Self-study questions – Appendix B and Ch. 1

Appendix B

Appendix B of A First Course in Atmospheric Thermodynamics offers a short but essential review of good problem-solving skills in the physical sciences.  The following self-study questions are designed to help you evaluate your own grasp of this material.

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1. Here, in random order, are what I call the Five Steps to Success (p. 282) for solving physical problems:
  • Validation
  • Understanding
  • Analysis
  • Knowledge
  • Execution
Put the above in the correct order, following the sequence outlined in the book.

2. Match the following short descriptions to the above Five Steps to Success:
  • drawing the appropriate lessons from the exercise
  • convincing yourself that your answer is correct
  • the mechanics of working and verifying your solution
  • applying familiar facts to unfamiliar problems
  • learning the relevant facts and theory
3. Actively answering which three questions in your own mind is an essential part of studying?  (p. 283)

4. What five questions should you answer for yourself as part of the process of planning your solution to a physical problem?

5. True or False: For your two-day trip from Madison to Chicago, it’s a sign of reasonable planning if your route passes through New York.

6. A key test of the validity of your path to the solution of a problem is that it satisfies the requirement for   .

7.  The following are typical steps used in executing your solution to a physical problem.  Put them in order:
  • Compute a numerical solution based on the specified values of the given variables.
  • Manipulate the symbols algebraically to obtain the solution to your problem expressed symbolically in terms of your givens.
  • Verify the dimensional consistency of your solution.
  • Specify values (including units) for those quantities, if applicable.
  • Assign suitable symbols to represent each relevant quantity.
8. A problem asks you to calculate the maximum possible radius of a hailstone that has been growing inside a strong thunderstorm. You come up with an answer of 1 meter.  Which of the four common sense tests given on p. 286 applies here, and what is your conclusion?

9. You have convinced yourself that your solution to a particular problem is correct and can safely be handed in. Is that all? What can you still do at that point, and why would you bother?

10. In the numbered list under “Recipe for disaster” (p. 288), identify those habits that you have been known to fall into when doing science problems. Then identify the reason(s) listed on the following page why those particular habits are worth unlearning.

10. Be able to explain and apply each of the following elements (habits) of a good solution write-up (p. 291-300):
  • Symbolic solution
  • Dimensional consistency
  • Mathematical consistency
  • Appropriate numerical precision
11. On page 303 is a “checklist for homework solutions.”  Identify the three items on that checklist that you, personally, are most likely to forget to do. Then make a point of thinking about those three things (or more) each time you work homework or test problems!

Atmospheric Thermal Structure

The following questions are drawn from pp. 18-28.

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1. How often are radiosonde balloons launched around the world, and what information do they provide?

2. When we make a plot of temperature vs. pressure from a balloon sounding, why do we make pressure decrease toward the top of the y-axis? And why are the pressure ticks spaced more closely near the bottom than near the top?

3. What are the troposphere, the tropopause, and the stratosphere, and how do you recognize these on a sounding diagram?

4. At altitude \(z_1\), the temperature is \(T_1\).  At altitude \(z_2 > z_1\), the temperature it \(T_2\).  What is the average lapse rate between \(z_1\) and \(z_2\)? Be sure to pay attention to the sign!

5. Give the name for the following cases:  (a) a temperature profile that increases with height, and (b) a temperature profile that is nearly constant with height.

6. What is the value of the standard lapse rate that we typically assume in the middle latitudes when we have no other direct information about the temperature profile?

7. Name and describe the five important ways that temperature inversions can form.

8. Fig. 1.7 gives an idealized (simplified) depiction of the temperature structure of the midlatitude atmosphere.  There are four “spheres” identified.  Be able to name them in the correct order (from the surface) and state whether temperature tends to decrease or increase with height in each one.

9. Explain the special significance of the troposphere. 10. During what season(s) (winter, fall, spring, summer) and/or in what latitude belt(s)  (tropical, midlatitude, polar) do you typically find the coldest/warmest tropopause temperatures and the highest/lowest tropopause heights?

Atmospheric pressure and density

The following questions are drawn from pp. 1-6:

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1. Identify the key similarities and differences between an atmosphere and an ocean (these could be on any planet!).

2. In what specific way is the atmosphere similar to a pot of water on a hotplate? What serves as the heat source for the atmosphere?

3. Fundamentally, what determines (to an excellent approximation) the atmospheric pressure at any particular point either at or above the surface?  Food for thought: Does the same general principle apply to points below the ocean or land surface?

4. What unit of pressure do most meteorologists generally prefer today?  What was the previous name for the same unit? Is it an SI unit?  If not, what is the appropriate SI unit, and what is the conversion between them?

5. If you visit this page, you can find current weather conditions at the top of our building, including pressure in hPa. From the current pressure, find the approximate mass of the atmosphere, in kg, within a square meter vertical column extending to outer space.

6. How and why can we use pressure as a vertical coordinate in the atmosphere? Will a particular pressure level over Madison always correspond to the same altitude in meters?

