Articles | Volume 9, issue 9
Development and technical paper
19 Sep 2016
Development and technical paper |  | 19 Sep 2016

Estimation of trace gas fluxes with objectively determined basis functions using reversible-jump Markov chain Monte Carlo

Mark F. Lunt, Matt Rigby, Anita L. Ganesan, and Alistair J. Manning

Abstract. Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.

Short summary
Bayesian inversions can be used to estimate emissions of gases from atmospheric data. We present an inversion framework that objectively defines the basis functions, which describe regions of emissions. The framework allows for the uncertainty in the choice of basis functions to be propagated through to the posterior emissions distribution in a single-step process, and provides an alternative to using a single set of basis functions.