Calculate the admittance and correlation spectra of two real functions.

Usage

admit, error, corr = SHAdmitCorr (gilm, tilm, [lmax])

Returns

admit : float, dimension (lmax+1)
The admittance function, which is equal to Sgt/Stt.
error : float, dimension (lmax+1)
The uncertainty of the admittance function, assuming that gilm and tilm are related by a linear isotropic transfer function, and that the lack of correlation is a result of uncorrelated noise.
corr : float, dimension (lmax+1)
The degree correlation function, which is equal to Sgt/sqrt(Sgg Stt).

Parameters

gilm : float, dimension (2, lmaxg+1, lmaxg+1)
The real spherical harmonic coefficients of the function G.
tilm : float, dimension (2, lmaxt+1, lmaxt+1)
The real spherical harmonic coefficients of the function T.
lmax : optional, integer, default = min(lmaxg, lmaxt)
The maximum spherical harmonic degree that will be calculated for the admittance and correlation spectra. This must be less than or equal to the minimum of lmaxg and lmaxt.

Description

SHAdmitCorr will calculate the admittance, admittance error, and correlation spectra associated with two real functions expressed in real spherical harmonics. The admittance is defined as Sgt/Stt, where Sgt is the cross-power spectrum of two functions G and T. The degree-correlation spectrum is defined as Sgt/sqrt(Sgg Stt), which can possess values between -1 and 1. The error of the admittance is calculated assuming that G and T are related by a linear isotropic transfer function: Gilm = Ql Tilm + Nilm, where N is noise that is uncorrelated with the topography. It is important to note that the relationship between two fields is often not described by such an isotropic expression.