Re: Tapered truncation in g2gsh, etc.

From: Dennis Shea <shea_at_nyahnyahspammersnyahnyah>
Date: Fri, 21 Jul 2006 22:36:05 -0600 (MDT)

> I would like to use g2gsh and f2gsh to regrid data while reducing the spatial
> resolution to T15 resolution. I would like to use the tapered truncation in
> spherical harmonic space (twave <0), as this reduces spectral ripples.
> However, I cannot find any documentation as to what the taper is. Does
> anyone know? Is it the Sardeshmukh and Hoskins taper that is used in
> exp_tapersh. If so, what exponent is used?
> _______________________________________________

The taper is the same used by the following:

    exp_tapershC 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. this is commonly 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:


     Spatial Smoothing on the Sphere
     P. D. Sardeshmukh and B. J. Hoskins
     Monthly Weather Review, December 1984, pp 2424-2529.
> _______________________________________________

I *think* r=4

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