CHAPTER #2
Energy: Warming the Earth and the Atmosphere





Energy: a property of system that has an ability or capacity to do work on a matter. The total amount of energy stored in a system is called internal energy and determines how much work that the object is capable of doing.

Potential energy: the energy that an object possesses by virtue of its position with respect to the object in the field of gravity. The potential energy of an object

PE = m g h

where m is the mass and h is the height of the object above the ground and g is the acceleration of gravity. A volume of air aloft has more potential energy than the volume of air at the ground.

Kinetic energy:the energy within an object that is result of its motion. The kinteic energy of an object is the half of its mass multiplied velocity squared.

KE = 1/2 m v^2

A strong wind possesses more kinetic energy than the light breeze on the same object, while the volume of water has more kinetic energy than the same volume of air at the same speed.


Heat: the total kinetic energy of the molecules or atoms composing a substance. The atoms and molecules in a substance do not always move at the same velocity meaning that there is a range of kinetic energy among the atoms and molecules.

Temperature: the average kinetic energy of individual atoms and molecules. The distinction between heat and temperature may be made by the following example: A cup of water at 80C (176F) is much hotter than a bathtub of water at 30C (86F) meaning average kinetic energy of individual water molecules at 80C is greater than at 30C. The bathtub, on the other hand, has the greater volume of water, it contains more total kinetic molecular energy than does the cup of water. As a result, a cup of water will cool down the room temperature much more rapidly than the bathtub of water. Much more heat energy must be removed from the bathtub water than from the cup of water in order for both to cool to the same temperature.

As a sample of air gains or loses heat, the amount of gained or lost heat is used for changes in temperature, phase of water, or volume of air sample, or combinatin of these.


For scientific purposes, temperature is described in terms of the Celsius scale, which was first proposed by the Swedish astronomer Andres Celsius in 1736. It has 100 interval between melting point of ice and boiling point of pure water. An alternative scale, Fahrenheit scale, which was introduced by German physicist Gabriel Fahrenheit in 1714, reads the melting point of ice at 32 degree and boiling point of water at 212 degree. The conversion between Celsius and Fahrenheit scale is as follows

F = (9/5)C +32

C = 5/9(F-32)

Absolute zero: the theoretical temperature at which a body emits no electromagnetic radiation and all molecular action ceases. It is equivalent to -273.15 degree C, -459.67 degree F, and 0 degree K, Kelvin scale which was introduced by Scottish physicist Lord Kelvin in 1844. Kelvin scale has 100 degree interval between melting point of ice (273.15 K) and boiling point of water (373.15 K). The conversion between the Kelvin scale and Celsius and Fahrenheit scales is given as follows:

K = (5/9)(F+459.67)

K = C + 273.15

Figure 2.2, page #34 (Ahrens)




Calorie (cal): the amount of heat needed to raise the temperature of one gram of water one Celsius degree from 14.5 to 15.5C. 1 cal = 4.1868 Joule.

British thermal unit (Btu): the amount of heat required to raise the temperature of one pound of water one Fahrenheit degree from 62F to 63F. 1 Btu = 252 cal = 1055 Joule.

Temperature gradient: a change in temperature with distance. For example, the temperature change between hot equator and cold polar regions, meridional (north-south) temperature gradient, the temperature change between relatively cold eastern US and relatively warm Antarctic ocean, zonal (east-west) temperature gradient, the temperature change between relatively mild earth's surface and relatively cold tropopause, vertical temperature gradient.

In response to temperature gradients, heat is transported via conduction, convection, and radiation following second order of thermodynamics, which states that all systems tend toward disorder.




Conduction: the transfer of kinetic energy of atoms and molecules by collision between neighboring atoms and molecules. No mass is exchanged, but a medium is required. Some substances conduct heat much more readily than the others: Solids are better conductor than liquids and liquids are better conductor than gases. Metals are excellent conductors of heat, whereas air is very poor conductor of heat.

Figure 2.5, page #37 (Ahrens)

A fresh snow cover has extremely low heat conductivity because of the air trapped between individual snowflakes. Therefore, a thick snow cover can prevent freezing of the underlying soil even though the temperature of the overlying air may drop well below freezing.

Table 2.2, page #37 (Ahrens)




Convection: the transport of heat within a fluid via motions of the fluid itself. Mass is exchanged and a medium is required. Convection occurs as a result of air density difference within the atmosphere. A convective circulation of air transports heat vertically from the earth's surface into the troposphere. Convection is much more important than conduction in transporting heat within the troposphere.

