CHAPTER 2. Solar Radiation and the Seasons
Chapter Overview:
The chapter defines and examines types of radiant energy and the propagation of that energy as
electromagnetic waves. In addition, temperature wavelength associations are developed. Earth’s
fluctuating orbital distance and the relationship between each hemisphere’s axis of rotation and the
Sun is explored. Relationships between solar geometry and hemispheric differences in solar angle
and length of day are also explored. <ME2.1>
Chapter at a Glance:
• Energy - Solar radiation is transferred to the Earth’s surface where it is absorbed. This
radiation provides energy for atmospheric motion, weather processes, biologic activity,
conversions of state, and many other activities.
A. Kinds of Energy - Most forms of energy can be classified as either kinetic or
potential energy. Kinetic energy, the energy of motion, can occur from very large to
very small scales. At the molecular scale, this energy describes molecular vibration
and determines an objects temperature. Potential energy is energy in reserve.
B. Energy Transfer Mechanisms - Energy may be transformed through
conduction, convection, or radiation.
1. Conduction - Conduction is essentially energy transfer through objects
without molecular displacement. This occurs mainly in solids whereby
energy passes through an object without the object being molecularly
altered. <Web>
2. Convection - Convection is energy transfer through fluids. Molecular
alteration takes place as density decreases in heated fluids leading to greater
buoyancy. The process regularly takes place in the atmosphere as solar
radiation heats the surface and the thin adjacent laminar layer. This heated
air then rises. <CD2.3> <Web>
3. Radiation - Radiation is an energy transfer mechanism, which requires
no physical medium. Radiation propagates energy transfer through the
vacuum of space.
• Radiation - Electromagnetic radiation is continually emitted by all substances.
Radiation types differ by their electrical and magnetic wave properties. In any type of
radiation, electrical and magnetic waves, although closely coupled, are perpendicular to
each other.
A. Radiation Quantity and Quality - Radiation quantity refers to the amount of
energy transferred and is expressed through wave amplitude. Wave quality relates
to radiation wavelength and identifies the type of radiant energy. <CD2.2>
Wavelength is expressed in µm, or micrometers. All electromagnetic energy travels
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at a constant, 300,000km/sec (186,000 mi/sec), the speed of light.
B. Intensity and Wavelengths of Emitted Radiation - All matter not only
radiates energy, but energy is emitted over a wide range of electromagnetic
wavelengths. Physical laws, which define the amount and the wavelength of
emitted energy, apply only to hypothetical perfect emitters of radiation known as
blackbodies. The Earth and Sun are similar to blackbodies. <CD2.2>
1. Stefan-Boltzmann Law - The amount of energy emitted by an object is
proportional to the object’s temperature. Hotter objects emit more energy
than cooler ones with energy emitted proportional to the fourth power of the
emitter’s absolute temperature. Stefan-Boltzmann Law describes this
mathematically as I=T4, where I is the intensity of the radiation in
watts/m2,  is the Stefan-Boltzmann constant (5.67x10-8 watts/m2/K4) and
T is the temperature of the body in K.
Graybodies denote objects that emit some percentage of the maximum
amount of radiation possible at a given temperature and therefore relate to
most liquids and solids. True radiation emitted by an object is a percentage
relative to a blackbody and reflects the emissivity of the object. Including
emissivity () into Stefan-Boltzmann yields I= T4.
2. Wein’s Law - Radiation emission is across a wide array of
electromagnetic wavelengths so it is useful to determine the wavelength of
peak emission. This is found through Wein’s Law which is max=2900/T,
where max refers to the wavelength of energy (in µm) radiated with greatest
intensity, 2900 equals a constant, and T is in K. Through Wein’s Law its
evident that hotter objects radiate at shorter wavelengths than cooler bodies.
Solar radiation peaks at 0.5 µm while terrestrial radiation peaks at 10 µm.
Further, most solar radiation is emitted as shortwave radiation with the
largest percentage in the visible portion of the spectrum. Conversely, the
majority of terrestrial radiation is emitted as longwave radiation. <Web>
Because hotter bodies radiate more at all wavelengths than do cooler ones,
the Sun emits not only more shortwave radiation than the Earth, but also
more longwave radiation.
