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Getting started

This guide illustrates how to use this package to perform continuous wavelet spectral analysis. We base our examples on the analysis presented by Torrence and Compo (1998)1 and we assume that you have a good understanding of the key concepts.

Please refer to the installation instructions for installing pycwt.

The pycwt package contains a collection of routines for wavelet transform and statistical analysis via the Fast Fourier Transform (FFT) algorithm, as well as cross-wavelet transforms and wavelet coherence tests.

Basic wavelet analysis

import pycwt
nino3 = pycwt.load_dataset("sst_nino3")  # Load sample time-series.
wavelet = pycwt.Morlet(w0=6)             # Instantiate mother wavelet.
result = wavelet.run(nino3)              # Run wavelet analysis.
result.plot()

NINO3 wavelet analysis

Note

Here, it is expected that nino3 is of type pandas.Series, has a constant sampling frequency dt, no data gaps (NaN values) and that time is given by the series index.

Parameters -- The default scale and significance parameters for this analysis are:

  • Starting scale: s0 = 2 * dt
  • Spacing between discrete scales: dj = 1 / 12 -- twelve sub-octaves per octave.
  • Number of scales: J = 7 / dj -- seven powers of two with dj sub-octaves.
  • Lag-1 autocorrelation for red noise: alpha = 1.
  • Significance level: significance_level = 0.95.

Methodology

  1. Normalization: detrending, Z-score normalization
  2. Calculate continuous wavelet transform
  3. Significance tests
  4. Plot results

Basic cross-wavelet analysis

import pycwt
jao = pycwt.load_dataset("jao")          # Load Artic-Oscillation time-series.
jbaltic = pycwt.load_dataset("jbaltic")  # Load Baltic Sea ice extent time-series.
wavelet = pycwt.Morlet(w0=6)             # Instantiate mother wavelet.
result = wavelet.run(jao, jbaltic)       # Run cross-wavelet analysis.
result.plot()

JAO-JBALTIC cross-wavelet analysis

  1. Torrence, C. and Compo, G. P.. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society, American Meteorological Society, 1998, 79, 61-78. DOI 10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2. ↩