Figure 2.6, page #37 (Ahrens)

Heat is also transported horizontally within the atmosphere and the process is called advection. The process of heat transport by both conduction and convection is known as sensible heating.

Figure 2.7, page#38 (Ahrens)




Radiation: a form of energy that travels as waves without exchanging mass in the presence or absence of a medium. It is the main tansport of energy between the sun and earth-atmosphere system. All objects absorb and emit radiation. At radiative equilibrium, absorption balances emission and the temperature of the object is constant. If absorption exceeds emission, the temperature rises, and if emission exceeds absorption, the temperature falls.

Electromagnetic radiation is the form of radiative energy that exhibits both electrical and magnetic properties. It travels through space as well as through gases, liquids, and solids. In a vacuum, electromagnetic radiation travel at its maximum speed, 300,000 km (186,000 mi.) per second. As electromagnetic radiation passes from one medium to another, it may be reflected or refracted at the interface. It can also be absorbed and converted to heat.

Electromagnetic radiation travels as waves, which is usually described in terms of wavelength and frequency. Wavelength is the distance between successive crests or successive troughs of a wave. Wave frequency is the number of crests or troughs that pass a given point in one second. Passage of one complete wave is called a cycle, and a frequency of one cycle per second equals one hertz (Hz). Frequency is inversely proportional to wavelength; that is, higher the frequency, the shorter the wavelength.




Electromagnetic spectrum: the range of different forms of electromagnetic radiation arranged by wavelength and frequency. It ranges from wavelengths of about 10-15 meter (or frequencies of 1024 Hz) to wavelengths of about 104 meter (or frequencies of 104 Hz) and includes gamma radiation, X-rays, ultraviolet radiation, visible light, infrared radiation, microwaves, and radio waves.

Gamma radiation ranges from about 10-11 meter to about 10-15 meter, while X-rays range from about 10-8 meter to about 10-13 meter, having a substantial overlap with the gamma radiation. Both are used to treat cancer patients.

Ultraviolet radiation (UV) ranges from 0.20 to 0.39 micrometer (µm); 0.20-0.29 µm (UVC), 0.29-0.32 µm (UVB), and 0.32-0.39 µm (UVA). The sun emits 7% of its radiation in this zone. UVC is absorbed by the ozone in the stratosphere, while UVB and UVA can be responsible for sunburn and skin redness, respectively.

Visible light ranges from 0.39 µm at the violet end to 0.76 µm at the red end. The colors within the visible light are violet, blue, green, yellow, orange, and red. Visible light stimulates the sensation of color, and regulates the timing of animal activities such as migration, and photosynthesis of plants. The sun emits nearly 44% of its radiation in this zone.




Infrared radiation (IR) ranges from 0.76 µm to about 1 mm. It is responsible for all the terrestrial radiation emitted by the Earth's surface and its atmosphere. The sun emits 49% of its radiation in this zone; nearly 37% is radiated between 0.76 and 1.5 µm (near IR), with only 12% radiated at wavelengths longer than 1.5 µm (far IR).

Microwave radiation ranges from about 1 mm to about 1 meter. It is used for the remote sensing of the atmosphere and also for microwave ovens. Radio waves range from a fraction of centimeter up to hundreds of kilometers, having a substantial overlap with the microwave radiation. It is used for radio communication including FM (frequency of modulation) waves which span from 88 to 108 million Hz.

Figure 2.8, page #39 (Ahrens)




Blackbody: a hypothetical object that absorbs all the incident radiation; that is, a perfect radiator neither reflects nor transmits any radiation. In reality, no perfect radiators exist, but the sun and the Earth are approximate blackbodies, therefore, blackbody radiation laws may apply to the solar and terrestrial radiation. There are four blackbody laws:

1) Planck's law states that the rate at which radiation is emitted by a blackbody depends on the absolute temperature of the blackbody and the specific wavelength (or frequency) of the radiation. It provides the amount of emitted radiation at some wavelength at a specific absolute temperature.

2) Stefan-Boltzmann law states that the total energy radiated by an object across all wavelength is proportional to the fourth power of its absolute temperature. Since the sun radiates at a much higher temperature than does the Earth-atmosphere system, the Stefan-Boltzmann law predicts that the sun's energy output per square meter is about 160,000 times that of the Earth-atmosphere system.

