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Recent Advances in Climate Change Research: Part I - Blackbody Radiation and Milankovic Cycles

Geoscience will probably play an important role in mitigating carbon dioxide emissions. In part one of this series, we discuss some history and physics behind the topic of climate change including the concepts behind blackbody radiation and Millankovic Cycles.
This article appeared in Vol. 16, No. 2 - 2019

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Recent Advances in Climate Change Research: Part I - Blackbody Radiation and Milankovic Cycles

“Available energy is the main object at stake in the struggle for existence and the evolution of the world.” Ludwig Eduard Boltzmann (1844–1906)

The Sun (1911) is one of several paintings by Edvard Munch that adorn the walls inside the Hall of Ceremonies at the University of Oslo. Inhuman itself, the sun provides Earth with the light and heat necessary to support life. The color of the sun is essentially all the colors mixed together, appearing to our eyes as white. At sunrise or sunset, the sun appears yellow, orange, or red, because its shorter-wavelength light colors (green, blue, purple) are scattered by the Earth’s atmosphere. Growing concerns about climate change and emissions of carbon dioxide (CO2) into the atmosphere are leading to changes in how the hydrocarbon industry operates. In a series of articles, we will discuss in simple terms some of the assumptions and basic physics behind these concerns and show how they might lead to new challenges and result in new ways to operate. We will discuss how CO2 might be stored in the subsurface to mitigate or reduce the amount of it emitted to the atmosphere. Geoscience will probably play an important role in this mitigation process. But first, we digress to discuss some history and physics behind the topic.

The Swedish physicist Svante Arrhenius (1859–1927) was among the first scientists to attempt to quantify the influence of CO2 and water vapor on the Earth’s temperature, in his quest to test a hypothesis that the ice ages were caused by a drop in CO2. His paper on the topic was published in The Philosophical Magazine and Journal of Science in April 1896. In the first two articles in this series we will discuss basic principles and the ideas behind Arrhenius’ work.

Arrhenius was very familiar with Stefan-Boltzmann’s Law, stating that the total radiant heat energy emitted from a surface is proportional to the fourth power of its absolute temperature. The law applies to blackbodies, which are theoretical surfaces that absorb all incident heat radiation. A great puzzle at the turn of the century was to explain the shape of the blackbody curve. In an act of desperation, in 1900 Max Planck (1858–1947) found that he could fit the shape of the black body curve if he postulated that the radiant energy could be emitted only in finite amounts of energy. His idea introduced the quantum principle into physics: certain quantities in nature occur only in discrete intervals, and the size of these intervals is determined by Planck’s constant, h.

Understanding blackbody radiation is one of the great triumphs of 20th century physics, since it led to the discovery of quantum theory. But blackbody radiation is manifest in the macroscopic world, and is determined by Planck’s radiation law, which depends only on temperature and wavelength. No objects are perfect blackbodies, but everything radiates – you, the Earth, and the sun. The sun is close to being a blackbody, and it emits radiation in the visible range. The Earth and its atmosphere emit in the infrared. Another rather more obvious concept is that radiation encountering matter is either transmitted through matter, absorbed by matter, or scattered by matter. The sum of energy that is transmitted, absorbed and scattered must equal the amount of incoming energy.

What is Blackbody Radiation?

A blackbody is a body that completely absorbs all the electromagnetic radiation (light, X-rays, gamma rays, and thermal radiation) falling on it. A surface covered with lampblack will absorb about 97% of the incident light and, for most purposes, can be considered a blackbody. The opposite of a blackbody would be a ‘whitebody’ where all energy is perfectly reflected. The concept of the blackbody as a perfect absorber of energy is very useful in the study of radiation phenomena.

When a blackbody absorbs radiant energy falling on it, it heats up, and the way that a blackbody can maintain thermodynamic balance is to emit radiation in order to maintain a constant temperature. The prefix black is used because at room temperature the blackbody would emit almost no visible light, appearing black to an observer.

