Calculate the admittance and correlation spectra of two real functions.

## Usage

call SHAdmitCorr (`gilm`

, `tilm`

, `lmax`

, `admit`

, `corr`

, `admit_error`

, `exitstatus`

)

## Parameters

`gilm`

: input, real*8, dimension (2,`lmaxg`

+1,`lmaxg`

+1)- The real spherical harmonic coefficients of the function
`G`

. `tilm`

: input, real*8, dimension (2,`lmaxt`

+1,`lmaxt`

+1)- The real spherical harmonic coefficients of the function
`T`

. `lmax`

: input, integer- 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`

. `admit`

: output, real*8, dimension (`lmax`

+1)- The admittance function, which is equal to
`Sgt/Stt`

. `corr`

: output, real*8, dimension (`lmax`

+1)- The degree correlation function, which is equal to
`Sgt/sqrt(Sgg Stt)`

. `admit_error`

: output, optional, real*8, 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. `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.

## Description

`SHAdmitCorr`

will calculate the admittance 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.

If the optional argument `admit_error`

is specified, then the error of the admittance will be calculated by 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.

## See also

shpowerspectrum, shcrosspowerspectrum

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