One-Third Resonance: Why Climate and the Sun Swing in Sync ✎

Original: "Nonlinear problems of complex natural systems: Sun and climate dynamics"
· A. Bershadskii
arXiv:1201.4679 · 2012-01-23 · arXiv non-exclusive · independent analysis · 3 min
Strong temperature and solar activity fluctuations arise from the same nonlinear mechanism: subharmonic resonance at one-third of the driving frequency.

A swing pushed once per second usually oscillates once per second. But if you push it harder and at the right rhythm, it can swing three times slower: one full swing for every three pushes. Physicists call this subharmonic resonance, and it seems to govern the most prominent climate and solar oscillations.

Earth's global temperature does not rise smoothly. On top of the warming trend lie strong fluctuations: from year to year, it warms and cools by amounts comparable to the trend itself. For a long time, these swings were dismissed as noise, random disturbances. But when the smooth trend was removed from temperature data since 1880, an unexpected rhythm emerged: a peak at a period of about 3 years. Three years is one-third of the annual cycle that Earth's orbit around the Sun imposes. So the climate responds to the yearly "push" three times slower than it is pushed.

The same pattern appears in Antarctic ice cores. In paleotemperature over the last 340,000 years, a cycle of 15,000 years dominates, which is one-third of the precession period of Earth's axis (about 45,000 years). The one-third resonance operates across all scales.

Solar activity follows the same rule. After removing the 11-year cycle from sunspot data, a peak remains at 3.7 years. This period coincides with the flip-flop phenomenon: the Sun's active longitudes alternate in dominance roughly every 3.7 years. Apparently, both phenomena draw from a single source: nonlinear resonance within the solar dynamo. Moreover, the spectrum of solar fluctuations decays exponentially with a characteristic time of 25.38 days, matching the Sun's rotation period at a latitude of 26 degrees. Chaos in the system is confirmed by a positive Lyapunov exponent (0.286 month⁻¹).

Subharmonic resonance is a system's response at a frequency that is an integer fraction of the driving frequency. A simple example: if you push a swing each time it reaches an extreme point, but with a force that depends on its position, it can swing with a period three times longer than the pushing period. This requires nonlinearity, meaning the response depends on amplitude.

Coherence between detrended solar activity and global temperature is high for periods longer than 20 years, even though the trends do not correlate. This means the Sun and climate exchange not slow trends but fast fluctuations amplified by a shared resonance mechanism. Previously, these links were lost in noise because they were sought at the wrong frequencies.

Now that a common rhythm has been found, climate models can incorporate nonlinear interactions instead of linear trends. This will not make weather forecasts accurate years ahead, because chaos limits predictability, but it will help explain why climate fluctuates so strongly and how these fluctuations relate to the Sun. The swing that oscillates three times slower than it is pushed turns out to be common across the entire solar system.

The 3.7-year period found in solar activity coincides with the period of the so-called flip-flop phenomenon: the Sun's active longitudes alternate in dominance roughly every 3.7 years. This points to a common source for both phenomena.

The idea that galactic turbulence affects Earth's climate echoes Isaac Asimov's novel "The End of Eternity," where changes in distant space cause cataclysms on Earth.

\ddot{x} + \omega_0^2 x + \gamma \dot{x} + \beta x^3 = F \sin(\omega t)
A nonlinear oscillator with cubic nonlinearity, which under certain conditions gives subharmonic resonance
E(f) \sim \exp(-2\pi \Delta f)
The width of the analytic strip Δ determines the rate of exponential decay of the spectrum
S_p(\tau) \propto \tau^{\zeta_p}, \quad \zeta_p \simeq p/3
The exponent ζ_p grows linearly with order p, which is characteristic of developed turbulence
Concepts
natural variability El Niño-Southern Oscillation ENSO seasonal cycle El Niño interannual variability seasonal forcing La Niña recharge oscillator model Multivariate ENSO Index Jin-Timmermann model Bjerknes feedback North Atlantic Oscillation ERSST relative ONI TAO/TRITON moorings North Equatorial Countercurrent climate solar cycle Indian Ocean capacitor effect