Atmospheric Inverse Modelling

Measured and modelled CH₄ mole fraction in Pallas-Sammaltunturi, Finland. The mole fractions are modelled with the global Eulerian atmospheric chemistry transport model TM5. When the prior emissions are used, the mole fractions are underestimated. Optimising the CH₄ emissions using atmospheric inversion model CarbonTracker Europe - CH₄ and data assimilation, the modelled mole fractions match better with the observations.

A primary aim of atmospheric inverse modelling is to estimate greenhouse gas (GHG) budgets based on atmospheric concentration observations. The modelling is based on Bayesian statistics, also known as a top-down method, in which observational data are used to infer information about GHG fluxes.

In our group we focus on the two most important GHGs, carbon dioxide (CO₂) and methane (CH₄). We study the global total GHG budgets and regional budgets for Finland, Europe, the high northern latitudes, and other regions such as Asia. We analyze total GHG budgets as well as source-specific emissions and sinks. We are developing inverse modelling methods for high resolution emission estimates utilising high intensity satellite data and machine learning techniques for analysis, interpretation, and evaluation of the modelled fluxes.

Our results contribute to international efforts to understand GHG budgets, including the Global Carbon Project, WMO IG3IS, and WMO G3W. These activities report our national, regional, and global scale CO₂ and CH₄ budget estimates to the Intergovernmental Panel on Climate Change (IPCC) and the United Nations Framework Convention on Climate Change (UNFCCC) Global Stocktake to support GHG verification and planning of effective climate change mitigation strategies.


We have active collaborations internationally, nationally, and internally within FMI. Our international collaborators include partners from several EU and global projects and institutions with whom we collaborate on estimation of the global and regional greenhouse gas budgets as well as in technical modelling and data aspects. Nationally our collaborators provide invaluable prior information and evaluation data for our modelling work related to greenhouse gas inventories, land use and land use change, atmospheric concentrations, and ecosystem flux observations and modelling. An important collaborator, the IT Center for Science Ltd, provides supercomputing facilities.

The experts in ecosystem modelling in our FMI Carbon Cycle group provide prior emission estimates from natural sources, an important part of atmospheric inverse modelling. Another important aspect of atmospheric inverse modelling is atmospheric concentration observations. We have close contacts with the Greenhouse Gases research group who conduct in situ measurements at several Finnish sites. Additionally, we use remotely sensed retrievals of GHG concentrations from satellites such as TROPOMI, GOSAT, and OCO. The Greenhouse Gases and Satellite Methods group has considerable expertise in these satellite products, and we work in close collaboration with them, particularly focusing on Arctic methane sources.


Our research has been supported by various national and international funding resources, including Finnish foundations such as the Nessling Foundationor Science Ltd, Nordic Centers of Excellence, Academy of Finland, the European Commission, the European Space Agency and the Japan Aerospace Exploration Agency (See Projects).

Atmospheric inverse modelling frameworks

CarbonTracker Europe-CH₄

CarbonTracker Europe-CH₄ (CTE-CH₄ [1]) is developed by the Finnish Meteorological Institute for estimating global CH₄ budgets. The model belongs to the family of CarbonTracker Data Assimilation Systems (CTDAS [2]), and its optimization method is based on the ensemble Kalman filter [3]. Using CTE-CH₄, we study Finnish national CH₄ budgets [4,5], trends and seasonality of CH₄ emissions in high northern latitudes [6], and their relation to climate drivers using machine learning techniques [7]. We contribute to the Global Methane Budget for model intercomparison and analysis of trends in global CH₄ emissions over the recent decades [8] as well as estimation of European methane budgets [9]. We also study the information derived from satellite data and develop methods for assimilating high resolution and high intensity data [10].

Community Inversion Framework

Community Inversion Framework (CIF [11]) is a modular atmospheric inverse modelling system developed under the EU H2020 project VERIFY. The system is applied to estimate CO₂ and CH₄ budgets, as well as other GHG such as N₂O. The optimization methods include analytical inversion, 4-dimensional variational inversion (4DVAR), and ensemble square root filter (EnSRF). It is coupled to various transport models. In our group we use TM5 and FLEXPART (see below) with CIF. Thanks to its applicability to high resolution inversion, we study detailed spatial distributions of source specific emissions and sinks, enhancing comparison with national inventories. Additionally, it is important that we have a system to evaluate the effect of transport models in atmospheric inverse modelling as it is one of the uncertainty sources.

Atmospheric Transport Models

In atmospheric inverse modelling, atmospheric transport models are key components that link emissions and atmospheric concentrations. Prior information about surface fluxes is transported to atmosphere which enables comparison to atmospheric observations. Atmospheric transport models account for atmospheric sinks, which are especially important for CH₄. We use the models as observation operators in atmospheric inverse modelling, as well as for evaluation of the inversion results. The transport models are computationally expensive, and therefore the models are run on high performance computing (HPC) services, such as LUMI, and with parallel computing architectures. Here we present the models that are used in our practices.

