wtc: Compute wavelet coherence

In biwavelet: Conduct univariate and bivariate wavelet analyses

Description

Compute wavelet coherence

Usage

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

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. Default is TRUE.
dj	spacing between successive scales. Default is 1/12.
s0	smallest scale of the wavelet. Default is 2*dt.
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. Default is morlet. Significance testing is only available for morlet wavelet.
param	nondimensional parameter specific to the wavelet function.
lag1	vector containing the AR(1) coefficient of each time series.
sig.level	significance level. Default is 0.95.
sig.test	type of significance test. If set to 0, use a regular χ^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. Default is 300.
quiet	Do not display progress bar. Default is 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 containg sig.level percentiles of wavelet coherence based on the Monte Carlo AR(1) time series

Note

The Monte Carlo randomizations can be extremely slow for large datasets. For instance, 1000 randomizations of a dataset consisting of 1000 samples will take ~30 minutes on a 2.66 GHz dual-core Xeon processor.

Author(s)

Tarik C. Gouhier ([e-mail])

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

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)

Example output

biwavelet 0.20.11 loaded.

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biwavelet documentation built on May 2, 2019, 5:10 p.m.