7. Explain why a log-linear plot is useful for plotting pressure vs. height and what it means mathematically when a function looks like a straight line on such a plot.  Extra: What kind of function looks like a straight line on a linear-log plot?  On a log-log plot?

8. Explain the concept of scale height for an exponential profile.  If, for example, the pressure at the surface is \(p_0\), how the pressure change with each additional scale height that you move upwards from the surface?

9. What physical property of air is responsible for the fact that pressure decreases more or less exponentially, taking into account your answers to questions 1 and 3, above?  What mathematical approximation for p(z) would you expect to be more appropriate in an ocean?

10. How do the observations in this section explain why mountain climbers usually need supplemental oxygen to climb mountains like Everest?  Specifically, what local property of the air are they having to compensate for?

Atmospheric composition

The following questions are drawn from pp. 6-12:

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1. Identify and describe the four broad categories of things that make up the terrestrial atmosphere.

2. What are three ways in which even seemingly minor constituents of the atmosphere can sometimes be considered “important?”

3. Below roughly what altitude are the so-called “permanent” constituents of the atmosphere found in nearly fixed proportions, and why?

4. Which three constituents make up all but a tiny proportion of the permanent gases in the atmosphere below 100 km, and how much is there of each, to the nearest 1%?

5. Why are things different above around 100 km?  What two processes affect the concentrations of various gases, and how?

6.  Why are some components of the atmosphere variable in proportion rather than fixed?  What factors control the degree of variability of any given constituent?

7. One variable component is water vapor.  Why do we treat it separately from all the others?

8. What would be typical maximum percentages of vapor by mass or by volume in extremely humid air?

9. What property of air sets an upper limit on how much water vapor can be present in any given case?

10. Describe the role carbon dioxide plays in the atmosphere and in the climate system, including its approximate concentration, its trend over time, natural and artificial sources and sinks, and importance for the energy balance of the climate.

11. Describe the process that forms ozone in the stratosphere, and explain the significance of the so-called ozone layer. Contrast that role with the role of ozone in the lower atmosphere.

Temperature

The following questions are drawn from pp. 13-17:

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1. True or false:  Your sense of touch is a reliable guide to the relative temperature of two different objects.

2. What fundamental process defines the relative temperature of two objects?

3. State the Zeroth Law of Thermodynamics in your own words.

4. Explain how the conduction of heat from one object to another occurs at the molecular level.

5. True or false:  An object can “have” a certain amount of heat.

6. In an ideal gas, the absolute temperature is proportional to

a) the average kinetic energy of the molecules
b) the average of the squared velocity of the molecules
c) the square of the average speed of the molecules
d) both (a) and (b)
e) none of the above.

6. Two gases have the same temperature. One of the gases is helium, the other is nitrogen.  In which of the gases are the molecules moving faster, on average, and why?

7. For every five degree change in temperature according to the Celsius scale, the temperature in Fahrenheit changes     degrees.

8. Whenever working with a physically derived equation involving temperature, that temperature generally needs to be expressed in degrees [Celsius, Fahrenheit, Kelvin] or you will get nonsense.

9. How many countries beside the U.S. use the Fahrenheit scale?

Wind chill

The following questions are drawn from pp. 33-35:

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1. On a particular day, the temperature is -5 degrees C and the wind is blowing at 40 km/hr. According to the Table 1.2, what is the wind chill temperature?  Based on that result, would you expect a jar of water left standing outside to freeze?  Why or why not?  What does the wind chill temperature purport to tell you?

Skew-T diagrams

The following questions are drawn from pp. 44-46:

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1. The horizontal lines on a Skew-T diagrams are called      and are lines of constant ; the straight lines slanted upward and to the right are called     and are lines of constant    .

2. True or false: By “skewing” the isotherms on a skew-T diagram,  the diagram becomes physically more meaningful than if they were vertical.

3. On a skew-T diagram, how does the spacing between the 1000 and 500 hPa isobars compare with the spacing between the 500 and 250 hPa isobars? In general, what determines the spacing between pairs of isobars, given that they’re evidently not equally spaced (i.e., the separation between 900 and 800 is smaller than the separation between 500 and 400)?

Upper air observations

The following questions are drawn from pp. 36-44:

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1. Upper air observations are typically taken around the world at what time(s) of day?

2. We typically think of a sounding as representing a vertical profile of temperature and humidity in the atmosphere. Is this in fact the case?  Why or why not?  If not, does it matter much?

3. List the six key components of a radiosonde package, and explain their function.

4. Explain the meaning of the following terms:  radiosonde, raob, rawinsonde, dropsonde, pibal, ceiling balloon.

5. In your own words, list the three key components of a radiosonde ground station and describe their function.

6. Study Table 1.3 and answer the following question: You have a radiosonde device that weighs 250 g.  What factor determines what size of balloon you would choose to launch it with?

5. What is the typical reason for the termination of an upper air sounding, and what can lead to premature termination?  What precautions must therefore be taken?