MakeGridPoint()

Evaluate a real function expressed in real spherical harmonics at a set of points.

Usage

value = MakeGridPoint (cilm, lat, lon, [lmax, norm, csphase, dealloc])

Returns

value : float, ndarray

Value of the function at (lat, lon).

Parameters

cilm : float, dimension (2, lmaxin+1, lmaxin+1)

The real spherical harmonic coefficients of the function. The coefficients C0lm and C1lm refer to the cosine (Clm) and sine (Slm) coefficients, respectively, with Clm=cilm[0,1,m] and Slm=cilm[1,l,m].

lat : float, array_like

The geocentric latitude of the point in degrees.

lon : float, array_like

The longitude of the point in degrees.

lmax : integer, array_like, optional, default = lmaxin

The maximum spherical harmonic degree used in evaluating the function.

norm : integer, array_like, optional, default = 1

1 (default) = Geodesy 4-pi normalized harmonics; 2 = Schmidt semi-normalized harmonics; 3 = unnormalized harmonics; 4 = orthonormal harmonics.

csphase : integer, array_like, optional, default = 1

1 (default) = do not apply the Condon-Shortley phase factor to the associated Legendre functions; -1 = append the Condon-Shortley phase factor of (-1)^m to the associated Legendre functions.

dealloc : integer, array_like, optional, default = 0

0 (default) = Save variables used in the external Legendre function calls. (1) Deallocate this memory at the end of the funcion call.

Description

MakeGridPoint will expand a function expressed in spherical harmonics at a given set of points. The input latitudes and longitudes are in degrees, and the maximum degree used in evaluating the function is the smaller of lmaxin and lmax. The employed spherical harmonic normalization and Condon-Shortley phase convention can be set by the optional arguments norm and csphase; if not set, the default is to use geodesy 4-pi normalized harmonics that exclude the Condon-Shortley phase of (-1)^m.