Methods of Ensemble Data Assimilation on Adaptive Moving Meshes
Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. In particular, neXtSIM is a 2D model of sea-ice that is numerically solved on a Lagrangian mesh that does not conserve the number of mesh points. In this dissertation, we present two novel approache...
Main Author: | |
---|---|
Other Authors: | , , , , , |
Format: | Doctoral or Postdoctoral Thesis |
Language: | English |
Published: |
University of North Carolina at Chapel Hill Graduate School
2019
|
Subjects: | |
Online Access: | https://doi.org/10.17615/bwc6-3891 https://cdr.lib.unc.edu/downloads/h702qb840?file=thumbnail https://cdr.lib.unc.edu/downloads/h702qb840 |
id |
ftcarolinadr:cdr.lib.unc.edu:1831cq45m |
---|---|
record_format |
openpolar |
spelling |
ftcarolinadr:cdr.lib.unc.edu:1831cq45m 2023-06-11T04:16:36+02:00 Methods of Ensemble Data Assimilation on Adaptive Moving Meshes Guider, Colin Thomas College of Arts and Sciences, Department of Mathematics Jones, Chris Budhiraja, Amarjit Sampson, Christian Carrassi, Alberto Newhall, Katie 2019 https://doi.org/10.17615/bwc6-3891 https://cdr.lib.unc.edu/downloads/h702qb840?file=thumbnail https://cdr.lib.unc.edu/downloads/h702qb840 English eng University of North Carolina at Chapel Hill Graduate School https://doi.org/10.17615/bwc6-3891 https://cdr.lib.unc.edu/downloads/h702qb840?file=thumbnail https://cdr.lib.unc.edu/downloads/h702qb840 http://rightsstatements.org/vocab/InC-EDU/1.0/ data assimilation ensemble kalman filter Mathematics moving mesh adaptive mesh Dissertation 2019 ftcarolinadr https://doi.org/10.17615/bwc6-3891 2023-05-28T20:56:03Z Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. In particular, neXtSIM is a 2D model of sea-ice that is numerically solved on a Lagrangian mesh that does not conserve the number of mesh points. In this dissertation, we present two novel approaches to the formulation of ensemble data assimilation for models with this underlying computational structure. Specifically, we map ensemble members onto a common reference mesh, where the Ensemble Kalman Filter (EnKF) can be performed. Numerical experiments are carried out using 1D prototypical models: Burgers and Kuramoto-Sivashinsky equations, with both Eulerian and Lagrangian synthetic observations assimilated. One of the approaches is very effective, while the other is significantly less so. We also present a novel approach in the formulation of the Local Ensemble Transform Kalman Filter (LETKF) on a conservative moving mesh model. This is also achieved by mapping the ensemble members onto a common reference mesh, but it done in a significantly different manner than from the previous two approaches. Specifically, the common mesh is formed by taking an equidistributing mesh for the previous output of the algorithm. The preliminary results of this method from an application to Burgers equation are encouraging. Doctor of Philosophy Doctoral or Postdoctoral Thesis Sea ice Carolina Digital Repository (UNC - University of North Carolina) |
institution |
Open Polar |
collection |
Carolina Digital Repository (UNC - University of North Carolina) |
op_collection_id |
ftcarolinadr |
language |
English |
topic |
data assimilation ensemble kalman filter Mathematics moving mesh adaptive mesh |
spellingShingle |
data assimilation ensemble kalman filter Mathematics moving mesh adaptive mesh Guider, Colin Thomas Methods of Ensemble Data Assimilation on Adaptive Moving Meshes |
topic_facet |
data assimilation ensemble kalman filter Mathematics moving mesh adaptive mesh |
description |
Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. In particular, neXtSIM is a 2D model of sea-ice that is numerically solved on a Lagrangian mesh that does not conserve the number of mesh points. In this dissertation, we present two novel approaches to the formulation of ensemble data assimilation for models with this underlying computational structure. Specifically, we map ensemble members onto a common reference mesh, where the Ensemble Kalman Filter (EnKF) can be performed. Numerical experiments are carried out using 1D prototypical models: Burgers and Kuramoto-Sivashinsky equations, with both Eulerian and Lagrangian synthetic observations assimilated. One of the approaches is very effective, while the other is significantly less so. We also present a novel approach in the formulation of the Local Ensemble Transform Kalman Filter (LETKF) on a conservative moving mesh model. This is also achieved by mapping the ensemble members onto a common reference mesh, but it done in a significantly different manner than from the previous two approaches. Specifically, the common mesh is formed by taking an equidistributing mesh for the previous output of the algorithm. The preliminary results of this method from an application to Burgers equation are encouraging. Doctor of Philosophy |
author2 |
College of Arts and Sciences, Department of Mathematics Jones, Chris Budhiraja, Amarjit Sampson, Christian Carrassi, Alberto Newhall, Katie |
format |
Doctoral or Postdoctoral Thesis |
author |
Guider, Colin Thomas |
author_facet |
Guider, Colin Thomas |
author_sort |
Guider, Colin Thomas |
title |
Methods of Ensemble Data Assimilation on Adaptive Moving Meshes |
title_short |
Methods of Ensemble Data Assimilation on Adaptive Moving Meshes |
title_full |
Methods of Ensemble Data Assimilation on Adaptive Moving Meshes |
title_fullStr |
Methods of Ensemble Data Assimilation on Adaptive Moving Meshes |
title_full_unstemmed |
Methods of Ensemble Data Assimilation on Adaptive Moving Meshes |
title_sort |
methods of ensemble data assimilation on adaptive moving meshes |
publisher |
University of North Carolina at Chapel Hill Graduate School |
publishDate |
2019 |
url |
https://doi.org/10.17615/bwc6-3891 https://cdr.lib.unc.edu/downloads/h702qb840?file=thumbnail https://cdr.lib.unc.edu/downloads/h702qb840 |
genre |
Sea ice |
genre_facet |
Sea ice |
op_relation |
https://doi.org/10.17615/bwc6-3891 https://cdr.lib.unc.edu/downloads/h702qb840?file=thumbnail https://cdr.lib.unc.edu/downloads/h702qb840 |
op_rights |
http://rightsstatements.org/vocab/InC-EDU/1.0/ |
op_doi |
https://doi.org/10.17615/bwc6-3891 |
_version_ |
1768374989453524992 |