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Calculating Relative Air Mass GLOBE
®
2002
Relative Air Mass Learning Activity - 1
Atmosphere
A
ppendix
W
elcome
Intr
oduction
P
r
otocols
L
earning A
ctivities
!
?
Calculating Relative Air Mass
Purpose
To introduce students to the concept of relative
air mass and demonstrate how solar elevation
angle affects the intensity of sunlight that
reaches an observer on the ground.
Overview
Students work in teams to calculate relative
air mass using simple geometry.
Student Outcomes
Students understand the relationship of solar
elevation angle to relative air mass.
Science Concepts
Earth and Space Science
Dynamic processes such as Earths
rotation influence energy transfer from
the sun to Earth.
Atmosphere Enrichment
The path length of incident sunlight
through the atmosphere (relative air
mass) varies as a function of the solar
elevation angle.
Scientific Inquiry Abilities
Identify answerable questions.
Use appropriate tools and techniques.
Use appropriate mathematics to analyze
data.
Develop and construct models using
evidence.
Communicate procedures and
explanations.
Time
Morning elevation readings: 5 minutes each;
sunny day is necessary
Calculating air mass: 20 minutes
Level
Middle and Secondary
Materials and Tools
Meter stick and/or tape measure marked
in centimeters
Pole, at least 50 cm high, to be used as a
solar gnomon (e.g. wooden dowel)
Calculating Relative Air Mass Data Sheet
Preparation
None
Prerequisites
Making a Sundial (suggested for younger
students) GLOBE
®
2002
Relative Air Mass Learning Activity - 2
Atmosphere
Teacher Support
Background
Relative air mass is a ratio indicating the amount
of atmosphere that light must pass through before
reaching an observer on the ground. When the
sun is directly overhead, sunlight passes through
the least amount of atmosphere to reach the
ground. This is defined as a relative air mass of
1.0. In this case, the sun is 90 above the horizon.
When the Sun is 30 above the horizon, sunlight
passes through twice as much atmosphere to reach
an observer on the ground, and the relative air
mass is 2.0. Thus, the relative air mass is a function
of the solar elevation angle.
In the Aerosol Protocol, the amount (the intensity)
of sunlight reaching the instrument depends on
the amount of atmosphere between the instrument
and the sun as well as the amount of aerosol in
the atmosphere. So, the relative air mass you
calculate in this activity is important for
interpreting data obtained using the GLOBE sun
photometer. In Looking At the Data for the Aerosol
Protocol, the technique is given for calculating
Observer on the Ground
The Earths Surface
Figure AT-AM-1
90
45
30
Sun
Sun
Sun
Atmosphere
aerosol optical thickness from the voltage readings
of the photometer. This calculation requires
knowing the relative air mass at the time of
observation.
In order to help students understand how the solar
elevation angle affects relative air mass, make some
sketches on the board like those shown above or
use an overhead projector to project the figure onto
a board or wall. Invite students to use a meter
stick to measure the distance from the top of the
atmosphere to the observer for solar elevation
angles of 90, 45, and 30 degrees. The students
should see that as the elevation angle of the sun
decreases, the pathlength of sunlight through the
atmosphere increases. Have the students find the
ratio of each pathlength to the 90 degree
pathlength. These ratios are the relative
pathlengths through the atmosphere and are the
same as the relative air masses.
Relative air mass can be calculated in the field
using the length of the shadow cast by a vertical
pole. A pole used for this purpose is called a solar
gnomon. In Figure AT-AM-2A, the pathlength GLOBE
®
2002
Relative Air Mass Learning Activity - 3
Atmosphere
A
ppendix
W
elcome
Intr
oduction
P
r
otocols
L
earning A
ctivities
through the atmosphere (p) is a function of the
elevation angle (e). The distance from the ground
to the top of the atmosphere (d) may be assumed
to be constant.
As shown in Figure AT-AM-2B , sunlight shining
on the solar gnomon casts a shadow creating a
right triangle. The three sides of this triangle are:
the height of the gnomon (h), the length of the
poles shadow on the ground (r), and the
hypotenuse (c).
The solar elevation angle ( e) is the same in the
right triangles in both figures, making them similar
triangles where the ratio of the hypotenuse to the
side opposite e is the same in both cases.
Therefore you can determine relative air mass (p/
d) by measuring the triangle formed by the solar
gnomom and its shadow.
