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15.2: Paleoclimatology- Historical Climate

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    Paleoclimatology is the study of the Earth’s climate before instrumental records were available. The demarcation between paleoclimatology and climatology is analogous to paleobiology and biology. Both fields study climate, but one is very much focused on our current climatic situation. Paleoclimatologists must tease out of the Earth the story of its climatic past. And, that past is full of evidence of change.

    Global average temperatures for the last 540 Ma, using graphs from various studies compressed together (Source: By Glen Fergus - Own work; data sources are cited below, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=31736468).
    Figure \(\PageIndex{1}\): Global average temperatures for the past 540 million years, using graphs from various studies compressed together. This graph shows a great deal of time, but at a very low resolution (CC BY-SA 3.0; By Glen Fergus – Own work; data sources are cited below, https://commons.wikimedia.org/w/index.php?curid=31736468).

    While we tend to focus on measuring our weather and climate using instrumentation on the ground and in space, the Earth has kept a record of its past climate in a wide variety of ways. In this chapter, we will explore a wide array of these kinds of paleoclimate evidence, including things like tree rings, layers of ice, and pollen. There are many more examples. Some of these record great detail over shorter periods of time while some record more coarse detail over much greater spans of time. In reality, this means that the Earth’s data stores are really no different than the data stores we create in instrumentation. Measurement of climate is a matter of time and resolution. The usefulness of a particular data set is limited by time and resolution. So, like studies of modern climate, paleoclimatologists ask questions and pursue investigations that are guided by data limited by time and resolution.

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    Figure \(\PageIndex{2}\): Earth’s various systems (Source: NASA).

    There are some important assumptions accepted when studying paleoclimate. Like in all of the geosciences, these assumptions are uniformitarian. That is, we assume past processes generally operated the same way as in the present. That does not mean changes in the Earth’s systems that affect climate always happen in the same way, but just that the processes that force or drive the changes do.

    A key assumption is that the Earth’s systems behaved throughout its history as they do today. And, we accept that the interactions among the Earth’s spheres also have remained consistent. An event that forces movement within one system will have effects in other systems. These can lead to amplifying feedbacks that further upset the system’s dynamic equilibrium and can lead to tipping points and a new set of system circumstances. Balancing feedbacks also still serve to work against such processes, as a natural means for the systems to right themselves and return to the former equilibrium.

    Climate models are made up of systems of equations that attempt to account for a wide variety of variables and their interactions. Known historical data is taken into account in creating those equations and physical processes, some of of which are listed in the inset here, are the focus. To run the model on a supercomputer, the globe and atmosphere are divided into a grid and the equations run (Source: NOAA).
    Figure \(\PageIndex{3}\): Climate models are made up of systems of equations that attempt to account for a wide variety of variables and their interactions. Known historical data is taken into account in creating those equations and physical processes, some of of which are listed in the inset here, are the focus. To run the model on a supercomputer, the globe and atmosphere are divided into a grid and the equations run (Source: NOAA).

    The study of paleoclimate has lead to a wide variety of insights into our modern climate and how it works. It has helped to refine the models we use to study current problems associated with anthropogenic (human caused) warming. Studies of paleoclimate have also led to deeper knowledge of how our solar system works. While Galileo and others discovered sunspots, their periodicity and effect on climate at different scales and magnitudes would not be known if it were not for paleoclimatic research. Likewise, we would perhaps not know that the Earth, like other planets, sees gradual changes in its orbital parameters that affect its climate. Knowledge about these exospheric impacts informs our current research, not only because it helps us understand how our climate should be responding under only natural influences, but also because we can eliminate them as mechanisms behind the current changes we are causing. Paleoclimate research is critically important to understanding our future.

    Intrinsic and Extrinsic Forcing Mechanisms

    The Earth system is a part of the solar system. Extrinsic climate change agents must come from outside of the Earth system and result from the solar environment, or the exosphere. The solar system is powered by mostly by our Sun and also contains a variety of other objects, including planets, dwarf planets, and chunks of rock or ice hurtling through space in the form of asteroids or comets.