The total solar energy absorbed by planet Earth is equal to the total terrestrial energy emitted by the Earth-atmosphere system back to space. The balance between energy input and energy output is called global radiative equilibrium.




3) Kirchhoff's law holds that a perfect absorber of radiation of a given wavelength is also a perfect emitter of radiation at the same wavelength (or frequency). In general, the efficiency of absorption, absorptivity, equals the efficiency of emission, emissivity. The absorptivity and emissivity of a black body are both 100%. The sum of emissivity, transmissivity, and albedo is 100% following energy conservation law. For opaque substances, such as ground, transmissivity is zero and the sum of emissivity and albedo equals 100%.

4) Wien's displacement law holds that the wavelength at which a blackbody emits the maximum intensity of radiation, lambdamax, is inversely proportional to the absolute temperature, T, of the blackbody:

lambdamax = 2897 µm K / T

For the sun, with a surface temperature of 6000 K,

lambdamax = 2897 µm kK / 6000 kK = 0.5 µm

For the Earth, with a surface temperature of 288 K,

lambdamax = 2897 µm K / 288 kK = 10 µm

Figures 2.9 and 2.10, pages #40-41 (Ahrens)




Sun: a gaseous body composed of hydrogen (about 80% by mass) and helium. It is our closest star, about 150 million km (93 million mi) from the earth. Based on the temperature of the region, the sun is divided into four layers: core, photosphere, chromosphere, and the corona.

The core is extremely hot, with temperatures exceeding 20 million C. The hydrogen nuclei (protons) collide at very high speeds that they fuse together to form helium nucleus (alpha particle). In this reaction, four hydrogen nuclei produce one helium nucleus, however, the mass of four hydrogen nuclei is 0.7% greater than the mass of one helium nucleus. The excess mass is converted to energy following the energy conservation equation of E = mc2, where c is the speed of the light (300,000 km/second).

The photosphere is visible surface of the sun. It is much cooler than the sun's interior, generally near 6000 C. The photosphere has a honeycomb appearance that is due to a network of huge, irregularly shaped convective cells, called granules. They have relatively cold spots, sunspots, and relatively hot spots, faculae.




The chromosphere consists of ions of hydrogen and helium at temperatures between 4000 and 40,000 C. It acts as a boundary between the photosphere and the corona.

The corona is region of hot (1 to 4 million C) and highly rarefied ionized gases that extends millions of kilometers into the space, the outer limits of the solar system. It is visible during a solar eclipse. Because of its low density, the corona radiates less energy than the photosphere. The solar wind originates in the corona and the solar flares that erupt from the photosphere into the corona intensify the solar wind.

Figure 8, page #52 (Ahrens)




Solar altitude (a): the angle of the sun above the horizon. It varies with the time of the day and the latitude. When sun is directly overhead, the solar altitude is 90 degree. The intensity of solar radiation decreases with decreasing solar altitude since solar radiation becomes less intense, spreading over larger area at lower solar altitude. The path of solar radiation also increases with decreasing solar altitude.

a = sin-1 [cos (l) * cos (d) * cos (h) + sin (l) * sin (d) ]

where l is local latitude, d is the declination angle, and h is the hour angle.

Declination (d): the angular distance of the sun from north or south of equator.

d = 23.45 sin [360/365 * 284 + day of the year]

Hour angle (h): the measure of the sun from solar noon.

h = 15 degree (hours from solar noon)




Reflection: a process whereby light bounces of a surface at an angle equal to the angle at which it initially strikes the surface.

Scattering: a process whereby light is actually absorbed by a particle and then quickly emitted in another direction. It is responsible for the color of the daytime sky. Since air molecules are smaller than wavelengths of visible light, they are more effective at scattering shorter wavelengths (blue and violet) of visible light than the longer wavelengths (red light). This property of being more effective at scattering particular wavelengths of light is named as Rayleigh scattering, which is responsible for the blue appearance of sky.

Another form of scattering called Mie Scattering, is responsible for the white appearance of clouds. Mie scattering occurs when the wavelengths of visible light are approximately, equally scattered. Water droplets and ice crystals, in even small clouds, as well as dust and haze particles effectively scatter all wavelengths of visible light in all directions, thus making clouds appear white, and the sky is a hazy white in the presence of high concentrations of aerosols.




Albedo: the ratio of reflected radiation to the incident radiation. It is generally expressed as a percentage. The incident radiation is the sum of direct and diffuse insolation. The light-colored surfaces have higher albedo than the dark-colored surfaces. The albedo of fresh-falling snow varies between 75% and 95%, while the albedo of alsfalt or dense forest may be as low as 5%.

