Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity
We introduce a method for quantifying the predictability of the event that the evolution of a deterministic dynamical system enters a specific subset of state space at a given lead time. The main idea is to study the distribution of finite-time growth rates of errors in initial conditions along the...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/9419024 |
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| author | A. E. Sterk D. L. van Kekem |
| author_facet | A. E. Sterk D. L. van Kekem |
| author_sort | A. E. Sterk |
| collection | DOAJ |
| description | We introduce a method for quantifying the predictability of the event that the evolution of a deterministic dynamical system enters a specific subset of state space at a given lead time. The main idea is to study the distribution of finite-time growth rates of errors in initial conditions along the attractor of the system. The predictability of an event is measured by comparing error growth rates for initial conditions leading to that event with all possible growth rates. We illustrate the method by studying the predictability of extreme amplitudes of traveling waves in the Lorenz-96 model. Our numerical experiments show that the predictability of extremes is affected by several routes to chaos in a different way. In a scenario involving intermittency due to a periodic attractor disappearing through a saddle-node bifurcation we find that extremes become better predictable as the intensity of the event increases. However, in a similar intermittency scenario involving the disappearance of a 2-torus attractor we find that extremes are just as predictable as nonextremes. Finally, we study a scenario which involves a 3-torus attractor in which case the predictability of extremes depends nonmonotonically on the prediction lead time. |
| format | Article |
| id | doaj-art-6be14003080b4f089ea3796ee97b22f2 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-6be14003080b4f089ea3796ee97b22f22025-02-03T06:13:42ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/94190249419024Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-PeriodicityA. E. Sterk0D. L. van Kekem1Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, NetherlandsJohann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, NetherlandsWe introduce a method for quantifying the predictability of the event that the evolution of a deterministic dynamical system enters a specific subset of state space at a given lead time. The main idea is to study the distribution of finite-time growth rates of errors in initial conditions along the attractor of the system. The predictability of an event is measured by comparing error growth rates for initial conditions leading to that event with all possible growth rates. We illustrate the method by studying the predictability of extreme amplitudes of traveling waves in the Lorenz-96 model. Our numerical experiments show that the predictability of extremes is affected by several routes to chaos in a different way. In a scenario involving intermittency due to a periodic attractor disappearing through a saddle-node bifurcation we find that extremes become better predictable as the intensity of the event increases. However, in a similar intermittency scenario involving the disappearance of a 2-torus attractor we find that extremes are just as predictable as nonextremes. Finally, we study a scenario which involves a 3-torus attractor in which case the predictability of extremes depends nonmonotonically on the prediction lead time.http://dx.doi.org/10.1155/2017/9419024 |
| spellingShingle | A. E. Sterk D. L. van Kekem Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity Complexity |
| title | Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity |
| title_full | Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity |
| title_fullStr | Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity |
| title_full_unstemmed | Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity |
| title_short | Predictability of Extreme Waves in the Lorenz-96 Model Near Intermittency and Quasi-Periodicity |
| title_sort | predictability of extreme waves in the lorenz 96 model near intermittency and quasi periodicity |
| url | http://dx.doi.org/10.1155/2017/9419024 |
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