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

knitr::opts_chunk$set(
  collapse = TRUE,
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Overview

This vignette documents all the steps needed to obtain the main results presented in Münch and Laepple (2018) along with the plotting of the respective main figures.

Obtaining the spectral data

library(proxysnr)
library(magrittr)

Produce the main spectral results for the DML1, DML2 and WAIS oxygen isotope datasets (i.e. the raw and corrected signal and noise spectra):

DWS <- WrapSpectralResults(
    dml1 = dml$dml1, dml2 = dml$dml2, wais = wais,
    diffusion = diffusion.tf,
    time.uncertainty = time.uncertainty.tf,
    df.log = c(0.15, 0.15, 0.1))

This function is only a wrapper for the main package functions ObtainArraySpectra() and SeparateSignalFromNoise() which calls the two functions for all the datasets that are specified as input to WrapSpectralResults(). The function ObtainArraySpectra() is used, for a specific dataset, to calculate all individual spectra, the corresponding mean spectrum and the spectrum of the stacked record (thus, of the average isotope record in the time domain); SeparateSignalFromNoise() is used to obtain the raw and corrected signal and noise spectra for this dataset.

The datasets analysed in the paper are provided along proxysnr in the variables ?dml and ?wais. The applied transfer functions to correct for the loss in high-frequency spectral power by the effects of diffusion and time uncertainty are included in the package datasets ?diffusion.tf and ?time.uncertainty.tf, respectively; see the vignette vignette("calculate-transfer-functions") for details on obtaining these functions.

The output from WrapSpectralResults() is a list of the spectral results for each of the datasets providing the estimated signal, noise and signal-to-noise ratio spectra (i) without any correction applied ("raw"), (ii) for only applying the diffusion correction ("corr.diff.only"), (iii) for only applying the time uncertainty correction ("corr.t.unc.only"), and (iv) for applying both corrections ("corr.full"):

ls.str(DWS)

For all or only for some of the datasets, you can omit both or one of the two transfer functions from the call to WrapSpectralResults() in which case only the raw, i.e. uncorrected, or only the partially corrected signal and noise spectra are returned for these datasets.

Plotting the main figures

Plot DML1 isotope array spectra (Figure 1)

dml$dml1 %>%
  ObtainArraySpectra(df.log = 0.12) %>%
  PlotArraySpectra(marker = DWS$dml1$corr.full$f.cutoff[2],
                   ylab = expression(
                     "Power spectral density " * "(\u2030"^{2}%.%"yr)"))

Plot DML and WAIS signal and noise spectra (Figure 2)

proxysnr:::muench_laepple_fig02(DWS)

Plot frequency dependence of signal-to-noise ratios (Figure 3)

Plot the final signal-to-noise ratio spectra from combining both DML datasets including additional logarithmic smoothing for visual purposes:

(SNR <- proxysnr:::PublicationSNR(DWS)) %>%
  PlotSNR(f.cut = TRUE, names = c("DML", "WAIS"),
          col = c("black", "dodgerblue4"))

Plot estimated correlation with common signal (Figure 4)

Calculate the estimated correlation of a stacked isotope record with the underlying common signal as a function of records averaged and the temporal averaging period (i.e. resolution) of the records, and plot it:

# for the DMl data
SNR$dml %>%
  ObtainStackCorrelation(N = 1 : 20,
                         limits = c(1 / 100, SNR$dml$f.cutoff[2])) %>%
  PlotStackCorrelation(label = expression(bold("a.")~"DML"),
                       ylim = c(NA, 50))

# for the WAIS data
SNR$wais %>%
  ObtainStackCorrelation(N = 1 : 20,
                         limits = c(1 / 100, SNR$wais$f.cutoff[2])) %>%
  PlotStackCorrelation(label = expression(bold("b.")~"WAIS"),
                       ylim = c(NA, 50))

Plot comparison of DML and Trench noise spectra (Figure 5)

We compare the noise spectrum of the DML firn-core array ("array scale") to the noise spectrum of the T15 trench oxygen isotope data ("local scale"). The latter is supplied in the internal package variable t15.noise and automatically loaded by the plotting function:

proxysnr:::muench_laepple_fig05(SNR)

Literature cited

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, doi: 10.5194/cp-14-2053-2018, 2018.

EarthSystemDiagnostics/proxysnr documentation built on June 9, 2025, 11:58 a.m.