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makemaggriddh.doc
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Create 2D cylindrical maps on a flattened ellipsoid of all three vector
components of the magnetic field, the magnitude of the magnetic field, and the
magnetic potential.
Usage
-----
rad, theta, phi, total, pot = MakeMagGridDH (cilm, r0, [lmax, a, f, sampling,
lmax_calc, extend])
Returns
-------
rad : float, dimension(nlat, nlong)
A 2D map of the radial component of the magnetic field that conforms to the
sampling theorem of Driscoll and Healy (1994). If sampling is 1, the grid is
equally sampled and is dimensioned as (n by n), where n is 2lmax+2. If
sampling is 2, the grid is equally spaced and is dimensioned as (n by 2n).
The first latitudinal band of the grid corresponds to 90 N, the latitudinal
sampling interval is 180/n degrees, and the default behavior is to exclude
the latitudinal band for 90 S. The first longitudinal band of the grid is 0
E, by default the longitudinal band for 360 E is not included, and the
longitudinal sampling interval is 360/n for an equally sampled and 180/n for
an equally spaced grid, respectively. If extend is 1, the longitudinal band
for 360 E and the latitudinal band for 90 S will be included, which
increases each of the dimensions of the grid by 1.
theta : float, dimension(nlat, nlong)
A 2D equally sampled or equally spaced grid of the theta component of the
magnetic field.
phi : float, dimension(nlat, nlong)
A 2D equally sampled or equally spaced grid of the phi component of the
magnetic field.
total : float, dimension(nlat, nlong)
A 2D equally sampled or equally spaced grid of the total magnetic field
strength.
pot : float, dimension(nlat, nlong)
A 2D equally sampled or equally spaced grid of the magnetic potential.
Parameters
----------
cilm : float, dimension (2, lmaxin+1, lmaxin+1)
The real Schmidt semi-normalized spherical harmonic coefficients to be
expanded in the space domain. The coefficients C1lm and C2lm refer to the
cosine (Clm) and sine (Slm) coefficients, respectively, with Clm=cilm[0,l,m]
and Slm=cilm[1,l,m]. Alternatively, C1lm and C2lm correspond to the positive
and negative order coefficients, respectively. The coefficients are assumed
to have units of nT.
r0 : float
The reference radius of the spherical harmonic coefficients.
lmax : optional, integer, default = lamxin
The maximum spherical harmonic degree of the coefficients cilm. This
determines the number of samples of the output grids, n=2*lmax+2, and the
latitudinal sampling interval, 90/(lmax+1).
a : optional, float, default = r0
The semi-major axis of the flattened ellipsoid on which the field is
computed.
f : optional, float, default = 0
The flattening of the reference ellipsoid: i.e., F=(R_equator-
R_pole)/R_equator.
sampling : optional, integer, default = 2
If 1 the output grids are equally sampled (n by n). If 2, the grids are
equally spaced (n by 2n).
lmax_calc : optional, integer, default = lmax
The maximum spherical harmonic degree used in evaluating the functions. This
must be less than or equal to lmax.
extend : input, optional, bool, default = False
If True, compute the longitudinal band for 360 E and the latitudinal band
for 90 S. This increases each of the dimensions of the grids by 1.
Description
-----------
MakeMagGridDH will create 2-dimensional cylindrical maps from the spherical
harmonic coefficients cilm of all three components of the magnetic field, the
total field strength, and the magnetic potential. The magnetic potential is
given by
V = R0 Sum_{l=1}^LMAX (R0/r)^{l+1} Sum_{m=-l}^l C_{lm} Y_{lm}
and the magnetic field is
B = - Grad V.
The coefficients are referenced to a radius r0, and the function is computed on
a flattened ellipsoid with semi-major axis a (i.e., the mean equatorial radius)
and flattening f.
The default is to use an input grid that is equally sampled (n by n), but this
can be changed to use an equally spaced grid (n by 2n) by the optional argument
sampling. The redundant longitudinal band for 360 E and the latitudinal band for
90 S are excluded by default, but these can be computed by specifying the
optional argument extend.
Reference
---------
Driscoll, J.R. and D.M. Healy, Computing Fourier transforms and convolutions on
the 2-sphere, Adv. Appl. Math., 15, 202-250, 1994.