## Abstract

Many situations in complex systems require quantitative estimates of the lack of information in one probability distribution relative to another. In short-term climate and weather prediction, examples of these issues might involve a lack of information in the historical climate record compared with an ensemble prediction, or a lack of information in a particular Gaussian ensemble prediction strategy involving the first and second moments compared with the non-Gaussian ensemble itself. The relative entropy is a natural way to quantify this information. Here a recently developed mathematical theory for quantifying this lack of information is converted into a practical algorithmic tool. The theory involves explicit estimators obtained through convex optimization, principal predictability components, a signal/dispersion decomposition, etc. An explicit computationally feasible family of estimators is developed here for estimating the relative entropy over a large dimensional family of variables through a simple hierarchical strategy. Many facets of this computational strategy for estimating uncertainty are applied here for ensemble predictions for two "toy" climate models developed recently: the Galerkin truncation of the Burgers-Hopf equation and the Lorenz '96 model.

Original language | English (US) |
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Pages (from-to) | 411-447 |

Number of pages | 37 |

Journal | SIAM Journal on Scientific Computing |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - 2005 |

## Keywords

- Ensemble predictions
- Predictability
- Relative entropy

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics