A Transdimensional, Hierarchical Bayesian Inversion Framework for Estimating Regional Trace Gas Emissions

Abstract:

Bayesian inverse modelling is very widely used for estimating trace gas flux fields using atmospheric observations. For reasons of computational expense, and to avoid under-determination, these high-dimensional fields are usually partitioned into a set of basis functions, or are estimated subject to some choice of correlation between grid cells. This partitioning or smoothing of the space is typically based on some set of subjective decisions made by the investigator. However, both the derived flux estimates, and their uncertainties, can be strongly dependent on these choices. Furthermore, traditional approaches do not allow for the uncertainty surrounding these choices to be propagated through to the derived fluxes. We outline a method whereby the number of basis functions, and therefore resolution at which fluxes are estimated, are determined using the data. A priori, we consider the number of flux basis functions and their configuration in the inversion domain to be unknown. In such a framework, the dimensionality of the inverse problem can change, and is therefore referred to as a “transdimensional” inversion. Reversible-jump Markov Chain-Monte Carlo tools to perform such dimension changing were first devised over two decades ago, but their uptake within atmospheric science has been limited. We present a novel application of this method for regional emissions estimation, also incorporating hierarchical Bayesian methods for the quantification of model-related and prior uncertainties. We show that, since the arrangement and geometry of the flux basis functions is no longer fixed, a relatively sparse, and therefore computationally efficient, partitioning can achieve a high effective spatial resolution of fluxes, where permitted by the data. We present an example of this new system for estimating fluxes in the UK, using data from the Deriving Emissions Related to Climate Change (DECC) network. This transdimensional, hierarchical approach is of particular relevance for the rapidly growing field of national emissions verification, where the use of fixed regions may result in the incorrect attribution of emissions, or correlated uncertainties, across country borders.