SPU 25 Energy and Climate: Vision for the Future, Spring 2018 Homework Set #1 Climate Basics, DUE Monday 2/12 (1:00 pm in lecture)
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Earth’s climate is a complex reflection of the distribution and movement of energy around the planet. The
primary source of Earth’s energy is radiation from the Sun. In this problem set, you will see how this energy is
received, lost, and stored, and the role of greenhouse gases in altering the climate. You will also understand
how the distribution of energy influences climate and get some practice with basic quantitative problems and
unit conversions. (40 points total)
You will only receive credit if you show all your work and write legibly.
I. Earth’s Energy Balance
Planet Earth (including the solid earth, oceans, and atmosphere) is best described as an isolated system:
energy, but not mass, can pass from Earth to space and vice versa. In this type of system, the energy balance
may be described by: Energy gained = Energy lost – change in storage.
1. Greenhouse gases in the atmosphere prevent the radiation of energy to space, so they impact which
term in the above equation? (1 point)
2. Changing surface and ocean temperatures reflect which term in the above equation? (1 point)
II. Energy from the Sun
3. True or False: Summer is warmer than winter because the Earth is closer to the Sun. (1 point)
4. Currently, the energy from the Sun arriving at Earth’s orbital position amounts to 1,379 W m-2,
measured perpendicular to the direction of the sunlight (see figure below).
a. Given that the Earth is a circular target for this energy and has a radius of 6.38 x 103 km,
calculate the total rate at which solar energy is intercepted by the Earth. Report your answer in
Watts. Recall that the area of a circle is πr2. (2 points)
Figure 1. The shadow formed by an
illuminated sphere has a circular
shape with a radius R equal to the
radius of the sphere.
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b. Assuming that the energy from the Sun is eventually distributed equally over the entire surface
area of the Earth, use your answer from part (a) to calculate the current average rate of
incoming solar radiation. Express your answer in Watts per meter squared. Recall that the
surface area of a sphere is 4πr2. (3 points)
III. The fate of energy from the Sun
5. Based on your answers from the previous problem and assuming a global average albedo of 0.3, how
much of the incoming solar radiation is reflected back into space? How much is absorbed? Express
your answers in Watts per meter squared. (2 points)
6. Much of the energy absorbed at the Earth’s surface is used for evaporation. The energy involved in
changing the phase of water is called latent heat. For water, the latent heat of evaporation (i.e. the
energy required to evaporate water) is 2.3 x106 Joules per kg water. Evaporation removes
approximately 1.2 m (depth) of water from the global oceans each year, which is later precipitated
over the continents and oceans. The oceans cover a total surface area of 3.6132 x 108 square
kilometers. Assume the density of the water is 1000kg/m3.
a. Calculate the total mass of water (in kg) evaporated from the oceans each year. (2 points)
b. Using your results from part a, calculate the total energy required to fuel the evaporation from
the oceans each year. Report your answer in Joules. (2 points)
c. Using your results from part b, calculate the energy absorbed by the oceans in Joules per
square meter. (2 points)
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d. Assuming that energy absorption takes place at a constant rate over the course of a year,
calculate the rate at which energy is used for evaporation from the oceans. Report your answer
in Watts per square meter. (2 points)
e. Compare your answer in part d to the global energy balance figure below. How does the latent
heat transfer term, averaged for the whole planet, on the figure compare to the energy
associated with ocean water evaporation you calculated? What does this tell you about the
energy required by evaporation over land versus the oceans? (2 points)
IV. Distributing Energy around the Planet
7. Which of the following statements regarding the global energy gradient is not true? (1 point)
a. Incoming solar radiation is more spread out at the poles and more concentrated at the equator.
b. The equator is warmer primarily because it is closer to the Sun than the poles.
c. The radiation imbalance results in more energy at the equator compared to the poles.
d. The radiation imbalance results in an energy gradient that moves energy from the equator toward
the poles.
Figure 3. Annual global energy
balance. Units are Watts per
meter squared. Source: IPCC
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8. Due to the Coriolis Effect, an air parcel in the northern hemisphere will appear to be deflected to the ________________ of its original direction. An air parcel in the southern hemisphere will appear to be
deflected to the ______________ of its original direction. (1 point)
V. The role of greenhouse gases in Energy Balance
9. Circle One: Energy reaching the Earth from the Sun is primarily shortwave (visible)/longwave
(infrared) radiation. (1 point)
10. Greenhouse gases are transparent to ________________ radiation, but trap ______________ radiation,
increasing temperatures. (1 point)
a. Ultraviolet, gamma
b. Longwave, shortwave
c. Shortwave, longwave
d. Outgoing, incoming
11. Which of the following are not greenhouse gases? (1 point)
CO2 N2O H2O N2 O3 O2 CH4 CFCs
VI. Climate Change
12. True or False. Although greenhouse gas emissions have been increasing rapidly since the Industrial
Revolution, global average surface temperatures have not increased because all of the emitted CO2 has
been absorbed by the oceans. (1 point)
13. On human time scales, what are the three major fates of anthropogenic carbon dioxide emitted to the atmosphere? (describe with a few words) (3 points)
a.
b.
c.
14. The figure below shows radiative forcing from different sources from the 2013 IPCC report. Take time to study this figure carefully, and then answer the following questions.
a. What is the IPCC? What do they do? (https://www.ipcc.ch/organization/organization.shtml) (2 points)
b. What is radiative forcing? (1 point)
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c. How does total anthropogenic forcing compare to total natural forcing? (1 point)
d. What drivers and emissions generally have a cooling effect on climate? (1 point)
e. What is the effect of deforestation of albedo? Would this be a positive (warming) or negative (cooling) radiative forcing? Explain your answer. (2 points)
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15. Navigate to https://www.esrl.noaa.gov/gmd/ccgg/trends/history.html and watch the “CO2 Movie.”
Answer the following questions:
a. Why are the seasonal variations in CO2 larger in the northern hemisphere than in the southern
hemisphere? (1 point)
b. How do scientists know what atmospheric CO2 concentrations were thousands of years ago?
(1 point)
c. The atmospheric concentrations of greenhouse gases are now higher than they have been in at
least the last _________________ years. (1 point)
16. On the same website, click on the “CO2 Emissions” tab. Read the description and watch the animation,
paying attention to how winds cause atmospheric mixing. Note that the animation is showing ONLY
the emissions accumulated over a two year period from fossil fuel combustion.
a. Which three regions are the major sources of CO2 from combustion? (1 point)