Cross-Curricular Project 1

How’s the Weather?

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction
USA TODAY, October 8, 2000

     Climate normals are a useful way to describe the average weather of a location. Several statistical measures are computed as part of the normals, including measures of central tendency, such as the mean or median, of dispersion or how spread out the values are, such as the standard deviation or inter-quartile range, and of frequency or probability of occurrence.

     Over the decades the term “normal”, to the lay person, has come to be most closely associated with the mean or average. In this context, a “climatic normal” is simply the arithmetic average of the values over a 30-year period. This period is generally, three consecutive decades. Someone who is unfamiliar with climate and climate normals may perceive the normal to be the weather that one should expect to happen.

     It’s important to note that the normal may, or may not, be what one would “expect” to happen. This is especially true with precipitation in dry climates, such as the U.S. Desert Southwest, and with temperatures at continental locations, which frequently experience large swings from cold air masses to warm air masses.

     Two discussions, with links below, will examine two examples that illustrate this misconception. The National Weather Service station at the Yuma, Ariz. airport serves as a typical example of the case of precipitation in dry climates. The Crosby, N.D., station serves as a typical example of the temperature swings at continental locations. The discussions, by Richard Heim of the National Climatic Data Center, go into statistical detail about normals.

     The point about normals is illustrated by snowfall in the Northeast so far during the 1990s. Since the winter of 1990-91, snow has been either well above or well below the seasonable average, or “normal.”

The Task
You are working as an assistant to a meteorologist for a local television station. The meteorologist wants to provide viewers with some interesting information about weather. She has asked you to research the relationship between latitude, longitude, and average monthly temperature. You need to prepare a portfolio of the data that you collect including any relationships shown by the data. If you prefer, you can prepare a Web page with this information that the TV viewers could access. Be sure that your portfolio or Web page contains the following information:

• the latitude and longitude for five pairs of U.S. cities, rounded to the nearest degree (pairs of cities must be located in different states);
• the average high or low temperature for each city for a month of your choice (the month must be the same for all cities);
• a scatter plot comparing the difference in latitude and the difference in monthly temperatures for each pair of cities;
• a scatter plot comparing the difference in longitude and the difference in monthly temperatures for each pair of cities;
• a scatter plot comparing the degree distance and difference in the monthly temperatures for each pair of cities (you will learn about degree distance in Lesson 1–3).

• Select five pairs of cities in the U.S. For each pair of cities, the distance between the cities should be greater than 100 miles. Search the Internet for the latitude, longitude, and average monthly temperature data for each city. For help, try these Web sites.
  www.usatoday.com/weather/wnormals.htm
  www.infoplease.com
  www.cpc.ncep.noaa.gov/products/predictions/new_climates/
  www.statistics.com
• Make a table to record the latitude, longitude, degree distance, and temperature for each pair of cities. For more information on degree distance, see the WebQuest exercise in Lesson 1–3 or try this Web site.
  http://www.indo.com/distance/
• Make scatter plots of your data. You must have at least three scatter plots as described below. (See the WebQuest Exercise in Lesson 1–3 for more detail on these scatter plots.)
  1. difference in latitude versus difference in temperature for the five pairs of cities
  2. difference in longitude versus difference in temperature for the five pairs of cities
  3. degree distance versus difference in temperature for the five pairs of cities
• Conjectures about the relationship between latitude, longitude, degree distance, and temperature. For information on distance between cities, try this Web site.
  www.infoplease.com
• Explain your findings and describe the changes that you predict in the U.S. due to an aging population.
• Be creative. Add some additional data, information, or even pictures to your portfolio or Web page.

1. Compare the difference in latitude, longitude, or degree distance for pairs of cities to the difference in the low or high record temperatures.
2. Make scatter plots for locations in the Southern Hemisphere.
3. Compare cities and locations in the Northern Hemisphere with locations in the Southern Hemisphere.
4. Compare the difference between the lowest and highest temperatures for the year of cities to the latitude and/or longitude.
5. Investigate the effect on the climate of a city located on an ocean or large lake.
6. Investigate the effect of altitude on climate.

• Present your project to your class or at a family night.
• Present the information on a Web page. Have other students critique your project and help you to make improvements to your project.
• Write a one–page summary of your project, including what you have learned from researching this topic.
• Interview a meteorologist. Find out what education is needed to pursue this career. Research the opportunities for employment in this field.

Lesson 1–3
Bonnie has decided to use the five pairs of cities shown in the table below for her research. She chose to use the average high temperature for July to make her comparisons. The latitude and longitude have been rounded to the nearest degree.

1. Fill in the Degree Distance column using the following directions. For each pair of cities, write an ordered pair (x, y) for each city such that x is the latitude and y is the longitude. Use the Distance Formula to find the degree distance for each pair of cities using the ordered pairs. (A pair of cities has only one degree distance.) The resulting value will be the distance between cities relative to the degrees of latitude and longitude.
2. Make a scatter plot comparing degree distance and temperature. For each pair of cities write the ordered pair (degree distance, |difference in temperature|). Plot the five ordered pairs and look for a relationship.
3. Make a second scatter plot comparing latitude and temperature. For each pair of cities write the ordered pair (|difference in latitude|, |difference in temperature|). Plot the five ordered pairs and look for a relationship.
4. Make a third scatter plot comparing longitude and temperature. For each pair of cities write the ordered pair (|difference in longitude|, |difference in temperature|). Plot the five ordered pairs and look for a relationship.

1. Make a conjecture about the relationship shown by each scatter plot.
2. Find the five pairs of cities you will use for your project. Make a table and three scatter plots for your chosen cities. Compare your scatter plots to those you made in Lesson 1–3.
3. Do the conjectures you made in Exercise 1 hold for the scatter plots you made in Exercise 2? Explain.

1. The ordered pair (latitude, longitude) for Washington, D.C., is (39, 77) and for Los Angeles, California, is (34,118). Find the degree distance for the two cities to the nearest tenth of a degree.
2. Find the distance to the nearest tenth of a mile between the two cities using the degree distance. Since these cities are not located at the pole, assume that a degree of latitude or longitude measures 69 miles.
3. Find the actual air distance between the two cities. Compare it to the distance you found in Exercise 1.
4. Compare the distance between other pairs of cities using the degree distance measure and the actual distance. What seems to be the relationship?