TM5 / TM5-MP

TM5 [12] is a global Eulerian atmospheric chemistry transport model. TM5-MP is a new version of TM5 that supports massive parallel runs. TM5/TM5-MP is run at 1° × 1° (latitude × longitude) resolution at the highest (in Europe or globally). With TM5/TM5-MP, we evaluate various emission and sink estimates by modelling global trends and seasonality of atmospheric GHG concentrations back in time and comparing them with observations [13,14,15].

Average lower tropospheric CH₄ mole fractions for 2021 modelled by TM5-MP at 1° × 1° (latitude × longitude) × daily resolution.


FLEXible PARTicle dispersion (FLEXPART) model [16] is a Lagrangian particle dispersion model. Source–receptor relationships from FLEXPART are used for atmospheric inverse modelling on regional scale, and it can be run at a higher resolution than TM5/TM5-MP. Currently in our research we run FLEXPART at resolutions up to 0.1° × 0.1° (latitude × longitude) resolution. With FLEXPART, we examine detailed emission paths to explain change in atmospheric concentrations and the potential of new sites to reduce uncertainty in flux estimations from atmospheric inverse modelling.

Backward trajectory from a point source on top of Pallas-Sammaltunturi in Finland, modelled by FLEXPART at 0.2° × 0.2° (latitude × longitude) × hourly resolution.


  1. Tsuruta, A. et al. Global methane emission estimates for 2000–2012 from CarbonTracker Europe-CH4 v1.0. GMD 10, 1261–1289, (2017).

  2. van der Laan-Luijkx, I. T. et al. The CarbonTracker Data Assimilation Shell (CTDAS) v1.0: implementation and global carbon balance 2001–2015. Geosci. Model Dev. 10, 2785–2800, (2017).

  3. Peters, W. et al. An ensemble data assimilation system to estimate CO2 surface fluxes from atmospheric trace gas observations. J. Geophys. Res. 110, D24304, (2005).

  4. Tsuruta, A. et al. Methane budget estimates in Finland from the CarbonTracker Europe-CH4 data assimilation system. Tellus B: Chemical and Physical Meteorology 71, 1565030, (2019).

  5. Tenkanen, M. K. et al. Using Atmospheric Inverse Modelling of Methane Budgets with Copernicus Land Water and Wetness Data to Detect Land Use-Related Emissions. Remote Sensing 16, 124, (2024).

  6. Tenkanen, M. et al. Utilizing Earth Observations of Soil Freeze/Thaw Data and Atmospheric Concentrations to Estimate Cold Season Methane Emissions in the Northern High Latitudes. Remote Sensing 13, 5059, (2021).

  7. Erkkilä, A., Tenkanen, M., Tsuruta, A., Rautiainen, K. & Aalto, T. Environmental and Seasonal Variability of High Latitude Methane Emissions Based on Earth Observation Data and Atmospheric Inverse Modelling. Remote Sensing 15, 5719, (2023).

  8. Saunois, M. et al. The Global Methane Budget 2000–2017. Earth System Science Data 12, 1561–1623, (2020).

  9. Petrescu A. et al. The consolidated European synthesis of CH4 and N2O emissions for the European Union and United Kingdom: 1990–2019. Earth Syst. Sci. Data, 15, 1197–1268, (2023)

  10. Tsuruta, A. et al. CH4 Fluxes Derived from Assimilation of TROPOMI XCH4 in CarbonTracker Europe-CH4: Evaluation of Seasonality and Spatial Distribution in the Northern High Latitudes. Remote Sensing 15, 1620, (2023).

  11. Berchet, A. et al. The Community Inversion Framework v1.0: a unified system for atmospheric inversion studies. Geoscientific Model Development 14, 5331–5354, (2021).

  12. Krol, M. et al. The two-way nested global chemistry-transport zoom model TM5: algorithm and applications. Atmos. Chem. Phys. 5, 417–432, (2005).

  13. Thum, T. et al. Evaluating two soil carbon models within the global land surface model JSBACH using surface and spaceborne observations of atmospheric CO2. Biogeosciences 17, 5721–5743, (2020).

  14. Kangasaho, V. et al. The Role of Emission Sources and Atmospheric Sink in the Seasonal Cycle of CH4 and δ13-CH4: Analysis Based on the Atmospheric Chemistry Transport Model TM5. Atmosphere 13, 888, (2022).

  15. Mannisenaho, V. et al. Global Atmospheric δ13CH4 and CH4 Trends for 2000–2020 from the Atmospheric Transport Model TM5 Using CH4 from Carbon Tracker Europe–CH4 Inversions. Atmosphere 14, 1121, (2023).

  16. Pisso, I. et al. The Lagrangian particle dispersion model FLEXPART version 10.4. Geoscientific Model Development 12, 4955–4997, (2019).