Cloud tops are the most important reflectors of insolation. The albedo of cloud tops ranges from under 40% for thin clouds (less than 50 meter thick) to 80% or more for thick clouds (more than 5000 meter thick). The average albedo for all cloud types and thickness is about 50%, and clouds cover about 60% of the planet at any given time.

The albedo of some but not all surfaces also varies with solar altitude. The variation of albedo with solar altitude is especially pronounced for ocean and lakes surfaces. The albedo of a water surface increases with decreasing solar altitude under clear skies. The increase in albedo is particularly sharp for solar altitudes less than 30, approaching 100% near sunrise and sunset.

On the other hand, when the sky is completely cloud covered, the variation of the albedo with solar altitude is uniformly very low (less than 10%). The average albedo of the ocean surface is only about 8% on a global basis; that is, the ocean is a strong absorber of solar radiation.




The surface albedo undergoes significant seasonal changes over land. It increases as a result of snow cover and the formation of sea ice over frozen lakes in winter and of loss of leaves in forested areas in autumn.

Planetary albedo: the fraction of solar radiation that is scattered and reflected back to space by the earth-atmosphere system. It is about 31% as indicated by satellite measurements, while the moon's albedo is only about 7% primarily because of the absence of clouds in the highly rarefied lunar atmosphere. The albedo of Venus is 78%, while the albedo of Mars is only 17%. Considering outer planets, Jupiter's and Saturn's albedos are 34%, while Uranus and Neptune have albdo of 30% and 29%, respectively.

Table 2.3, page #49 (Ahrens)

Absorption: the process whereby a portion of the radiation incident on an object is converted to heat. The amount of absorbed is generally expressed as a percentage (one minus albedo). The earth-atmosphere system absorbs 69% of solar radiation; 23% by the atmosphere and 46% by the earth' surface, mainly due to low average albedo of oceans, covering 71% of the globe.




Water vapor, oxygen, ozone, and various aerosols are the principal absorbers of the solar radiation. Absorption by an atmospheric gases is wavelength dependent, that is, these gases absorbs the solar radiation at particular wavelengths.

The clear sky is essentially transparent to solar radiation at the wavelengths of the visible light . Ozone and oxygen are the strong absorbers of solar ultraviolet radiation in the stratosphere. Oxygen absorbs very short UV (less than 0.2 µm), while ozone absorbs UVC radiation. As a result of this absorption, a significant reduction in UV radiation at the earth's surface and a warming of upper stratosphere are both observed.

Water vapor absorbs solar IR radiation at wavelengths greater than 0.8 mm. Clouds are poor absorbers of solar radiation. Typically, clouds absorb less than 10% of the radiation that strikes the cloud top.

Absorption of solar radiation by ocean and lakes is also wavelength dependent: red light is totally absorbed within about 15 m (49 ft) of the surface, while blue-violet light may penetrates to depths of 250 m (820 ft) within clear, clean water. However, suspended sediments significantly increase the rate of absorption, in fact, sunlight rarely reaches below 10 m (33 ft.).




Absorption of infrared radiation by the atmospheric gases is wavelength dependent as well. Absorptivity is very low or close to zero near 8 µm and 11 µm, called atmospheric window. The gases that absorb the IR radiaiton are water vapor (principical), carbon dioxide, ozone, methane, and nitrous oxide, called greenhouse gases. They are responsible for rising the average surface temperature of lower atmosphere by 33 C.

Figure 2.13, page #46(Ahrens)

A greenhouse effect also operates on Mars and Venus where the principal greenhouse gas is carbon dioxide. The Martian atmosphere is thinner than the Earth's atmosphere; the average surface temperature of Mars raises by about 10 ûC (18 ûF). Venusian atmosphere, on the other hand, is denser than the Earth's atmosphere; the average surface temperature raise is estimated at 523 C (941 F).




Clouds, which are composed of water droplets and/or ice crystals, also produce a greenhouse effect. They reflect the solar radiation as they cool the earth's surface; they absorb and re-radiate the IR radiation as they warm the earth's surface. However, on a global scale, a greater cloud cover would tend to cool the planet.

