratories/networks have their own scale, namely AGAGE who uses the SIO-1998 scale and NIES who use the NIES-94 scale. Even different laboratories operating on the same scale have differences between measurements. For this reason, the calibration differences with respect to NOAA-2006A are determined and specified by a regression coefficient and bias. These are found by either comparing the measurements made by a given laboratory with those of NOAA at the same location, where these both exist, or for laboratories with no sites co-located with a NOAA site, by inter-comparison of gas standards by the different laboratories. A summary of the calibration differences is given in Fig. 3. Using the regression coefficient and bias for each laboratory the observations are corrected to the NOAA-2006A scale.

Figure 3: Calibration comparison to the NOAA scale (NOAA-2006A). The regression coefficient is shown for the comparison of the other laboratories scale with that of NOAA. For some laboratories/networks there is more than one site (i.e. AGAGE and CSIRO) and the comparison for each site where a comparison is possible.

Data from ground-based in-situ sites are generally assimilated into the inversion as daily afternoon averages (between 12:00 and 17:00), however, for mountain sites, a night-time average (between 00:00 and 06:00) is used to avoid times with complex circulation patterns, such as upslope winds, which cannot be reproduced with the current resolution of global atmospheric transport models. Aircraft and ship data are assimilated as the average of all observations falling in each grid-cell and time step of the transport model.

3. Prior fluxes

A prior estimate of the total N₂O flux with monthly resolution and inter-annually varying fluxes is prepared from a number of models and inventories (see Table 2). For the natural and agricultural soil fluxes an estimate from the land surface model DLEM is used, which is driven by observation-based climate data, N-fertilizer statistics and modelled N-deposition (Tian et al. 2024). DLEM is one of the models that participates in the Nitrogen Model Intercomparison, NMIP (Tian et al. 2019). For the ocean fluxes, an estimate from the ocean biogeochemistry model Bern3D is used (Battaglia and Joos, 2018), which is one of the models participating in the GCP N₂O budget. In this model, the global ocean source is 3.8 TgN y^-1 and is higher than the prior estimates used in CAMS-r20 (2.6 TgN y^-1). For biomass burning fluxes, the GFED-v4.1s data is used, which is based on fire activity data from the MODIS satellite and emission factors from Akagi et al. (2011). Lastly, for non-agricultural anthropogenic emissions (industry, waste and fuel combustion), the EDGAR inventory data are used. In this revision, r21, EDGAR-v8 estimates are used, which cover the period 1970 to 2022. EDGAR-v8 provides annual estimates per source sector, but also monthly profiles for each sector and country, which were used to give monthly estimates. All flux data are interpolated/averaged from their original resolution to that of the atmospheric transport model. In this version, r22, the new version of LMDz is used with a horizontal resolution of 2.5° × 1.26° (longitude by latitude) and 79 vertical levels. The prior flux estimates for land (ocean) are allocated specifically to the land (ocean) grid cells as defined on the LMDz model grid, after averaging. This was to account for instances along the coast where the coarser LMDz grid cells contained both land and ocean grid cells in the finer data input grid.

Table 2. Overview of prior fluxes (totals are given for the year 2010).

4. Atmospheric transport model and input

Atmospheric transport is modelled using an offline version of the Laboratoire de Meteorologie Dynamique model, LMDz6, which computes the evolution of atmospheric compounds using archived fields of winds, convection mass fluxes and planetary boundary layer (PBL) exchange coefficients that have been calculated using the online version nudged to ECMWF ERA interim winds. LMDz6 uses a Eulerian grid of 2.5° × 1.26° (longitude by latitude) and 79 hybrid pressure levels. Stratospheric losses of N₂O through reaction with O(¹D) and photolysis are calculated for each time-step and grid-cell using pre-calculated fields of O(¹D) and photolysis rate from the online LMDz6-INCA model.

Initial conditions, in this case, 3D fields of N₂O mixing ratios for the 79 level model were prepared starting from a fields for the pre-industrial time (provided by Karine Laurent) and uniformly scaling these to give a global mean mixing ratio of 308 ppbv in the lowest layer consistent with the observed global mean in 1993. A spin-up of 29 years was calculated using actual mass fluxes for 1993-2021 but with climatological emissions of 12 Tg yr^-1, which approximately equals the atmospheric sink.

5. Uncertainty estimates

5.1. Uncertainty in the observation space

Uncertainty in the observation space is calculated as the quadratic sum of the measurement and transport uncertainties. The measurement uncertainty is assumed to be 0.3 ppb (approximately 0.1%) based on the recommendations of data providers. The transport uncertainty includes estimates of uncertainties in advective transport (based on the method of Rödenbeck et al. (2003)) and from a lack of subgrid-scale variability (based on the method of Bergamaschi et al. (2010)). The calculated total model transport uncertainty varied typically between 0.1 and 1.0 ppb, depending on the synoptic situation and the location, and had a mean of 0.2 ppb. It is assumed that there are no cross-correlations between observations (i.e. the observation error covariance matrix is diagonal), which is a reasonable approximation considering that the observations are assimilated as afternoon (or night-time) means for ground-based data and at the grid-cell and time-step of the model for aircraft and ship data.

5.2. Uncertainty in the state space

For the error in each land grid cell, the maximum magnitude of the flux in the cell of interest and its 8 neighbours is used, while for ocean grid cells the magnitude of the cell of interest only is used. This is done to allow the more degrees of freedom to change the fine spatial patterns of the fluxes on land, whereas on in the ocean, this method is not used to avoid having too large uncertainties in grid cells close to coastlines. The covariance was calculated as an exponential decay with distance and time using correlation scale lengths of 500 km over land and 1000 km over ocean and 3 months. The prior error covariance matrix is scaled so that the sum of its elements was equal to a global uncertainty of 2 TgN y^-1, which is chosen to reflect an approximate uncertainty of about 12% in the total source.

