Appendix A
The Chemistry and Physics of Global Warming:
An Overview

The regulating factor for global climate change depends on a fundamental principle, the First Law of Thermodynamics, also known as the Law of Conservation of Energy. Mathematically this can be represented as follows:

where dQ = heat added to the system, dU = change in the internal energy of the system, and dW = work extracted. Heat can be transported to and from a system in three ways [59]. This law states that the total amount of energy added should be equal to the amount of energy removed from a stable system to keep the system stable. Energy cannot be gained or lost in a stable system; it can only change forms. Such a system is said to follow an “Energy Balance Model.” To maintain stability, the Earth-ocean-atmosphere system absorbs energy from the Sun, radiates it in the form of infrared (heat) energy, and transports it in the form of both latent and sensible heat flux. Several natural events (volcanic eruptions, forest fires, fluctuating intensity of solar radiation, varying cloud cover, and others) and human activities (fuel combustion, aerosol production, industrial and land use practices that release or remove heat-trapping greenhouse gases, and others) can affect the balance between the absorption and emission of radiation.

The absorption of light by fluids (here, greenhouse gases [GHGs]) can be measured by the following simple relation:

where A is the absorbance or optical density of the solute (here, a GHG), epsilon (liters per mole per centimeter) is the molar extinction coefficient of the GHG at the wavelength of measurement, c (moles per liters) is the concentration of the GHG, d is the optical pathlength in centimeters, and T is the transmittance [60]. When a molecule absorbs light, it normally goes from the ground state to an excited or “hot” state. The hot molecule can release its excess energy primarily in three ways: chemical reaction, quenching, and emission. Because greenhouse gases are fairly stable, chemical reaction is not a common pathway for releasing the excess energy. Excited or hot greenhouse molecules release excess energy mostly through emission and quenching. Quenching is the process of transferring excess energy to other molecules in a ground state, thereby increasing the temperature of the other molecules. The other hot molecules can also emit excess energy in the form of radiation.

At the top of the atmosphere, the shortwave energy flux received from the Sun is about 1,368 watts per square meter [61]. Because of its spherical shape, at any instant the Earth receives on average half the incident solar flux, that is, 684 watts per square meter. Due to the Earth's rotation, the average radiative flux received over a day-night cycle is half of this value, that is, 342 watts per square meter, approximately 105 watts per square meter of which is reflected by the Earth's surface and the atmosphere. According to measurements made from satellites, the outgoing longwave, or infrared, radiation is 237 watts per square meter. Approximately 169 watts per square meter of solar radiation is absorbed by the Earth's oceanic and land surfaces and 68 watts per square meter by the atmosphere. About 90 watts per square meter of latent heat flux and 16 watts per square meter of turbulent heat flux are estimated to leave the surface and enter the atmosphere. These latent and turbulent heat fluxes do not necessarily become part of the infrared radiation emitted by the surface and the atmosphere. This relatively shortwave radiation either can be absorbed by water (including clouds), ozone, and/or oxygen, or it can be simply added to the outgoing reflected solar radiation in the global energy balance model [62] [63].

Radiation from the Sun varies greatly in energy, from high-energy gamma rays to low-energy microwaves (Table A1). Shortwave ultraviolet (UV) radiation includes wavelengths from 160 billionths of a meter (nanometers or nm) to the threshold of visible light at 400 nm. In wavelengths longer than one millionth of a meter (micrometer or µm), energy takes the form of heat. These wavelengths are grouped into the infrared and microwave bands. The spectrum of sunlight from the zenith at the surface of the Earth (Figure A1) reflects dips in the ultraviolet (290-365 nm) [64] and red to infrared (650-1100 nm) [65] regions, which are due to absorption by water vapor.

Table A1. Electromagnetic Spectrum
Spectral Band	Wavelength Range	Photon Energy (electronvolts)
Microwave	0.1 - 100 cm	0.000001 - 0.001
Infrared - C	3.0 - 1,000 µm	0.001 - 0.4
Infrared - B	1.4 - 3.0 µm	0.4 - 0.9
Infrared - A	0.76 - 1.4 µm	0.9 - 1.6
Visible	400 - 760 nm	1.6 - 3.1
Ultraviolet - A	320 - 400 nm	3.1 - 3.9
Ultraviolet - B	280 - 320 nm	3.9 - 4.4
Ultraviolet - C	100 - 280 nm	4.4 - 12.4
Vacuum Ultraviolet	10 - 100 nm	12.4 - 124
X-rays	0.1 - 10 nm	100 - 100,000
Gamma-rays	0.0001 - 0.1 nm	10,000 - 10,000,000
cm = Centimeter. µm = Micrometer. nm = Nanometer. Notes: 100 cm = 1 meter; 1 million µm = 1 meter; 1 thousand nm = 1 µm; 1 billion nm = 1 meter. Source: L.I. Grossweiner, The Science of Photobiology, ed. K.C. Smith (New York: Plenum Press, 1989), pp. 1-77.