  • Blackbody curves showing the intensity of light emitted at various wavelengths for four different blackbodies, each at a different temperature. Temperature is the only quantity that distinguishes one blackbody from another. Intensity is defined to be the amount of energy emitted each second per square meter of the body’s surface. Blackbody spectra are important in physics because of their universality. Virtually any hot body emits electromagnetic radiation in the form of a blackbody spectrum. The object becomes visible as red, then yellow, and eventually a bluish-white as the temperature rises. When the object appears white, it is emitting a substantial fraction of its energy as ultraviolet radiation. The sun, with an effective temperature of 5,778 K, is an approximate blackbody with an emission spectrum peaked in the central part of the visible spectrum, but with significant power in the ultraviolet as well.

  • Solar radiation spectrum for direct light at both the top of the Earth’s atmosphere (represented by yellow area) and at sea level (red area). The temperature of an ideal blackbody that would radiate energy at the same rate as the sun is 5,778 K (5,505°C), which is the sun’s surface temperature. This effective temperature is obtained by setting the area under the intensity-wavelength curve for the sun’s radiation equal to the area under the intensity-wavelength curve for the ideal blackbody, and solving for temperature. As light passes through the atmosphere, specific wavelength ranges are absorbed by carbon dioxide and water vapor. Oxygen and ozone absorb light in the UV spectrum on the left side of the graph, shielding plants from harmful radiation. Meanwhile, the atmosphere is relatively transparent to visible light from the sun. Additional light is redistributed by Raleigh scattering, which is responsible for the atmosphere’s blue color. The curves are based on the American Society for Testing and Materials (ASTM) Terrestrial Reference Spectra. Source: wikimedia.org

As discussed, Max Planck was the first to find the mathematical relation between the radiationemitted by a blackbody as a function of temperature and wavelength. His efforts laid the foundation of the quantum theory, for which he received the Nobel prize in 1918. The key observation is that blackbody radiation depends on only one parameter: the temperature of the blackbody. The radiation thus is independent of the shape and size and material of the blackbody.

Scientists study many real objects as ideal blackbodies. Examples are the Earth, non-terrestrial objects like the moon, the sun and stars, and humans and non-humans. We may use the blackbody radiation model to determine the temperature of our sun or to determine the body temperature at various locations on a horse or human.

The Electromagnetic Spectrum

The entire range of light energy is called the electromagnetic spectrum. The light we can see with our eyes is within the optical spectrum, which ranges in color from red up to violet, with wavelengths from 380 nm to 740nm. All objects in our universe absorb, reflect and emit electromagnetic radiation in their own distinctive ways. Light that is given off, or radiated from an object, is called radiation.

Frequency is related to wavelength by λ=c/ν, where c is the speed of light. Temperature is related to wavelength by the Wien displacement law. 

The energy of electromagnetic radiation is called radiant energy. It is measured in Joules (J). In many situations it is more interesting to consider the rate at which energy is transferred per time. The corresponding quantity is called power, which has dimensions J/s, or Watt (W). However, when talking about radiant power that is emitted by, passing through or incident on a surface, the term flux is more common. Therefore, the radiant energy emitted, reflected, transmitted or received, per unit time, is called radiant flux. Spectral flux is the radiant flux per unit frequency or wavelength (W/m). The term flux density refers to the spatial density of radiant flux; hence, radiant flux density is the radiant flux per unit area at a point on a surface, measured in W/m2. If flux is leaving the surface due to emission or reflection, the radiant flux density is referred to as radiant exitance, while if the flux is arriving at the surface the radiant flux density is referred to as irradiance. Thus, irradiance is the amount of light power from one object hitting a square meter of a second object. Radiant exitance and irradiance are sometimes called ‘intensity’, since the SI-unit of intensity is also W/m2. Spectral radiant exitance and spectral irradiance are the corresponding quantities per unit frequency or wavelength. For wavelengths, the SI-unit is W/m3.

