# 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 = 62shaec(g,a,b)tri_trunc(a,b,T) ;triangularly truncate the spherical harmonic coefficientsexp_tapersh(a,b, 45, 2) ;taper the spherical harmonic coefficientsshsec(a,b,h) ;perform the spherical harmonic synthesis on the truncated coefficients, store results in h