Model selection for the sound speed perturbation of GNSS-A using the widely applicable Bayesian information criterion (WBIC)

Analysis methods for GNSS-A seafloor geodetic observations have become sophisticated in recent years. A Bayesian statistical approach with the Markov-Chain Monte Carlo (MCMC) method enables observers to flexibly estimate seafloor positions simultaneously with the perturbation of the sound speed in the ocean under several spatiotemporal patterns. To select the perturbation model appropriately and quantitatively, we implemented the widely applicable Bayesian Information Criterion (WBIC) in our software. The WBIC value is an approximation of the Bayes free energy that indicates the statistical appropriateness of the given model, which is available after running an MCMC sequence with a certain inverse temperature. Applying the WBIC-based model selection method to the actual data obtained at the seafloor GNSS-A sites along the Japanese archipelago by the Japan Coast Guard, we found that a simpler model, where the perturbation field is characterized by a uniformly inclined layer is more preferable than models with more degrees of freedom, especially in regions, where the Kuroshio current is strong. For the sites in the area where the cold and warm currents tend to cause multi-scale eddies, the model with more degrees of freedom was occasionally selected.