The Truth of Global Warming: Part 4 - Global warming and the energy balance of sunligh

Published: Feb. 6, 2024, 3:18 p.m. (UTC) / Updated: May 22, 2024, 4:05 a.m. (UTC) 🔖 3 Bookmarks
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Overview of Sunlight's Energy Balance

The figure below shows the estimated annual energy balance of the Earth. Incoming Solar Radiation is $342 W m^{-2}$ from the sun, which follows various paths and ultimately is released into space. Of the solar radiation, $107 W m^{-2}$ is not absorbed at the Earth's surface but is reflected by the atmosphere, clouds, water surfaces, etc., and emitted into space (Reflected Solar Radiation). On the other hand, the energy absorbed at the Earth's surface is released into the atmosphere as heat, as water vapor into the atmosphere, and as infrared radiation into the atmosphere. Furthermore, when clouds absorb upward fluxes from these, effects such as energy radiation from the clouds back to the Earth's surface, warming the Earth's surface, etc., occur. However, ultimately, $235 W m^{-2}$ of energy is emitted from the clouds to space, so that the amount entering and leaving is balanced.

When this balance is disrupted and the amount of incident energy exceeds the output energy, Earth accumulates energy, leading to global warming. Such data is fundamental to various simulators and is extremely important, so it is desirable to systematically update and publish the data annually through fixed-point observations.

By the way, in the case of the diagram above, since it is balanced, Earth warming would not occur. In fact, the explanation above only considers a short time interval of one year, during which the effect of global warming is negligible and therefore not mentioned. Upon closer inspection of the diagram, there are greenhouse gases on the right side, which appear to be related to radiation returning to the surface (Back Radiation). Let's examine this part in more detail.

Micro Mechanism of Greenhouse Gases

Blackbody Radiation: Different Spectrum Distribution between the Sun and the Earth's Surface

Let's first review the energy coming from the Sun. The surface temperature of the Sun is approximately $6000{}^\circ K$, and from there, very intense energy becomes light and shines down on the Earth. As many people know, this sunlight contains ultraviolet, visible light, and infrared radiation.

For example, visible light ranges from approximately $0.4 \mu m$ to $0.8 \mu m$ ($1 \mu m = 0.001 mm$). The figure below shows the energy magnitude included in each wavelength, with the horizontal axis representing the wavelength of light and the vertical axis representing the magnitude of energy contained in that wavelength. The thin orange peak represents the wavelength (spectrum) distribution of light emitted by the Sun, while the broad green tail represents the spectrum distribution of infrared radiation emitted by the Earth's surface (average $14{}^\circ C = 287{}^\circ K$) after absorbing sunlight. (See the Appendix for details on how the figure was created.)

Please note that the left vertical axis corresponds to the blackbody radiation intensity from the Sun, while the right vertical axis corresponds to the blackbody radiation intensity from the Earth's surface. The radiation intensity from the Sun is orders of magnitude larger, around ten million times greater.

A crucial point to understand here is that the spectra of sunlight incident from the Sun and emitted from the Earth's surface rarely overlap precisely. As seen in the chapter on the "History of Research", the mathematical physicist Fourier stated in his papers from the 1820s that "the atmosphere is transparent to the energy coming from the Sun, so it does not warm up due to it, but it captures and warms up due to the energy (infrared radiation) emitted from the Earth". At that time, this detailed mechanism was not understood, but it is clear to us in modern times. When it comes to gases like greenhouse gases being "transparent" to sunlight, it means that gas molecules do not interfere with sunlight's wavelengths and simply pass through. In the above diagram, this occurs around the orange peaks below $3-4\mu m$, but gas molecules in the atmosphere do not absorb this range of infrared radiation. If atmospheric gas molecules were to absorb this infrared radiation, they would receive a large amount of energy, causing them to vigorously collide with surrounding gas molecules, leading to increased movement of the surrounding gas molecules. When gas molecule movement becomes more vigorous, atmospheric temperature rises. In other words, the atmosphere absorbs sunlight, causing it to warm up. However, as Fourier discovered, atmospheric gas molecules are unresponsive to the sunlight shining down from the sun, and therefore do not warm up as a result.

On the other hand, for the green-colored infrared radiation, greenhouse gases are not transparent; they absorb light. As seen in the green-colored infrared spectrum above, this is the spectrum distribution when the energy from the sun, absorbed by the Earth's surface, warms the surface, and the warmed surface then releases that energy into the atmosphere as infrared radiation. Greenhouse gases absorb this range of infrared radiation. Therefore, when the Earth's surface warms up, the atmospheric temperature also rises.

By the way, greenhouse gases, after absorbing infrared radiation, eventually re-emit it, with roughly half directed back toward the Earth's surface and the other half emitted toward space. This portion corresponds to the back radiation described in the lower right part of the figure from the previous section. Through this cycle of absorption and emission, as described earlier, most of the energy is eventually emitted toward space. However, if even a small portion remains within the Earth, it would contribute to warming the planet. To explain further, when the atmosphere absorbs the infrared radiation emitted from the Earth's surface, the CO2 molecules, for example, hold onto this energy for a certain period before re-emitting it as infrared radiation. Then, nearby CO2 molecules (or other greenhouse gases) capture this radiation. In this way, the energy is passed back and forth among CO2 molecules until some of it gradually reaches the upper layers of the atmosphere. Eventually, when a CO2 molecule emits the infrared radiation toward space, if no other gas molecule captures it, the energy would be lost to space, resulting in a cooling effect on Earth.

