Non-Gaussian bivariate spatio-temporal statistical models for atmospheric trace gas inversions

Atmospheric trace gas inversion is a method for assessing the spatial distribution of gas emissions/sinks, or flux, from (i) mole fraction measurements and (ii) atmospheric simulations from deterministic computer models. Studies to date are predominantly of a data assimilation flavour, implicitly considering univariate statistical models with the spatially distributed flux as the variate of interest. Here, we show that a more appropriate approach to the problem is through a non-Gaussian bivariate statistical model constructed via a conditional approach, where the atmospheric simulator is used to explicitly elicit the distribution of the mole fraction field (variate #2) given the flux field (variate #1). This model offers several interpretable and computational advantages. First, through the conditional approach we can cater explicitly for inaccuracies in the spatio-temporal simulator, which are usually ignored. Second, following a Box-Cox transformation of the flux field, we obtain interpretable quantities for the expectations of, and the covariance between, the mole-fraction field and the flux field, as well as all the auto- and cross-cumulant functions of the joint process. Third, the decoupling of the observation locations from those at which the processes are evaluated allows us to use computationally-efficient spatio-temporal model representations. These offer a way forward for the inversion of large to massive datasets, which will soon be available from remote sensing instruments. We show how a Markov Chain Monte Carlo (MCMC) scheme can be used to make inferences on the model parameters and non-Gaussian flux field using moderate computational resources. The approach is illustrated on a simple one-dimensional simulation study as well as a case study of methane (CH4) emissions in the United Kingdom and Australia.

This is joint work with Noel Cressie and Anita Ganesan.