Lunt, M. F., Rigby, M., Ganesan, A. L., Manning, A. J. (2016):
Estimation of trace gas fluxes with objectively determined basis functions using reversible jump Markov chain Monte Carlo
Geoscientific Model Development, 3213-3229, 20161–27. doi: 10.5194/gmd-2016-41
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 size 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 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, it allows the uncertainty in our choice of aggregation to be carried through to the solution. 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 allows methane emissions over north-west Europe to be resolved.
Received: 17 Feb 2016 – Accepted: 22 Apr 2016 – Published in Geosci. Model Dev. Disc.: 27 Apr 2016
Revised: 20 Jul 2016 – Accepted: 25 Aug 2016 – Published: 19 Sep 2016