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We present a hierarchical Bayesian method for at- mospheric trace gas inversions. This method is used to esti- mate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDFs) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more com- plete estimation of emissions and their uncertainties than tra- ditional Bayesian inversions, which rely heavily on expert judgment. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model repre- sentation uncertainties, in particular, can lead to the deriva- tion of emissions and associated uncertainties that are un- realistic and show that those derived using the hierarchical method are likely to be more representative of the true uncer- tainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties than traditional methods.

Characterization of uncertainties in atmospheric trace gas inversions using hierarchical Bayesian methods