Quantifying uncertainty for non-gaussian ensembles in complex systems

Rafail V. Abramov, Andrew J. Majda

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)411-447
Number of pages37
JournalSIAM Journal on Scientific Computing
Issue number2
StatePublished - 2005


  • Ensemble predictions
  • Predictability
  • Relative entropy

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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