CHAPTER 2. Solar Radiation and the Seasons Chapter Overview ...

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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 h
emisphere’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.

Chapter at a Glance:

• Energy


Solar radiation is transferred to t
he 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 e
ither 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


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 sol
ids whereby
energy passes through an object without the object being molecularly

2. Convection

Convection is energy transfer through fluids. Molecular
alteration takes place as density decreases in heated fluids leading to greater
uoyancy. 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.
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3. Radiation


Radiation is an energy transfer mechanism, which requi
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.

Wavelength is expressed in
, or micrometers. All electromagnetic energy travels


at a constant, 300,000km/sec (186,000 mi/sec), the speed of light.

B. I
ntensity 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 hypothe
tical perfect emitters of radiation known as
blackbodies. The Earth and Sun are similar to blackbodies.

1. Stefan
Boltzmann Law

The amount of energy emitted by an object is
proportional to the object’s temperature. Hotter objects emit more

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=

, where I is the intensity of the radiation in

is the Stefan
ann constant (5.67x10

) 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 r
adiation 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=


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



refers to the wavelength of energy (in
) radiated w
ith 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

while terrestrial radiation peaks at 10
Further, mos
t 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.

Because hotter bodies radiate more at all wav
elengths 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 red
uction 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 f
rom the Sun yields a solar constant of 1367 W/m
. Slight
alterations may occur in reference to the solar constant.

• Causes of Earth’s Seasons

Variations in the relationship between the orbital alignment
of Earth and the Sun are responsible fo
r variations of incoming solar radiation (insolation)
at the Earth’s surface.


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

Earth rotation about its axis occurs once every 24 hours. The axis of rotation is
offset 23.5

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.

Examining Earth’s axis with a full 90

tilt may help in th
e 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 Su
occurs on only two dates for each hemisphere, however, the hemispheres
are in opposition relative to the Sun.

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 w
here 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 23.5
N, the Tropic of
Cancer. For the N.H. winter solstice, the subsolar po
int is located at the
Tropic of Capricorn (23.5
S). Exactly opposite conditions occur relative to
these dates for the S.H. Thus the subsolar point fluctuates 47

between the

Temporally centered between the solstices are the equinoxes.

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 dire
ctly proportional to solar angle.
Higher solar angles incorporate reduced radiational beam spreading which
leads to greater heating through energy concentration.

angles induce less intense illumination through greater beam spreading.
(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


are bisected unequally by the circle of illuminati
on. A hemisphere
maximally aligned toward (away from) the sun will have constant daylight
(night) poleward of 66.5
. 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 i
ncreases (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

4. Atmospheric Beam Depletion


olar radiation is diminished relative to
the amount of atmosphere the radiation passes through.

solar angles see little reduction in intensity as the path from the top of the
atmosphere to the surface is short. Significant beam reduction occ
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


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
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
mispheres have a mean surplus of energy resulting in warmer

Chapter Boxes:

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 worldw
ide. Conversion formulas
between the scales are given.

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 wh
en 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

Unlike solids and liquids that emit and absorb wide arrays of electromagnetic


energy, atmospheric gases are very selective absorbers and emitters of energy.

3 Physical Principles: The Sun

Our Sun, a rather average star, has a high temp
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 pronounce
d 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. Thr
ee 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 distanc
e between Earth and the Sun. Beams arriving
at latitudes 0

and 90

are nearly identical with regard to angle.
Animations of Solar radiation traveling through space to Earth and
graphics quantitatively detailing beam alignment highlight the

. 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 max
imum margin of error of
only 0.5

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 consta
nt 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 lati
tude 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.


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 thr
ough 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 augmen
ts 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 gr
aphics 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 are
a of the CD highlights topics discussed in the beam
depletion area of the text.

Related Web Sites:

Solar Constant:





Longwave Radiation; Conduction:

Astronomical data


Media Enrichment:



A January 1998 ice storm movie from visible satellite imagery.



Movie of a solar eclipse.


January and July global cloud cover and SST movie.

Key Terms:







nuclear fusion




convection zone



Boltzmann law






solar disk


kinetic energy

Kelvin scale



potential energy



Tropics of Cancer and Capricorn


shortwave radiation




longwave radiation



inverse square law


Arctic and Antarctic


solar constant solar wind




ecliptic plane

beam spreading


Review Questions:


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 ch
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 molecu
lar 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 radiati
on 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? T
hat 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 molecu
les) whereas longer
wavelengths may be absorbed into, or reflected from, objects.

5. Place the following wavelength bands in correct order of wavelength: visible, X
ultraviolet, microwave, infrared.

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
C and



F and

C are the same temperat

7. Convert the following Fahrenheit temperatures to Celsius:
F, 50
F, 113

C, 10
C, 45

8. Convert the following Celsius temperatures to Fahrenheit:
C, 10
C, 40

F, 38
F, 54

9. Why is the Kelvin scale superior to the Fahrenheit and Celsius scales in many scientific


Because there are no negative values.

10. Describe how the wavelengths and total energy emitted change as the temperature of an object

Emitted energy increases to the 4

power of an object’s absolute temperature.

11. The solar constant is about 1367W/m
. If the distance between Earth and Sun were to double,
what would be the new value?

3.865 x 10
W / 4 (3.14) (3 x 10
2 =


= 0.0342W/m

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

13. Describe the annual march of solar declination.

The solar declination migrates between the Tropic of Cancer (23.5
N) and the Tropic of
Capricorn (23.5
S) through the year. On the summer solstice, the solar declination reaches
its farthest poleward migration for that hemisphere. In the opposite hemis
phere, 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 10
, where would the Arctic and Antarctic Circles be found?
Would this cause a change in the dates of the solstices, equinoxes, and perihelion and

The solar declination is sim
ply 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 10

both north and south

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

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 t


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 s
olar 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

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

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

Actually, this questio
n 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, da
y 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 d
epletion). 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 23.5

N, the Tropic
of Cancer. At the pole, the sun would be at its highest po
int in the sky, 23.5

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 eq
uator one would
experience a non solar angle of 66.5

while at the Tropic of Cancer the noon solar
angle would be 90
. After this point, the noon solar angle would decrease to a
minimum of 23.5

above the horizon at the North Pole. Moving from the equator

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, 66.5


2. The difference in radiation received across the latitudes wo
uld 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 la
titude 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. Burling
ton, Vermont, is located at 44.5

N. What is the angle of the noontime Sun on either of
the equinoxes and on the solstices?

Equinoxes = 45
; summer solstice =68.5
; winter solstice = 21.5