CLIMATE 105 Assignment 2 Answer Key.docx
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Course
105
Subject
Geography
Date
Jun 4, 2024
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4
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CLIMATE 105: Our Changing Atmosphere (Spring 2024)
Assignment 2
Due Friday, May 24: please show all work!
1.
Calculate the energy of photons with the following wavelengths: (10 points)
E =
ℎ𝑐
λ
(Planck’s constant, h = 6.626 × 10
-34
m
2
kg/s; velocity of light, c = 3 x 10
8
m/s)
a.
1 m
E = (6.626 x 10
-34
x 3 x 10
8
/ 1) J
E = 1.987 x 10
-25
J
b.
1 cm
E = (6.626 x 10
-34
x 3 x 10
8
/ 1) J
E = 1.987 x 10
-23
J
c.
0.5 μm
E = (6.626 x 10
-34
x 3 x 10
8
/ 0.5 x 10
-6
) J
E = 3.975 x 10
-19
J
d.
250 nm
E = (6.626 x 10
-34
x 3 x 10
8
/ 250 x 10
-9
) J
E = 7.951 x 10
-19
J
2.
Calculate the energy flux and peak wavelengths of the energy radiated from the
following celestial objects: (10 points)
𝐹
=
𝜎 𝑇
4
λ = 2989
𝑇
(Stefan – Boltzmann constant, σ = 5.67 × 10
−
8
W m
−
2
K
−
4
;
a.
The Sun’s photosphere or “surface”: T = 5700 K
F = (5.67 × 10
−8
x 5700
4
) W/m
2
F = 59852525.67 W/m
2
= 5.985 x 10
7
W/m
2
λ
max
= (2898 / 5700) μm
λ
max
= 0.508 μm
b.
Neutron star: T = 600,000 K
F = (5.67 × 10
−8
x 600000
4
) W/m
2
F = 7.348 x 10
15
W/m
2
λ
max
= (2898 / 600000) μm
λ
max
= 0.00483 μm = 4.83 nm
c.
Supernova: T = 100 billion K
F = (5.67 × 10
−8
x (100 x 10
9
)
4
) W/m
2
F = 5.67 x 10
36
W/m
2
λ
max
= (2898 / (100 x 10
9
)) μm
λ
max
= 2.898 x 10
-8
μm
d.
Earth’s atmosphere: T = 290 K
F = (5.67 × 10
−8
x 290
4
) W/m
2
F = 401.028 W/m
2
λ
max
= (2898 / 290) μm
λ
max
= 9.993 μm
3.
Calculate the effective equilibrium surface temperature and magnitude of the greenhouse
effect (rise in temperature) for the following moons of Jupiter (Jupiter orbits the sun at
roughly 5 times the distance of Earth, i.e.
5 AU
). (10 points)
S
J
= S
o
(
)
2
𝑟𝑜
𝑟
(Solar constant at Earth, S
o
= 1370 W/m
2
)
S
J
= 1370 x
(1/5)
2
S
J
= 54.8 W/m
2
a.
Callisto
: Albedo, A = 0.22; Actual surface Temperature T
S
= 134 K
T
e
= [(1 – 0.22) x (54.8 / 4 x 5.67 x 10
-8
)]
1/4
K
T
e
= 117.167 K
ΔT
g
= 134 – 117.167 = 16.833 K
b.
Europa
: Albedo, A = 0.67; Actual surface Temperature T
S
= 102 K
T
e
= [(1 – 0.67) x (54.8 / 4 x 5.67 x 10
-8
)]
1/4
K
T
e
= 94.495 K
ΔT
g
=102–94.495=7.5K
4.
List the different layers of the Earth’s atmosphere and the altitudes over which they
extend. How are they defined? (5 points)
Troposphere
, (10-15 km from the surface) where the temperature decreases with altitude.
Stratosphere
, (10-15 to 50 km from the surface) where the temperature increases with
altitude.
Mesosphere
, (50 to 90 km from the surface) where the temperature again decreases with
altitude.
Ionosphere
or
Thermosphere
(Above 90 km from the surface) where the temperature
again increases with altitude.
Exosphere
, the very outermost fringe of the atmosphere, where the gas is so tenuous that
collisions between molecules become infrequent.
5.
In the Northern Hemisphere’s summer, the sun does not set at the North Pole. Although
the Sun is the major source of heat for Earth, why is the North Pole colder than the
Tropics in the summer? (5 points)
The amount of solar energy incident on surfaces near the North Pole is much less than
near the equator. This is due to the curvature of Earth as the same amount of solar energy
spreads out over a larger surface area at the poles than at the equator. Each square meter
of the surface receives proportionately less energy as we move to higher latitudes.
6.
a. What role does humidity play in the global climate? (5 points)
Humidity is composed of water vapor, which is a greenhouse gas. More humidity
generally causes an increase in temperatures, and higher temperatures increase the
atmosphere's capacity to hold water vapor. Water vapor also condenses to form clouds,
which can increase the reflection of incoming solar energy, thereby increasing albedo and
lowering temperatures. However, clouds can also absorb infrared radiation, causing
warming. The interplay of these competing processes can help shape global climate.
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b. Using your answer from the question above, draw a system diagram to illustrate the
relationship between Earth’s temperature, humidity, and albedo. (5 points)
Note: This diagram applies for when shortwave scattering is greater than longwave
absorption for cloud feedback mechanisms.
EXTRA CREDIT
(5 points)
A.
Why is the lower atmosphere, say less than 1 km above Earth's surface, so much warmer
than the upper atmosphere? Be sure to state any assumptions you might make.
Most of the energy from the sun passes through the atmosphere and reaches the surface,
where some of it is absorbed and reemitted as heat energy. After the surface is warmed by
the sun, this energy is distributed upwards thorough the troposphere. Thus, the farther
away you get from the surface (the main heat source), the colder it will be. Additionally,
as air rises, it expands, and this also contributes to cooling.