    Fallen trees resulting from the Tunguska Event, Hushmo River, Siberia (Source: By ru:Евгений Леонидович Кринов, member of the expedition to the Tunguska event in 1929. - [1] (original, black and white version of photo) / Vokrug Sveta, 1931 (current, color version of photo), Public Domain, https://commons.wikimedia.org/w/index.php?curid=200531).
    Figure \(\PageIndex{4}\): Fallen trees resulting from the Tunguska Event, Hushmo River, Siberia (Public Domain; By ru:Евгений Леонидович Кринов, member of the expedition to the Tunguska event in 1929. – [1] (original, black and white version of photo) / Vokrug Sveta, 1931 (current, color version of photo), https://commons.wikimedia.org/w/index.php?curid=200531).

    Extrinsic forcing agents typically have a global effect, but in some cases effects can be more limited, such as the impact of a Tunguska-like asteroid versus a Chicxulub-like asteroid. The Tunguska asteroid impact, which happened over Siberia in 1908, had a wide variety of local effects, whereas the Chicxulub asteroid impact at 65 Ma devastated the planet’s biosphere, killing off the dinosaurs and eventually giving mammals the evolutionary reins. The devastation of this impact led to massive global climate effects that contributed mightily to the extinction.

    Likewise, intrinsic climate change agents come from within the Earth system. Overall, these forcing mechanisms can tend to be more limited in their impact, occurring on more local or regional scales rather than global. The Earth system consists of the atmosphere, hydrosphere, geosphere, cryosphere, and biosphere. Massive perturbation in any one of these could have climatic effects. From the geosphere, volcanic eruptions provide an excellent example of scale-dependent intrinsic climate forcing. In April 1815, Mt. Tambora, a stratovolcano in Indonesia, erupted. This eruption was very large and led to three years of significant climate change, particularly for the northern Hemisphere where Europe recorded the three coldest years in centuries and saw major crop failure and famine.

    Projected ashfall resulting from the 1815 eruption of Mt. Tambora. While localized here, it was enough to force significant cooling over large parts of the globe for that year and into the next, leading to the "Year without a summer" (Source: Wikimedia - The base map was taken from NASA picture Image:Indonesia_BMNG.png and the isopach maps were traced from Oppenheimer (2003).[1], CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1266774).
    Figure \(\PageIndex{5}\): Projected ashfall resulting from the 1815 eruption of Mt. Tambora. While localized here, it was enough to force significant cooling over large parts of the globe for that year and into the next, leading to the “Year without a summer” (CC BY-SA 3.0; Wikimedia – The base map was taken from NASA picture Image:Indonesia_BMNG.png and the isopach maps were traced from Oppenheimer (2003).[1], https://commons.wikimedia.org/w/index.php?curid=1266774).

    This calamity pales in comparison, however, to the major flood basalt eruptions of Earth’s past. The Siberian Trap eruptions that took place at the Permian/Triassic boundary caused the largest mass extinction in the planet’s history. This large igneous province in northern Siberia covered 7 million km\(^2\) in lava and lasted for perhaps hundreds of thousands of years. \(\ce{CO2}\) emissions from the lava led to runaway global warming and oceanic stagnation. Almost everything on Earth died.

    EXTRINSIC CHANGE AGENTS

    There are some key extrinsic change agents that affect Earth’s climate from our exosphere. Below is a brief explanation of some of them. Ultimately, extrinsic factors do one of two things. They either adjust the amount of incoming solar radiation, like turning a handle on a spigot, or they cause direct perturbations to the Earth system. Most notably, changes in the hydrologic cycle and carbon cycle are good examples of systems that can be heavily affected by bolide impacts, for example. For this chapter, we will focus on three specific extrinsic change agents. These are Milankovitch Cycles, bolide impacts, and changes in solar energy output.

    Milankovitch Cycles

    Born in the rural Serbian village of Dalj in 1879, Milutin Milankovitch would make his mark on the study of climate in a big way. Through his research on insolation variation during Earth’s seasons, he discovered a mathematical theory of climate that helped predict changes in Earth’s climate due to changes in its orbit . His theory stated that as the Earth travels in its orbit around the sun, three cycles of variability will have an effect on changes in its climate. These are orbital eccentricity, axial obliquity, and axial precession.

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    Figure \(\PageIndex{6}\): A perfectly circular orbit, which does not happen in planetary systems. Yet, it provides a model for what the other end of Milankovitch eccentricity is like. Note the position of the Sun at the center of the orbit. (Source: NASA)
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    Figure \(\PageIndex{7}\): A highly elliptical orbit during an eccentricity cycle. Note the position of the Sun being located at one of the foci of the ellipse. (Source: NASA).

