Controllability, not chaos, key criterion for ocean state estimation
The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or <q>4D-VAR</q>) has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2017-07-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://www.nonlin-processes-geophys.net/24/351/2017/npg-24-351-2017.pdf |
| _version_ | 1819266977335607296 |
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| author | G. Gebbie T.-L. Hsieh T.-L. Hsieh T.-L. Hsieh |
| author_facet | G. Gebbie T.-L. Hsieh T.-L. Hsieh T.-L. Hsieh |
| author_sort | G. Gebbie |
| collection | DOAJ |
| description | The Lagrange multiplier method for combining observations and
models (i.e., the adjoint method or <q>4D-VAR</q>) has been avoided or
approximated when the numerical model is highly nonlinear or chaotic. This
approach has been adopted primarily due to difficulties in the initialization
of low-dimensional chaotic models, where the search for optimal initial
conditions by gradient-descent algorithms is hampered by multiple local
minima. Although initialization is an important task for numerical weather
prediction, ocean state estimation usually demands an additional task – a
solution of the time-dependent surface boundary conditions that result from
atmosphere–ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the
forced chaotic pendulum. Contrary to previous assertions, it is demonstrated
that the Lagrange multiplier method can track multiple chaotic transitions
through time, so long as the boundary conditions render the system
controllable. Thus, the nonlinear timescale poses no limit to the time
interval for successful Lagrange multiplier-based estimation. That the key
criterion is controllability, not a pure measure of dynamical stability or
chaos, illustrates the similarities between the Lagrange multiplier method
and other state estimation methods. The results with the chaotic pendulum
suggest that nonlinearity should not be a fundamental obstacle to ocean state
estimation with eddy-resolving models, especially when using an improved
first-guess trajectory. |
| first_indexed | 2024-12-23T21:09:50Z |
| format | Article |
| id | doaj.art-3137343d3d3848c4b4827277fce2a742 |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-12-23T21:09:50Z |
| publishDate | 2017-07-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-3137343d3d3848c4b4827277fce2a7422022-12-21T17:31:07ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462017-07-012435136610.5194/npg-24-351-2017Controllability, not chaos, key criterion for ocean state estimationG. Gebbie0T.-L. Hsieh1T.-L. Hsieh2T.-L. Hsieh3Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA, USADepartment of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA, USASummer Student Fellow, Woods Hole Oceanographic Institution, Woods Hole, MA, USAProgram in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USAThe Lagrange multiplier method for combining observations and models (i.e., the adjoint method or <q>4D-VAR</q>) has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization of low-dimensional chaotic models, where the search for optimal initial conditions by gradient-descent algorithms is hampered by multiple local minima. Although initialization is an important task for numerical weather prediction, ocean state estimation usually demands an additional task – a solution of the time-dependent surface boundary conditions that result from atmosphere–ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the forced chaotic pendulum. Contrary to previous assertions, it is demonstrated that the Lagrange multiplier method can track multiple chaotic transitions through time, so long as the boundary conditions render the system controllable. Thus, the nonlinear timescale poses no limit to the time interval for successful Lagrange multiplier-based estimation. That the key criterion is controllability, not a pure measure of dynamical stability or chaos, illustrates the similarities between the Lagrange multiplier method and other state estimation methods. The results with the chaotic pendulum suggest that nonlinearity should not be a fundamental obstacle to ocean state estimation with eddy-resolving models, especially when using an improved first-guess trajectory.https://www.nonlin-processes-geophys.net/24/351/2017/npg-24-351-2017.pdf |
| spellingShingle | G. Gebbie T.-L. Hsieh T.-L. Hsieh T.-L. Hsieh Controllability, not chaos, key criterion for ocean state estimation Nonlinear Processes in Geophysics |
| title | Controllability, not chaos, key criterion for ocean state estimation |
| title_full | Controllability, not chaos, key criterion for ocean state estimation |
| title_fullStr | Controllability, not chaos, key criterion for ocean state estimation |
| title_full_unstemmed | Controllability, not chaos, key criterion for ocean state estimation |
| title_short | Controllability, not chaos, key criterion for ocean state estimation |
| title_sort | controllability not chaos key criterion for ocean state estimation |
| url | https://www.nonlin-processes-geophys.net/24/351/2017/npg-24-351-2017.pdf |
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