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An approach to localization for ensemble-based data assimilation
- Source :
- PLoS ONE, PLoS ONE, Vol 13, Iss 1, p e0191088 (2018)
- Publication Year :
- 2018
- Publisher :
- Public Library of Science (PLoS), 2018.
-
Abstract
- Localization techniques are commonly used in ensemble-based data assimilation (e.g., the Ensemble Kalman Filter (EnKF) method) because of insufficient ensemble samples. They can effectively ameliorate the spurious long-range correlations between the background and observations. However, localization is very expensive when the problem to be solved is of high dimension (say 106 or higher) for assimilating observations simultaneously. To reduce the cost of localization for high-dimension problems, an approach is proposed in this paper, which approximately expands the correlation function of the localization matrix using a limited number of principal eigenvectors so that the Schür product between the localization matrix and a high-dimension covariance matrix is reduced to the sum of a series of Schür products between two simple vectors. These eigenvectors are actually the sine functions with different periods and phases. Numerical experiments show that when the number of principal eigenvectors used reaches 20, the approximate expansion of the correlation function is very close to the exact one in the one-dimensional (1D) and two-dimensional (2D) cases. The new approach is then applied to localization in the EnKF method, and its performance is evaluated in assimilation-cycle experiments with the Lorenz-96 model and single assimilation experiments using a barotropic shallow water model. The results suggest that the approach is feasible in providing comparable assimilation analysis with far less cost.
- Subjects :
- Cartography
Shallow Water
010504 meteorology & atmospheric sciences
lcsh:Medicine
Geometry
Research and Analysis Methods
01 natural sciences
010104 statistics & probability
Matrix (mathematics)
Data assimilation
Applied mathematics
0101 mathematics
lcsh:Science
Physics::Atmospheric and Oceanic Physics
Eigenvalues and eigenvectors
0105 earth and related environmental sciences
Mathematics
Latitude
Multidisciplinary
Covariance
Geography
Covariance matrix
Applied Mathematics
Simulation and Modeling
lcsh:R
Random Variables
Eigenvalues
Kalman filter
Models, Theoretical
Probability Theory
Correlation function (statistical mechanics)
Algebra
Linear Algebra
Radii
Longitude
Physical Sciences
Earth Sciences
lcsh:Q
Ensemble Kalman filter
Hydrology
Eigenvectors
Kalman Filter
Algorithms
Research Article
Subjects
Details
- ISSN :
- 19326203
- Volume :
- 13
- Database :
- OpenAIRE
- Journal :
- PLOS ONE
- Accession number :
- edsair.doi.dedup.....930b9869d8ff8981de919c704e2dea36