Download Atmospheric Sciences 101, Summer 2003 Homework #1 Solutions

Atmospheric Sciences 101, Summer 2003
Homework #1 Solutions
1. Atmospheric vertical temperature profile
a. Describe how the stratosphere is primarily heated.
The stratosphere is primarily heated by the absorption of ultraviolet (UV) radiation from
the sun.
b. Describe how the troposphere is primarily heated.
The troposphere is primarily heated by transfer of heat, mostly through convection, from
solar energy absorbed by the Earth’s surface below.
c. The upper stratosphere is warmer than the upper troposphere (see Fig. 1.7 of EOM if you
need confirmation) but not because the stratosphere is closer to the sun than the troposphere.
Those different methods of heating in parts (a) and (b) are one reason why. Give another
argument for why proximity to the sun does not explain why the upper stratosphere is
warmer than the upper troposphere.
Possible answers may include:
• The top of the stratosphere is only about 35km closer to the sun than the top of the
troposphere, which is trivial compared to the average 150,000,000km Earth-Sun
distance.
• Only during daylight hours when the sun is high is the sky is the stratosphere over a
location even that ~35km closer to the sun; at night it is farther away.
2. Ozone
a. Why is ozone in the stratosphere beneficial to life?
Ozone absorbs ultraviolet (UV) radiation, which is harmful to living tissue in organisms.
b. Why is ozone in the troposphere harmful to life?
Ozone itself is a pollutant, which is damaging to plants and an irritant to the eyes and
throat. It is also a primary component in photochemical smog.
3. Heat transfer (at dinnertime)
For each situation listed below choose the primary method of heat transfer that is occurring:
conduction, convection, or radiation. Then justify your choice by briefly describing the physical
process by which the heat is moving. An example is done for you:
Example: The Earth is heated by the sun.
Radiation
Energy through electromagnetic waves moves through space from the sun to the Earth.
a. Hot pizza burns the roof of your mouth after you take a bite.
Conduction
Heat is transferred by the contact between the pizza and your mouth.
b. You warm up some leftovers in the microwave.
Radiation
Radiation generated from the microwave is absorbed by the food and heats it.
c. Soup at the bottom of a pan heats up soon after the range is turned on.
Conduction
The pan is heated in some manner, and the soup at the bottom of the pan is heated because
it is in direct contact with the hot pan.
d. Some time later the soup at the top of the pan is warmed.
Convection
Heat has dispersed throughout the soup by movement of the soup itself.
4. Emission of electromagnetic radiation
a. Which is hotter, a red star or a blue star? Why?
The blue star is hotter. Blue light has a shorter wavelength than red light, and the color of
the star is a good indicator of the peak wavelength of emission of the star. As described by
Wien’s Law, hotter objects emit most radiation at shorter wavelengths than colder objects,
so the blue star must be hotter.
b. Assuming both stars are the same size, which one is emitting energy at a greater rate? Why?
The blue star is emitting more intense radiation. As described by the Stefan-Boltzmann
Law hotter objects emit radiation at a greater rate than colder objects.
5. Explain the process by which sweating helps cool the body.
Sweating puts liquid water from your sweat glands onto the surface of your skin. Heat
from your body is conducted into the water, and some of that heat goes into evaporating
the liquid into water vapor. When the vapor leaves the skin, it takes away that now latent
heat (that changed that phase of the water from liquid to gas) it gained from the body, thus
leaving the body with less heat and therefore cooler.
6. Weather satellite images
On the class Assignments web page there are links to two satellite images of western North
America and the eastern Pacific Ocean. They are not labeled, but one is a visible image, and one
is an infrared (IR) image, not an “enhanced” IR image. Use the images to answer the following
questions. Information on pp. 235-237 in EOM may also be helpful. (Note: Do not print out the
satellite images to turn in with this assignment.)
Which image (1 or 2) is the IR image? #2
Which image (1 or 2) is the visible image? #1
Explain how you determined which image was the IR and which image was the visible.
Several possible ways including:
• Space in the upper right corner is black in the visible (since it does not reflect visible
light) and white in the IR (since it emits essentially no IR radiation).
• Clouds in IR images span a greater range of gray and white shades, whereas in
visible images there is much more consistent white and light gray among the clouds.
• In visible image, water appears darker since it has a lower albedo than land.
On or nearby three cloud formations are labels (A, B, C) on both satellite images. Write whether
each formation features high clouds or low clouds.
A:
Low
B:
High
C:
Low
Explain how you determined which clouds were high or low.
Higher clouds appear white in the visible image and also white in the IR image (since they
are colder and thus emit less IR radiation, which shows up as a lighter color). Lower
clouds also appear white in the visible image, but a darker shade of gray in the IR image
(since they are warmer and emit more IR radiation, which shows up as a darker color).