Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

Journal Article · Fri Feb 15 04:00:00 EST 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2012.11.006· OSTI ID:22233556

Harlim, John ^[1]

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1. Department of Mathematics, North Carolina State University, NC 27695 (United States)

In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable.

• OSTI ID: 22233556
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 235; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
ERRORS
INTERPOLATION
KRIGING
LAYERS
LIMITING VALUES
MIXING
RANDOMNESS
SEAS
SIGNALS
STOCHASTIC PROCESSES
TURBULENCE