• Solar Constant - The intensity of electromagnetic radiation is not reduced with distance
through the vacuum of space. A reduction of intensity is proportional to increasing
distance only as energy is disbursed over a larger area. Due to this, radiation intensity
decreases in proportion to the distance squared. Calculating this inverse square law for
Earth’s average distance from the Sun yields a solar constant of 1367 W/m2. Slight
alterations may occur in reference to the solar constant. <Web>
• Causes of Earth’s Seasons - Variations in the relationship between the orbital alignment
of Earth and the Sun are responsible for variations of incoming solar radiation (insolation)
at the Earth’s surface.
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A. Earth’s Revolution and Rotation - Through the year Earth revolves about the
Sun along an ecliptic plane. Distance along this plane varies between the
perihelion, (Jan 3; 147 mil km, 91 mil mi), and the aphelion (July 3; 152 mil km, 94
mil mi). Earth’s orbital distance, therefore, varies by about 3%. Using the inverse
square law, radiation intensity varies by approximately 7% between perihelion and
aphelion. <ME2.2>
Earth rotation about its axis occurs once every 24 hours. The axis of rotation is
offset 23.5o from a perpendicular plane through the ecliptic plane. Because the axis
of rotation is never changing, the northern axis aligns with the star Polaris.
Hemispheric orientation, therefore, changes as the Earth orbits the Sun. A
particular hemisphere will either align toward or away from the Sun, or occupy a
position between the extremes. <CD1.3> Examining Earth’s axis with a full 90o
tilt may help in the visualization of the changing circle of illumination relative to
hemispheric lines of latitude through revolution.
1. Solstices and Equinoxes - Maximum axial tilt in relation to the Sun
occurs on only two dates for each hemisphere, however, the hemispheres
are in opposition relative to the Sun. <CD1.3> On approximately June 21,
the June solstice, the Northern (Southern) Hemisphere (N.H.) axis of
rotation is fully inclined toward (away from) the Sun, ensuring maximum
(minimum) insolation absorption throughout the hemisphere. Exactly
opposite conditions occur on the December solstice, on or around
December 21. Astronomically, these two dates designate the first days of
winter or summer where appropriate. During the N.H. summer solstice, the
subsolar point (solar rays at a right angle to the surface, the latitudinal
position of which equals solar declination) is at 23.5oN, the Tropic of
Cancer. For the N.H. winter solstice, the subsolar point is located at the
Tropic of Capricorn (23.5oS). Exactly opposite conditions occur relative to
these dates for the S.H. Thus the subsolar point fluctuates 47o between the
Tropics.
Temporally centered between the solstices are the equinoxes. <Web> The
March equinox occurs on or about March 21 while the September equinox
occurs on approximately September 21. During the equinoxes, the subsolar
point (solar declination) lies at the equator.
2. Solar Angle - Incident radiation is directly proportional to solar angle.
Higher solar angles incorporate reduced radiational beam spreading which
leads to greater heating through energy concentration. <CD1.4> Lower
angles induce less intense illumination through greater beam spreading.
Less (more) energy per unit area leads to less (more) warming.
3. Period of Daylight - Axial tilt influences day length. During
hemispheric alignment either toward or away from the Sun, lines of latitude
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are bisected unequally by the circle of illumination. A hemisphere
maximally aligned toward (away from) the sun will have constant daylight
(night) poleward of 66.5o. This line of latitude is designated the Arctic
Circle in the N.H. and the Antarctic Circle in the S.H. Due to this geometry,
day length increases (decreases) from the equator to the pole of the summer
(winter) hemisphere. Lines of latitude are equally split for both
hemispheres on the equinoxes ensuring equal day/night conditions
everywhere.
4. Atmospheric Beam Depletion - Solar radiation is diminished relative to
the amount of atmosphere the radiation passes through. <CD1.5> High
solar angles see little reduction in intensity as the path from the top of the
atmosphere to the surface is short. Significant beam reduction occurs
where energy is diffused through larger amounts of atmosphere. Such a
situation occurs at high latitudes and is magnified during the winter season.
5. Overall Effects of Period of Daylight, Solar Angle, and Beam
Depletion - Combined effects of the aforementioned caused hemispheric
extremes on the solstices and “between” conditions on the equinoxes.
Further, higher latitudinal locations will experience reduced energy yields
due to low solar angle and increased beam depletion which offsets
increased period of daylight during the warm season.
