A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation
In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this boundary, a scalar unknown (buoyancy or surface temperature...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-02-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2016-6019 |
| _version_ | 1828355334566051840 |
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| author | Jolly Michael S. Martinez Vincent R. Titi Edriss S. |
| author_facet | Jolly Michael S. Martinez Vincent R. Titi Edriss S. |
| author_sort | Jolly Michael S. |
| collection | DOAJ |
| description | In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this boundary, a scalar unknown (buoyancy or surface temperature of the fluid) satisfies the surface quasi-geostrophic equation. The feedback nudging is done on this two-dimensional model, yet ultimately synchronizes the streamfunction of the three-dimensional flow. The main analytical difficulties are due to the presence of a nonlocal dissipative operator in the surface quasi-geostrophic equation. This is overcome by exploiting a suitable partition of unity, the modulus of continuity characterization of Sobolev space norms, and the Littlewood–Paley decomposition to ultimately establish various boundedness and approximation-of-identity properties for the observation operators. |
| first_indexed | 2024-04-14T02:40:34Z |
| format | Article |
| id | doaj.art-e28ec813707149ce8c66d5c6b888226e |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-14T02:40:34Z |
| publishDate | 2017-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-e28ec813707149ce8c66d5c6b888226e2022-12-22T02:17:09ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752017-02-0117116719210.1515/ans-2016-6019A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic EquationJolly Michael S.0Martinez Vincent R.1Titi Edriss S.2Department of Mathematics, Indiana University, Bloomington, IN 47405, USA Department of Mathematics, Tulane University, New Orleans, LA 70118, USA Department of Mathematics, Texas A& M University, College Station,TX 77843-3368, USA; and Department of Computer Science and Applied Mathematics, Weizmann Institute of Science,Rehovot, 76100, Israel In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this boundary, a scalar unknown (buoyancy or surface temperature of the fluid) satisfies the surface quasi-geostrophic equation. The feedback nudging is done on this two-dimensional model, yet ultimately synchronizes the streamfunction of the three-dimensional flow. The main analytical difficulties are due to the presence of a nonlocal dissipative operator in the surface quasi-geostrophic equation. This is overcome by exploiting a suitable partition of unity, the modulus of continuity characterization of Sobolev space norms, and the Littlewood–Paley decomposition to ultimately establish various boundedness and approximation-of-identity properties for the observation operators.https://doi.org/10.1515/ans-2016-6019data assimilationnudgingsurface measurementsquasi-geostrophic and surfacequasi-geostrophic equationfractional poincaré inequalities35q30 37c50 76b75 34d06 |
| spellingShingle | Jolly Michael S. Martinez Vincent R. Titi Edriss S. A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation Advanced Nonlinear Studies data assimilation nudging surface measurements quasi-geostrophic and surfacequasi-geostrophic equation fractional poincaré inequalities 35q30 37c50 76b75 34d06 |
| title | A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation |
| title_full | A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation |
| title_fullStr | A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation |
| title_full_unstemmed | A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation |
| title_short | A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation |
| title_sort | data assimilation algorithm for the subcritical surface quasi geostrophic equation |
| topic | data assimilation nudging surface measurements quasi-geostrophic and surfacequasi-geostrophic equation fractional poincaré inequalities 35q30 37c50 76b75 34d06 |
| url | https://doi.org/10.1515/ans-2016-6019 |
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