This dataset contains simulation results for the region of Fennoscandia from atmospheric inversion model Carbon Tracker Europe - CH4 (CTE-CH4). These simulations were performed to study the sensitivity of optimised biospheric methane emissions to choice of the prior data. The prior data are simulated biospheric methane fluxes from two ecosystem process models, JSBACH-HIMMELI, and LPX-Bern v.1.4, and from Global Carbon Project prior for inversion modeling. The CTE-CH4 simulated methane fluxes are given as monthly means over 14 years and cover the region of Fennoscandia in one-degree resolution. The optimised fluxes using the three priors are contained in three separate files.