6. Inversion Methodology

PyVAR-N₂O uses the Bayesian inversion method to find the optimal fluxes of N₂O given prior information about the fluxes and their uncertainty, and observations of atmospheric N₂O mole fractions. The method is the same as that used in Thompson et al. (2014) and the reader is referred to this paper for full details about the method. In summary, the optimal fluxes are those that minimize the following cost function (for derivation of the cost function see Rodgers et al. (2000)):

 where the flux uncertainties are described by the error covariance matrix B, the observation uncertainties are described by the error covariance matrix R and H is a non-linear operator for atmospheric transport and chemistry (in Eq. 1, the matrix transpose is indicated by ^T). We use the variational approach to solve Eq. 1, which is an iterative process where the gradient of J is calculated
at each iteration using a conjugate gradient algorithm (Lanczos 1950). This involves using an adjoint of the chemistry transport model (CTM) (Chevallier et al. 2005).

Posterior flux uncertainties are calculated from a Monte Carlo ensemble of inversions, based on the method of Chevallier et al. (2005). In each ensemble member, the prior fluxes were randomly perturbed to introduce errors consistent with those described by the prior error covariance matrix, B. The standard deviation of the posterior fluxes were assumed to be consistent with the probability distribution of the true fluxes.

7. Flux and concentration output

The optimized N₂O fluxes are saved as NetCDF files, where each file contains fluxes for one year at monthly temporal, and 2.5° × 1.26° (longitude by latitude) spatial, resolution. In addition, 3D N₂O concentration fields, generated using the optimized fluxes, are saved. These are also NetCDF files with one file per month containing the N₂O concentration every 3 hours for the 79 vertical layers and 2.5° × 1.26° (longitude by latitude) horizontal resolution.

8. References

Akagi, S. K., Yokelson, R. J., Wiedinmyer, C., Alvarado, M. J., Reid, J. S., Karl, T., Crounse, J. D. and Wennberg, P. O.: Emission factors for open and domestic biomass burning for use in atmospheric models, Atmos. Chem. Phys., 11(9), 4039-4072, doi:10.5194/acp-11-4039-2011, 2011.

Bergamaschi, P., Krol, M., Meirink, J. F., Dentener, F., Segers, A., van Aardenne, J., Monni, S., Vermeulen, A. T., Schmidt, M., Ramonet, M., Yver, C., Meinhardt, F., Nisbet, E. G., Fisher, R. E., O'Doherty, S. and Dlugokencky, E. J.: Inverse modeling of European CH₄ emissions 2001-2006, J. Geophys. Res, 115(D22), D22309, doi:10.1029/2010jd014180, 2010.

Buitenhuis, E. T., Suntharalingam, P., & Le Quéré, C.: Constraints on global oceanic emissions of N₂O from observations and models. Biogeosciences, 15(7), 2161–2175, doi:10.5194/bg-15-2161-2018, 2018

Chevallier, F., Fisher, M., Peylin, P., Serrar, S., Bousquet, P., Bréon, F. M., Chédin, A. and Ciais, P.: Inferring CO₂ sources and sinks from satellite observations: Method and application to TOVS data, J. Geophys. Res., 110(D24309), doi:10.1029/2005jd006390, 2005.

Dutreuil, S., Bopp, L. and Tagliabue, A.: Impact of enhanced vertical mixing on marine biogeochemistry: lessons for geo-engineering and natural variability, Biogeosciences, 6(5), 901-912, doi:10.5194/bg-6-901-2009, 2009.

Hall, B. D., Sutton, G. S. and Elkins, J. W.: The NOAA nitrous oxide standard scale for atmospheric observations, J. Geophys. Res., 112(D09305), doi:10.1029/2006JD007954, 2007.

Machida, T., Matsueda, H., Sawa, Y., Nakagawa, Y., Hirotani, K., Kondo, N., Goto, K., Nakazawa, T., Ishikawa, K. and Ogawa, T.: Worldwide measurements of Atmospheric CO₂ and Other Trace Gas Species Using Commercial Airlines, J. Atmos. Ocean. Tech, 25, 1744-1754, doi:10.1175/2008JTECHA1082.1, 2008.

Rödenbeck, C., Houweling, S., Gloor, M. and Heimann, M.: CO₂ flux history 1982-2001 inferred from atmospheric data using a global inversion of atmospheric transport, Atmos. Chem. Phys, 3, 1919-1964, 2003.

Thompson, R. L., Chevallier, F., Crotwell, A. M., Dutton, G., Langenfelds, R. L., Prinn, R. G., Weiss, R. F., Tohjima, Y., Nakazawa, T., Krummel, P. B., Steele, L. P., Fraser, P., Ishijima, K. and Aoki, S.: Nitrous oxide emissions 1999 - 2009 from a global atmospheric inversion, Atmos. Chem. Phys., 14, 1801-1817, doi: 10.5194/acp-14-1801-2014, 2014.

Xiong, X., Maddy, E. S., Barnet, C., Gambacorta, A., Patra, P. K., Sun, F. and Goldberg, M.: Retrieval of nitrous oxide from Atmospheric Infrared Sounder: Characterization and validation, J. Geophys. Res., 119(14), 9107-9122, doi:10.1002/2013JD021406, 2014.

Zaehle, S., Ciais, P., Friend, A. D. and Prieur, V.: Carbon benefits of anthropogenic reactive nitrogen offset by nitrous oxide emissions, Nature Geosci, 4(9), 601-605, 2011.

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