    The longest of these cycles is eccentricity, lasting from 90,000 to 100,000 years per cycle. As this cycle progresses, the Earth’s orbit stretches from more circular to more elliptical. The shift occurs because, while the Earth orbits the Sun, the giant planets Jupiter and Saturn over time exert gravitational forces on the Earth, which causes the Earth to shift over this period. As Johannes Kepler discovered well before Milankovitch, no planetary orbits are perfectly circular; all are elliptical (Kepler’s First Law).

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    Figure \(\PageIndex{8}\): Image of Earth at aphelion and perihelion and the associated dates at present. Also shown here are positions of our Moon relative to its distance from Earth, apogee (farthest distance) and perigee (nearest distance). (Source: NOAA)

    However, Milankovitch discovered that the shape of our orbit changes enough to have a significant effect on our climate. Currently, our orbit is in the phase of this cycle where it is more circular, leading to only a 6% increase in incoming solar radiation from January to July. In January, the Earth is at its closest approach to the Sun for the year (called perihelion) and in July, it is at its furthest approach (aphelion). When the orbit is more highly elliptical, the difference in incoming solar radiation at perihelion can be 20% to 30% greater than it is today. This would mean a much different climate than we have today. And, as you can see in the figure below, it is this 100,000-year cycle that governs cold and hot periods (glacials and interglacials) during the Pleistocene epoch.

    Insolation, methane, and carbon dioxide data extracted from the Vostok ice core, Antarctica. This ice core records in detail the last four glacial/interglacial cycles of the Pleistocene and the start of the Holocene Epochs. Note the approximately 100,000 year cyclicity that emerges in the data.
    Figure \(\PageIndex{9}\): Insolation, methane, and carbon dioxide data extracted from the Vostok ice core, Antarctica. This ice core records in detail the last four glacial/interglacial cycles of the Pleistocene and the start of the Holocene Epochs. Note the approximately 100,000 year cyclicity that emerges in the data.
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    Figure \(\PageIndex{10}\): Changes in Earth’s obliquity over ~41,000 years. (Source: NASA)

    While the Earth’s orbital path is changing, there are also at least two cycles of obliquity that will occur at about 41,000 years each. During one of these cycles, the Earth’s tilt ranges from a minimum of 22.1\(^{\circ}\) to a maximum of 24.5\(^{\circ}\). Currently, our orbital tilt is 23.5\(^{\circ}\), meaning that we are in the middle of one of these cycles rather than at one end or the other. 10,700 years ago, the planet was last at its maximum tilt. In 9,800 years, it will reach its minimum tilt. As the tilt of the Earth is the main factor that determines the behavior of our seasons, changes in this variable can also have significant effects on global climate. Greater tilt leads to more severe seasons while lesser tilt leads to milder changes between seasons. We think the greatest impact on climate occurs at times of greater tilt, as ice builds up and causes major changes in insolation albedo, leading to an amplifying feedback toward cooler climate. Higher reflectivity of the Earth’s surface reflects more of the sun’s radiation back to space. When this happens, ice sheets expand. As ice sheets continue to expand, even more sunlight is reflected back to space, cooling the planet.

    Changes in Earth's precession occur over the course of about 26,000 years. The Earth's axis "wobbles" like a top does when it begins to lose energy. (Source: NASA)
    Figure \(\PageIndex{11}\): Changes in Earth’s precession occur over the course of about 26,000 years. The Earth’s axis “wobbles” like a top. (Source: NASA)

    Finally, precession is the shortest of the Milankovitch cycles. Over the course of about 26,000 years, the Earth’s axis (the imaginary line defining our geographic north and south poles) wobbles. As the axis does wobbles, it marks out a kind of circle on the celestial sphere over the course of that time. Currently, the axis is pointing toward the star Polaris, the North Star, making it the only star that stays in a “constant” position in the night sky. This is why it can be used for navigation. This has not always been the case over longer periods, however. At times, there is no north star, much like there is currently no “south star.” At other times, other stars have that title, as the star Thuban did in 2000 BC when ancient Egyptians might used it to navigate through the desert. In terms of climate, the changes in precession alter the dates for aphelion and perihelion during the year, which affects how seasonal insolation affects the northern and southern hemisphere. As such, the effect of precession in global climate is significant, but more difficult to tease out of data as it is not nearly as powerful as obliquity and eccentricity.

