Physics-based Bayesian inference from oceanographic data

Geoff Nicholls
Auckland University

Authors: Ian McKeague, Geoff Nicholls and Kevin Speer
Mathematics Department
Auckland University, New Zealand

We describe ongoing work to estimate ocean flow and property fields (pressure,
temperature, salinity and oxygen). The data is made up of spatialy and
temporally nonuniform point measurements of related fields including
temperature, salinity, wind-stress curl and tracers. We fit a physics-based
model, accounting for geostrophy, hydrostatics and mass and tracer
conservation. The fit is made using Bayesian inference and Markov chain Monte
Carlo simulation. Solution of the forward problem, mapping the property fields
of interest to the data, is computationaly intensive. In effect we must solve a
system of partial differential equations at each likelihood evaluation. We
present algorithmic innovations, relevant for the MCMC setting, which allow
rapid evaluation of the likelihood.


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