An analysis of the effects of Milankovitch cycles and terrestrial albedo on the Earth\’s climate

Abstract

This article explores the effect of natural changes on the Earth’s climate, with a particular focus on the Milankovitch cycles and terrestrial albedo. Milankovitch cycles owe their name to the Serbian astronomer, geophysicist and mathematician Milutin Milankovitch who derived a mathematically developed theory suggesting the changes related to the Earth’s position relative to the Sun were responsible for the long term variations in climate. Terrestrial albedo describes the surface composition of the Earth and how that relates to the amount of sunlight that is reflected or absorbed. It is important to note that both Milankovitch cycles and changes in terrestrial albedo act over the space of tens of thousands of years and produce long term, periodical changes in the Earth\’s climate.

Introduction

Milankovitch cycles are the collective term describing the variations in the Earth’s obliquity, eccentricity and precession. Up until recently, these variations have been due to what is considered natural causes e.g. volcanic explosions, solar insolation, the tilt of the Earth, its surface composition etc. Obliquity describes the angle between the plane of the Earth’s equator and the plane of its orbit around the sun. Orbital eccentricity is the degree to which an object’s orbit deviates from a perfect circle. Precession is the change in the direction of the axis of a rotating object as it circumnavigates the Sun. These changes have been consistent since the Earth’s formation around 4.5 billion years ago. Milankovitch cycles were initially developed by James Croll: a Scottish scientist who utilised the formula for orbital variations from Urbain Le Verrier, a French astronomer and mathematician. They stemmed from the idea that variations in the Earth’s orbit can produce variations in climate, as these changes dictate the extent of solar radiation received. There are also factors that do not change the amount of solar radiation received, but the amount of it that is absorbed into the Earth’s atmosphere, or reflected back into space. One such factor is terrestrial albedo: the measure of the reflectivity of a substance. Unlike Milankovitch cycles which produce more global effects, terrestrial albedo has the ability to change the climate on a smaller scale. One such example is the existence of urban heat islands. Urban areas tend to be characterised by a range of materials with high and low albedos which, when in close proximity to each other, are perfect for increasing local temperatures.

Obliquity

Obliquity refers to the angle a planet’s spin axis makes with its orbital plane. It is due to the gravitational attraction between the Earth, its neighbouring planets and the Sun. Earth’s obliquity ranges from 22.1 to 24.5 degrees, with its current obliquity at 23.4 degrees. These changes occur over a period of 41,000 years, accounting for the seasons we experience. Substantial changes in obliquity are mainly due to orbital resonances, which in turn are caused by a planet’s rate of precession – the rate at which the orientation of a planet’s rotational axis changes. Orbital resonance occurs when two celestial bodies exert periodic gravitational influence on each other as their orbital periods are related by a small ratio of integers. Once a planet’s rate of precession reaches a set of core values, orbital resonance results in substantial changes in obliquity.
With less axial tilt, shortwave solar radiation is distributed more evenly throughout the seasons causing them to be less extreme. Less axial tilt also increases the variation in the amount of radiation received in the polar and equatorial regions^[1]. One explanation for this is that a smaller degree of tilt would promote the growth of ice sheets. This is as winters will be warmer and summers will be cooler to the point we might need our ski gloves during this season- as seasons are less extreme with smaller axial tilt – allowing for more evaporation of moisture and therefore more snowfall when temperatures reach sub-zero. In other words, with a smaller degree of axial tilt less solar radiation reaches the polar latitudes, therefore less of the previous year’s snow and ice will melt. Colder summers may allow for the build-up of snow and ice in the polar latitudes. Over the space of a few years, ice sheets would eventually form, fueling a positive feedback system as more solar radiation is reflected into space, thus causing additional cooling.

