Wavelet Coherence
Also known as: WTC, Wavelet coherency, Continuous wavelet coherence
Wavelet coherence (WTC) is a normalized measure of correlation between two time series in the time-frequency domain, eliminating the amplitude-dependence of the raw cross-wavelet transform. Introduced by Torrence and Webster (1999) and formalized by Grinsted, Moore, and Jevrejeva (2004), WTC quantifies how tightly two signals are coupled at each time-frequency point, independent of their individual power levels. It is the wavelet analog of classical spectral coherence, revealing time-localized relationships across all frequencies.
Key highlights
- Normalized measure (0 to 1) that is independent of signal amplitude, allowing fair comparison across different scales
- Combines phase and power information into a single interpretable statistic
- Can reveal frequency-specific and time-localized relationships missed by global correlation
- Natural handling of non-stationary signals with time-varying interactions
- Provides intuitive visual maps of coherence regions in time-frequency space
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use wavelet coherence when you need to assess the strength of association between two signals without being biased by amplitude differences. It is ideal for comparing signals of different scales (e.g., global climate indices), studying coupled oscillations, identifying frequency-specific relationships, and detecting intermittent connections. WTC is superior to simple correlation when relationships are localized in time and frequency.
Strengths & limitations
- Normalized measure (0 to 1) that is independent of signal amplitude, allowing fair comparison across different scales
- Combines phase and power information into a single interpretable statistic
- Can reveal frequency-specific and time-localized relationships missed by global correlation
- Natural handling of non-stationary signals with time-varying interactions
- Provides intuitive visual maps of coherence regions in time-frequency space
- Requires careful choice of smoothing parameters in the time-frequency domain to avoid over-smoothing or creating artifacts
- Statistical significance testing is non-trivial—inferred coherence values can appear high by chance even between uncorrelated signals
- Interpretation is subjective; no universal threshold for 'significant' coherence exists beyond formal hypothesis testing
- Computationally expensive for long signals or high-resolution analysis requiring many scales
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What does a wavelet coherence value of 0.7 mean?
It means that at that particular time-frequency point, the two signals are about 70% correlated. This is moderately strong coupling but not perfect. Combine with visual inspection and phase information for full interpretation.
How do I determine if coherence values are statistically significant?
Use Monte Carlo simulations against the null hypothesis of independent AR(1) or white noise. Grinsted's software includes built-in significance tests that produce confidence contours overlaid on the coherence plot.
What is the cone of influence and why does it matter?
Edge effects distort wavelet coefficients near signal boundaries because wavelets lack data to convolve with. The cone of influence marks these unreliable regions (typically 1/√2 of wavelet duration from edges). Exclude these regions from interpretation.
Can I compare coherence across different frequency bands?
Yes, but use caution: wider frequency bands have intrinsically higher degrees of freedom and may show spurious coherence. Narrow bands at specific frequencies (e.g., annual cycle) are more meaningful than broad bands.
How does wavelet coherence differ from spectral coherence?
Spectral coherence averages over the entire time series, giving a single global correlation per frequency. Wavelet coherence is local in time, revealing when and for how long coherence exists—it is the time-localized version.
Sources
- 1.Torrence, C., & Webster, P. J. (1999). Interdecadal changes in the ENSO–monsoon system. Journal of Climate, 12(8), 2679–2690.
- 2.Grinsted, A., Moore, J. C., & Jevrejeva, S. (2004). Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 11(5–6), 561–566.
- 3.Maraun, D., Kurths, J., & Holschneider, M. (2007). Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing. Physical Review E, 75(1), 016707.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Wavelet Coherence. ScholarGate. https://scholargate.app/time-series/wavelet-coherence