An Improved Framework for the Dynamic Likelihood Filter

We significantly extend the capabilities of the Dynamic Likelihood Filter, a Bayesian data assimilation scheme that uses a computational model and its inherent uncertainties to generate a prior and exploits hyperbolicity in wave problems to time-evolve the likelihood in order to formulate approximations of the conditional probabilities. The methodology is particularly effective when observations have small inherent measurement errors and are sparse in space and time, as is often the case in geophysical wave problems.

A unique capability of the scheme is that it can generate approximate likelihoods in the near future, by exploiting hyperbolicity and the finite propagation of information, enabling Bayesian forecasting. With these dynamic likelihoods, the method produces better calibrated Bayesian estimates of priors created by model outcomes. Computed results and analysis will show that the Dynamic Likelihood Filter is computationally competitive and capable of outperforming the ensemble Kalman filter as applied to linear and nonlinear wave problems, with respect to both mean prediction and probabilistic uncertainty calibration, particularly in sparse observation networks.