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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:aakash_sane@brown.edu

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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:aakash.sane@princeton.edu

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We propose a metric for measuring internal and forced variability in ensemble atmosphere, ocean, or climate models using information theory: Shannon entropy and mutual information. This metric differs from the standard ensemble-variance approaches. 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 as well as a change of units or scale. Finally, we use an example featuring a highly skewed probability distribution (Arctic sea surface temperature) to show that the new metric is robust even with a sharp nonlinear cutoff (the freezing point). We apply these two metrics to quantify internal vs forced variability in (1) idealized Gaussian data, (2) an initial condition ensemble of a realistic coastal ocean model, (3) the Community Earth System Model large ensemble. Each case illustrates the advantages of the proposed metric over variance-based metrics. Furthermore, in the coastal ocean model, the new metric is adapted to further quantify the impact of different boundary forcing choices to aid in prioritizing model improvements–i.e., comparing different choices of extrinsic forcing. The 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.