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Internal vs Forced Variability Metrics for Geophysical Flows Using Information Theory
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  • Aakash Sane,
  • Baylor Fox-Kemper,
  • David Ullman,
  • Aakash Sane
Aakash Sane
Brown University, Brown University

Corresponding Author:[email protected]

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Baylor Fox-Kemper
Brown University, Brown University, Brown University
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David Ullman
University of Rhode Island, University of Rhode Island, University of Rhode Island
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Aakash Sane
Brown University

Corresponding Author:[email protected]

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Abstract

We demonstrate the use of information theory metrics, Shannon entropy and mutual information, for measuring internal and forced variability in ensemble atmosphere, ocean, or climate models. This metric delineates intrinsic and extrinsic variability reliably in a wider range of circumstances. Information entropy quantifies variability by the size of the visited probability distribution, as opposed to variance that measures only its second moment. Shannon entropy and mutual information manage correlated fields, apply to any data, and are insensitive to outliers and a change of units or scale. In the first part of this article, we use climate model ensembles to illustrate an example featuring a highly skewed probability distribution (Arctic sea surface temperature) to show that the new metric is robust even under sharp nonlinear behavior (freezing point). We apply these two metrics to quantify internal vs forced variability in (1) idealized Gaussian and uniformly distributed data, (2) an initial condition ensemble of a realistic coastal ocean model (OSOM), (3) the GFDL-ESM2M climate model large ensemble. Each case illustrates the advantages of information theory metrics over variance-based metrics. Our chosen metric can be applied to any ensemble of models where intrinsic and extrinsic factors compete to control variability and can be applied regardless of if the ensemble spread is Gaussian. In the second part of this article, mutual information and Shannon entropy are used to quantify the impact of different boundary forcing in a coastal ocean model. Information theory is useful as it enables ranking the potential impacts of improving boundary and forcing conditions across multiple predicted variables with different dimensions.