Heavy Tails in the NWP Ensemble Perturbation Subspace

Recent studies have pointed to the presence of heavy tails in the climatological distributions of some common geophysical variables.  Since NWP forecast ensemble distributions effectively become samples from climatology when integrated for sufficient duration, it follows that the NWP ensemble subspace might also display heavy tails.  The potential presence of heavy tails is not only of academic interest but also has practical implications for various forecasting applications in terms of sampling, estimation, and balance.  Further, the emergence of heavy tails in geophysical distributions is not well understood from the standpoint of phenomenology / physical processes.  Here, standard diagnostics for the detection of heavy tails are applied to a handful of NWP ensembles, and the findings are found to support the presence of heavy tails in the ensemble subspace.  The synoptic phenomenology surrounding the most extreme values of ensemble perturbation total energy (PTE) is also examined, and it is shown that the tails in the ensemble perturbation subspace are not necessarily associated with extreme physical events.  Rather, the heavy tails tend to occur in association with outlying ensemble members at tropospheric jet levels in the case of a dry PTE norm, and at near-surface levels in the case of a moist PTE norm.  The large perturbations associated with the extreme end of the PTE tail tend to emerge rapidly and can manifest in any of the major state variables including the zonal and meridional wind components (U,V), air temperature (T), and specific humidity (q).  However, for the cases examined, the extreme perturbations under the dry PTE norm occur more frequently in the V-wind component.  The extreme perturbations under the dry PTE norm also tend to be coincident with regions of low ensemble effective dimension, consistent with the presence of an outlying ensemble member.  Further, the heavy tails are found not only when the ensemble perturbations are near saturation, but also during the growth phase of the perturbations.