Orbital eccentricity

Orbital eccentricity is the measure of the degree of distortion of a planet’s orbit from a perfect circle. The eccentricity of an object’s orbit is caused by the initial location of the object before drifting into its current orbit and gravitational attraction of the Sun and any other celestial objects in close proximity. A circular orbit is given a value of 0, as they do not deviate from the shape of a perfect circle. A parabolic orbit is given an eccentricity value of between 0 and 1. Parabolic orbits are defined as an orbit that lies in the border region between an elliptical orbit – a closed orbit that repeats itself – and a hyperbolic orbit, which is an orbit that extends indefinitely and will not traverse itself ^[2]. Hyperbolic orbits are given an eccentricity value of greater than 1^[3].

_{Figures 1 and 2: a visualisation of orbits with eccentricity values of 0 and 0.5.}^[4]

Earth’s current eccentricity is 0.0167, varying between 0.0034 to 0.058 every 100,000 years. In comparison, Pluto has a highly eccentric orbit at 0.2488^[5].
Due to the Earth’s parabolic orbit, the distance between the Earth and the Sun is not constant throughout the year. There is a 6% increase in received solar radiation in January and July, although this may increase by up to 30% during perihelion – early January – when the Earth’s eccentricity is at its highest (0.058). This leads to a greater disparity between seasons, as weather events become more extreme.

Precession

Precession is the change caused by the gravitational pull of the Sun and Moon on Earth’s equatorial bulge resulting in slow circular motion. It results from the gravitational pull of the Sun and the Moon on the Earth\’s equatorial bulge and has a periodicity of 25,000 years causing the climate to alter significantly. When the axis is towards Vega, the brightest star in the Northern constellation Lyra located just 25±0.07 light-years from Earth, the Northern Hemisphere’s summer and winter solstice will correspond to the perihelion and aphelion. When the axis is toward Polaris Aa, the largest star in the constellation Ursa Minor located 323 light-years from Earth, summer and winter switch in the Northern hemisphere.

_{Figure 3: a visualisation of the fluctuations in the direction of the Earth’s axis.}[6]

Aphelion is the point in the orbit of a celestial body at which it is furthest from the Sun. It occurs around 2 weeks after the June solstice during the northern hemisphere’s summer. Perihelion is the point in the orbit of a celestial body at which it is closest to the Sun, occurring when the Earth’s orbit is most eccentric. It occurs around two weeks after the December solstice during the northern hemisphere’s winter^[6][7]. A solstice occurs bi-annually when the Sun reaches its most northerly/southerly point in relation to the earth’s tilt.

Terrestrial albedo

Terrestrial albedo refers to the amount of sunlight that is reflected away from a celestial body. It refers to the ‘whiteness’ of a substance. With 0 indicating a ‘perfect absorber and 1 indicating a ‘perfect reflector’. The terrestrial albedo of Earth and Venus is 0.30^[8] and 0.77^[9] respectively. Venus has a surface temperature of 700K, the highest in our solar system. Although, due to its high terrestrial albedo, its effective temperature is lower than Earth’s at only 227K. The effective temperature is defined as the temperature a planet would have if it acted like a black body – a hypothetical object that absorbs and emits 100% of incident radiation. The high terrestrial albedo can be accredited to the various sulfur species which exist on Venus in the gaseous state in addition to the water and carbon dioxide that complete its atmospheric composition, combined with high atmospheric pressure of 9.3Mpa. This creates a set of thick clouds composed of sulfuric acid droplets which reflect the majority of the solar radiation incident on the planet. In comparison, the atmospheric pressure on Earth is 0.10Mpa at sea level. These factors offset the proximity of Venus to the Sun, leaving Venus colder than Earth, when treated as a black body, despite the fact that Venus is only 0.723 AU from the Sun.
The effective temperature is affected by three factors; the distance of the object from the sun, the terrestrial albedo of the object and its atmospheric composition. Treated as a black body, the Earth absorbs an average of 239Wm^-2 of incoming solar radiation, leaving its effective temperature at 252K (-21 degrees Celsius). The difference between this and the Earth’s surface temperature 288K, (15 degrees Celsius) is due to the greenhouse effect. The greenhouse effect occurs naturally, allowing Earth to maintain its climate, although human contributions, particularly over the last two centuries, have led to an unprecedented increase in the concentrations of CO₂ in the Earth’s atmosphere. Thus leading to an increase in the thickness of the ozone layer, amount of solar radiation trapped within the Earth’s atmosphere and therefore Earth’s surface temperature.
As Earth’s surface temperature increases, global ice cover decreases. This ,in turn, decreases the Earth’s albedo as ice has a high albedo of 0.90, indicating ice has a high capacity to reflect solar radiation. However, as global forest cover decreases, terrestrial albedo increases. This is as canopy has a low albedo of 0.15, indicating that forest cover has a high capacity to absorb solar radiation. This provides an explanation for the global fluctuations in the Earth’s terrestrial albedo as shown in Figure 4.

