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Abstract:
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Steadily increasing atmospheric carbon dioxide (CO2) concentration is largely responsible for the observed radiative forcing in Earth's climate system over the last century. Inference from land-air carbon fluxes from satellite-based CO2 observations helps uncover the responsible locations and mechanisms. Doing this is an ill-posed, likelihood-free inverse problem for which a Bayesian data assimilation is the usual approach to obtain regularized estimation and uncertainty quantification. From a frequentist perspective, such estimates can have nonnegligible bias and coverage issues. Using a specialized Monte Carlo method for evaluating the posterior uncertainty and a simulation study involving a realistic global atmospheric transport model, we investigate the extent to which these issues affect the flux inversions. We demonstrate that inflating the prior uncertainty can lead to more realistic uncertainties that nevertheless remain well-constrained over regional spatio-temporal scales. We therefore argue that in order to mitigate these problems, one should prefer implicit regularization using spatio-temporal aggregates, instead of explicit regularization using the prior distribution.
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