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Abstract:
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Non-Gaussian multivariate spatial models are needed for the statistical analysis of several geophysical phenomena. Here, we propose a constructive approach to non-Gaussian spatial bivariate modelling based on conditioning, and illustrate 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 Bayesian inference is facilitated by approximating the likelihood in a hierarchical framework. We apply this model to atmospheric trace-gas inversion, where the aim is to infer the sources and sinks (fluxes) of a gas from mole-fraction observations at ground stations. This application 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 (and typically non-Gaussian). These two fields are related through meteorology, which is assumed known from a Lagrangian particle dispersion model. We demonstrate the validity of the approach in a controlled-experiment study for methane flux estimation in the UK and Ireland.
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