Calculate ensemble power spectra using 4 spectral methods:

1. Lomb-Scargle periodogram

2. REDFIT (Mudelsee et al, 2009)

3. Multitaper Method (Thomson et al. 1982)

4. nuspectral (Mathias et al 2004) (no confidence estimation)

For REDFIT and MTM, only the 95 For multiple ensemble members, the median of the ensemble of 95 For Lomb-Scargle, the parameter probs determines the quantiles of the surrogate spectrum distribution extracted as confidence limits.

computeSpectraEns(
time,
values,
max.ens = NA,
method = "mtm",
probs = 0.95,
gaussianize = TRUE,
ofac = 4,
tbw = 3,
sigma = 0.02,
mtm_null = "power_law"
)

## Arguments

time

LiPD "variable list" or vector of year/age values

values

LiPD "variable list" or vector of values

max.ens

Maximum number of ensemble members to analyze

method

Method used to compute the spectra. Choose from:

• 'mtm': The multi-taper method (MTM) of Thomson (1982), a mainstay of spectral analysis (Ghil et al. 2002) designed for evenly spaced timeseries. From the astrochron package.

• 'redfit': a version of the Lomb-Scargle periodogram tailored to paleoclimatic data (Mudelsee et al. 2009). From the dplR package.

• 'lomb-scargle': the Lomb-Scargle periodogram (VanderPlas et al. 2018), which uses an inverse approach to harmonic analysis in unevenly-spaced timeseries. From the lomb package.

• 'nuspectral':The wavelet-based method of Mattias et al. (2004). This method is quite similar to the Weighted Wavelet Z-transform algorithm of Foster (1996), though it is prohibitively slow in this implementation. From the nuspectral package.

probs

vector of probabilities for the siginificance levels. To avoid such computations, pass probs = NA.

gaussianize

Boolean flag indicating whether the values should be mapped to a standard Gaussian prior to analysis.

ofac

oversampling factor for lomb::lsp and dplR::redfit

tbw

time-bandwidth product for astrochron::mtm___ functions

radius of the nuspectral nuwaveletcoeff weight function (non-dimensional units)

sigma

decay parameter of the nuspectral nuwaveletcoeff wavelets

mtm_null

Method to estimate null hypothesis if method = "mtm". Valid choices are 'AR(1)', 'power_law' (default), or 'ML96'

## Value

a list of ensemble spectra results

• freqs: vector of frequencies

• power: vector of spectral powers

• power.CL: matrix of confidence limits for spectral power

## Details

Calculate ensemble power spectra

## Long-form example

View a full-fledged example of how to use this function.

## References

Ghil, M., Allen, R. M., Dettinger, M. D., Ide, K., Kondrashov, D., Mann, M. E., Robertson, A., Saunders, A., Tian, Y., Varadi, F., and Yiou, P.: Advanced spectral methods for climatic time series, Rev. Geophys., 40, 1003–1052, 2002.

Foster, G.: Wavelets for period analysis of unevenly sampled time series, Astron. Jour., 112, 1709, https://doi.org/10.1086/118137, 1996.

Mudelsee, M., D. Scholz, R. Röthlisberger, D. Fleitmann, A. Mangini, and E. W. Wolff (2009), Climate spectrum estimation in the presence of timescale errors, Nonlinear Processes in Geophysics, 16(1), 43–56, doi:10.5194/npg-16-43-2009.

Mathias, A., F. Grond, R. Guardans, D. Seese, M. Canela, and H. Diebner (2004), Algorithms for spectral analysis of irregularly sampled time series, Journal of Statistical Software, Articles, 11(2), 1–27, doi:10.18637/jss.v011.i02.

Thomson, D. J. (1982), Spectrum estimation and harmonic analysis, Proc. IEEE, 70(9), 1055–1096.

VanderPlas, J. T.: Understanding the Lomb–Scargle Periodogram, The Astrophysical Journal Supplement Series, 236, 16, https://doi.org/10.3847/1538-4365/aab766, 2018.

Mann, M. and Lees, J.: Robust Estimation of Background Noise and Signal Detection in Climatic Time Series, Clim. Change, 33, 409–445.

Other spectra: ar1Surrogates(), createSyntheticTimeseries(), periodAnnotate(), plotSpectrum(), reverselog10_trans()