    Asteroid Impacts

    Asteroid impacts are both exciting and terrifying. We hope that, should we ever be in danger of a massive bolide collision, NASA or some other space agency will see it coming. If they do, perhaps we will get a chance to do something about it. Until then – such imaginings make for excellent disaster B-movie plots!

    However, these are very real hazards. Certainly, small impacts like the Tunguska event mentioned earlier are not likely to be seen by any NEA (Near Earth Asteroid) observatory, like the Center for NEO Studies, run by NASA through the Jet Propulsion Laboratory at Caltech. According to their data, there have been 822 recorded fireballs between April 15, 1988 and March 4th, 2020:

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    Most of these are small and cause only localized disturbances. To better quantify risks associated with impacts, the IAU (International Astronomical Union) in 1999 created the Torino Scale. This metric communicates to the public the hazard level of a particular NEA that is being watched by specialists. Displayed using colors from white (no hazard) to red (certain collisions), it is simple and conveys important information on the type of resulting hazards associated at that level. Fortunately for Earth, none of the currently monitored NEA objects are listed as greater than 0 on the Torino Scale.

    The Torino Scale measures the severity of an impact hazard based upon two variables, the probability of an impact and the kinetic energy (in Megatons) involved.
    Figure \(\PageIndex{12}\): The Torino Scale measures the severity of an impact hazard based upon two variables, the probability of an impact and the kinetic energy (in Megatons) involved.

    Asteroid impacts are important extrinsic climate change forcing mechanisms because of the effect they convey on the atmosphere, hydrosphere, geosphere, and biosphere. Impactors heat the atmosphere on their way in and then, as their ejecta return to Earth, heat the global atmosphere more evenly, possibly to temperatures as high as several thousand degrees. But this is a short-term effect of the impact. Post-impact, dust, ash, and other materials may block incoming solar radiation for many years to come, creating a long-term cooling effect. These are just two of the climate effects. As the oceans acidify from dissolved gases and rock debris, climate-regulating currents may be upended. New tectonic or volcanic activity from the geosphere can also contribute to climatic change.

    Manicouagan Crater Reservoir, northern Quebec, Canada. Photographed here by ISS Expedition 38 crewmembers, this crater is so visible from space that it is one of the most photographed. It was created during the Triassic Period, 215.5 Ma. (Source: NASA)
    Figure \(\PageIndex{13}\): Manicouagan Crater Reservoir, northern Quebec, Canada. Photographed here by ISS Expedition 38 crewmembers, this crater is so visible from space that it is one of the most photographed. It was created during the Triassic Period, 215.5 Ma. (Source: NASA)

    In the time periods where we study paleoclimate, none of these warning agencies existed. In the Earth’s history, we know of many large impacts that have occurred, many of which have left lasting scars on the surface. One of the most photographed is of Manicouagan Crater in northern Quebec, which was created by a bolide that hit that part of Canada 215.5 Ma (during the Triassic period). The impactor is estimated to have been about 5 km in diameter (85km diameter crater), very close to the size of the Chicxulub impactor that caused the extinction of the dinosaurs at the K/Pg boundary (6km impactor and 150km crater).

    Figure \(\PageIndex{14}\): The Earth Impact Database world map. Note that the colors indicate a rough time period of impact. These are also known impacts. There are very likely many, many more yet to be discovered. Hovering over a circle brings up more information about it.

    Changes in solar insolation over time

    Over the course of a year, the fraction of the energy Earth receives from the Sun is measured as insolation (the energy received), and varies by about 0.1%. While this fraction is small, it actually represents quite a bit of energy. Changes in short-term solar insolation are of great interest to climate modelers. Such changes result over time spans longer than a year due to the 11-year sunspot cycle, where the Sun’s surface experiences a cycle running from cooler to hotter due to magnetic changes. These can affect the planet’s climate over these time spans, though the evidence is clear that current climate change cannot be explained by this. To study changes in solar output, NASA in 2003 launched the Solar Radiation and Climate Experiment mission (SORCE).

