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Bred vector

In applied mathematics, bred vectors are perturbations related to Lyapunov vectors, that capture fast-growing dynamical instabilities of the solution of a numerical model. They are used, for example, as initial perturbations for ensemble forecasting in numerical weather prediction. They were introduced by Zoltan Toth and Eugenia Kalnay.[1]

The growth rates of bred vectors in the Lorenz system. Red indicates the fastest-growing bred vectors while blue the slowest.

Method edit

Bred vectors are created by adding initially random perturbations to a nonlinear model. The control (unperturbed) and the perturbed models are integrated in time, and periodically the control solution is subtracted from the perturbed solution. This difference is the bred vector. The vector is scaled to be the same size as the initial perturbation and is then added back to the control to create the new perturbed initial condition. After a short transient period, this "breeding" process creates bred vectors dominated by the naturally fastest-growing instabilities of the evolving control solution.

References edit

  1. ^ Toth, Zoltan; Kalnay, Eugenia (December 1993). "Ensemble Forecasting at NMC: The Generation of Perturbations". Bulletin of the American Meteorological Society. 74 (12): 2317–2330. Bibcode:1993BAMS...74.2317T. doi:10.1175/1520-0477(1993)074<2317:EFANTG>2.0.CO;2. S2CID 121674874.
  • Kalnay, E. (2003). Atmospheric Modeling, Data Assimilation and Predictability. Cambridge: Cambridge University Press. ISBN 978-0-521-79629-3.
  • Glickman, T. S., ed. (2000). Glossary of Meteorology (Second ed.). Boston, Massachusetts: American Meteorological Society.


bred, vector, applied, mathematics, bred, vectors, perturbations, related, lyapunov, vectors, that, capture, fast, growing, dynamical, instabilities, solution, numerical, model, they, used, example, initial, perturbations, ensemble, forecasting, numerical, wea. In applied mathematics bred vectors are perturbations related to Lyapunov vectors that capture fast growing dynamical instabilities of the solution of a numerical model They are used for example as initial perturbations for ensemble forecasting in numerical weather prediction They were introduced by Zoltan Toth and Eugenia Kalnay 1 The growth rates of bred vectors in the Lorenz system Red indicates the fastest growing bred vectors while blue the slowest Method editBred vectors are created by adding initially random perturbations to a nonlinear model The control unperturbed and the perturbed models are integrated in time and periodically the control solution is subtracted from the perturbed solution This difference is the bred vector The vector is scaled to be the same size as the initial perturbation and is then added back to the control to create the new perturbed initial condition After a short transient period this breeding process creates bred vectors dominated by the naturally fastest growing instabilities of the evolving control solution References edit Toth Zoltan Kalnay Eugenia December 1993 Ensemble Forecasting at NMC The Generation of Perturbations Bulletin of the American Meteorological Society 74 12 2317 2330 Bibcode 1993BAMS 74 2317T doi 10 1175 1520 0477 1993 074 lt 2317 EFANTG gt 2 0 CO 2 S2CID 121674874 Kalnay E 2003 Atmospheric Modeling Data Assimilation and Predictability Cambridge Cambridge University Press ISBN 978 0 521 79629 3 Glickman T S ed 2000 Glossary of Meteorology Second ed Boston Massachusetts American Meteorological Society nbsp This mathematical physics related article is a stub You can help Wikipedia by expanding it vte nbsp This mathematical analysis related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Bred vector amp oldid 1220479230, wikipedia, wiki, book, books, library,

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