_{Figure 4: Global fluctuations in albedo between March 1 2000 and December 31 2011.}^[8]

However, there is no overall trend indicating a global change in albedo. Despite this, there have been substantial regional changes, as shown in Figure 5.
Albedo has decreased substantially in the North pole mainly due to three reasons. Firstly due to declining Arctic sea ice. Secondly due to the increased melting of Arctic permafrost, releasing methane which further contributes to global warming, creating a positive feedback effect. Thirdly due to the increased appearance of sediment on top of the sea ice. Ice sheets that are formed in shallow Arctic waters often have sediments from the seafloor embedded in them. Over time these sediments concentrate on the top of the ice sheet as seasonal melting and freezing move them upward through the ice. This darkens the sea ice, reducing its albedo.
Urban areas have typically experienced increases in albedo due to high population densities and the use of darker, absorbent materials e.g concrete, asphalt combined with lighter, reflective materials e.g. glass and reflective surfaces. The urban heat island effect is exacerbated by tall buildings with reflective surfaces which increase the absorption and reflection of solar radiation and block wind which prevents cooling. However, there is a relatively manageable solution to this problem^[10]. Replacing many of the darker surfaces with lighter ones e.g. lighter rooftops, pavements and roads could offset some of the effects produced by global warming as they would increase the region\’s albedo, and may reduce the urban heat island.

_{Figure 5: A representation of the changes in reflectivity across oceanic and continental parts of Earth between March 1 2000 and December 31 2011.}^[8]

Conclusion

Once again, it is important to note that Milankovitch cycles and changes to the Earth\’s terrestrial albedo take place over vast time scales and in our lifetimes, would only produce very small variations in global temperature. According to the Earth’s current obliquity (23.4 degrees), orbital eccentricity (0.0167) and precession, we are in an interglacial period named the Holocene. A period of warmer than average global temperatures which began over 11,000 years ago. On average, global temperatures rose by a maximum of 2 degrees Celsius during the Holocene Optimum, which lasted from 5000 to 3000 BC^[11]. In comparison, global temperatures have increased by 1 degree Celsius in the last 140 years. There is a stark difference in the rate of increase in global temperatures pre and post-industrial era. The contribution of human activities to the unprecedented increase in global temperatures is undeniable. Another 1 degree Celsius increase in global temperatures could lead to the increased frequency and severity of tropical storms, the increased frequency of heatwaves, crop failures, increased sea levels, greater flood risk and unprecedented economic damage. This is a mere snapshot of the possible consequences.

