Atmospheric inversion of greenhouse gas fluxes

The ultimate goal of the inverse modelling performed in our group is a better quantification in terms of magnitude, distribution and uncertainty range of net fluxes of anthropogenic and natural greenhouse gases (GHG) to the atmosphere. We develop and adapt methods that can be applied both to the re-gional as well as to the global scale and a large suite of GHGs ranging from CO2, CH4, N2O to halocarbons. On the one hand, our results help to validate so called bottom-up estimates of anthropogenic emissions as they are reported in the frameworks of the Montreal and Kyoto protocols. On the other hand, a better quantification of the net fluxes helps improving our understanding of the emitting/absorbing processes and their representation in biogeochemistry models of the land surface. The latter is essential when the future climate system and its interactions and feedbacks with the land surface should be successfully simulated.
Elements of inverse modelling.
The first element of every inverse modelling is observations of atmospheric constituents. These can either come from surface networks of stations, mobile platforms (aircraft) or even satellites. The second element is a numeric model of atmospheric transport and chemistry of these constituents. However, this model is not only used to simulate the concentration of a certain species at the location of the observations, but it needs to be able to estimate the sensitivity of these concentrations towards the surface flux of the species (flux sensitivities). Thereby the surface flux can be represented as individual grid cells, split into sub-categories and also sub-regions. The parameters, here surface fluxes, to be optimised are commonly referred to as state vector. The inversion algorithm is then used to optimally adjust the state vector to find a better match between observed and simulated concentrations. In most cases this process is guided by the use of a set of previously known surface fluxes (a priori). As a result of the inversion algorithm one obtains an updated set of surface fluxes (a posteriori) and their uncertainties.
Regional scale
Average per capita halocarbon emissions per region in 2009 weighted by their GWPs. Numbers below the bars indicate total aggregated emissions in kilograms of CO2 equivalents per capita and year.

On the regional scale we use backward simulations of the Lagrangian Particle Dispersion Model FLEXPART to obtain flux sensitivities for limited areas. These describe the sensitivity towards surface fluxes within the given domain, whereas surface fluxes outside the domain are not explicitly treated but are taken as part of the baseline concentration entering the domain.
We implemented two regional scale inversion systems: a Bayesian inversion and an extended Kalman Filter inversion. In the Bayesian approach a cost function is optimised that contains a term penalising the misfit between model and observations and a term penalising deviations from the a priori state. The weighting between these two terms is controlled by two uncertainty covariance matrices that give the combined uncertainty of the model and the observation and an estimate of the a priori uncertainty. Using covariance matrices allows including spatiotemporal correlations in the involved uncertainties, which can further guide the inversion algorithm to find a realistic solution to the posed problem. In the Bayesian approach observations form different times and locations are used in the same optimisation step to obtain the a posteriori fluxes. In addition, to the surface fluxes other parameters, like the baseline concentrations at different times, can be part of the optimisation problem. A typical application of the Bayesian inversion technique is to the estimation of European scale halocarbon emissions by using the observations from the AGAGE stations Jungfraujoch, Mace Head and Monte Cimone (Keller et al., 2011, 2012). Similar analyses were done for north-eastern China (An et al., 2012, Vollmer et al., 2009).


Distribution of annual mean emissions (left) and their uncertainties (right) of HFC-125, HFC-152a and HCFC-141 in Europe in 2009.
As a second inversion framework we implemented an extended Kalman Filter (extKF) inversion (Brunner et al., 2012). In contrast to the Bayesian approach that uses observations from different times in one step to estimate the surface fluxes, the extKF assimilates the observations sequentially from time step to time step. In each step observations from different sites but not from different times are incorporated. This allows for a more flexible temporal evolution of the surface fluxes as in the Bayesian approach and keeps the involved matrices small, potentially allowing the treatment of very large inversion problems that might not fit into the Bayesian framework. Under certain conditions the Kalman Filter and Bayesian inversion can be shown to be mathematically equivalent. In addition, the Kalman filter approach can be used to estimate the logarithm of the surface fluxes rather than the fluxes itself, therefore enforcing positive solutions. As in the Bayesian inversion the extKF can use a priori information and describes the uncertainties of these and the model-observation uncertainty through their respective covariance matrices In addition to these, the extKF requires a covariance matrix that gives the uncertainty with which the state vector can change from one time step to the next. Previously, we applied the extKF to European halocarbon fluxes (Brunner et al.,2012).
Global scale