    Variability in the Sun's luminosity (brightness), radius, and temperature over time, looking at past trends and future trends. The Sun will continue to increase its radius and continue to become more luminous over time as it moves toward the red giant phase of its life. Associated temperatures will rise some and affect climate over that time. (By RJHall - Own work, based on figure 1, Ribas, Ignasi (February 2010). "Solar and Stellar Variability: Impact on Earth and Planets, Proceedings of the International Astronomical Union, IAU Symposium". Error: journal= not stated 264: 3–18. DOI:10.1017/S1743921309992298., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=16799327)
    Figure \(\PageIndex{15}\): Variability in the Sun’s luminosity (brightness), radius, and temperature over time, looking at past trends and future trends. The Sun will continue to increase its radius and continue to become more luminous over time as it moves toward the red giant phase of its life. Associated temperatures will rise some and affect climate over that time. (CC BY-SA 3.0; By RJHall – Own work, based on figure 1, Ribas, Ignasi (February 2010). “Solar and Stellar Variability: Impact on Earth and Planets, Proceedings of the International Astronomical Union, IAU Symposium”. Error: journal= not stated 264: 3–18. DOI:10.1017/S1743921309992298., https://commons.wikimedia.org/w/index.php?curid=16799327)

    The Sun itself changes over very long time spans also. Since its early days, it has been steadily warming and will continue to do so. The warming trend is significant, but does pale in comparison to the increases over time in the star’s radius and luminosity. These two variables are related, as greater radius leads to greater surface area which leads to greater luminosity. In the figure to the left, it is predicted that the Sun will continue to grow larger. One misleading piece of data here is temperature. While the Sun’s temperature may not increase as dramatically as its radius, as that radius increases, the surface of the Sun and its very hot atmosphere will inch ever closer to Earth. This effect on Earth will be very significant, very likely making within a billion years or less most life on Earth as we know it no longer possible. Ultimately, whether at this point the Earth is pushed outward be the Sun’s lower mass or pulled inward by drag and enveloped is a matter of some lively scientific debate.

    Lunar effects (stabilization, etc.)

    What about forcing factors outside of the Sun and bolide impacts? Certainly, while there may be some climatic effects caused by phenomena such as supernova explosions and the passing of our solar system through dense interstellar clouds, these effects are tiny, if they exist.

    What about the Moon?

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    Figure \(\PageIndex{16}\): Animation of the lunar tidal effect. The combined pull of the Moon and Sun (the Moon’s effect is much greater) during New and Full lunar phases create the largest tidal bulges and ranges and are called spring tides. (Source: NOAA)

    The Earth’s natural satellite (as that is really the proper term to use), the Moon, has two demonstrable effects, though small, on our climate. Both of these effects are related to the tidal gravitational forces that the Moon exerts on the Earth. When we think of tidal forces, we usually think of shorelines. This is correct, of course, but the effect on the shorelines is really a gravitational effect, as the Moon is pulling and releasing the water in the ocean as the Earth rotates and as a 29.5 day lunar cycle passes. As you may have learned, there are one to two diurnal high and low tides per day. During a lunar month, there are also times of greatest tidal range that occur during the New and Full phases of the Moon, the spring tides. The tidal range is the difference between the elevation of high and low tide. There are also what are called neap tides, when the tidal range is lowest during a lunar cycle, during the 1st and 3rd quarter phases (half moons).

    These tidal effects actually affect climate on a small scale, by affecting the amount of precipitation that occurs. It does this not by pulling on Earth’s water, however, but by exerting its gravitational pull on the atmosphere. When the Moon is overhead, a full moon in particular, air pressure is actually higher. This slightly depresses the chance for precipitation. The effect is tiny, but it does exist.

    The Distribution of Earth's seasons relative to the Sun. The tilt of the Earth and its stability are what allow for the predictable cycle of seasonality we experience in temperate latitudes. At the time of the autumnal or vernal (spring) equinoxes, the equator faces most directly toward the Sun. At the time of summer solstice, the northern hemisphere experiences summer and at the time of winter solistice, the southern hemisphere is experiencing summer.
    Figure \(\PageIndex{17}\): The Distribution of Earth’s seasons relative to the Sun. The tilt of the Earth and its stability are what allow for the predictable cycle of seasonality we experience in temperate latitudes. At the time of the autumnal or vernal (spring) equinoxes, the equator faces most directly toward the Sun. At the time of summer solstice, the northern hemisphere experiences summer and at the time of winter solistice, the southern hemisphere is experiencing summer.