A solid angle Ω is equal to the ratio of the viewed surface area A divided by the square of the viewed distance r; whence, Ω = A/r2 sr. (Solid angle is expressed in the SI unit steradian (sr)). When the area is A = r2, then the solid angle is Ω = 1 sr. A steradian ‘cuts out’ an area of a sphere equal to r2, in the same way that a radian ‘cuts out’ a length of a circle’s circumference equal to the radius. There are 2π radians along a circle and 4π steradians over a sphere. Source: wikimedia.org Sources of radiation are objects rather than point sources; each point of the surface of the object is characterized individually rather than the entire source. Radiance is the radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit area. It is a directional quantity, measured in W/(sr m2)

Unlike radiant flux density, the definition of radiance does not distinguish between flux arriving at or leaving a surface. Spectral radiance is radiance of a surface per unit frequency or wavelength, the latter measured in W/(sr m3).

The radiance B and irradiance U are related by: B = dU/cos θ dΩ

where represents the differential of solid angle and θ is the angle between a beam of radiation and the direction normal to the surface (usually horizontal) on which the radiance is measured. Radiation whose radiance is independent of direction is called isotropic radiation. In this case the equation can be integrated to yield: U = πB

Absorption Spectra of Earth’s Atmosphere

Absorption spectra of some atmospheric gases for wavelengths between 0.1 and 100 micrometers. Notice that water vapor has a wider ‘blocking’ spectrum compared to, for instance, CO2. (Source: T.J. Nelson Cold Facts on Global Warming https://www. randombio.com/ co2.html) As observed above, the Earth (and the moon) emits blackbody radiation mainly within the infrared band, peaking around 17 micrometers. This outgoing radiation from the Earth is absorbed by various gases in the atmosphere, and the figure top of page 42 shows for which wavelengths this absorption effect is most effective. For CO2, we observe that there are three relatively thin bands: one around 2.5 micrometers, the next around 4 micrometers and a wider band ranging from 12–18 micrometers. 

Water vapor has several bands, and acts as a blocker for wavelengths above 15–20 micrometers. It is evident from this figure that if we increase the amount of some of these gases, then less terrestrial blackbody radiation will escape, leading to global warming. In most climate models there are complex coupling between an increase in CO2 leading to a corresponding increase in water vapor and so on, often referred to as positive feedback.

Benthic δ18O Records and Milankovic Cycles

When Arrhenius published his 1896 paper on CO2 and temperature (to be discussed further in Part II), the famous work of the Serbian scientist Milutin Milankovic (1879–1958) was not known. Milankovic suggested in 1920 that the Earth’s eccentricity, the tilt of its axis and the precession will cause systematic variations in how much energy the

Earth receives from the sun, and hence, such variations might cause climate changes. One way to establish a link between this theory and observations is to use benthic sedimentary records obtained from deep sea drilling experiments (see Lisiecki and Raymo (2005) for a comprehensive discussion). By measuring the variation in δ18O (the relative difference of the O18 to O16 ratio measured in parts per thousand) it is possible to link this ratio to the temperature. Epstein et al. (1953) suggested the following empirical relation between δ18O and temperature: T(°C) = 16.5 – 4.3 δ + 0.14 δ2

  • a) Benthic sedimentary record composed of 57 globally distributed sites of measured δ18 O and b) the corresponding temperature estimate. Notice the gradual colder climate from three million years ago to present, and also that the magnitude of the temperature oscillations is larger towards present time.

The figure above shows just such a comprehensive record (using Lisiecki and Raymo’s data) and the corresponding temperature estimate using this equation.

The figure below shows the amplitude spectrum of the temperature curve (Fourier spectrum), and we can clearly observe three distinct maxima in the spectrum: one corresponding to a cycle of approximately 100,000 years (coupled to the eccentricity of the Earth’s orbit), another cycle peaking at approximately 41,000 years (corresponding to the tilt of the Earth’s axis) and a third cycle of approximately 23,000 years (corresponding to the precession of the Earth orbit). 

  • Amplitude spectrum of the temperature series obtained from sedimentary measurements of delta O18. The three peaks shown here actually

Today, Milankovic models are accepted as a cornerstone in our understanding ofclimate variations in the past. However, this does not exclude other effects like variations in atmospheric gases, and in 1896 Arrhenius suggested that CO2 could actually be a cause for ice ages.

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