Internal vs Forced Variability Metrics for Geophysical Flows Using
Information Theory
Abstract
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.