### Abstract

The Galerkin truncated inviscid Burgers equation has recently been shown by the authors to be a simple model with many degrees of freedom, with many statistical properties similar to those occurring in dynamical systems relevant to the atmosphere. These properties include long time-correlated, large-scale modes of low frequency variability and short time-correlated "weather modes" at smaller scales. The correlation scaling in the model extends over several decades and may be explained by a simple theory. Here a thorough analysis of the nature of predictability in the idealized system is developed by using a theoretical framework developed by R.K. This analysis is based on a relative entropy functional that has been shown elsewhere by one of the authors to measure the utility of statistical predictions precisely. The analysis is facilitated by the fact that most relevant probability distributions are approximately Gaussian if the initial conditions are assumed to be so. Rather surprisingly this holds for both the equilibrium (climatological) and nonequilibrium (prediction) distributions. We find that in most cases the absolute difference in the first moments of these two distributions (the "signal" component) is the main determinant of predictive utility variations. Contrary to conventional belief in the ensemble prediction area, the dispersion of prediction ensembles is generally of secondary importance in accounting for variations in utility associated with different initial conditions. This conclusion has potentially important implications for practical weather prediction, where traditionally most attention has focused on dispersion and its variability.

Original language | English (US) |
---|---|

Pages (from-to) | 15291-15296 |

Number of pages | 6 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 99 |

Issue number | 24 |

DOIs | |

State | Published - Nov 26 2002 |

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### ASJC Scopus subject areas

- Genetics
- General

### Cite this

**Quantifying predictability in a model with statistical features of the atmosphere.** / Kleeman, Richard; Majda, Andrew J.; Timofeyev, Ilya.

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 99, no. 24, pp. 15291-15296. https://doi.org/10.1073/pnas.192583699

}

TY - JOUR

T1 - Quantifying predictability in a model with statistical features of the atmosphere

AU - Kleeman, Richard

AU - Majda, Andrew J.

AU - Timofeyev, Ilya

PY - 2002/11/26

Y1 - 2002/11/26

N2 - The Galerkin truncated inviscid Burgers equation has recently been shown by the authors to be a simple model with many degrees of freedom, with many statistical properties similar to those occurring in dynamical systems relevant to the atmosphere. These properties include long time-correlated, large-scale modes of low frequency variability and short time-correlated "weather modes" at smaller scales. The correlation scaling in the model extends over several decades and may be explained by a simple theory. Here a thorough analysis of the nature of predictability in the idealized system is developed by using a theoretical framework developed by R.K. This analysis is based on a relative entropy functional that has been shown elsewhere by one of the authors to measure the utility of statistical predictions precisely. The analysis is facilitated by the fact that most relevant probability distributions are approximately Gaussian if the initial conditions are assumed to be so. Rather surprisingly this holds for both the equilibrium (climatological) and nonequilibrium (prediction) distributions. We find that in most cases the absolute difference in the first moments of these two distributions (the "signal" component) is the main determinant of predictive utility variations. Contrary to conventional belief in the ensemble prediction area, the dispersion of prediction ensembles is generally of secondary importance in accounting for variations in utility associated with different initial conditions. This conclusion has potentially important implications for practical weather prediction, where traditionally most attention has focused on dispersion and its variability.

AB - The Galerkin truncated inviscid Burgers equation has recently been shown by the authors to be a simple model with many degrees of freedom, with many statistical properties similar to those occurring in dynamical systems relevant to the atmosphere. These properties include long time-correlated, large-scale modes of low frequency variability and short time-correlated "weather modes" at smaller scales. The correlation scaling in the model extends over several decades and may be explained by a simple theory. Here a thorough analysis of the nature of predictability in the idealized system is developed by using a theoretical framework developed by R.K. This analysis is based on a relative entropy functional that has been shown elsewhere by one of the authors to measure the utility of statistical predictions precisely. The analysis is facilitated by the fact that most relevant probability distributions are approximately Gaussian if the initial conditions are assumed to be so. Rather surprisingly this holds for both the equilibrium (climatological) and nonequilibrium (prediction) distributions. We find that in most cases the absolute difference in the first moments of these two distributions (the "signal" component) is the main determinant of predictive utility variations. Contrary to conventional belief in the ensemble prediction area, the dispersion of prediction ensembles is generally of secondary importance in accounting for variations in utility associated with different initial conditions. This conclusion has potentially important implications for practical weather prediction, where traditionally most attention has focused on dispersion and its variability.

UR - http://www.scopus.com/inward/record.url?scp=0037180483&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037180483&partnerID=8YFLogxK

U2 - 10.1073/pnas.192583699

DO - 10.1073/pnas.192583699

M3 - Article

C2 - 12429863

AN - SCOPUS:0037180483

VL - 99

SP - 15291

EP - 15296

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 24

ER -