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We present a modelling framework for fossil fuel CO2 emissions in an urban environment, which allows constraints from emission inventories to be combined with atmospheric observations of CO2 and its co-emitted species CO, NOx , and SO2. Rather than a static assignment of average emission rates to each unit area of the urban domain, the fossil fuel emissions we use are dynamic: they vary in time and space in relation to data that describe or approximate the activity within a sector, such as traffic density, power demand, 2m temperature (as proxy for heating demand), and sunlight and wind speed (as proxies for renewable energy supply). Through inverse modelling, we optimize the relationships between these activity data and the resulting emissions of all species within the dynamic fossil fuel emission model, based on atmospheric mole fraction observations. The advantage of this novel approach is that the optimized parameters (emission factors and emission ratios, N D 44) in this dynamic emission model (a) vary much less over space and time, (b) allow for a physical interpretation of mean and uncertainty, and (c) have better defined uncertainties and covariance structure. This makes them more suited to extrapolate, optimize, and interpret than the gridded emissions themselves. The merits of this approach are investigated using a pseudo-observation-based ensemble Kalman filter inversion set-up for the Dutch Rijnmond area at 1km-1km resolution. We find that the fossil fuel emission model approximates the gridded emissions well (annual mean differences < 2 %, hourly temporal r2 D 0:21-0.95), while reported errors in the underlying parameters allow a full covariance structure to be created readily. Propagating this error structure into atmospheric mole fractions shows a strong dominance of a few large sectors and a few dominant uncertainties, most notably the emission ratios of the various gases considered. If the prior emission ratios are either sufficiently well-known or well constrained from a dense observation network, we find that including observations of co-emitted species improves our ability to estimate emissions per sector relative to using CO2 mole fractions only. Nevertheless, the total CO2 emissions can be well constrained with CO2 as the only tracer in the inversion. Because some sectors are sampled only sparsely over a day, we find that propagating solutions from day-to-day leads to largest uncertainty reduction and smallest CO2 residuals over the 14 consecutive days considered. Although we can technically estimate the temporal distribution of some emission categories like shipping separate from their total magnitude, the controlling parameters are difficult to distinguish. Overall, we conclude that our new system looks promising for application in verification studies, provided that reliable urban atmospheric transport fields and reasonable a priori emission ratios for CO2 and its co-emitted species can be produced.