Abstract
Abstract. We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate 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 complete estimation of emissions and their uncertainties than traditional 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 representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties 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.
Highlights
Inverse modeling is widely used to estimate sources and sinks of trace gas fluxes and their distributions using measurements of atmospheric mole fractions and chemical transport models (CTMs)
The results of the hierarchical Bayesian inversion (HB) inversion show that (1) SF6 emissions from the UK, France and Germany have deceased from the scaled EDGAR emissions and are smaller than 2008 EDGAR emissions; (2) East Asian SF6 emissions have decreased from scaled EDGAR values but have increased compared to 2008 EDGAR emissions; (3) emissions from the western coast of North America have largely decreased from 2008 EDGAR emissions; (4) Australian emissions have approximately remained the same as the scaled EDGAR emissions
We present an application of a hierarchical Bayesian method for trace gas inversions
Summary
Inverse modeling is widely used to estimate sources and sinks of trace gas fluxes and their distributions using measurements of atmospheric mole fractions and chemical transport models (CTMs). The model error can be split into several components: structural errors within the CTM or meteorological model (Peylin et al, 2002; Thompson et al, 2011); model representation error, which describe errors in the representation of a point measurement in representing a grid volume (Chen and Prinn, 2006); aggregation errors, which result from averaging parameters over space and time and assuming fixed distributions within those domains (Kaminski et al, 2001; Thompson et al, 2011) Knowledge of these uncertainties is critical for robustly estimating posterior fluxes and their uncertainties; they are largely elicited through “expert judgment”. We present a hierarchical Bayesian method to estimate trace gas emissions and additional parameters, which we call “hyper-parameters”, that describe the a priori emissions PDF and the model-measurement uncertainty PDF. We utilize this method to estimate regional sulfur hexafluoride (SF6) emissions using measurements from the Advanced Global Atmospheric Gases Experiment (AGAGE) network and the UK Met Office Numerical Atmospheric-dispersion Modelling Environment v3 (NAME) transport model (Jones et al, 2007; Ryall and Maryon, 1998)
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