Dynamic Likelihood Filter: A Data Assimilation Scheme that Exploits Hyperbolicity in Wave Problems to Propagate Observations

Abstract:

We significantly extend the capabilities of the Dynamic Likelihood Filter, a data assimilation scheme tailor made for linear and nonlinear wave problems with inherent uncertainties in both the initial and boundary data as well as wave speed and forcing. A unique capability of the scheme is that it can generate likelihoods at times when no observations are available, including the near future, by exploiting hyperbolicity and the finite propagation of information. 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.