Inverse modelling

Two inverse models are used for estimating methane fluxes for high northern latitudes.



NILU has developed FLEXINVERT, a regional inverse model based on the Lagrangian particle dispersion model, FLEXPART, and a Bayesian optimisation method. FLEXINVERT is designed to be flexible in terms of the species to be optimised and to the scale of the problem, from hemispheric to regional scale. FLEXINVERT can be coupled to the output of a Eulerian model to provide initial conditions for the high-resolution Lagrangian model. FLEXINVERT can be used to optimise the fluxes of species that undergo atmospheric chemistry so long as this can be approximated as a linear process, and must be incorporated into the FLEXPART runs. FLEXINVERT is continuously undergoing development and a version for CO2 is planned this year. In addition, developments for a version to handle very large problems, such as using satellite observations, are planned and will involve using a Variational (or gradient) method for the optimisation.

About the code

FLEXINVERT is programmed in Fortran90 and requires the LAPACK and NetCDF4 libraries. FLEXINVERT requires pre-computed FLEXPART output. Details about FLEXPART can be found on the FLEXPART homepage.

CarbonTracker Europe-CH4

CarbonTracker Europe – Methane (CTE-CH4) is a state-of-the-art atmospheric inverse model developed at FMI for estimating global methane emissions. The model emission estimates are constrained by a global network of atmospheric concentration observations, which are assimilated in the model system. The model system is based on an ensemble Kalman filter (EnKF), and uses a the atmospheric chemistry-transport model, TM5, for modelling the transport and chemical loss of methane in the atmosphere. The modelled chemical loss atmospheric loss of methane includes those due to reaction with e.g. the OH radical, the largest sink of methane. CTE-CH4 is a flexible model and can choose emission sources to be optimized. In this project, anthropogenic (e.g. fossil fuel, agriculture and lanfill) and natural biospheric sources (e.g. wetlands and peatlands) are optimised in CTE-CH4.

Variants of the CarbonTracker model system are being used in many countries for many applications. The development work, focusing on carbon dioxide, originated at NOAA-ESRL with CarbonTracker North America and was continued at Wageningen University, Netherlands, with CarbonTracker Europe. Since then the model has been developed for other greenhouse gases and their isotopes and new regions of interest (China and Australasia). The Finnish Meteorological Institute is working on developing CarbonTracker Europe with a focus on Europe and the high northern latitudes.

About the code

The CTE-CH4 optimization scheme is coded in Python (CarbonTracker Data Assimilation Shell CTDAS; van der Laan-Luijkx et al., 2017). To run CTDAS, Python2.x version, and modules numpy and netCDF4 are required. CTDAS is coupled with TM5 atmospheric transport model, which is coded in Fortran90 and run by Python. To run TM5, the HDF4, HDF5, NetCDF4 and LAPACK libraries must be installed, and parallel computing capabilities (e.g. MPI) are highly recommended. For more details on the TM5 code, see the TM5 webpage and the SourceForge page. For CTE-CH4 specific TM5 code please contact the Finnish Meteorological Institute.


Model specific inputs


  • FLEXPART output files from a backwards mode run.
  • Global coarse resolution fields of atmospheric concentration to be used for the initial conditions.


  • Meteorological fields for TM5 atmospheric transport model, e.g. European Centre for Medium-Range Weather Forecasts ERA Interim meteorological fields (ECMWF).
  • Global fields of atmospheric concentration to be used for the inital conditions.
  • Monthly tropospheric OH concentrations* to account for atmospheric chemical loss calculated in off-line chemistry in TM5. Furthermore, stratospheric sink due to reaction with OH, Cl and O(1D) is included by applying reaction rates based on a 2D photochemical Max-Planck-Institute (MPI) model.

* For OH concentration fields and the simulated methane atmospheric loss rates, please contact TM5 development team (TM5 webpage) and/or the Finnish Meteorological Institute.

Atmospheric observations

In this project, observations of atmospheric concentrations of mainly methane and carbon dioxide were used. However, the inverse models presented here are capable of integrating some other tracers. The atmospheric observations can be obtained from following sites, e.g.

Prior emissions

A global or regional methane emissions, calculated from various inventories and process models can be used as prior emission estimates for different sources such as those from anthropogenic activities, wetlands, forest fires, microbes in termites, geological activities and ocean. Anthropogenic methane emissions contribute to more than half of the global total methane sources and natural (e.g. wetland) sources are the second largest source. Other emissions account for a minor part (< 20%) of total methane emissions. Note that the combinations of these inputs are carefully chosen in each simulation to account for important sources and avoid double counting.

The example of prior emission estimates used in this project are:

  • Wetland emissions (incl. peatlands and minral soils): from process-based ecosystem models, such as LPX-Bern (versions 1.0 and DYPTOP) and LPJG-WHyME.
  • Anthropogenic emissions (incl. fossil fuel, enteric fermentation and waste decomposition): from the Emission Database for Global Atmospheric Research inventory (EDGAR v4.2 FT2010)
  • Rice cultivation emissions: from process-based ecosystem models LPX-Bern, EDGAR
  • Wild fire and biomass burning emissions: from the Global Fire Emissions Database (GFED; GFED v3.1 GFED v3.2, GFED v4)
  • Geological (natural thermogenic) emissions: based on the estimate of Etiope et al. 2009
  • Wild animals: from Houweling et al. 1999, Ito and Inatomi (2012)
  • Termites: from Sanderson et al. 1996
  • Oceans: from Lambert et al. 1993, Tsuruta et al. 2017

** For the flux data based on publications, please contact the authors


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