6. Changes in Energy Receipt with Latitude - The combined effects of
solar angle, day length, and beam depletion, cause winter hemispheres to
run a deficit of energy, leading to cooler temperatures. Summer
hemispheres have a mean surplus of energy resulting in warmer
temperatures. <M2.3>
Chapter Boxes:
2-1 Physical Principles: The Three Temperature Scales - Because both the Celsius and
Fahrenheit scales permit negative values, implying an impossible negative heat, scientists
use the Kelvin scale for temperature measurements. Zero K refers to a temperature in
which no molecular vibrations take place. In the US, the most common temperature scale
is Fahrenheit. Celsius is used virtually everywhere else worldwide. Conversion formulas
between the scales are given.
2-2 Physical Principles: The Nature of Radiation, Absorption, and Emission Electromagnetic radiation behaves as a particle at elementary levels. Photos are released
from hydrogen molecules when orbital changes in electrons occur. The photons are bound
to shells, or limited orbits about the nucleus, with each shell representative of a given
energy level. Excited atoms may have electrons hopping to higher shells but if the
electrons jump back, energy is released in the form of the photon. Photon energy is fixed
and relative to a given shell and is dependent upon wavelength. In the atmosphere,
emission and absorption involve decreases or increases in energy as photons are released or
absorbed. Unlike solids and liquids that emit and absorb wide arrays of electromagnetic
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energy, atmospheric gases are very selective absorbers and emitters of energy.
2-3 Physical Principles: The Sun - Our Sun, a rather average star, has a high temperature,
high density core which generates energy through nuclear fusion. Hydrogen is combined
to form helium, and in the process radiant energy is released. Core energy, slowly migrates
to the convection zone where upwelling transfers the energy to the outer photosphere. The
photosphere is heavily imprinted by granules, the top of individual convection cells.
Sunspots, large cool areas formed through strong localized magnetic fields which blocks
upwelling, also dot the surface. There exists a pronounced 11 year sunspot cycle, with
notable periods of high and low activity superimposed upon this. Attempts to link climatic
variables to this phenomena have been inconclusive.
CD Rom Unit 1 - Solar Geometry:
1. Introduction - Unit 1 of the CD Tutorial begins with an explanation of the unit topics.
Quizzes separate each topical section.
2. Simplifying Assumptions - The basis of scientific assumptions is described and
may be used as a foundation for this topic. Three underlying assumptions are given
in the CD and are explained graphically through animations and quantitatively
using mathematics. The assumptions are:
A. Solar radiation arrives in parallel beams. The assumption is justified
due to the great distance between Earth and the Sun. Beams arriving
at latitudes 0o and 90o are nearly identical with regard to angle.
Animations of Solar radiation traveling through space to Earth and
graphics quantitatively detailing beam alignment highlight the
section.
B. Light reaching Earth is emitted from the center of the solar disk. Again,
due to the vast distances involved, angles of radiation emitted from
the Sun’s poles are virtually identical. This is reiterated through
graphics that mathematically prove a maximum margin of error of
only 0.5o.
C. Earth orbits the Sun in a perfect circle. The true orbit is slightly elliptical
but the effect negligible.
3. Daylength Variations - Parallelism of axis is described through an animation
detailing the constant angle and direction of Earth’s axis through orbit. The
equinoxes and solstices are labeled in an animation describing relationships
between axial tilt and the Sun. The circle of illumination is illustrated with an
animation showing solar rays and latitude lines unequally bisected at the June
solstice. Animations allow changing views of Earth’s latitudinal daylength
variations. Animations are repeated for the December solstice and the equinoxes.
This CD section should be used in association with the sections on Earth’s
revolution and rotation and the equinox, solstice section.
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4. Solar Position Variations - The nature of changes between Earth tilt and
seasonal and latitudinal changes in solar position are detailed. A graphic illustrates
this through an examination of three parallel solar beams at different latitudes
during N.H. summer. Different angles of incidence are shown and related to Earth
curvature. With increasing latitude (either direction) comes a lower sun angle.
This section augments topics presented in the solar angle division of the textbook.
5. Effects of Solar Position - The effect of solar altitude on radiation intensity at
the surface is demonstrated through animations of beam spreading over various
solar angles. The graphics highlight the fact that with high (low) solar altitudes,
little (great) changes in intensity occur with small variations in solar altitude. A
second animation details beam attenuation with increasing travel lengths through
the atmosphere. This area of the CD highlights topics discussed in the beam
depletion area of the text.
