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NCL: Eliassen-Palm flux; Eady Growth Rate

Brunt-Vaisala; Gradient Richardson Number

The Glossary of Meteorology defines Eliassen-Palm flux (EP-flux) as:

   A vector quantity with nonzero components in the latitude-height plane, 
   the direction and magnitude of which determine the relative importance 
   of eddy heat flux and momentum flux.
   When the Eliassen-Palm flux (EPF) vector points upward, the meridional heat flux 
   dominates; when the EPF vector points in the meridional direction, the meridional 
   flux of zonal momentum dominates. The divergence of the Eliassen-Palm flux is more 
   frequently used as a diagnostic tool, as it is proportional to the eddy potential 
   vorticity flux. In the special case when the EPF divergence is zero, as for steady, 
   frictionless, linear waves, thermal wind balance is maintained in an idealized 
   zonally symmetric atmosphere through the induction of a mean meridional circulation, 
   even though the waves produce significant eddy heat and momentum fluxes.

The NCL function, epflux works for NCEP Reanalysis data. The function is based upon code developed by J. Barsugli (NOAA/PSD) and adapted by C. Smith (NOAA/PSD). The original NCL script is at:

A guide to the EP-flux computations and sample results are at:"

   Edmon, H.J., B.J. Hoskins, and M.E. McIntyre,1980:
   Eliassen-Palm cross sections for the troposphere.
   J. Atmos. Sci., 37:2600-2616
Eliassen-Palm flux (EP-flux) is a non-linear quantity. Hence, the correct way to compute time averaged EP-flux is to compute it every time step and average the results. Computing EP-flux from monthly mean U, V, T quantities will result in smooth results that may compare well in terms of patterns but will likely lack the detailed structure of the 'correct' monthly mean EP-flux.

epflux_1.ncl: The example reads daily mean daily data for a specified period. The data source is NOAA's Physical Sciences Division's NCEP Reanalysis. The variables are of type short and must be unpacked (short2flt) prior to use. The contours are for the acceleration (dudt, showacc=1)
epflux_2.ncl: The example reads daily mean daily data for Dec 7, 2016. The data source is NOAA's Physical Sciences Division's NCEP Reanalysis daily mean for 2016. The contours are for the EP-divergence (showacc=0) The image generated by NOAA/PSD is here.
BrRiEgr_1.ncl: Using WRF model input, calculate the Brunt-Vaisala frequency (brunt_vaisala_atm), the gradient Richardson number (rigrad_bruntv_atm) and the Eady maximum growth rate eady_growth_rate. The level chosen is within the boundary layer.