    Perhaps a larger lunar impact is related to the Earth’s obliquity cycle. Joutel and Robutel (1993) were able to demonstrate the Moon’s gravity stabilizes our planet’s tilt. In essence, it keeps our obliquity cycle stable, which prevents much more massive long term climatic changes. This also helps stabilize our seasons, which the Earth’s tilt is critical in defining. In times when the tilt angle could be nearly 0\(^{\circ}\) or much greater than 24.5\(^{\circ}\) maximum our planet currently has, the seasons would be very different. In a situation where there is zero to little tilt angle, there would be no seasonality on the planet, or very little. In a situation where the tilt might reach greater than 30\(^{\circ}\), the difference between summer and winter would be quite harsh in temperate latitudes and nearly impossible to bear in polar regions. As such, our Moon works to stabilize our climate.

    The leading idea on the formation of the Moon is that it resulted from a massive impact, probably of an object about the size of Mars. In its early years then, the Moon was much, much closer to the Earth. Over time, it has gradually been moving farther and farther away. However, this also means that its gravitational tidal forces have also been lessening over time. One notable effect of this is the gradual change in the length of a day on Earth and, consequently, the number of days in a solar year. This is born out by fossil mollusks and corals from 80 Ma (and other time periods) that show that a year was 372 days at the time.

    There are also potentially effects over time on other orbital parameters that affect climate. The affect of our natural satellite on our climate is still an active and exciting area of research.

    INTRINSIC CHANGE AGENTS

    Within the Earth system, there are a wide variety of factors that can affect the Earth’s climate. These intrinsic factors all have one thing in common. In one way or another, they disrupt, or place in a state of disequilibrium, one or more biogeochemical cycles. There are many biogeochemical cycles and all of them interact with more than one of the Earth’s subsystems, or spheres. Examples include the carbon cycle, nitrogen cycle, hydrologic cycle, phosphorus cycle, etc.

    Earth's greenhouse effect (Source: EPA)
    Figure \(\PageIndex{18}\): Earth’s greenhouse effect (Source: EPA).

    The Earth’s climate is regulated by the greenhouse effect, or the retention of re-radiated longwave radiation through the absorption of this energy by greenhouse gases in our atmosphere. Earth is not the only planet that has a greenhouse effect. Venus has this also, in spades. It is what leads to surface temperatures on Venus exceeding 400 \(^{\circ}\)C (~800 \(^{\circ}\)F) in some instances. Mars has very little atmosphere and though what it does have it almost entirely carbon dioxide, it cannot retain much of the Sun’s energy. Mars lacks a magnetic field and thus cannot hold onto its atmosphere. One other location in our solar system, Titan, a very large and gassy natural satellite of Saturn, has a moderate greenhouse effect, but due to the high concentration of methane in its atmosphere.

    On Earth, the greenhouse effect is moderate, but absolutely critical for life. This is due in part to its distance from the Sun, but also because of its very different mix of atmospheric gases due to the presence of life. Photosynthesis has altered our atmosphere so that it contains 21% oxygen on average. 80% of the gas in our atmosphere is nitrogen, which also has biogenic sources. Life on Earth has, thus, reduced the carbon dioxide so prevalent in the atmospheres of Venus and Mars (from volcanism) to a mere 0.04% of the total gas content. As of this writing today, this amounts to a carbon dioxide concentration of about 416ppm. Common greenhouse gases include carbon dioxide, methane (another carbon compound), oxides of nitrogen (\(\ce{NO_x}\)), HCFCs (anthropogenic chlorofluorocarbons), and water vapor.

    Ultimately, all of the elements that make up compounds in our atmosphere share a primordial source from the Earth’s interior. Biogeochemical cycling, aided by plate tectonics, makes these elements accessible. Biogeochemical cycles are cycles driven not only by geological processes (geo), but also biological processes (bio). As such, Earth’s versions of these cycles are unique.


    This page titled 15.2: Paleoclimatology- Historical Climate is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Callan Bentley, Karen Layou, Russ Kohrs, Shelley Jaye, Matt Affolter, and Brian Ricketts (VIVA, the Virginia Library Consortium) via source content that was edited to the style and standards of the LibreTexts platform.