Performs a Laplacian operation on spectral data.
A spherical harmonic function can be expressed as:
(4.13)
By performing a horizontal Laplacian operation
(4.14)
on (4.13), and from the properties of a spherical harmonic function, we obtain:
(4.15)
Now, by substituting
(4.16)
into (4.15), we obtain:
(4.17)
Conversely, when
(4.18)
we can use
(4.19)
to rewrite (4.18) as
(4.20)
The present subroutine calculates
from Amn when IND=1, and
from Amn when IND=-1.
SHTLAP(MM,IND,A,B)
MM (I) Input parameter. The cut-off wavenumber (M). IND (I) Input parameter. Specifies the type of Laplacian operation. (See above definition.) A (R) Input parameter. The array in which Amn is stored. (For length and arrangement of array, see SHTNML.) B (R) Output parameter. The array in which Bmn is stored. (For length and arrangement, see SHTNML.)
- (a)
- B00=0 is substituted when IND=-1.