A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation
Abstract The Kuroshio Current in the North Pacific displays path changes on an interannual‐to‐decadal time scale. In an idealized barotropic quasi‐geostrophic model of the double‐gyre wind‐driven circulation under stochastic wind‐stress forcing, such variability can occur due to transitions between...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Geophysical Union (AGU)
2023-05-01
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| Series: | Journal of Advances in Modeling Earth Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1029/2022MS003456 |
| _version_ | 1797800154699399168 |
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| author | René M. vanWesten Sourabh Kotnala Sven Baars Fred W. Wubs Henk A. Dijkstra |
| author_facet | René M. vanWesten Sourabh Kotnala Sven Baars Fred W. Wubs Henk A. Dijkstra |
| author_sort | René M. vanWesten |
| collection | DOAJ |
| description | Abstract The Kuroshio Current in the North Pacific displays path changes on an interannual‐to‐decadal time scale. In an idealized barotropic quasi‐geostrophic model of the double‐gyre wind‐driven circulation under stochastic wind‐stress forcing, such variability can occur due to transitions between different equilibrium states. The high‐dimensionality of the problem makes it challenging to determine the probability of these transitions under the influence of stochastic noise. Here we present a new method to estimate these transition probabilities, using a Dynamical Orthogonal (DO) field approach. In the DO approach, the solution of the stochastic partial differential equations system is decomposed using a Karhunen–Loève expansion and separate problems arise for the ensemble mean state and the so‐called time‐dependent DO modes. The original method is first reformulated in a matrix approach which has much broader application potential to various (geophysical) problems. Using this matrix‐DO approach, we are able to determine transition probabilities in the double‐gyre problem and to identify transition paths between the different states. This analysis also leads to the understanding which conditions are most favorable for transition. |
| first_indexed | 2024-03-13T04:30:50Z |
| format | Article |
| id | doaj.art-4924dfa351414d97984efa83f55eec73 |
| institution | Directory Open Access Journal |
| issn | 1942-2466 |
| language | English |
| last_indexed | 2024-03-13T04:30:50Z |
| publishDate | 2023-05-01 |
| publisher | American Geophysical Union (AGU) |
| record_format | Article |
| series | Journal of Advances in Modeling Earth Systems |
| spelling | doaj.art-4924dfa351414d97984efa83f55eec732023-06-19T13:40:46ZengAmerican Geophysical Union (AGU)Journal of Advances in Modeling Earth Systems1942-24662023-05-01155n/an/a10.1029/2022MS003456A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean CirculationRené M. vanWesten0Sourabh Kotnala1Sven Baars2Fred W. Wubs3Henk A. Dijkstra4Institute for Marine and Atmospheric Research Utrecht Utrecht University Utrecht The NetherlandsBernoulli Institute for Mathematics, Computer Science and Artificial Intelligence University of Groningen Groningen The NetherlandsBernoulli Institute for Mathematics, Computer Science and Artificial Intelligence University of Groningen Groningen The NetherlandsBernoulli Institute for Mathematics, Computer Science and Artificial Intelligence University of Groningen Groningen The NetherlandsInstitute for Marine and Atmospheric Research Utrecht Utrecht University Utrecht The NetherlandsAbstract The Kuroshio Current in the North Pacific displays path changes on an interannual‐to‐decadal time scale. In an idealized barotropic quasi‐geostrophic model of the double‐gyre wind‐driven circulation under stochastic wind‐stress forcing, such variability can occur due to transitions between different equilibrium states. The high‐dimensionality of the problem makes it challenging to determine the probability of these transitions under the influence of stochastic noise. Here we present a new method to estimate these transition probabilities, using a Dynamical Orthogonal (DO) field approach. In the DO approach, the solution of the stochastic partial differential equations system is decomposed using a Karhunen–Loève expansion and separate problems arise for the ensemble mean state and the so‐called time‐dependent DO modes. The original method is first reformulated in a matrix approach which has much broader application potential to various (geophysical) problems. Using this matrix‐DO approach, we are able to determine transition probabilities in the double‐gyre problem and to identify transition paths between the different states. This analysis also leads to the understanding which conditions are most favorable for transition.https://doi.org/10.1029/2022MS003456model order reduction techniqueswind‐driven ocean circulationtransition probabilities and pathsmulti‐stable stochastic dynamical systemsnumerical methods |
| spellingShingle | René M. vanWesten Sourabh Kotnala Sven Baars Fred W. Wubs Henk A. Dijkstra A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation Journal of Advances in Modeling Earth Systems model order reduction techniques wind‐driven ocean circulation transition probabilities and paths multi‐stable stochastic dynamical systems numerical methods |
| title | A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation |
| title_full | A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation |
| title_fullStr | A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation |
| title_full_unstemmed | A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation |
| title_short | A New Method to Compute Transition Probabilities in Multi‐Stable Stochastic Dynamical Systems: Application to the Wind‐Driven Ocean Circulation |
| title_sort | new method to compute transition probabilities in multi stable stochastic dynamical systems application to the wind driven ocean circulation |
| topic | model order reduction techniques wind‐driven ocean circulation transition probabilities and paths multi‐stable stochastic dynamical systems numerical methods |
| url | https://doi.org/10.1029/2022MS003456 |
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