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Solutions
ATM S 211
Homework 3
Due Monday October 29 at 11:45 pm PDT
Problem #1: Temperature Cycles (6 pts)
Consider the following June / December average temperatures:
( i ) 70 ◦ F / -10 ◦ F
( iv ) 80 ◦ F / 76 ◦ F
( ii ) 65 ◦ F / 40 ◦ F
( v ) 40 ◦ F / 65 ◦ F
( iii ) 70 ◦ F / 35 ◦ F
( vi ) 75 ◦ F / 65 ◦ F
Which of the above is the best match for the following cities?
¦ Seattle, Bali (Indonesia), Los Angeles, Sydney (Australia), Moscow (Russia), New York City .
Pair each city with a unique answer above (i.e. you cannot use the same answer for more than one city).
¦ Sydney : ( v ) . As it is in the Southern Hemisphere, December is cooler than June.
¦ Bali : ( iv ) . Being very close to water and the equator, its seasonal temperature cycle is very small.
¦ Moscow : ( i ) . High latitude and continental.
¦ Los Angeles : ( vi ) . Lower latitude than the remaining three.
¦ New York City : ( iii ) . Slightly lower latitude than Seattle
¦ Seattle : ( ii ) .
Problem #2: Poleward energy transport
(12 pts)
ATM S 211 Homework 3 Solutions
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The above figure (also figure 4-2 on page 61 of the book) shows the present-day distributions of the annual
average absorbed solar energy (net shortwave, blue curve) and of the annual average emitted infrared energy
(net longwave, red curve) as functions of latitude. Please note that the emitted infrared energy includes
energy emitted by the Earth’s surface and by the atmosphere. As discussed in class, there is a surplus of
energy in the tropics (latitudes between 30◦ South and 30◦ North), where absorbed solar energy is greater
than the emitted infrared energy. In the polar regions, the situation is reversed; there is a deficit of energy
where absorbed solar energy is less than the emitted infrared energy.
The surplus of energy is redistributed from the tropics to the polar regions jointly by atmospheric and
oceanic currents in a process called the poleward energy transport.
For parts (a), (b) and (c), consider the situation a short time after a volcanic eruption which caused the
albedo of the tropics to increase, but did not affect the albedo of locations outside the tropics. Under this
condition,
(a) Is the temperature difference (or gradient) between the tropics and the polar regions either greater than,
less than or equal to its present day value ? (2 pts)
The tropics cooled but the temperature in the polar regions, which are not affected by the volcanic
eruption, remained the same. So, the temperature difference is less.
(b) Is the energy surplus either greater than, less than or equal to its present day value ? Assume that the
surface and the atmosphere had time to cool to equilibrium. (2 pts)
An increased albedo causes a decrease in absorbed solar energy in the tropics which in turn causes a
cooling of both the Earth and the atmosphere. Net longwave energy depends on temperature; hence, it
decreases accordingly (via Stefan-Boltzmann) and the energy surplus remains constant.
(c) Is the magnitude of poleward energy transport either greater than, less than or equal to its present day
value ? (2 pts)
The energy surplus in the tropics is constant, from part (b), and the energy deficit is constant; therefore,
the same amount of energy is being redistributed from the tropics to the polar regions by the poleward
energy transport.
This question was meant to illustrate that the energy surplus (and not the temperature difference) induces or results in the poleward energy transport.
Now, for parts (d) and (e), suppose that Earth was shaped like an American football, with the pointy ends
being the North and South poles. Take everything else to be the same as present-day Earth; e.g. the surface
area, the albedo, the tilt angle, the rotation and revolution period, etc. Under these conditions,
(d) Is the difference in absorbed solar energy between the equator and the 45◦ (North or South) latitude
band either greater than, less than or equal to the present day value ? (2 pts)
Solar energy reaching the Earth’s surface in spread more uniformly with latitude (draw the picture).
Hence, if the albedo remains the same, the difference in absorbed solar energy is less.
(e) Is there still a surplus of energy in the tropics and deficits in the polar regions? Yes or no?
(2 pts)
ATM S 211 Homework 3 Solutions
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Yes, because, as seen in class, the albedo and the atmospheric water vapor concentration are not constant with latitude. These effects combine to create an energy surplus in the tropics.
In class, we discussed that the Sahara desert (located between 22◦ and 30◦ North) acts as an energy sink for
Earth. Compared to other regions on the planet, a greater fraction of the infrared energy emitted from the
surface in the Sahara is lost to space. Now, suppose that water vapor is added into the air column over the
Sahara. Under these conditions,
(f ) Is the energy surplus be greater than, less than or equal to its present day value ?
(2 pts)
Water vapor absorbs a fraction of the Earth’s emitted infrared energy, then emits it in all directions
and at a cooler temperature as temperature decreases with height in the atmosphere (more specifically
the troposphere). This results in a decrease in net longwave energy (again via Stefan-Boltzmann) and
consequently, as the shortwave part of the energy budget is left unchanged, a greater energy surplus. In
other words, the presence of water vapor in the Sahara would trap even more energy in the tropics.
Problem #3: Land breezes (12 pts)
A land breeze is a wind that originates from the land near the shore and blows towards the nearby sea. In
other words, it is a sea breeze acting in reverse. They occur when land is cooler than the nearby sea.
(a) Briefly explain why land breezes occur at night. 2 sentences suffice.
(4 pts)
At night, in the absence of solar energy, the Earth’s surface (both land and sea) cools. Due to its lower
heat capacity, land cools more rapidly then the sea creating temperature / pressure difference and surface winds blowing from cold to warm.
(b) Are land breezes either more likely, less likely or equally likely to occur if there are clouds strictly covering the land? (2 pts)
Clouds at night increase the greenhouse effect without reflecting solar energy. This results in a warming
of the land and consequently a weaker temperature difference with respect to the sea.
(c) Are land breezes either more likely, less likely or equally likely to occur if there are clouds strictly covering the sea? (2 pts)
An increased greenhouse effect over the sea results in a more pronounced temperature difference.
(d) In a land breeze, is the surface pressure over land either greater than, less than or equal to the surface
pressure over the sea? (2 pts)
Winds blow (in the absence of the Coriolis force) from high the low pressure. We need high pressure
over land to observe a land breeze.
(e) Now consider the air about 2 km above the surface. Is the pressure above the land either greater than,
less than or equal to the pressure of the air above the sea? (2 pts)
Pressure in a warm air column drops less rapidly with height than in a cold air column (via hydrostatic
balance). Here, the relatively warm air is over the sea. So, there is high pressure above the sea and low
pressure above the land.