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Atmospheric trace-gas inversion is the procedure by which the sources andsinks of a trace gas are identified from observations of its mole fraction atisolated locations in space and time. This is inherently a spatio-temporalbivariate inversion problem, since the mole-fraction field evolves in space andtime and the flux is also spatio-temporally distributed. Further, the bivariatemodel 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 wedescribe some of its properties through auto- and cross-cumulant functions. Abivariate non-Gaussian, specifically trans-Gaussian, model is then achievedthrough the use of Box--Cox transformations, and we facilitate Bayesianinference by approximating the likelihood in a hierarchical framework.Trace-gas inversion, especially at high spatial resolution, is frequentlyhighly sensitive to prior specification. Therefore, unlike conventionalapproaches, we assimilate trace-gas inventory information with theobservational data at the parameter layer, thus shifting prior sensitivity fromthe inventory itself to its spatial characteristics (e.g., its spatial lengthscale). We demonstrate the approach in controlled-experiment studies of methaneinversion, using fluxes extracted from inventories of the UK and Ireland and ofNorthern Australia.

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