On the global scale we use an adapted version of FLEXPART in a forward mode to continuously simulate atmospheric concentrations (Henne et al., 2013). In this configuration the whole atmosphere is filled with model particles that follow the atmospheric flow and are allowed to interact with the surface to take up emissions. The model also includes first order OH chemistry and, hence, is suited for the description of atmospheric methane. Each model particle is allowed to carry a large number of tracers. In this way we simulate concentrations for different types of emissions, different emission regions but, most importantly, emission times. The latter information together with the fact that, thanks to the first order chemistry, simulated concentrations linearly depend on emissions, allows us to construct the required flux sensitivities from the model output. We apply a Kalman smoother technique (Bruhwiler et al., 2005) to derive a posteriori flux estimates for the different emission types as a function of time. Currently the transport model and the inversion technique are applied to derive methane surface fluxes for the period 1990 to 2012 in the project MAIOLICA-II.


  • Brunner, D., Arnold, T., Henne, S., Manning, A., Thompson, R. L., Maione, M., O'Doherty, S., and Reimann, S.: Comparison of four inverse modelling systems applied to the estimation of HFC-125, HFC-134a and SF6 emissions over Europe, Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2017-19, in review, 2017.
  • Henne, S., Brunner, D., Oney, B., Leuenberger, M., Eugster, W., Bamberger, I., Meinhardt, F., Steinbacher, M., and Emmenegger, L.: Validation of the Swiss methane emission inventory by atmospheric observations and inverse modelling, Atmos. Chem. Phys., 16, 3683-3710, doi:10.5194/acp-16-3683-2016, 2016.
  • An, X., Henne, S., Yao, B., Vollmer, M., Zhou, L., and Li, Y.: Estimating emissions of HCFC-22 and CFC-11 in China by atmospheric observations and inverse modeling, SCIENCE CHINA Chemistry, 55, 2233-2241, doi: 10.1007/s11426-012-4624-8, 2012.
  • Bruhwiler, L. M. P., Michalak, A. M., Peters, W., Baker, D. F., and Tans, P.: An improved Kalman Smoother for atmospheric inversions, Atmos. Chem. Phys., 5, 2691-2702, doi: 10.5194/acp-5-2691-2005, 2005.
  • Brunner, D., Henne, S., Keller, C. A., Reimann, S., Vollmer, M. K., O'Doherty, S., and Maione, M.: An extended Kalman-filter for regional scale inverse emission estimation, Atmos. Chem. Phys., 12, 3455-3478, doi: 10.5194/acp-12-3455-2012, 2012.
  • Henne, S., Schnadt Poberaj, C., Reimann, S., and Brunner, D.: Global-scale tropospheric Lagrangian particle models with linear chemistry, in: Lagrangian Modeling of the Atmosphere, edited by: Lin, J. C., Gerbig, C., Brunner, D., Stohl, A., Luhar, A., and Webley, P., Geophysical Monographs, AGU, Washington, DC, 235-250, 2013.
  • Keller, C. A., Hill, M., Vollmer, M. K., Henne, S., Brunner, D., Reimann, S., O'Doherty, S., Arduini, J., Maione, M., Ferenczi, Z., Haszpra, L., Manning, A. J., and Peter, T.: European Emissions of Halogenated Greenhouse Gases Inferred from Atmospheric Measurements, Environ. Sci. Technol., 46, 217-225, doi: 10.1021/es202453j, 2012.
  • Keller, C. A., Brunner, D., Henne, S., Vollmer, M. K., O'Doherty, S., and Reimann, S.: Evidence for under-reported western European emissions of the potent greenhouse gas HFC-23, Geophys. Res. Lett., 38, L15808, doi: 10.1029/2011GL047976, 2011.
  • Vollmer, M. K., Zhou, L., Greally, B. R., Henne, S., Yao, B., Reimann, S., Stordal, F., Cunnold, D. M., Zhang, X., Maione, M., Zhang, F., Huang, J., and Simmonds, P. G.: Emissions of ozone-depleting halocarbons from China, Geophys. Res. Lett., 36, L15823, doi: 10.1029/2009GL038659, 2009.



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