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shsgc_R42

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

Prototype

	function shsgc_R42 (
		a  : numeric,  
		b  : numeric   
	)

Arguments

a
b

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. The return type is floating point if the input is floating point, and double if the input is of type double.

Description

shsgc_R42 performs the spherical harmonic synthesis via the arrays a and b.

NOTE: This function does not allow for missing values.

Examples

The following offer some typical scenarios.

Example 1

The file contains coefficients for one grid.

  f      = addfile("foo.nc","r")
  a      = f->A                     ; a(43,43)
  b      = f->B                     ; b(43,43)
  x      = shsgc_R42(a,b)           ; x(108,128)

  ; Use shsgc_R42_Wrap if metadata retention is desired
  ; 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("foo.nc","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(108,128)

  ; Use shsgc_R42_Wrap if metadata retention is desired
  ; 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("foo.nc","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,108,128)

  ; Use shsgc_R42_Wrap if metadata retention is desired
  ; 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("foo.nc","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)

       ; Use shsgc_R42_Wrap if metadata retention is desired
       ; x = shsgc_R42_Wrap(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.