Forecast Uncertainty and Regional Mixture Distributions in the Ensemble Subspace

A simple but fundamental relationship is shown between regional-average
forecast uncertainty and regional mixture distributions. The structure of
regional mixtures of perturbation energy (PE) in the ensemble subspace is
examined using standard diagnostics including log-quantile plots and
numerical shape-parameter estimation. These diagnostics show that regional
mixtures of wind PE and air temperature PE can have heavy-tailed (i.e.
sub-exponential) structure through a great portion of the tail, even if the
extremity of the tail is exponential or bounded in nature. The
sub-exponential structure appears in a wide variety of circumstances
including during the growth phase of the ensemble perturbations and in
ensembles generated from both dynamically conditioned and random analysis
perturbations, suggesting that the structure may be an endemic feature of
the regional mixtures of PE.

The sub-exponential structure in the mixtures implies that, regionally,
moderate to large forecast errors occur with greater frequency than would be
expected from standard distributions like the exponential. This can have
notable practical consequences for distribution fitting, for assessments of
sampling variability, and for estimation of the maximum forecast error
magnitude within a region of interest. Synoptically, the most extreme values
in the tails of the regional mixtures of PE are not associated with extreme
physical events, but rather with ensemble outliers.