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exp_tapersh

Performs tapering (filtering) of the spherical harmonic coefficients.

Prototype

	procedure exp_tapersh (
		a  : float or double,  
		b  : float or double,  
		N  : numeric,          
		r  : integer           
	)

Arguments

a
b

spherical harmonic coefficients returned to the user by the NCL procedures shagc/shaec.

N

mode at which the taper weight will equal exp(-1) [=0.3678795 ]. (N < maximum-wave-number possible)

r

power of exponent. This determines the rate at which the coefficients decrease (see below).

Description

exp_tapersh performs tapering on the spherical harmonic coefficients.

The effect is to perform (spatial) isotropic smoothing by reducing the amplitude of the coefficients at higher modes. Most frequently, this is done for graphical purposes. The formula used is:

S(n) = EXP{-[ n(n+1)/N(N+1)]^r }
n = total wavenumber, N,r defined above. This is equation (9) in the following reference:

Reference:

Spatial Smoothing on the Sphere
P. D. Sardeshmukh and B. J. Hoskins
Monthly Weather Review, December 1984, pp 2424-2529.
exp_tapersh is the procedural version of exp_tapershC.

See Also

exp_tapershC, exp_tapersh_wgts, shagc, shaec

Examples

Example 1

a and b are calculated from a procedure (say shagc/shaec). Array space for a and b must be preallocated by the user prior to calling the NCL procedures shagc/shaec. g is a data array dimensioned ntim x nlat x nlon, h is a preallocated, equally-spaced grid, and no cyclic points are included

  a  = new ( nlat, nlat )
  b  = new ( nlat, nlat )

  T  = 62
  shaec(g,a,b)
  tri_trunc (a,b,T)			;triangularly truncate the spherical harmonic coefficients
  exp_tapersh (a,b, 45, 2)		;taper the spherical harmonic coefficients

  shsec(a,b,h)			;perform the spherical harmonic synthesis on the truncated coefficients, store results in h