An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that significantly accelerates the computational efficiency of Lagra...
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ftdatacite:10.48550/arxiv.2108.00855 2023-05-15T18:18:08+02:00 An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models Chen, Nan Fu, Shubin Manucharyan, Georgy E 2021 https://dx.doi.org/10.48550/arxiv.2108.00855 https://arxiv.org/abs/2108.00855 unknown arXiv https://dx.doi.org/10.1016/j.jcp.2022.111000 Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 CC-BY Atmospheric and Oceanic Physics physics.ao-ph Numerical Analysis math.NA Fluid Dynamics physics.flu-dyn FOS Physical sciences FOS Mathematics article-journal Article ScholarlyArticle Text 2021 ftdatacite https://doi.org/10.48550/arxiv.2108.00855 https://doi.org/10.1016/j.jcp.2022.111000 2022-04-01T09:58:41Z Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that significantly accelerates the computational efficiency of Lagrangian data assimilation. The algorithm starts with a Fourier transform of the high-dimensional flow field, which is followed by an effective model reduction that retains only a small subset of the Fourier coefficients corresponding to the energetic modes. Then a linear stochastic model is developed to approximate the nonlinear dynamics of each Fourier coefficient. Effective additive and multiplicative noise processes are incorporated to characterize the modes that exhibit Gaussian and non-Gaussian statistics, respectively. All the parameters in the reduced order system, including the multiplicative noise coefficients, are determined systematically via closed analytic formulae. These linear stochastic models succeed in forecasting the uncertainty and facilitate an extremely rapid data assimilation scheme. The new Lagrangian data assimilation is then applied to observations of sea ice floe trajectories that are driven by atmospheric winds and turbulent ocean currents. It is shown that observing only about $30$ non-interacting floes in a $200$km$\times200$km domain is sufficient to recover the key multi-scale features of the ocean currents. The additional observations of the floe angular displacements are found to be suitable supplements to the center-of-mass positions for improving the data assimilation skill. In addition, the observed large and small floes are more useful in recovering the large- and small-scale features of the ocean, respectively. The Fourier domain data assimilation also succeeds in recovering the ocean features in the areas where cloud cover obscures the observations. Text Sea ice DataCite Metadata Store (German National Library of Science and Technology) |
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Atmospheric and Oceanic Physics physics.ao-ph Numerical Analysis math.NA Fluid Dynamics physics.flu-dyn FOS Physical sciences FOS Mathematics |
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Atmospheric and Oceanic Physics physics.ao-ph Numerical Analysis math.NA Fluid Dynamics physics.flu-dyn FOS Physical sciences FOS Mathematics Chen, Nan Fu, Shubin Manucharyan, Georgy E An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models |
topic_facet |
Atmospheric and Oceanic Physics physics.ao-ph Numerical Analysis math.NA Fluid Dynamics physics.flu-dyn FOS Physical sciences FOS Mathematics |
description |
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that significantly accelerates the computational efficiency of Lagrangian data assimilation. The algorithm starts with a Fourier transform of the high-dimensional flow field, which is followed by an effective model reduction that retains only a small subset of the Fourier coefficients corresponding to the energetic modes. Then a linear stochastic model is developed to approximate the nonlinear dynamics of each Fourier coefficient. Effective additive and multiplicative noise processes are incorporated to characterize the modes that exhibit Gaussian and non-Gaussian statistics, respectively. All the parameters in the reduced order system, including the multiplicative noise coefficients, are determined systematically via closed analytic formulae. These linear stochastic models succeed in forecasting the uncertainty and facilitate an extremely rapid data assimilation scheme. The new Lagrangian data assimilation is then applied to observations of sea ice floe trajectories that are driven by atmospheric winds and turbulent ocean currents. It is shown that observing only about $30$ non-interacting floes in a $200$km$\times200$km domain is sufficient to recover the key multi-scale features of the ocean currents. The additional observations of the floe angular displacements are found to be suitable supplements to the center-of-mass positions for improving the data assimilation skill. In addition, the observed large and small floes are more useful in recovering the large- and small-scale features of the ocean, respectively. The Fourier domain data assimilation also succeeds in recovering the ocean features in the areas where cloud cover obscures the observations. |
format |
Text |
author |
Chen, Nan Fu, Shubin Manucharyan, Georgy E |
author_facet |
Chen, Nan Fu, Shubin Manucharyan, Georgy E |
author_sort |
Chen, Nan |
title |
An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models |
title_short |
An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models |
title_full |
An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models |
title_fullStr |
An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models |
title_full_unstemmed |
An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models |
title_sort |
efficient and statistically accurate lagrangian data assimilation algorithm with applications to discrete element sea ice models |
publisher |
arXiv |
publishDate |
2021 |
url |
https://dx.doi.org/10.48550/arxiv.2108.00855 https://arxiv.org/abs/2108.00855 |
genre |
Sea ice |
genre_facet |
Sea ice |
op_relation |
https://dx.doi.org/10.1016/j.jcp.2022.111000 |
op_rights |
Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 |
op_rightsnorm |
CC-BY |
op_doi |
https://doi.org/10.48550/arxiv.2108.00855 https://doi.org/10.1016/j.jcp.2022.111000 |
_version_ |
1766194567183335424 |