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eady_growth_rate

Compute the maximum Eady growth rate.

Available in version 6.4.0 and later.

Prototype

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"

	function eady_growth_rate (
		th      : numeric,  ; float, double, integer only
		u       : numeric,  
		z       : numeric,  
		lat     : numeric,  
		opt [1] : integer,  
		dim [1] : integer   
	)

	return_val [dimsizes(z)] :  float or double

Arguments

Potential temperature (K).

Zonal wind (m/s). Same dimensionality as th.

Geometric height (m). Same dimensionality as th.

lat

Latitudes (degrees). Same dimensionality as th. NOTE: This may require the user to use conform or conform_dims prior to using the function.

opt

opt=0, Return the Eady growth rate
opt=1, Return the Eady growth rate and the vertical gradient of the zonal wind (du/dz)
opt=2, Return the Eady growth rate and the vertical gradient of the zonal wind (du/dz) and the Brunt-Vaisala frequency

dim

The dimension number of z which corresponds to th.

Return value

A multi-dimensional array of the same size and shape as th. The output will be double if th is of type double.

Description

The maximum Eady growth rate is a measure of baroclinic instability.

  eady_growth_rate = 0.3098*g*abs(f)*abs(du/dz)/brunt_vaisala

where f is the Coriolis parameter (1/s) and g is gravity (m/s).

References: 
   E. Eady (1949):
   Long waves and cyclone waves
   Tellus, 1, 33-52
     http://dx.doi.org/10.1111/j.2153-3490.1949.tb01265.x

   R. S. Lindzen and Brian Farrell, 1980: 
   A Simple Approximate Result for the Maximum Growth Rate of Baroclinic Instabilities. 
   J. Atmos. Sci., 37, 1648-1654. 
    http://dx.doi.org/10.1175/1520-0469(1980)037<1648:ASARFT>2.0.CO;2

   Simmonds, I., and E.-P. Lim (2009): 
   Biases in the calculation of Southern Hemisphere mean baroclinic eady growth rate 
   Geophys. Res. Lett., 36, L01707 
     http://dx.doi.org/10.1029/2008GL036320

Examples

Example 1: Read data from a WRF file and calculate assorted quantities.

;----------------------------------------------------------
;                     WRF DATA
;----------------------------------------------------------

   a  = addfile("wrfout_d01_2013-05-17_12","r") ;[Time|1]x[bottom_top|40]x[south_north|324]x[west_east|414]
                                               ;     0            1              2              3

   th = wrf_user_getvar(a,"theta",-1)      ; potential temperature (degK)
   z  = wrf_user_getvar(a,"z",-1)          ; model height
   ua = wrf_user_getvar(a,"ua"   ,-1)      ; u at mass grid points

;--- Read latitudes 
;    The 'eady_growth_rate' function requires that 'lat' and 'th' agree
;    Use 'conform' the propogate the lat values

   xlat = a->XLAT                          ; [Time|1]x[south_north|324]x[west_east|414] 
   printVarSummary(xlat)

   XLAT = conform(th, xlat, (/0,2,3/))     ; (1,40,324,414)

   egr = eady_growth_rate(th, ua, z, XLAT, 0,  1)
   printVarSummary(egr)
   printMinMax(egr, 0)

; print all vertical values at an arbitrarily chosen grid point

   nt =  0        ; print 1st time step
   ix = 20        ; arbitrary
   jy = 21

   pr = wrf_user_getvar(a,"pressure"   ,-1)      ; for printing 

   print( sprint("%7.1f" ,   pr(nt,:,jy,ix)) \
        + sprintf("%7.1f" ,    z(nt,:,jy,ix)) \
        + sprintf("%15.5e",  egr(nt,:,jy,ix)) \
        + sprintf("%7.2f",  egr(nt,:,jy,ix)*86400) )

The (edited) output is: