Climate data are always noisy: monthly temperature fluctuations are comparable in magnitude to the trend itself. These fluctuations are usually treated as random or attributed to weather, but their origin has remained unclear. This work fits into research on solar-climate links and nonlinear ocean-atmosphere dynamics, alongside studies of the solar thermal pump, solar tidal rhythms, magnetic cycles, and invisible ocean waves. However, this paper stands out by focusing not on external forcing or a specific mechanism, but on the internal resonance of the climate system that converts the annual signal into a three-year one.
The author used monthly global temperature anomaly series (land and ocean) from 1880 to 2009 from NOAA data, as well as global sea surface temperature anomaly series from 1850 to 2008. For detrending, he applied nonparametric wavelet regression with symlets and a soft VisuShrink threshold. He then computed spectra of the detrended fluctuations using the maximum entropy method, which provides good resolution even on short series. To test the connection with Rossby waves, he compared the autocorrelation defect with the analogous quantity from satellite measurements of sea surface height (TOPEX/Poseidon, ERS-1/2).
The spectrum of detrended global temperature fluctuations showed a huge peak at a period of about three years and only a small peak at the annual period (Fig. 3). A similar pattern emerged for global sea surface temperature (Fig. 5). The author interprets the three-year peak as a third-order subharmonic resonance: a nonlinear system with a natural frequency near 1/3 year is excited by the annual forcing and responds at a frequency equal to one-third of the forcing frequency. The autocorrelation defect for ocean temperature and for the El Niño index follows a power law with an exponent of about 0.6, consistent with the spectral slope observed for sea surface height, where Rossby waves dominate. This suggests that Rossby waves may serve as the physical carrier of the resonance and link it to El Niño.
This work differs from neighboring studies by shifting the focus from external factors (solar activity, tides) to the internal nonlinear dynamics of the climate system. If the three-year oscillations are indeed a subharmonic response to annual forcing, then the climate contains a mechanism that itself converts one period into another without additional external signals. This changes the view on the origin of interannual variability and may explain why El Niño has a characteristic quasi-three-year rhythm.
The topic could develop toward more detailed modeling of nonlinear oscillators with distributed natural frequencies to test the conditions for synchronization and the emergence of subharmonic resonance in realistic ocean-atmosphere models. The method could also be applied to other climate indices and longer records, including paleodata, to test the universality of the found resonance.
The result may influence the interpretation of climate spectra and approaches to El Niño forecasting, as well as the assessment of the contribution of natural variability to observed warming.
Test the reproducibility of the resonance on independent data and in models of varying complexity; assess how the subharmonic response depends on nonlinearity and dissipation parameters.
This work touches on a fundamental problem in climatology: separating the forced signal from internal variability. If the three-year oscillations are a resonant response to the annual cycle, then part of the interannual variability does not require an external explanation, which is important for climate change attribution.
Third-order subharmonic resonance means that the system responds at a frequency three times lower than the forcing frequency: an annual push generates a three-year cycle. Such behavior is familiar in nonlinear electrical circuits and mechanical oscillators, but in climate it appears unexpected.