Carbon dioxide, on the other hand, could rise the average surface temperature between 1.5 to 4.5 C (2.7 to 8.1 F) if it doubles its present value. The numerical models based on the rise in carbon dioxide concentration observed in Mauna Loa Observatory, Hawaii predicts that CO2 will double by the middle of this century(2050). However, many uncertainties in numerical models particularly with regard to timing, magnitude, and regional patters of climate change exist.

Fossil fuel combustion accounts for 80% increase in CO2 concentration, while deforestation is likely responsible for the balance. The burning of coal, oil, and natural gas produces carbon dioxide as a byproduct.




The increase of the other greenhouse gases, methane, nitrous oxide, and CFCs, is also evident. Although their concentration is considerably less than the carbon dioxide, they are more efficient absorbers of IR radiation since they strongly absorb within the atmospheric window.

Ozone in the troposphere help to global warming, while the carbon dioxide in the stratosphere cools the atmosphere. The aerosols resulting from sulfur emissions may have offset a significant part of the greenhouse warming in the Northern Hemisphere during the past several decades.

Global mean surface temperature has increased by 0.3û to 0.6û over the last 100 years, is consistent with predictions of climate models, but it is also the same magnitude as natural climate variability. Natural climate variability and other human factors could have offset a still larger human-induced greenhouse warming.




Ozone, which is produced mainly by the subsequent combination of oxygen atoms and oxygen molecules at altitudes between 10 to 50 km in the atmosphere, absorbs the ultraviolet radiation at wavelengths less than 0.30 µm. It exists at peak concentrations of 10 ppm at altitudes of 20 to 25 km.

Ozone is destroyed by colliding with other molecules and atoms. Chlorofluorocarbons (CFCs), which is used as refrigerants, propellants in aerosol sprays, and blowing agents for foam insulation, is one of the major source for ozone destruction. CFCs in the stratosphere breaks down into chlorine (Cl) atoms by UV radiation. Chlorine which acts as a catalyst in chemical reactions, converts ozone to oxygen. A single chlorine atom destroys perhaps tens of thousands of ozone molecules before it undergoes chemical reaction with another substance.

Fortunately, Cl atoms do not exist in the stratosphere, forever. They are removed as chlorine monoxide (ClO) combines with nitrogen dioxide (NO2) to form chlorine nitrate (ClONO2). Free Cl atoms combine with methane (CH4) to form hydrogen chloride (HCl) and a new substance, CH3.




The depletion of ozone layer was first reported over Antarctica by British Antarctic Survey team in 1985. It is attributed to the exceptionally high concentrations of ClO. The Antarctic ozone hole exists during the Southern Hemisphere spring (mainly September and October) and disappears by November. It is about the size of the continental United States.

Satellite measurements show a negative trend in ozone concentration in both hemispheres except near the equator where no significant change was indicated. The ozone depletion in midlatitudes is observed in late winter and early spring.

The concentration of ozone is expressed in Dobson units. It is the depth of ozone produced if all the ozone in a column of the atmosphere is brought down to sea-level temperature and pressure. One Dobson unit is a hundredth of millimeter. A typical value of stratospheric ozone concentration measured by the total ozone mapping spectrometer (TOMS) or ozone monitoring instrument (OMI) abroad different satellite is about 200 to 400 Dobson units.

Figure 18.11, page #530 (Ahrens)

Figure 2, page #531 (Ahrens)


The reduction of ozone concentration in the stratosphere allows more UV radiation to reach to the earth's surface, following a greater risk of skin cancer, eye damage etc. In general, every 1% decline in stratospheric ozone translates into a 2% increase in UV radiation. At the same time, 2.5% decrease in ozone layer could increase the incidence of human skin cancer by 10%.

The most dangerous UV radiation for the human health is its UVB band. Sand reflects up to 50% of the incident UVB, therefore one would still expose to dangerous radiation even in the shade of beach umbrella. Water transmits UVB to a depth of a meter or so, and a wet T-shirt allow 20% to 30% of incident UVB to reach skin. One is also exposed to high levels of UVB radiation at high mountain elevations during skiing. Snow reflects UVB radiation more than the beach sand.

In general, if your shadow is shorter than your height, you should apply a sunscreen, otherwise it is not a problem. Sunscreens have ingredients that selectively block UV radiation. The sun protection factor (SPF) is a measure of the time that the skin can safely exposed to the sun. The higher the SPF value, the longer the protection lasts. It should be noted that suntan lotions help to keep the skin moist, but they do not provide any protection from UV radiation.

Figure 4, page #43 (Ahrens)




Energy