A Physical–Mathematical Approach to Climate Change Effects through Stochastic Resonance

Abstract

The aim of this work is to study the effects induced by climate changes in the framework of the stochastic resonance approach. First, a wavelet cross-correlation analysis on Earth temperature data concerning the last 5,500,000 years is performed; this analysis confirms a correlation between the planet's temperature and the 100,000, 41,000, and 23,000-year periods of the Milankovitch orbital cycles. Then, the stochastic resonance model is invoked. Specific attention is given to the study of the impact of the registered global temperature increase within the stochastic model. Further, a numerical simulation has been performed, based on: (1) A double-well potential, (2) an external periodic modulation, corresponding to the orbit eccentricity cycle, and (3) an increased value of the global Earth temperature. The effect of temperature increase represents one of the novelties introduced in the present study and is determined by downshifting the interaction potential used within the stochastic resonance model. The numeric simulation results show that, for simulated increasing values of the global temperature, the double-well system triggers changes, while at higher temperatures (as in the case of the absence of a global temperature increase although with a different threshold) the system goes into a chaotic regime. The wavelet analysis allows characterization of the stochastic resonance condition through the evaluation of the signal-to-noise ratio. On the basis of the obtained findings, we hypothesize that the global temperature increase can suppress, on a large time scale corresponding to glacial cycles, the external periodic modulation effects and, hence, the glacial cycles.Climate 2019, 7, 21 2 of 16 the oceans [6][7][8][9]. Equilibrium temperature at these times represents an upper stationary regime. On the other hand, climate variations can give rise to harsh conditions that are of interest for the study of extremophile organisms [10][11][12][13] for biotechnological applications [14][15][16][17][18][19][20][21][22].Temperature determinations performed at the Vostok scientific station (Figure 1) revealed a strong correlation with the Milankovitch cycles [23][24][25][26][27][28][29][30][31][32], and are shown in Figure 2.

Parametric Resonance Climate Model

“…In this case, after a transient phase, the forced oscillations become stationary and acquire the same frequency as the external force. Furthermore, when the frequency of the external force is close to the natural frequency of the oscillator, the amplitude of the oscillations can reach significant values giving rise to a phenomenon of resonance [30][31]. Another way to energize the system oscillation can be obtained through a suitable periodic variation of the system parameters.…”

Controlled Symmetry with Woods-Saxon Stochastic Resonance Enabled Weak Fault Detection

“…Over the past two decades, SR has been used in many different fields, including meteorology [11], pharmacology [12], nanomechanics [13][14][15], and medicine [16]. SR-aided signal processing is particularly useful for wireless communication [17], mechanical fault diagnosis [18], underwater target identification [19], image enhancement [20], and other applications.…”

On the Breaking of the Milankovitch Cycles Triggered by Temperature Increase: The Stochastic Resonance Response

“…These occurrences determine an increase of the energy reflected by the Earth (i.e., albedo), and in turn a further temperature decrease, i.e., a positive feedback. Glacial ages end with a temperature increase, which, inversely, provokes a water transfer from the cryosphere [5][6][7][8].…”