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<p>We present a modelling framework for fossil fuel <span class="inline-formula">CO₂</span> emissions in an urban environment, which allows constraints from emission inventories to be combined with atmospheric observations of <span class="inline-formula">CO₂</span> and its co-emitted species <span class="inline-formula">CO</span>, <span class="inline-formula">NO_<i>x</i></span>, and <span class="inline-formula">SO₂</span>. 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, 2&thinsp;m 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, <span class="inline-formula"><i>N</i>=44</span>) 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 <span class="inline-formula">1 km×1 km</span> resolution.</p> <p>We find that the fossil fuel emission model approximates the gridded emissions well (annual mean differences <span class="inline-formula">&lt;2</span>&thinsp;%, hourly temporal <span class="inline-formula"><i>r</i>²=0.21</span>–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 <span class="inline-formula">CO₂</span> mole fractions only. Nevertheless, the total <span class="inline-formula">CO₂</span> emissions can be well constrained with <span class="inline-formula">CO₂</span> 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 <span class="inline-formula">CO₂</span> 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 <span class="inline-formula">CO₂</span> and its co-emitted species can be produced.</p>