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We present a method to derive atmosphericobservation-based estimates of carbon dioxide (CO 2 ) fluxes at the national scale, demonstrated using data from a network of surface tall-tower sites across the UK and Ireland over the period 2013-2014. The inversion is carried out using simulations from a Lagrangian chemical transport model and an innovative hierarchical Bayesian Markov chain Monte Carlo (MCMC) framework, which addresses some of the traditional problems faced by inverse modelling studies, such as subjectivity in the specification of model and prior uncertainties. Biospheric fluxes related to gross primary productivity and terrestrial ecosystem respiration are solved separately in the inversion and then combined a posteriori to determine net ecosystem exchange of CO 2 . Two different models, Data Assimilation Linked Ecosystem Carbon (DALEC) and Joint UK Land Environment Simulator (JULES), provide prior estimates for these fluxes. We carry out separate inversions to assess the impact of these different priors on the posterior flux estimates and evaluate the differences between the prior and posterior estimates in terms of missing model components. The Numerical Atmospheric dispersion Modelling Environment (NAME) is used to relate fluxes to the measurements taken across the regional network. Posterior CO2 estimates from the two inversions agree within estimated uncertainties, despite large differences in the prior fluxes from the different models. With our method, averaging results from 2013 and 2014, we find a total annual net biospheric flux for the UK of 8±79 TgCO 2 yr -1 (DALEC prior) and 64±85 TgCO 2 yr -1 (JULES prior), where negative values represent an uptake of CO 2 . These biospheric CO 2 estimates show that annual UK biospheric sources and sinks are roughly in balance. These annual mean estimates consistently indicate a greater net release of CO 2 than the prior estimates, which show much more pronounced uptake in summer months.