The Earth as a Parametric Oscillator, Instability and non-equilibrium thermodynamics


The earth has a multitude of variable cycles, the longest is the galactic orbital cycle, but they all contribute to its climate. The shortest cycle is the daily insolation cycle which is responsible for the energy which powers the climate and the biosphere. The most important are the cycles to do with the staff of life, these are the H2O cycle and the CO2 cycle. The cycles all contribute to the climate of the earth but the earth can be described in general with a few variables, which while they act over the short term, they are only significant over millenial timescales, due to resonance.

I intend to show that the Earth behaves as a parametric Oscillator, and can be modeled with the acting forces being equivalent to thermal variables and the internal components/processes as a capacitive/reactive network, i.e. a thermal amplifier with time dependent load. A parametric oscillator is a system which can be described by some or all of its internal cycles, without specific reference to the external force acting on it. Insolation is the acting force, but the internal equivalent process is the blackbody temperature as derived from

T_E=T_S\sqrt{\frac{R_S\sqrt{\frac{1-\alpha}{\overline{\epsilon}}}}{2D}}

 Initial conditions Albedo = 0.0 T ave = 278 °K = +05 °C (top of atmosphere)

attenuated Albedo = 0.3 T ave = 254 °K = -19 °C ( current surface conditions)

This gives a average Thermal Potential Difference of 24 °C, with cyclical variations at 1 day, 1 year, and 1 MC ( Milankovitch Cycle) as well as sunspot cycles etc.

From the 5 Myr temperature graph it can be seen that the principle resonant frequency at low resolution of the thermal system is the principle MC i.e 27 kyr approximate sine wave.

The current temperature of the earth is usually expressed in terms of 0.0 °C Vostok equivalent which is 5 °C below the theoretical maximum available thermal equilibrium condition.

The current temperature is a product of the attenuated albedo Temperature and oceanic and atmosphere thermal capacitance (GWP). This gives a theoretical value of 19-24 °C for these systemic thermal effects.

The system operates such that (unless the input conditions are attenuated by a greater degree than currently) the coarse variations as recorded by geological records exhibit a resonance with astronomical cycles. Other resonances may also be apparent in current measurements, that various mathematical analysis can isolate, but due to the long term cyclical nature of the geological, thermal and biological processes which occur these have no significant effect on the system.

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About madmikedavies

Retired Communications Engineer, living in Portugal. Interests are Cosmology, Earth Sciences, Organic farming, Climatology, Football, Golf, Birdwatching, and Dogs
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