Correlation Coefficient of ENSO Power Spectra

The model fit to ENSO takes place in the time domain. However, the correlation coefficient between model and data of the corresponding power spectra is higher than in the time series. Below in Figure 1 the CC is 0.92, while the CC in the time series is 0.82.

Fig.1 : Power spectra of ENSO data against model

The model allows only 3 fundamental lunar frequencies along with the annual cycle, plus the harmonics caused by the non-linear orbital path and the seasonally impulsed modulation.

What this implies is that almost all the peaks in the power spectra shown above are caused by interactions of these 4 fundamental frequencies. Figure 2 shows a satellite view of peak splitting (also shown here).

Fig 2: Frequency sideband plot identifying components created by modulation of a biennial cycle with the lunar cycles (originally described here).

One of the reasons that the power spectrum gives a higher correlation coefficient — despite the fact that the spectrum wasn’t used in the fit — is that the lunar tides are precisely determined and thus all the harmonics should align well in the frequency domain. And that’s what is observed with the multiple-peak alignment.

Furthermore, according to Ref [1], this result is definitely not a characteristic of noise-driven system, and it also possesses a very low dimension of chaotic content. The same frequency content is observed largely independent of the prediction time profile, i.e. training interval.


1. Bhattacharya, Joydeep, and Partha P. Kanjilal. “Revisiting the role of correlation coefficient to distinguish chaos from noise.” The European Physical Journal B-Condensed Matter and Complex Systems 13.2 (2000): 399-403.

2 thoughts on “Correlation Coefficient of ENSO Power Spectra

  1. Time-domain modelling of global barotropic ocean tides

    “Traditionally, ocean tides have been modelled in frequency domain with forcing of selected tidal constituents. It is a natural approach, however, non-linearities of ocean dynamics are implicitly neglected. An alternative approach is time-domain modelling with forcing given by the full lunisolar potential, i.e., all tidal constituents are included. This approach has been applied in several ocean tide models, however, a few challenging tasks still remain to solve, for example, the assimilation of satellite altimetry data. In this thesis, we present DEBOT, a global and time-domain barotropic ocean tide model with the full lunisolar forcing. DEBOT has been developed “from scratch”. The model is based on the shallow water equations which are newly derived in geographical (spherical) coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a physically consistent form. The numerical model employs finite differences in space and a generalized forward-backward scheme in time. The validity of the code is demonstrated by the tests based on integral invariants. DEBOT has two modes for ocean tide modelling: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. We introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing…”
    This DEBOT model is what is needed. I have tried to generate the full lunisolar potential but it’s tough to get correct.


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