Abstract. Wavelet coherence is a method that is commonly used in hydrology to extract
scale-dependent, nonstationary relationships between time series. However,
we show that the method cannot always determine why the time-domain
correlation between two time series changes in time. We show that, even for
stationary coherence, the time-domain correlation between two time series
weakens if at least one of the time series has changing skewness. To
overcome this drawback, a nonlinear coherence method is proposed to
quantify the cross-correlation between nonlinear modes embedded in the time
series. It is shown that nonlinear coherence and auto-bicoherence spectra
can provide additional insight into changing time-domain correlations. The
new method is applied to the El Niño–Southern Oscillation (ENSO) and
all-India rainfall (AIR), which is intricately linked to hydrological
processes across the Indian subcontinent. The nonlinear coherence analysis
showed that the skewness of AIR is weakly correlated with that of two ENSO
time series after the 1970s, indicating that increases in ENSO skewness
after the 1970s at least partially contributed to the weakening ENSO–AIR
relationship in recent decades. The implication of this result is that the
intensity of skewed El Niño events is likely to overestimate India's
drought severity, which was the case in the 1997 monsoon season, a time
point when the nonlinear wavelet coherence between AIR and ENSO reached its
lowest value in the 1871–2016 period. We determined that the association
between the weakening ENSO–AIR relationship and ENSO nonlinearity could
reflect the contribution of different nonlinear ENSO modes to ENSO
diversity.
Simulation of the influence of the ocean and the El-Niño – Southern Oscillation phenomenon on the structure and composition of the atmosphere