Quantifying uncertainty in climate change science through empirical information theory

Andrew J. Majda, Boris Gershgorin

Research output: Contribution to journalArticlepeer-review


Quantifying the uncertainty for the present climate and the predictions of climate change in the suite of imperfect Atmosphere Ocean Science (AOS) computer models is a central issue in climate change science. Here, a systematic approach to these issues with firm mathematical underpinning is developed through empirical information theory. An information metric to quantify AOS model errors in the climate is proposed here which incorporates both coarse-grained mean model errors as well as covariance ratios in a transformation invariant fashion. The subtle behavior of model errors with this information metric is quantified in an instructive statistically exactly solvable test model with direct relevance to climate change science including the prototype behavior of tracer gases such as CO2. Formulas for identifying the most sensitive climate change directions using statistics of the present climate or an AOS model approximation are developed here; these formulas just involve finding the eigenvector associated with the largest eigenvalue of a quadratic form computed through suitable unperturbed climate statistics. These climate change concepts are illustrated on a statistically exactly solvable one-dimensional stochastic model with relevance for low frequency variability of the atmosphere. Viable algorithms for implementation of these concepts are discussed throughout the paper.

Original languageEnglish (US)
Pages (from-to)14958-14963
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number34
StatePublished - Aug 24 2010


  • Model errors
  • Practical algorithms
  • Unbiased empirical estimates

ASJC Scopus subject areas

  • General


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