In this game of catch, increasing the concentration of CO2 prolongs the number of times the "ball" (infrared radiation) is passed among molecules before reaching the upper layers of the atmosphere. Consequently, it takes longer for the energy to be released. In other words, more heat is retained by the Earth, leading to what is commonly known as global warming.

Absorption by Greenhouse Gases

It is known that there is a spectrum distribution emitted from the Earth's surface to the atmosphere, as seen above. If this were to be released directly into space, the radiation spectrum observed from satellites at the upper boundary of the atmosphere would exhibit the same distribution. The figure below compares the upward radiation from the Earth's surface with the distribution observed at the upper atmosphere.

The blue line represents the thermal energy emitted from the Earth's surface to the atmosphere, while the red line represents the thermal energy emitted from the top of the atmosphere to space. The difference between the blue and red lines represents the intensity of infrared absorption by the atmosphere, indicating the strength of the greenhouse effect. In the figure, $H_2O$ and $CO_2$ indicate the wavelength regions where absorption of infrared radiation occurs due to these molecules. It can be observed that the red line around where it is labeled as $CO_2$ is concave. This indicates that $CO_2$ has an absorption band around $15\mu m$. The difference between the blue and red lines is called radiative forcing, measured in ($W m^{-2}$) of net radiative flux at the top of the troposphere. The sign indicates that radiation from space or the greenhouse effect causing temperature rise is positive, while radiation to space causing temperature decrease is negative.

Now, let's see how much influence each of these greenhouse gases has on the greenhouse effect. The following figure shows the radiative forcing ($W m^{-2}$) for "Water vapor ($H_2O$)", "Carbon dioxide (CO_2)", "Ozone ($O_3$)", and "Others", as well as the contribution of each gas to the total radiative forcing for both clear-sky and cloudy-sky conditions. The results for cloudy skies are provided in parentheses. The sum of all values represents the atmospheric greenhouse effect. Particularly, pay attention to the section labeled "Combined with overlap effects," which decomposes the greenhouse effect to show where gases overlap and contribute jointly.

In clear-sky conditions, water vapor is the most important greenhouse gas, accounting for 60% of the total greenhouse effect. The second most important greenhouse gas is CO2, with a contribution of $32 W m^{-2}$. From this, an important insight can be gleaned. Even if human activities lead to an increase in CO2, the resulting temperature rise may be only marginal. However, the crucial point is that the increased CO2 content in the atmosphere can raise the saturation vapor pressure, allowing more water vapor to accumulate in the atmosphere, ultimately leading to a much larger greenhouse effect.

This is a crucial point. The argument that the concentration of CO2 in the atmosphere is only about 0.04%, so a slight increase wouldn't be a significant problem, is not necessarily accurate. The result is that water vapor ends up heating the Earth like a sauna, even if CO2 increases only slightly. Understanding this is essential, and the impact of water vapor is a major issue when quantitatively verifying future scenarios of global warming. I believe that the lack of thorough explanation of this aspect in reports like those of the IPCC, even if it is a result of political compromises among various countries, is somewhat dishonest to humanity's descendants (our children).

Continuity of Absorption Spectra of Gas Molecules (Reference)

If you've understood everything up to this point, you may skip this section as it's for reference only. However, those with a deeper understanding of physics (quantum mechanics) might have the following question. Providing an answer to this question and understanding the details of how molecules, which constitute only 0.04% of the atmosphere, actually absorb light could be valuable. So, let's explain.

And the simple answer to the question is as follows: Indeed, light absorbed by molecules such as $CO_2$ corresponds to specific wavelengths, and in quantum mechanical interpretation, their absorption spectrum appears as spikes (line spectrum). This is because the absorption spectrum of molecules corresponds to transitions between specific energy levels. Therefore, the depiction where spikes appear at specific wavelengths, rather than a continuous absorption band, is correct. However, in the actual absorption spectrum of gases like $CO_2$ in the atmosphere, due to the different energy levels of individual molecules, the overlapping of multiple molecules results in the appearance of a continuous absorption band. This occurs because of interactions between molecules and the surrounding environmental conditions, which broaden the absorption spectrum.

To revisit the basics, CO2 molecules absorb only light wavelengths corresponding to the modes of motion they can undergo based on their structure. To understand what types of motion are possible, it's helpful to visit sites like this, where animations depict the movements of molecular modes as shown in the figure below. Intuitively, you can grasp the variety of movements of the hands attached to the central carbon atom, which are bound to oxygen atoms, representing carbon dioxide molecules.

In both the initial and final vibrational states, a molecule can adopt a multitude of rotational states, each separated by energy much smaller than the energy difference between the vibrational states. Consequently, there are many transitions between the various rotational states associated with the ground and first excited vibrational states. These transitions between many pairs of states are facilitated by the absorption of infrared radiation at wavelengths appropriate to each pair, leading to the absorption of such radiation across a range of energies.

That is to say, absorption spectra of many polyatomic molecules or compounds typically exhibit absorption bands characterized by broad peaks rather than discrete lines composed of comb-like discontinuous lines. The point of maximum absorption within these bands is referred to as the absorption maximum, and the corresponding wavelength is termed the maximum absorption wavelength.

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