D

Most of the high-energy radiation from the Sun--for example, gamma rays--does not pass through the mesosphere [66]. In the stratosphere [67], ozone and oxygen absorb virtually all ultraviolet (UV) light in band C (wavelengths of from 100 to 280 nanometers [nm]), the UV light with the shortest wavelengths and highest energy (see Figure 2). All cellular constituents, including all the proteins (such as deoxyribonucleic acid [DNA] and ribonucleic acid [RNA]), absorb UV-C. Without the stratospheric ozone layer, all living things in the biosphere would suffer enormously from UV-induced diseases, including radiation-induced alterations/mutations of genetic fingerprints (DNA and RNA) and ocular diseases. In the stratosphere, oxygen uses this energy to produce ozone, and ozone absorbs most of the UV light in band B (280 to 320 nm), preventing it from reaching the surface of the Earth. Still further down, in the troposphere [68], water vapor and clouds absorb on average more than 60 percent of the remaining incoming radiation with wavelengths between 290 and 365 nm. Because the water vapor content varies from 0 to 4 percent, the amount of radiation with wavelengths between 290 and 365 nm and between 650 and 1100 nm reaching the Earth's surface also varies (Figure A1).

What happens after the GHG molecules absorb infrared radiation? The hot molecules release their energy, usually at lower energy (longer wavelength) radiation than the energy previously absorbed. The molecules cannot absorb energy emitted by other molecules of their own kind. Methane molecules, for example, cannot absorb radiation emitted by other methane molecules. This constraint limits how often GHG molecules can absorb emitted infrared radiation. Frequency of absorption also depends on how long the hot GHG molecules take to emit or otherwise release the excess energy.

Emission of radiative heat from excited greenhouse molecules to some extent is independent of surroundings. Transport of the heat emitted, however, can be facilitated by wind patterns and sensible heat flux. The absorption coefficients of some of the greenhouse gases are temperature dependent [69].

Albedo is defined as the ratio of energy incident to energy reflected. It exercises a tremendous influence on absorption, reflection, and emission of radiation in the Earth-ocean-atmosphere system. Snow or white clouds have relatively high albedo values due to their reflective surfaces, whereas water has a low albedo value.

Vertical mixing of atmospheric constituents occurs in the troposphere because of the turbulence that characterizes the region. Temperature inversions and mountains surrounding cities inhibit this mixing. However, in the upper atmosphere, this process is mostly controlled by molecular diffusion (that is, conduction of heat by collisions of atoms and molecules), which depends solely on molecular size, and by thermal diffusion, which depends on the temperature gradient between hot molecules and their surroundings.

Assuming steady incident radiation, the radiating power of a GHG molecule depends largely on the absorption coefficients for that GHG, which determine how much of the available radiation it absorbs in each of the wavelength ranges where it absorbs radiation. Other important factors are the concentration of the gas and its residence time, or decay time, in the atmosphere. The residence time of GHGs depends mostly on two factors, namely reactivity of GHGs and the GHG sinks in the biosphere. Plants and trees, for example, store carbon and thus serve as sinks for carbon dioxide.

The radiating power of a GHG is usually expressed as its global warming potential (GWP). The decay time or residence time for carbon dioxide ranges from around 150 to about 500 years [70] [71]. Without carbon dioxide absorbers (sinks), the carbon dioxide residence time would be only 3.9 years, which is precisely its exchange rate. The lifetime of the hydrological cycle is estimated to be approximately 2 to 4 weeks. The replacement time for deep ocean water is believed to be on the order of a thousand years [72], and the replacement time for deep ice in the Arctic may be on the order of tens of thousands of years. Most of the GWPs found in scientific literature are expressed in relation to the carbon dioxide GWP. The GWP of a GHG is expressed in the following relationship [73]:

where tau_i and tau_j are the residence times of the GHG of interest, i, and the reference GHG, j (usually carbon dioxide), respectively, in years; ai and aj are the instantaneous radiative forcings of GHGs per unit mass due to a unit increase in the concentration of GHG of interest i and the reference GHG j, respectively [74]; t is the integration time in years; and GWP(C_i) and GWP(C_j) are the GWPs of the GHG of interest i and the reference GHG j, respectively, at a given concentration C remaining at time t after their release.

This relation can be further simplified by defining the GWP for carbon dioxide as a reference GHG with a value of 1 (see (Table 5). This equation was derived by assuming that the concentration of a greenhouse gas is independent of altitude, and other factors. GWP calculations assume homogeneous mixing of GHGs in the troposphere. Homogeneity must be defined in terms of an appropriate scale, because given a sufficiently fine scale, all matter is heterogeneous in view of its atomic and molecular constitution [75]. Moreover, according to the United Nations' Intergovernmental Panel on Climate Change (IPCC), carbon dioxide equivalency (GWP) values are generally within the range of plus or minus 35 percent. GWPs obtained for GHGs, therefore, are very rough approximations and their reliability varies greatly.

