Compute the power spectrum of the magnetic field given the Schmidt seminormalized magnetic potential spherical harmonic coefficients.
call SHMagPowerSpectrum (c, a, r, lmax, spectrum, exitstatus)
c : input, real(dp), dimension (2, lmax+1, lmax+1)
: The Schmidt seminormalized spherical harmonic coefficients of the magnetic potential.
a : input, real(dp)
: The reference radius of the magnetic potential spherical harmonic coefficients.
r : input, real(dp)
: The radius to evaluate the magnetic field.
lmax : input, integer
: The maximum spherical harmonic degree to calculate the power spectrum.
spectrum : output, real(dp), dimension (lmax+1)
: The power spectrum of the magnetic field.
exitstatus : output, optional, integer
: If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.
SHMagPowerSpectrum will calculate the power spectrum of the magnetic field at radius r given the magnetic potential Schmidt seminormalized spherical harmonic coefficients c evaluated at radius a. For a given degree l, this is explicitly calculated as (Lowes 1966):
S(l) = (l+1) (a/r)**(2l+4) Sum_{m=0}^l [ c(1, l+1, m+1)**2 + c(2, l+1, m+1)**2 ].
Lowes, F. J., Mean-square values on sphere of spherical harmonic fields, J. Geophys. Res., 71(8), 2179, 1966.