Spatio-temporal bivariate statistical models for atmospheric trace-gas inversion

TL;DR

This paper introduces a novel bivariate spatio-temporal statistical model for atmospheric trace-gas inversion, improving prediction accuracy and computational efficiency by jointly modeling mole-fraction and flux fields with a lognormal process and inventory integration.

Contribution

It extends univariate models to a bivariate framework, employs a lognormal spatial process for flux, and develops a new geostatistical method to incorporate flux inventories.

Findings

Enhanced prediction of methane fluxes and mole-fractions.

Significant computational savings over univariate models.

Data-driven flux field posterior distribution achieved.

Abstract

Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a data-assimilation flavour, which implicitly consider univariate statistical models with the flux as the variate of interest. This univariate approach typically assumes that the flux field is either a spatially correlated Gaussian process or a spatially uncorrelated non-Gaussian process with prior expectation fixed using flux inventories (e.g., NAEI or EDGAR in Europe). Here, we extend this approach in three ways. First, we develop a bivariate model for the mole-fraction field and the flux field. The bivariate approach allows optimal prediction of both the flux field and the mole-fraction field, and it leads to significant computational savings over the univariate approach. Second, we employ a lognormal spatial process for the flux field that captures both the lognormal characteristics of the flux field (when appropriate) and its spatial dependence. Third, we propose a new, geostatistical approach to incorporate the flux inventories in our updates, such that the posterior spatial distribution of the flux field is predominantly data-driven. The approach is illustrated on a case study of methane (CH$_4$) emissions in the United Kingdom and Ireland.