There are several ways to find relative air mass
depending on the mathematical sophistication of
your students. If your students only know
arithmetic, have them measure c directly as
suggested in the steps below.
Equation 1 Relative Air Mass =
If your students know a bit of geometry and
understand square roots, then you can measure
the length of the shadow (r) and the height of the
gnomon (h), and:
Equation 2 Relative Air Mass =
If your students understand trigonometric
functions, you can measure e, and:
Equation 3 sin(e)=h/c
Equation 4 Relative Air Mass = c/h = 1/sin(e)
Ask the students to speculate about how the
relative air mass will affect the intensity of the
sunlight that an observer on the ground would
see. The important concept for the students to
understand is that the longer the pathlength, the
less sunlight shines through. This happens even
in a clear atmosphere, as students can see by
observing that sunlight is not as strong near
sunrise and sunset as it is at noontime.
Also note that outside the tropics, the sun is never
directly overhead and the relative air mass is
always greater than one.
Students may ask why the sun looks redder at
sunrise and sunset than at noontime. Sunlights
path through the atmosphere is longest at sunrise
and sunset, so the number of gas molecules and
particles that can scatter the sunlight is greatest
at these times. The gases in the atmosphere scatter
blue light more strongly than red light. At sunset,
when the relative air mass is high, the orange and
red color dominates because almost all the violet,
blue, green, and yellow light has been scattered
leaving only the red and orange hues
(wavelengths). The relative amounts of different
wavelengths in sunlight combined with the
relative amount of scattering by gases in the
atmosphere gives us our blue sky. During most of
the day when we look at the sky and not at the
sun, the light reaching our eyes is scattered
sunlight, and blue is the predominant color.
Aerosols in the sky tend to make the sky look
less blue and more milky.
What To Do and How To Do It
1. Organize the class into working groups of
three students per group.
2. Select a day that is sunny. Unless your
school is at relatively high latitude (higher
than ~ 50 N or S), this activity is best
done before mid morning or after mid
afternoon.
3. Find a flat site outside that will not be
shaded during the activity. Place a solar
gnomon (wooden dowel or other straight
object) at least 50 cm in height in the
ground. Use a string with a weight on the
end or a level to make sure that the pole is
perpendicular to the ground. Measure the
length of the gnomon above the ground
c
h
=
r
2
h
2
1 +
=
h
2
+ r
2
h
2
c
h GLOBE
®
2002
Relative Air Mass Learning Activity - 4
Atmosphere
h
Sun
Solar Elevation Angle
Solar Gnomon
The Earths Surface
Figure AT-AM-2B: Simple Model of Relative Air Mass
e
c
r
Length of the Gnomons Shadow
d
Sun
Top of Atmosphere
Solar Elevation Angle
Distance to the
T
op of the
Atmosphere
Pathlength
Through the Atmosphere
Air Mass = 1
The Earths Surface
Figure AT-AM-2A: Simple Model of Relative Air Mass
e
p GLOBE
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Relative Air Mass Learning Activity - 5
Atmosphere
A
ppendix
W
elcome
Intr
oduction
P
r
otocols
L
earning A
ctivities
and record it on the Calculating Relative
Air Mass Work Sheet. Next, measure the
distance from the top of the pole to the
end of the shadow. This is the hypotenuse
of the triangle. Use a tape measure or a
string to measure the distance. Have the
three students in each group do this
reading independently and record the
readings on the Calculating Relative Air
Mass Work Sheet.
4. Have students average the hypotenuse
lengths.
Deriving Relative Air Mass
1. Calculate the relative air mass value for
each of five days using Equations 1 or 2.
2. Ask students the following questions:
How do you think the relative air mass
readings might change if your readings
were taken at different times throughout
the day? How might relative air mass
readings taken at the same time of the
day, differ at different times of year?
Variations for Older Students
Have students measure and average the length of
the shadow instead of the hypotenuse and
calculate relative air mass using Equation 2.
Have students measure the solar elevation angle
and use Equations 3 and 4 to calculate relative
air mass. GLOBE
®
2002
Relative Air Mass Learning Activity - 6
Atmosphere
Calculating Relative Air Mass
Data Sheet
1. During a day that will be sunny in the morning, set up a solar gnomon outside. Work in
groups of three and measure the height of the gnomon and length of the hypotenuse of the
triangle formed by the solar gnomon and the shadow it casts using a me