Non-Gaussian bivariate modelling with application to atmospheric trace-gas inversion

TL;DR

This paper develops a non-Gaussian bivariate model for atmospheric trace-gas inversion, incorporating Bayesian inference and prior information assimilation, to improve source-sink identification from spatially and temporally distributed data.

Contribution

It introduces a trans-Gaussian bivariate model using Box--Cox transformations and a hierarchical Bayesian framework for trace-gas inversion, emphasizing prior sensitivity reduction.

Findings

Effective in controlled methane inversion experiments

Reduces prior sensitivity by integrating inventory data at the parameter level

Demonstrates improved flux estimation accuracy

Abstract

Atmospheric trace-gas inversion is the procedure by which the sources and sinks of a trace gas are identified from observations of its mole fraction at isolated locations in space and time. This is inherently a spatio-temporal bivariate inversion problem, since the mole-fraction field evolves in space and time and the flux is also spatio-temporally distributed. Further, the bivariate model is likely to be non-Gaussian since the flux field is rarely Gaussian. Here, we use conditioning to construct a non-Gaussian bivariate model, and we describe some of its properties through auto- and cross-cumulant functions. A bivariate non-Gaussian, specifically trans-Gaussian, model is then achieved through the use of Box--Cox transformations, and we facilitate Bayesian inference by approximating the likelihood in a hierarchical framework. Trace-gas inversion, especially at high spatial resolution, is frequently highly sensitive to prior specification. Therefore, unlike conventional approaches, we assimilate trace-gas inventory information with the observational data at the parameter layer, thus shifting prior sensitivity from the inventory itself to its spatial characteristics (e.g., its spatial length scale). We demonstrate the approach in controlled-experiment studies of methane inversion, using fluxes extracted from inventories of the UK and Ireland and of Northern Australia.