Related Web Sites:
Solar Constant: www.ucar.edu/publications/lasers/sun
Equinox: www.stcloud.msus.edu/~physcrse/astr106/emapautumn.html
Seasons: http://aa.usno.navy.mil/data/docs/EarthSeasons.html
Convection: http://ghrc.msfc.nasa.gov/camex3
Sunspots: http://spencer.thmech.nottingham.ac.uk/~etzjgw/sun.html
Longwave Radiation; Conduction: www.arts.ouc.bc.cal/geog/G111/6ilong.html
Astronomical data: http://aa.usno.navy.mil/data/docs/AltAz.html
Sunrise: http://www.srrb.noaa.gov/highlights/sunrise/sunrise.html
Media Enrichment:
M2.1 - A January 1998 ice storm movie from visible satellite imagery.
M2.2 - Movie of a solar eclipse.
M2.3 - January and July global cloud cover and SST movie.
Key Terms:
energy
wavelength
joule
micrometers/microns
power
blackbody
watt
Stefan-Boltzmann law
electromagnetic
radiation
Polaris
kinetic energy
equinox
potential energy
Tropics of Cancer and Capricorn
solar declination
convection
buoyancy
inverse square law
radiation
solar constant solar wind
insolation
ecliptic plane
Review Questions:
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core
nuclear fusion
convection zone
photosphere
graybody
Kelvin scale
photon
conduction
longwave radiation
corona
amplitude
beam spreading
revolution
perihelion
aphelion
rotation
solar disk
granules
sunspots
shortwave radiation
chromosphere
Arctic and Antarctic
Circles
flares
1. Describe the different ways kinetic and potential energy may exist on Earth.
Kinetic energy: light and other forms of radiation, heat, motion, and electrical power.
Potential energy: reservoir behind hydroelectric dam, high pressure, five types of chemical
potential energy (battery, gasoline, explosives, firewood, food).
2. Conduction and convection are alike in that both transfer heat within a substance. What is the
critical difference between them?
In conduction, heat transfers without molecular motion taking place. It is, therefore,
restricted to solids. In fluids, heat energy transfers through molecular displacement, which
is known as convection.
3. We have discussed sunlight, X-rays, etc., as electromagnetic radiation. Describe radiation as a
wave phenomenon, and explain what is meant by “electromagnetic”.
Energy propagates from an emitter in a pulsating wave form. These waves have both an
electrical and a magnetic component.
4. Why is wavelength important in radiation transfer? That is, when discussing radiation, why
isn’t it enough to specify the amount or rate of energy transfer?
Wavelength differentiates the type of radiation emitted. Shorter wavelengths may
penetrate objects (as the waves are smaller than the object’s molecules) whereas longer
wavelengths may be absorbed into, or reflected from, objects.
5. Place the following wavelength bands in correct order of wavelength: visible, X-rays,
ultraviolet, microwave, infrared.
X-rays, ultraviolet, visible, infrared, microwave
6. Is there a temperature that has the same value on both the Fahrenheit and Celsius scales? If so,
find that temperature. (Hint: Draw a graph of oC and oF.)
- 40 o F and -40 o C are the same temperature.
7. Convert the following Fahrenheit temperatures to Celsius: -22 oF, 50 oF, 113 oF.
-53 oC, 10 oC, 45 oC
8. Convert the following Celsius temperatures to Fahrenheit: -20 oC, 10 oC, 40 oC.
13 oF, 38 oF, 54 oF
9. Why is the Kelvin scale superior to the Fahrenheit and Celsius scales in many scientific
applications?
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Because there are no negative values.
10. Describe how the wavelengths and total energy emitted change as the temperature of an object
increases.
Emitted energy increases to the 4th power of an object’s absolute temperature.
11. The solar constant is about 1367W/m2. If the distance between Earth and Sun were to double,
what would be the new value?
3.865 x 1026W / 4 (3.14) (3 x 1011)2 = 3.86527/1.1309429 = 0.0342W/m2
12. What is the most important factor responsible for seasons on Earth?
Earth’s axial tilt and its subsequent relationship (orientation) to the Sun through Earth
orbit.
