The theory that humans are causing climate change has a small but often vociferous number of doubters. Often heard in discussions with those who do not accept anthropological causes is “…it’s part of the nature cycle for the climate to change”. And indeed the latter is partly correct, there are cyclical changes in Earth’s atmosphere due to the orbital and rotational motion of the Earth; but they are not causing the climate changes we are seeing today.
This short article seeks to explain why the natural cycles and consequently why ‘doubters’ are incorrect. It is intended to be a reference article if you are having discussions with climate changer deniers. I’ve included a short glossary of orbital terms at the end of this article.
Milankovitch cycles
The cycles most often cited (whether by theory name or not) are the Milankovitch cycles. In 1941 the Serbian mathematician Milutin Milankovitch proposed that specific cycles of the rotation and orbit of the Earth were associated with long-term climate changes and ice ages. The Milankovitch cycles refer to three specific aspects of the dynamical nature of the Earth’s rotation and revolution. These are the cyclical changes of the direction of the Earth’s axial rotation, the equatorial tilt (inclination) of the Earth’s orbit around the Sun, and the change in orbital eccentricity.
The ‘wobble’ in the axial rotation has been known about for more than 2000 years; its discovery is usually ascribed to Hipparchus in the 2nd century BC. It has an approximately 25,770-year cycle and is due to the tidal torque (from both the moon and the sun) on the non-spherical (equatorial bulge) shape of the Earth. Note that the equatorial bulge is not caused by tidal effects; it is caused by inertia within a rotating sphere. The tidal effects causing axial tilt arises because of the Earth’s oblate spheroid shape.
The scale of the oscillation, ɛ, is (currently) 23.4°in radius and the precessional path follows an imaginary circle centred on the pole of the ecliptic (the normal to the ecliptic plane). The displacement circle has the same angular radius as the Earth’s orbital inclination. Axial rotation precession affects the direction of the North Celestial pole and longitude of celestial objects. It is important to note that it does not affect latitude; i.e. it does not affect the net orbital inclination of the ecliptic to the celestial equator. It is the plane of the ecliptic that is rotating; the plane does not ‘vertically oscillate’ due to axial rotational precession.
The Earth’s orbit: Keplerian and non-Keplerian
The orbit of the Earth is not unfixed and unchanging. All orbital elements are changing, with most changing on a cyclical basis. These are all caused by perturbation effects of gravitational and non-gravitational forces outside the 2-body gravitational model (principally the other major planets). The terms Keplerian and non-Keplerian are applied to the non-perturbed and perturbed orbits respectively.
The non-Keplerian nature of the orbits is due to gravitational perturbations within the 2-body problem. Gravitational effects of the other planets within the solar system cause the orbital acceleration to vary. Analytically this can be considered by an additional force being included in the Keplerian description / equations for gravitational acceleration. In maths form:
The changes in the orbital eccentricity and orbital inclination (often referred to as obliquity) have been known about since the late 17th century. Each of the major planets has an effect on the forcing function f and thus the net result is the summation of a series of sinusoidal forces; effectively a multi-element Fourier series.
Earth’s orbital inclination varies between limits of 22.1° to 24.5° over an approximate 40.3 x 103 years period. There are also smaller scale oscillation periods of 29 x 103 and 54 x 103 years. Our orbital inclination is currently 23.44 (23°26’) and is currently reducing to reach 22.7° over the next 8 x 103 years before rising again to an interim peak of ~24° in about 38 x 103 years-time.
The eccentricity of the Earth’s orbit is currently 0.0167. Over the past million years it has varied between 0.002 to 0.0558 (these limits were extant 33 x 103 years ago and 970 x 103 years ago respectively). Several perturbing functions give rise to these changes and are cyclic on periods from 94 x 103 to 130 x 103 years; with a dominant cycle also having a periodicity of 405 x 103 years. Our orbital eccentricity is also slowly reducing; in this case to a minimum of ~0.005 in about 25 x 103 years-time.
Effect on Earth’s climate.
These effects have a demonstrable effect upon the Earth’s climate. Although the effects cause very little change to the mean annual global insolation (the amount of energy the Earth receives from the Sun), they do affect the distribution. To understand the global effects of the changes the landmass and oceans distribution between the hemispheres need to be considered, as do the local effects at latitudes.
In summary; changes in axial rotation precession alter the season within which the hemispheres are in winter/summer with respect to perihelion/aphelion; inclination changes affect the variation in winter and summer temperatures; and changes in Eccentricity affect differences in summer and winter solar insolation. Certainly there appears to be a 100,000 year cycle of ice coverage over the last million years which can be related to changes particularly in the Earth’s orbital eccentricity.
Obliquity is the dominant shorter-term driver in astronomical climate changes because it affects the mildness or harshness of the winters (and corresponding heat during summers). Where the northern hemisphere seasons are mild ice will accumulate and not be reduced by mild summers. Where winter and summer seasons are very different the Earth will experience very hot summers and very cold winters. And whilst ice will readily build up in extreme winters; it is temporary and more than compensated for by ice-reduction in hot summers.
The Milankovitch cycles are frequently cited inappropriately to seek to explain the current global warming and ice reduction at the polar regions. However, these effects operate over a period of many thousands of years; the ‘shortest-cycle’ being 26,000 years. Hence they cannot explain the change in our climate over the past 200 years.
It is also worth noting that the driving functions of eccentricity and inclination change are currently reducing climate warming processes.
Hence, we can state categorically the anthropological sourced increase in atmospheric carbohydrates and carbon dioxide, and thus the reduction in global albedo due to ice loss, and consequential atmospheric water vapour (through sublimated ice), are the primary causes of the global warming and extreme weather events currently being seen.
Glossary of terms used
Albedo The amount of sunlight which is reflected by a planet.
Aphelion The point in a planet’s orbit where it if furthest away from the sun
Axial rotation The rotating/spinning of the Earth (every 24 hours)
Celestial equator An artificial project of the line of the Earth’s equator onto the celestial sphere
Celestial sphere The apparent sphere of stars viewed from the Earth (the sphere’s centre)
Ecliptic The plane of the Earth’s orbit as it revolves around the sun.
Eccentricity A measure of how elliptical an orbit is. Zero is a circle. 1 is an open parabola
Inclination The same as obliquity.
Obliquity The tilt of a planet’s rotational axis measured against the plane of its orbit
Oblate spheroid An out-of-shape sphere, often slightly ‘fatter’ in the middle.
Orbit The path a planet takes around the sun.
Perihelion The point in a planet’s orbit where it is closest to the sun
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