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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 ofaverage emission rates to each unit area of the urban domain, the fossilfuel emissions we use are dynamic: they vary in time and space in relationto data that describe or approximate the activity within a sector, such astraffic density, power demand, 2 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 theseactivity data and the resulting emissions of all species within the dynamicfossil 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=44 ) in this dynamic emissionmodel (a) vary much less over space and time, (b) allow for a physicalinterpretation of mean and uncertainty, and (c) have better defineduncertainties and covariance structure. This makes them more suited toextrapolate, 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 theDutch Rijnmond area at 1 km×1 km resolution. We find that the fossil fuel emission model approximates the griddedemissions well (annual mean differences  %, hourly temporal r2=0.21 –0.95), while reported errors in the underlying parameters allow afull covariance structure to be created readily. Propagating this errorstructure into atmospheric mole fractions shows a strong dominance of a fewlarge sectors and a few dominant uncertainties, most notably the emissionratios of the various gases considered. If the prior emission ratios are either sufficientlywell-known or well constrained from a dense observation network,we find that including observations of co-emitted species improves ourability to estimate emissions per sector relative to using CO2 molefractions only. Nevertheless, the total CO2 emissions can bewell constrained with CO2 as the only tracer in the inversion. Because some sectors are sampled only sparsely over a day, we find that propagatingsolutions from day-to-day leads to largest uncertainty reduction andsmallest CO2 residuals over the 14 consecutive days considered. Although wecan technically estimate the temporal distribution of some emissioncategories like shipping separate from their total magnitude, thecontrolling parameters are difficult to distinguish. Overall, we concludethat our new system looks promising for application in verification studies,provided that reliable urban atmospheric transport fields and reasonablea priori emission ratios for CO2 and its co-emitted species can be produced.

geoscientific model development

Optimizing a dynamic fossil fuel CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; emission model with CTDAS (CarbonTracker Data Assimilation Shell, v1.0) for an urban area using atmospheric observations of CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, CO, NO&amp;lt;sub&amp;gt;&amp;lt;i&amp;gt;x&amp;lt;/i&amp;gt;&amp;lt;/sub&amp;gt;, and SO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;