13. Describe the annual march of solar declination.
The solar declination migrates between the Tropic of Cancer (23.5o N) and the Tropic of
Capricorn (23.5o S) through the year. On the summer solstice, the solar declination reaches
its farthest poleward migration for that hemisphere. In the opposite hemisphere, that day
marks the winter solstice.
14. What is the significance of the Arctic and Antarctic Circles?
The Arctic and Antarctic Circles denote the farthest latitudinal migrations of the circle of
illumination (the boundary between the lighted and darkened halves of the Earth).
15. If the solar declination were 10o, where would the Arctic and Antarctic Circles be found?
Would this cause a change in the dates of the solstices, equinoxes, and perihelion and
aphelion?
The solar declination is simply the latitudinal position of the subsolar point. As such, the
Arctic and Antarctic Circles, the solstices, equinoxes, and perihelion and aphelion would
remain exactly as they are. In fact, the solar declination is at 10o both north and south
latitude, four times per year.
16. Pick a day in the Northern Hemisphere winter. Describe the changes in daylength and solar
position you would encounter if you were to travel from the North Pole to South Pole. Do
the same for a day in the Northern Hemisphere summer.
Daylength and solar position will decrease with increasing latitude in Northern
Hemisphere winter and increase with latitude in the Southern Hemisphere summer.
Therefore, a trip from the North Pole to the South Pole will begin in the darkness of the
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central Arctic and end in the perpetual light of the South Pole. As one travels south from
the North Pole, daylength and solar position will increase. Maximum solar position will be
along a line of latitude in the tropics which receives the vertical solar ray. Maximum
daylength will occur within the Antarctic Circle where the day is 24 hours long.
Exactly opposite conditions will occur during Northern Hemisphere summer (Southern
Hemisphere winter).
17. Explain why the equator always has 12 hours of sunlight.
It is always equally divided between the lighted and darkened halves of the Earth.
18. Explain how changes in solar position influence the intensity of radiation on a horizontal
surface.
Energy concentration is greatly affected by changes in solar position. Energy intensity is
greater when solar position in high. This concentrates more energy per unit area. Lower
solar angles decreases the intensity of energy per unit area as a greater surface area is
illuminated.
19. If you were to travel from the equator to the North Pole, on what day would variations in solar
radiation be smallest? Why? Explain how day length and solar angle change as you move
poleward.
Actually, this question could be answered in two ways depending on the viewpoint:
1. The latitudinal radiation gradient would be least for a hemisphere on the summer
solstice. This is due to the fact that the subsolar point is at its greatest poleward
latitude. Therefore, day length increases poleward with latitude. Thus, the entire
high latitude “circle” region receives 24 hours of light which partially offsets
radiation attenuation factors such as beam spreading, low solar declinations, and
atmospheric attenuation (beam depletion). These factors are reflected in the small
latitudinal thermal gradients characteristic of summer.
So, on June 21, the summer solstice, the solar declination is at 23.5o N, the Tropic
of Cancer. At the pole, the sun would be at its highest point in the sky, 23.5o above
the horizon. Thus the difference in energy receipt would be minimized on this day.
Traveling from the equator to the North Pole one would see increasing solar angles
at noon from the equator to the Tropic of Cancer. At the equator one would
experience a non solar angle of 66.5o while at the Tropic of Cancer the noon solar
angle would be 90o. After this point, the noon solar angle would decrease to a
minimum of 23.5o above the horizon at the North Pole. Moving from the equator to
pole would also bring about a change in day length. At the equator, one would
experience a day length of 12 hrs. This will increase to a maximum of 24 hrs at the
Arctic Circle, 66.5o.
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2. The difference in radiation received across the latitudes would be least on either the
equinox. This is due to the fact that all latitudes receive exactly the same amount of
radiation at the top of the atmosphere as every line of latitude is equally bisected by
the circle of illumination. Because every line of latitude is equally bisected, every
location on Earth experiences a 12 hour day and a 12 hour night. However, due to
beam spreading, beam depletion, and low solar angles, polar regions will receive
less radiation than low latitude locations.
20. Burlington, Vermont, is located at 44.5o N. What is the angle of the noontime Sun on either of
the equinoxes and on the solstices?
Equinoxes = 45o; summer solstice =68.5o; winter solstice = 21.5o.
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