skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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 linearmore » interpolations are comparable.« less

Authors:
 [1]
  1. Department of Mathematics, North Carolina State University, NC 27695 (United States)
Publication Date:
OSTI Identifier:
22233556
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 235; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; ERRORS; INTERPOLATION; KRIGING; LAYERS; LIMITING VALUES; MIXING; RANDOMNESS; SEAS; SIGNALS; STOCHASTIC PROCESSES; TURBULENCE

Citation Formats

Brown, Kristen A., E-mail: kabrown6@ncsu.edu, and Harlim, John. Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters. United States: N. p., 2013. Web. doi:10.1016/J.JCP.2012.11.006.
Brown, Kristen A., E-mail: kabrown6@ncsu.edu, & Harlim, John. Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters. United States. https://doi.org/10.1016/J.JCP.2012.11.006
Brown, Kristen A., E-mail: kabrown6@ncsu.edu, and Harlim, John. Fri . "Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters". United States. https://doi.org/10.1016/J.JCP.2012.11.006.
@article{osti_22233556,
title = {Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters},
author = {Brown, Kristen A., E-mail: kabrown6@ncsu.edu and Harlim, John},
abstractNote = {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.},
doi = {10.1016/J.JCP.2012.11.006},
url = {https://www.osti.gov/biblio/22233556}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 235,
place = {United States},
year = {2013},
month = {2}
}