# Local low dimensionality of atmospheric dynamics.

@article{Patil2001LocalLD, title={Local low dimensionality of atmospheric dynamics.}, author={D. J. Patil and Brian R. Hunt and Eugenia Kalnay and James A. Yorke and Edward Ott}, journal={Physical review letters}, year={2001}, volume={86 26 Pt 1}, pages={ 5878-81 } }

A statistic, the BV (bred vector) dimension, is introduced to measure the effective local finite-time dimensionality of a spatiotemporally chaotic system. It is shown that the Earth's atmosphere often has low BV dimension, and the implications for improving weather forecasting are discussed.

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#### References

SHOWING 1-10 OF 12 REFERENCES

Chaos: An Introduction to Dynamical Systems

- Physics
- 1997

One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential… Expand

Linear algebra with applications

- Computer Science
- 1991

Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra. Expand

Mon. Weather Rev

- Mon. Weather Rev
- 1997

Scheick, Linear Algebra with Applications (McGraw

- 1997

Ten bred vectors are made available, but five of them are the result of subtracting the perturbations from the main solution; hence we average the pairs of the perturbations to give five bred vectors

- Ten bred vectors are made available, but five of them are the result of subtracting the perturbations from the main solution; hence we average the pairs of the perturbations to give five bred vectors

Bull

- Am. Meteorol. Soc. 72, 2317
- 1993

Bull. Am. Meteorol. Soc

- Bull. Am. Meteorol. Soc
- 1993

Email address: dpatil@ipst.umd.edu ‡ Department of Meteorology

- Email address: dpatil@ipst.umd.edu ‡ Department of Meteorology

Institute for Plasma Research and Departments of Physics and of Electrical Engineering

- Institute for Plasma Research and Departments of Physics and of Electrical Engineering

The NWS global model output requires almost a gigabyte of data; hence only a few key fields are posted

- The NWS global model output requires almost a gigabyte of data; hence only a few key fields are posted