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<p>We present a novel high-resolution inverse modelling system (“FLEXVAR”) based on FLEXPART-COSMO back trajectories driven by COSMO meteorological fields at <span class="inline-formula">7 km×7 km</span> resolution over the European COSMO-7 domain and the four-dimensional variational (4DVAR) data assimilation technique. FLEXVAR is coupled offline with the global inverse modelling system TM5-4DVAR to provide background mole fractions (“baselines”) consistent with the global observations assimilated in TM5-4DVAR. We have applied the FLEXVAR system for the inverse modelling of European CH<span class="inline-formula">₄</span> emissions in 2018 using 24 stations with in situ measurements, complemented with data from five stations with discrete air sampling (and additional stations outside the European COSMO-7 domain used for the global TM5-4DVAR inversions). The sensitivity of the FLEXVAR inversions to different approaches to calculate the baselines, different parameterizations of the model representation error, different settings of the prior error covariance parameters, different prior inventories, and different observation data sets are investigated in detail. Furthermore, the FLEXVAR inversions are compared to inversions with the FLEXPART extended Kalman filter (“FLExKF”) system and with TM5-4DVAR inversions at <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M5" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><msup><mi/><mo>∘</mo></msup><mo>×</mo><mn mathvariant="normal">1</mn><msup><mi/><mo>∘</mo></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="34pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="d308210e38ed1a4940972a050836d54c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-13243-2022-ie00001.svg" width="34pt" height="11pt" src="acp-22-13243-2022-ie00001.png"/></svg:svg></span></span> resolution over Europe. The three inverse modelling systems show overall good consistency of the major spatial patterns of the derived inversion increments and in general only relatively small differences in the derived annual total emissions of larger country regions. At the same time, the FLEXVAR inversions at <span class="inline-formula">7 km×7 km</span> resolution allow the observations to be better reproduced than the TM5-4DVAR simulations at <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><msup><mi/><mo>∘</mo></msup><mo>×</mo><mn mathvariant="normal">1</mn><msup><mi/><mo>∘</mo></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="34pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="2f0cd8b2e0fda9823788cc41d80ac5a2"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-22-13243-2022-ie00002.svg" width="34pt" height="11pt" src="acp-22-13243-2022-ie00002.png"/></svg:svg></span></span>. The three inverse models derive higher annual total CH<span class="inline-formula">₄</span> emissions in 2018 for Germany, France, and BENELUX compared to the sum of anthropogenic emissions reported to UNFCCC and natural emissions estimated from the Global Carbon Project CH<span class="inline-formula">₄</span> inventory, but the uncertainty ranges of top-down and bottom-up total emission estimates overlap for all three country regions. In contrast, the top-down estimates for the sum of emissions from the UK and Ireland agree relatively well with the total of anthropogenic and natural bottom-up inventories.</p>