wtc: Compute wavelet coherence

Description

Compute wavelet coherence

Usage

wtc(
  d1,
  d2,
  pad = TRUE,
  dj = 1/12,
  s0 = 2 * dt,
  J1 = NULL,
  max.scale = NULL,
  mother = "morlet",
  param = -1,
  lag1 = NULL,
  sig.level = 0.95,
  sig.test = 0,
  nrands = 300,
  quiet = FALSE
)

Value

Return a biwavelet object containing:

coi: matrix containg cone of influence
wave: matrix containing the cross-wavelet transform
wave.corr: matrix containing the bias-corrected cross-wavelet transform using the method described by Veleda et al. (2012)
power: matrix of power
power.corr: matrix of bias-corrected cross-wavelet power using the method described by Veleda et al. (2012)
rsq: matrix of wavelet coherence
phase: matrix of phases
period: vector of periods
scale: vector of scales
dt: length of a time step
t: vector of times
xaxis: vector of values used to plot xaxis
s0: smallest scale of the wavelet
dj: spacing between successive scales
d1.sigma: standard deviation of time series 1
d2.sigma: standard deviation of time series 2
mother: mother wavelet used
type: type of biwavelet object created (wtc)
signif: matrix containing sig.level percentiles of wavelet coherence based on the Monte Carlo AR(1) time series

Arguments

d1: Time series 1 in matrix format (n rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
d2: Time series 2 in matrix format (n rows x 2 columns). The first column should contain the time steps and the second column should contain the values.
pad: Pad the values will with zeros to increase the speed of the transform.
dj: Spacing between successive scales.
s0: Smallest scale of the wavelet.
J1: Number of scales - 1.
max.scale: Maximum scale. Computed automatically if left unspecified.
mother: Type of mother wavelet function to use. Can be set to morlet, dog, or paul.
param: Nondimensional parameter specific to the wavelet function.
lag1: Vector containing the AR(1) coefficient of each time series.
sig.level: Significance level.
sig.test: Type of significance test. If set to 0, use a regular \(\chi^2\) test. If set to 1, then perform a time-average test. If set to 2, then do a scale-average test.
nrands: Number of Monte Carlo randomizations.
quiet: Do not display progress bar.

Author

Tarik C. Gouhier (tarik.gouhier@gmail.com)

Code based on WTC MATLAB package written by Aslak Grinsted.

References

Cazelles, B., M. Chavez, D. Berteaux, F. Menard, J. O. Vik, S. Jenouvrier, and N. C. Stenseth. 2008. Wavelet analysis of ecological time series. Oecologia 156:287-304.

Grinsted, A., J. C. Moore, and S. Jevrejeva. 2004. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics 11:561-566.

Torrence, C., and G. P. Compo. 1998. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society 79:61-78.

Torrence, C., and P. J. Webster. 1998. The annual cycle of persistence in the El Nino/Southern Oscillation. Quarterly Journal of the Royal Meteorological Society 124:1985-2004.

Veleda, D., R. Montagne, and M. Araujo. 2012. Cross-Wavelet Bias Corrected by Normalizing Scales. Journal of Atmospheric and Oceanic Technology 29:1401-1408.

Examples

Run this code

t1 <- cbind(1:100, rnorm(100))
t2 <- cbind(1:100, rnorm(100))

## Wavelet coherence
wtc.t1t2 <- wtc(t1, t2, nrands = 10)

## Plot wavelet coherence and phase difference (arrows)
## Make room to the right for the color bar
par(oma = c(0, 0, 0, 1), mar = c(5, 4, 4, 5) + 0.1)
plot(wtc.t1t2, plot.cb = TRUE, plot.phase = TRUE)

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