References

1. Indiana University. “Milankovitch Cycles and Glaciation.” Accessed March 25 2019. https://geol105.sitehost.iu.edu/images/gaia_chapter_4/milankovitch.htm
2. NASA. “Trajectories and Orbits.” Accessed May 30 2020. https://history.nasa.gov/conghand/traject.htm#:~:text=TRAJECTORIES%20AND%20ORBITS,-A.&text=The%20terms%20trajectory%20and%20orbit,of%20a%20body%20in%20space.&text=In%20discussions%20of%20space%20flight,satellite%20orbits%20around%20the%20Earth.
3. Tate, Jean. “Eccentricity.” Universe Today. April 26 2016. Accessed March 28, 2019. www.universetoday.com/57964/eccentricity/.
4. NASA. “Milutin Milankovitch.” Earth Observatory. March 24, 2000. Accessed March 30 2019 https://earthobservatory.nasa.gov/features/Milankovitch.
5. Williams, David R. “Pluto Fact Sheet.” Accessed May 30 2020. https://nssdc.gsfc.nasa.gov/planetary/factsheet/plutofact.html.
6. Keller, Sarah B. “Precession of Earth.” Sara\’s Astronomy Blog. January 25 2016. Accessed April 20, 2019. https://sarabkeller.wordpress.com/2016/01/25/precession-of-earth.
7. Kher, Aparna. “Perihelion, Aphelion and the Solstices.” Timeanddate.com. Accessed April 20 2019 www.timeanddate.com/astronomy/perihelion-aphelion-solstice.html.
8. NASA “Measuring Earth\’s Albedo.” Earth Observatory. Accessed April 29 2019 https://earthobservatory.nasa.gov/images/84499/measuring-earths-albedo.
9. Williams, David R. “Venus Fact Sheet.” NASA. Accessed December 15, 2019. https://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html.
10. Akbari, Hashem, H Damon Matthews, and Donny Seto. \”The long-term effect of increasing the albedo of urban areas.\” Environmental Research Letters. April 12 2012. Accessed July 1 2020. https://iopscience.iop.org/article/10.1088/1748-9326/7/2/024004#erl422949s5
11. University of Arizona. \”The Climate of the Holocene.\” ATMO 336. Accessed 20 June 2020. http://www.atmo.arizona.edu/students/courselinks/fall12/atmo336/lectures/sec5/holocene.html
12. Various information was obtained from an evening lecture at UCL titled ‘Milankovitch Cycles: Ice Ages and Climate Change’ held by Prof. Alan Aylward on December 7 2018.

Bibliography

1. Malhotra, Renu. “Orbital Resonances and Chaos in the Solar System.” PDF file. Accessed May 30 2020. www.lpl.arizona.edu/~renu/malhotra_preprints/rio97.pdf
2. Loenen, E,. and Marco Westerkamp. “How Did Pluto Form (Is It An Asteroid or A Planet?).” Kapteyn Institute. Accessed May 30 2020. http://www.astro.rug.nl/~etolstoy/ACTUEELONDERZOEK/JAAR2000/pluto/aosorbit.html
3. Star Facts. “Polaris.” Accessed May 30 2020. www.star-facts.com/polaris/.
4. Exploratorium. “Background: Ice.” Global Climate Change Explorer. Accessed June 1 2020. https://www.exploratorium.edu/climate/background-ice
5. National Snow & Ice Data Centre. “Thermodynamics: Albedo.” All About Sea Ice. Accessed June 1 2020. https://nsidc.org/cryosphere/seaice/processes/albedo.html
6. Skeptical Science. “The Runaway Greenhouse Effect On Venus.” Accessed June 1 2020. https://skepticalscience.com/print.php?r=366/.
7. Volgyesi, Lajos. \”Revision of the physical backgrounds of Earth\’s ro-tation.\” PDF file. Accessed July 1 2020. www.researchgate.net/publication/268016194
8. Monroe, Rob, Scripps Institution of Oceanography, and María-José Viñas. \”NASA Satellites See Arctic Surface Darkening Faster.\” February 18 2014. Accessed July 1 2020. https://climate.nasa.gov/news/1041/nasa-satellites-see-arctic-surface-darkening-faster/#:~:text=The%20retreat%20of%20sea%20ice,fly%20aboard%20several%20NASA%20satellites.
9. Shapiro Ledley, T,. and Stephanie Pfirman. \” The Impact of Sediment-Laden Snow and Sea Ice in the Arctic on Climate.” Climate Change 37, 641-664 (1997). https://doi.org/10.1023/A:1005354912379

About the Author

Shannon is an aspiring astrophysicist who also has a love for the planetary sciences. She is also a senior member of the Young Scientists Journal team. In her spare time she enjoys sports, reading and horror movies.