Bayesian spatio-temporal inference of trace gas emissions using an integrated nested Laplacian approximation and Gaussian Markov random fields

Abstract

Abstract. We present a method to infer spatially and spatio-temporally correlated emissions of greenhouse gases from atmospheric measurements and a chemical transport model. The method allows fast computation of spatial emissions using a hierarchical Bayesian framework as an alternative to Markov chain Monte Carlo algorithms. The spatial emissions follow a Gaussian process with a Matérn correlation structure which can be represented by a Gaussian Markov random field through a stochastic partial differential equation approach. The inference is based on an integrated nested Laplacian approximation (INLA) for hierarchical models with Gaussian latent fields. Combining an autoregressive temporal correlation and the Matérn field provides a full spatio-temporal correlation structure. We first demonstrate the method on a synthetic data example and follow this using a well-studied test case of inferring UK methane emissions from tall tower measurements of atmospheric mole fraction. Results from these two test cases show that this method can accurately estimate regional greenhouse gas emissions, accounting for spatio-temporal uncertainties that have traditionally been neglected in atmospheric inverse modelling.

Implementation of a Gaussian Markov random field sampler for forward uncertainty quantification in the Ice-sheet and Sea-level System Model v4.19

“…4, these parameters have a major impact on the uncertainty in mass balance estimates. Therefore, these parameters should ideally be constrained through data assimilation methods, modelling efforts, and inverse methods, including Bayesian inference; see, for instance Cameletti et al (2012) and Western et al (2020), for Bayesian spatio-temporal inference with hidden Gaussian random fields. Lastly, we assumed the spatial correlation to be constant on the PIG.…”

“…Among the families of covariance functions, the Matérn family is a popular choice to represent spatial correlation in geostatistics. Applications include spatial modelling of greenhouse gas emissions (Western et al, 2020), temperature or precipitation anomalies (Furrer et al, 2006), soil properties (Minasny and McBratney, 2005), acoustic wave speeds in seismology (Bui-Thanh et al, 2013), and basal friction in glaciology (Isaac et al, 2015;Petra et al, 2014). The Matérn covariance function is defined as…”

“…Temporal correlation between samples (for transient simulation) is represented with a first-order autoregressive model (AR1 process) (Cameletti et al, 2012;Western et al, 2020):…”

A new sampling capability for uncertainty quantification in the Ice-sheet and Sea-level System Model v4.19 using Gaussian Markov random fields

“…4, these parameters have a major impact on the uncertainty in mass balance estimates. Therefore, these parameters should ideally be constrained through data assimilation methods, modeling efforts, and inverse methods, including Bayesian inference; see, for instance Cameletti et al (2012) and Western et al (2020), for Bayesian spatio-temporal inference with hidden Gaussian random fields. Lastly, we assumed the spatial correlation to be constant on the PIG.…”

“…Among the families of covariance functions, the Matérn family is a popular choice to represent spatial correlation in geostatistics. Applications include spatial modeling of greenhouse gas emissions (Western et al, 2020), temperature or precipitation anomalies (Furrer et al, 2006), soil properties (Minasny and McBratney, 2005), acoustic wave speeds in seismology (Bui-Thanh et al, 2013), and basal friction in glaciology (Isaac et al, 2015;Petra et al, 2014). The Matérn covariance function is defined as…”