Radiative forcing is defined as a change in average net radiation at the boundary between troposphere and stratosphere (known as the tropopause). A positive radiative forcing tends on average to warm the surface; there is a net heat flow from troposphere to stratosphere. A negative forcing on average tends to cool the surface; there is a net heat flow from stratosphere to troposphere. The global average radiative forcing is based on the assumption that the vertical irradiance gradient is significant at the tropopause and that the horizontal irradiance gradient along the tropopause and both the regional horizontal irradiance gradient and vertical irradiance gradient in the troposphere and stratosphere are not significant. Radiative forcing (also known as climate forcing), therefore, is an empirical tool designed for policy makers. Possibly policy makers would find the carbon dioxide equivalency or GWP values more useful when coupled with cost and other economic variables. Table A2 provides an explanation for some units for commonly used measures to describe energy.

Table A2. Radiometric Units
Radiometric Quantity	Concept	SI Unit
Radiant energy (Q)	Quantity of light	Joule (J)
Radiant flux (F)	Power	Watt (W)
Radiant energy density (W)	Energy content per unit volume	Joule per cubic meter
Radiant irradiance (E)	Flux per unit area incident on a small plane surface	Watt per square meter
Radiant intensity (I)	Flux emitted into a unit solid angle	Watt per steradiana
Radiant radiance (L)	Flux in a given direction per unit solid angle per unit area normal to the direction of propagation	Watt per square meter-steradian
Radiant exposure (Q)	Energy per unit area incident on one side of a small-plane area	Joule per square meter
a A steradian is a unit of measure equal to the solid angle subtended at the center of a sphere by an area equal to the radius squared on the surface of the sphere. Source: L.I. Grossweiner, Photophysics--The Science of Photobiology, 2nd ed., ed. K.C. Smith (New York: Plenum Press, 1989), pp. 1-77.

Another important piece in the global warming maze is the tropospheric lapse rate. The lapse rate is mathematically defined by

where Gamma = tropospheric lapse rate, the partial derivative of T = change in temperature (T), and partial derivative of z = change in altitude (z). This indicates the rate of cooling with height, and the decrease in temperature with increase in altitude in the troposphere. The global average tropospheric lapse rate is 6.5^oC per kilometer. The lapse rate varies with altitude, season, and latitude.

At present, the most accurate models for projecting the impact of the greenhouse effect are General Circulation Models (GCMs). GCMs attempt to take into account the entire climate system over an extended period of time, including the roles of the oceans, the atmosphere, the biosphere, the polar regions, and other important features. GCMs usually treat the atmosphere and the ocean as fluids, calculating how various factors such as the concentration of carbon dioxide interact with atmosphere and oceans to generate the entire climate system [76]. Both proponents and critics of global warming models agree that GCMs have well-documented inadequacies that significantly impair their capacity to project global warming. Most GCMs, for example, cannot predict cloud formation well.

Based on preliminary data from satellite measurements, Ramanathan and his colleagues concluded that clouds appear to cool Earth's climate, possibly offsetting the atmospheric greenhouse effect [77] [78]. This observation supports the theory that sulfur dioxide creates “cool clouds.” That is, sulfur dioxide emissions not only acidify rain, but also combine with water to form “aerosols” that brighten the clouds, increase their albedo, and thus enhance the reflection of radiation away from Earth. Some scientists advocate considering sulfur dioxide effects together with carbon dioxide effects on evaporation and hence on cloud cover and convection. As carbon dioxide speeds up the hydrological cycle, increased convection in turn increases clouds and cooling.

Recently, some models like the Community Climate Model (CCM) have incorporated clouds into climate calculations, including clouds' radiative properties and their effects on the global energy balance. Recent satellite observations indicate that clouds absorb four times more shortwave radiation (from 25 watts per square meter to 30 watts per square meter) than indicated by previous model simulations. This absorption of shortwave radiation occurs in addition to reflection of solar radiation and absorption of infrared radiation emitted by the Earth's surface and the atmosphere. The enhanced cloud absorption observed may lead to an important reinterpretation of the energetics of the models. Increased water vapor in the atmosphere increases the number of cirrus-anvil clouds, which effectively absorb shortwave radiation, thus reducing the emission of infrared radiation [79] [80] [81]. The observations may be due to aggregation phenomena of water molecules in the crystalline phase. As is very common for a large number of compounds, the spectra either broaden or shift to shorter wavelengths as aggregation increases. Most current infrared spectra of water available in the literature are for water in the vapor phase. Infrared spectral characteristics of ice crystals and liquid mist should be explored to understand the behavior of cirrus-anvil clouds fully.

Proceed to Appendix B