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DCL:MATH2:SHTLIB: Spherical Harmonic Function: Explanation of Subroutines

4.3.23 SHTLFW

1.

Function

Performs forward Legendre transformation.

2.

Definition

The following are performed on floating-point wave data W^m_(&phi) for a zonal wavenumber.

When ISW=0, a normal forward Legendre transformation is performed.

When ISW=1, the longitudinal derivative of the forward Legendre transform is calculated.

When ISW=-1, the meridional derivative of the forward Legendre transform is calculated.

3.

Call

SHTLFW(MM,JM,M,ISW,WM,SM,WORK)

4.

Explanation of Parameters

MM	(I)	Input parameter. The cut-off wavenumber (M).
JM	(I)	Input parameter. 1/2 of the NS partition number (J)
ISW	(I)	Input parameter. Specifies the type of transformation. (See above definition.)
M	(I)	Input parameter. The zonal wavenumber (m) on which to perform transformation.
WM	(R)	Input parameter. Wave data. (For length and arrangement, see SHTLBW.)
SM	(R)	Output parameter. Spectral data. (For length and arrangement, see SHTLBW.)
WORK	(R)	Working area initialized by SHTINT.

5.

Notes

(a)

When ISW=0 and the wave data WM has been created by SHTLBW with the condition of ISW=0, the above integral will be free of aliasing and can be exactly evaluated.

(b)

When ISW=±1 and the wave data WM has been created by SHTLBW with the condition of ISW, the above integral will be free of aliasing and can be exactly evaluated.

(c)

Must be M≥0.