NCL Website header
NCL Home > Documentation > Functions > Spherical harmonic routines


Computes spherical harmonic synthesis of a scalar quantity via rhomboidally truncated (R42) spherical harmonic coefficients onto a (108x128) gaussian grid. (creates metadata).

Available in version 4.2.0.a033 and later.


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

	function shsgc_R42_Wrap (
		a  : numeric,  
		b  : numeric   

	return_val  :  float or double



Real and imaginary spherical harmonic coefficients (input, array with two or more dimensions). The rightmost dimensions must be of size (43,43).

Return value

This function is "hard-wired" to return one or more latitude x longitude grids of size 108 x 128. Coordinate arrays are assigned. If metadata is available it is copied. The return type is floating point if the input is floating point, and double if the input is of type double.


shsgc_R42_Wrap performs the spherical harmonic synthesis via the arrays a and b.

NOTE: This function does not allow for missing data input values.

See Also



The following offer some typical scenarios. Of course, the _Wrap version of the function can be used if metadata is desired. Example 1

The file contains coefficients for one grid.

  f      = addfile("","r")
  a      = f->A                     ; a(43,43)
  b      = f->B                     ; b(43,43)
  x      = shsgc_R42(a,b)           ; x(108,128)
  x      = shsgc_R42_Wrap(a,b)      ; x(108,128)
Example 2

Same as Example 1 but the coefficients are stored as a one-dimensional array (AB). Use onedtond to make the required 43x43 array. For clarity, one-dimensional coefficients will be created separately.

  f      = addfile("","r")
  a1     = f->AB(0::2)              ; a1(43*43) ==> a(1849)
  b1     = f->AB(1::2)              ; b1(43*43) ==> b(1849)
  a      = onedtond(a1, (/43,43/) )
  b      = onedtond(b1, (/43,43/) )
  x      = shsgc_R42(a,b)           ; x(108,124)
  x      = shsgc_R42_Wrap(a,b)      ; x(108,128)
Example 3

Let the coefficients be stored as (ntim,klevel,43,43). The following illustrates recreating the entire variable array.

  f      = addfile("","r")
  a      = f->A                     ; a(ntim,klevel,43,43)
  b      = f->B                     ; b(ntim,klevel,43,43)
  x      = shsgc_R42(a,b)           ; x(ntim,klevel,108,124)
  x      = shsgc_R42_Wrap(a,b)      ; x(108,128)
Of course, it is possible to process one array at a time via do loops.
  f      = addfile("","r")
  do nt=0,ntim-1
    do kl=0,klevel-1
       a = f->A(nt,kl,:,:)          ; a(43,43)
       b = f->B(nt,kl,:,:)          ; b(43,43)
       x = shsgc_R42(a,b)           ; x(108,128)
    end do
  end do
Example 4

Same as Example 3 but the real and imaginary coefficients are in an alternating sequence. Use of both onedtond and ndtooned is required.

  f      = addfile("","r")
  A      = f->AB(:,:,0::2)          ; A(ntim,klevel,1849)
  B      = f->AB(:,:,1::2)          ; B(ntim,klevel,1849)
  a      = onedtond( ndtooned(A), (/ntim,klevel,43,43/) )
  b      = onedtond( ndtooned(B), (/ntim,klevel,43,43/) )
  x      = shsgc_R42(a,b)           ; x(ntim,klevel,108,124)
  x      = shsgc_R42_Wrap(a,b)      ; x(108,128)