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Logarithmic bred vectors in spatiotemporal chaos: structure and growth
Sarah Hallerberg1, Diego Pazó, Juan M López
1Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, E-39005 Santander, Spain. sarah.hallerberg@physik.tu-chemnitz.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
Logarithmic bred vectors in atmospheric models resemble leading Lyapunov vectors, enabling a new scaling law for their growth rates. This research clarifies chaos prediction in weather models.
Area of Science:
- Atmospheric Science
- Chaos Theory
- Numerical Modeling
Background:
- Bred vectors are finite perturbations used in atmospheric models with spatially extended chaos.
- Understanding bred vector behavior is crucial for improving prediction accuracy.
Purpose of the Study:
- To investigate the structure, spatial correlations, and growth rates of logarithmic bred vectors.
- To establish a relationship between bred vector growth rates and Lyapunov exponents.
Main Methods:
- Analysis of logarithmic bred vector structure and correlations.
- Derivation of a scaling law for bred vector growth rates.
- Simulation using the Lorenz 1996 model.
Main Results:
- Logarithmic bred vectors are piecewise copies of the leading Lyapunov vector after transformation.
- A scaling law for bred vector growth rate was deduced based on amplitude.
- Growth rates correlate with Lyapunov exponents for expanding directions.
Conclusions:
- The study provides a theoretical framework for understanding bred vector dynamics in chaotic atmospheric models.
- Results enhance the predictability of atmospheric phenomena by characterizing perturbation growth.
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