StackCorrelation: Correlation with common signal

In EarthSystemDiagnostics/proxysnr: Separate Signal and Noise in Climate Proxy Records

Correlation with common signal

Description

This function calculates the theoretical correlation of a "stacked" proxy record with the common signal depending on the number of records in the stack and the time resolution of the records, given estimates of the average proxy signal and noise spectra.

Usage

StackCorrelation(
  input,
  N = 1,
  f1 = 2,
  f2 = "max",
  freq.cut.lower = NULL,
  freq.cut.upper = NULL
)

Arguments

input	a list of the spectral objects lists signal and noise, usually to be obtained from a call to SeparateSpectra
N	integer vector with the number of records in the assumed stack; correlations are then calculated for stacks with record numbers according to each element of N
f1	index of the the minimum frequency from which to integrate the signal and noise spectra for calculating the correlation; per default the lowest frequency of the spectral estimates is omitted
f2	index of the maximum frequency until which to integrate the signal and noise spectra for calculating the correlation; defaults to use the maximum frequency of the given spectral estimates
freq.cut.lower	lower frequency (not index!) at which to cut the spectra: this provides a direct way for specifying a minimum frequency for the integration different from the minimum frequency of the spectral estimates. Setting freq.cut.lower overrides the frequency corresponding to the index set in f1.
freq.cut.upper	upper frequency (not index!) at which to cut the spectra: this provides a direct way for specifying a maximum frequency for the integration different from the maximum frequency of the spectral estimates. Setting freq.cut.upper overrides the frequency corresponding to the index set in f2.

Details

The function is an implementation of Eqs. (6) and (7) in Münch and Laepple (2018). The integral in (6) is approximated by the cumulative sum of the integration arguments from f.int1 to f.int2, where f.int1 = f1 and f.int2 consecutively increases from f1 to f2.

Value

a list of two components:

freq:

numeric vector of frequencies corresponding to the upper ends of the cumulative integrations

correlation:

a n * m matrix where n corresponds to length(N) and m is given by length(freq) providing the correlation values as a function of the number of averaged records and the record resolution (= increasing upper frequency of the integration)

Author(s)

Thomas Münch

References

Münch, T. and Laepple, T.: What climate signal is contained in decadal- to centennial-scale isotope variations from Antarctic ice cores? Clim. Past, 14, 2053–2070, https://doi.org/10.5194/cp-14-2053-2018, 2018.

EarthSystemDiagnostics/proxysnr documentation built on April 27, 2024, 8:24 p.m.