Optimal representation of source-sink fluxes for mesoscale carbon dioxide inversion with synthetic data

The inversion of CO₂ surface fluxes from atmospheric concentration measurements involves discretizing the flux domain in time and space. The resolution choice is usually guided by technical considerations despite its impact on the solution to the inversion problem. In our previous studies, a Bayesian formalism has recently been introduced to describe the discretization of the parameter space over a large dictionary of adaptive multiscale grids. In this paper, we exploit this new framework to construct optimal space-time representations of carbon fluxes for mesoscale inversions. Inversions are performed using synthetic continuous hourly CO₂ concentration data in the context of the Ring 2 experiment in support of the North American Carbon Program Mid Continent Intensive (MCI). Compared with the regular grid at finest scale, optimal representations can have similar inversion performance with far fewer grid cells. These optimal representations are obtained by maximizing the number of degrees of freedom for the signal (DFS) that measures the information gain from observations to resolve the unknown fluxes. Consequently information from observations can be better propagated within the domain through these optimal representations. For the Ring 2 network of eight towers, in most cases, the DFS value is relatively small compared to the number of observations d (DFS/d < 20%). In this multiscale setting, scale-dependent aggregation errors are identified and explicitly formulated for more reliable inversions. It is recommended that the aggregation errors should be taken into account, especially when the correlations in the errors of a priori fluxes are physically unrealistic. The optimal multiscale grids allow to adaptively mitigate the aggregation errors.