An aircraft-based Bayesian inversion of Berlin CO₂ emissions with explicit background treatment

Abstract. Quantifying greenhouse gas (GHG) emissions from urban areas is critical for assessing progress toward climate goals. Aircraft-based measurements provide valuable information on urban emission fluxes; however, their interpretation is often limited by uncertainties in atmospheric background concentrations. Here, we present an emission estimate of Berlin city emissions that explicitly includes background concentrations from a Eulerian background run as state vector elements in a Bayesian inversion framework. Using data from the 20^th of July flight of the 2018 3DO aircraft campaign of the [UC]² (“Urban Climates Under Change”) project over Berlin and high-resolution GHG and meteorological simulations using Weather Research and Forecasting (WRF) model, we derive a CO₂ emission estimate for the city of Berlin. We find an optimized Berlin emission rate of 13.4 ± 4.6 MtCO₂a⁻¹. The emissions rate is about 48 % higher than the prior total annual emissions of the TNO anthropogenic bottom-up inventory (time-scaled emissions, 10.8 MtCO₂a⁻¹) and VPRM biogenic (time-varying, -1.7 MtCO₂a⁻¹) and about 30 % of the estimate from the traditional mass balance approach (44 ± 24 MtCO₂a⁻¹), while reducing the uncertainty by over a factor of five. We verify our posterior background concentration with independent concentration measurements above the boundary layer. This study provides an improved independent estimate of urban emissions and demonstrates that explicit treatment of background concentrations in inversions improves aircraft-based urban flux estimates.