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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

th

Potential temperature (K).

u

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

z

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

See Also

coriolis_param, brunt_vaisala_atm, pot_temp, rigrad_bruntv_atm, static_stability

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:

   Variable: egr
   Type: float
   Total Size: 20925216 bytes
               5231304 values
   Number of Dimensions: 4
   Dimensions and sizes:   [Time | 1] x [bottom_top | 39] x [south_north | 324] x [west_east | 414]
   Coordinates: 
   Number Of Attributes: 3
     _FillValue :  1e+20
     long_name :   maximum eady growth rate
     units :       
   (0)     maximum eady growth rate: min=6.5775e-13   max=0.00406928

 
            P       Z       EGR (1/s)    EGR (1/day)
    (0)	 1009.1    29.2   -6.51605e-06  -0.56
    (1)	 1001.0    99.1   -4.83609e-06  -0.42
    (2)	  990.3   192.9   -2.27035e-06  -0.20
    (3)	  976.8   313.0   -9.32204e-07  -0.08
    (4)	  960.0   463.0    3.49967e-06   0.30
    (5)	  939.6   647.4    1.24992e-05   1.08
    (6)	  915.3   872.0    1.05712e-05   0.91
    (7)	  886.7  1142.9    2.63051e-06   0.23
    (8)	  853.8  1463.4    3.39886e-06   0.29
    (9)	  817.2  1835.1    4.34887e-06   0.38
    (10)  777.3  2258.8    2.34866e-06   0.20
    (11)  734.6  2733.7    5.76828e-07   0.05
    (12)  689.6  3259.3    3.18521e-06   0.28
    (13)  642.9  3835.0    4.51157e-06   0.39
    (14)  596.3  4442.5    2.02051e-06   0.17
    (15)  552.0  5057.9    9.44995e-07   0.08
    (16)  510.4  5674.7    1.08149e-06   0.09
    (17)  471.4  6292.0    5.79138e-06   0.50
    (18)  434.8  6907.9    1.05950e-05   0.92
    (19)  400.5  7523.3    5.64395e-06   0.49
    (20)  368.4  8139.1    3.27011e-07   0.03
    (21)  338.4  8755.4    8.26907e-07   0.07
    (22)  310.3  9372.1    3.56708e-06   0.31
    (23)  284.1  9988.7    7.66039e-06   0.66
    (24)  259.7 10606.4    1.39343e-05   1.20
    (25)  236.9 11225.7    1.61388e-05   1.39
    (26)  215.7 11845.9    1.17152e-05   1.01
    (27)  195.9 12465.8    4.51332e-06   0.39
    (28)  177.6 13085.9    5.23316e-06   0.45
    (29)  160.6 13707.9    1.15163e-05   1.00
    (30)  144.8 14335.0    7.09510e-06   0.61
    (31)  130.2 14971.9    5.89672e-06   0.51
    (32)  116.7 15621.2    6.78411e-06   0.59
    (33)  104.3 16288.0    4.65560e-06   0.40
    (34)   92.8 16976.2    4.16494e-06   0.36
    (35)   82.2 17686.4    4.20652e-06   0.36
    (36)   72.6 18420.1    2.95023e-06   0.25
    (37)   63.7 19185.4    2.68033e-06   0.23
    (38)   54.7 20094.5    3.04996e-06   0.26