# As Time Goes By in Weather Forecasting: For Teachers

This WebQuest is designed to help students learn some basic concepts in statistics using real-time, self-collected weather forecast data. The project involves research and reporting, web searching and data gathering, mathematical calculation, and interpretive reasoning. The project is designed as a group activity. The suggested evaluation rubric includes components for a student’s individual contribution, as well as for the group effort.

This WebQuest is appropriate for grades 5-12.

### Objectives

At the end of this activity, students will have accomplished the following:

• Gathered data using the web
• learned the statistical concepts of mean, error, bias and lag
• compared the accuracy of weather forecasts using the concepts of ‘mean absolute errors’ and ‘mean relative errors’
• evaluated the accuracy of weather forecasts as a function of lag time
• prepared individual and group reports using data gathered form the web
• referenced information sources
• collaboratively analyzed an environmental problem (the accuracy of weather forecasts)
• learned to make interpretations of statistical results

### Requirements

An Internet-connected computer. Students may use home computers if they wish. (If this is not available, the project can still be accomplished using traditional media: newspapers, television and radio.)

### Time

This project requires three weeks.

• Week 1: data gathering (collect forecasts)
• Week 2: data gathering (collect forecasts)
• Week 3: calculations, analysis and preparation of reports

### Other Ideas

• Each group could evaluate weather forecasts for a different city. Results from different groups could be prepared to answer the following questions:
• Does a certain network (ABC, FOX, etc.) tend to produce more accurate forecasts?
• Are high temperature forecasts more accurate in certain cities? (In other words, are the mean forecast errors smaller for certain cities?)
• Does the deterioration of forecast accuracy with increasing lag times change for different cities?
• Discuss the difficulties in comparing 1-day forecast results with 4-day forecast results. How does the different sample size (more 1-day forecasts than 4-day forecasts) affect the comparison? How might the problem of different sample sizes be eliminated?
• Examine the interpretation of different values of relative errors.
• Discuss the concept of bias (relative error consistently positive or negative).
• Discuss how a relative error near zero does not necessarily indicate a good forecaster (for example, very high overpredictions could balance out very low underpredictions).
• Discuss how the absolute error does not provide any information about bias.
• Examine the difference between relative and absolute errors.
• What’s better – a small mean relative error or a small mean absolute error? Why?
• Why isn’t just one type of mean error (relative or absolute) enough to describe the accuracy of a forecaster?
• Why is the following equation incorrect?:
AAE=|ARE|

(in other words, why isn’t the average absolute forecast error simply the absolute value of the average relative forecast error?)

• Examine some relevant meteorological considerations.
• What might be some reasons for differing quality of forecasts for different cities? For different Lags? Is the weather more complex (harder to forecast) at certain cities? Why?
• Do you think the results might change if the forecasts were collected during a different two week period? Why?
• Why isn’t just one type of mean error (relative or absolute) enough to describe the accuracy of a forecaster?
• Would the results be different if the forecasts were made in degrees Celsius instead of degrees Fahrenheit? Why or why not?
• This WebQuest addresses the issue of ‘Who is the best weather forecaster’ in any particular location. This is a relative question. In other words, we’re only comparing the forecasters to each other. It might be interesting to ask the question in an absolute sense: Are the forecasters really any good? This question can be addressed by adding a new forecaster, called “Persistence”. A persistence forecast works like this: tomorrow’s high temperature will be the same as today’s high temperature. A good forecaster should achieve results that are consistently better than persistence forecasts.

### Standards

This WebQuest specifically addresses the following National Science Education Standards, but may also touch on other standards not listed:

#### Science as Inquiry – Content Standard A

• Use appropriate tools and techniques to gather, analyze and interpret data.
• Think critically and logically to make the relationships between evidence and explanations.
• Recognize and analyze alternative explanations and predictions.
• Use mathematics in all aspects of scientific inquiry

#### Earth and Space Science – Content Standard D

• Structure of the earth system
• atmosphere
• clouds
• global patterns of atmospheric movement

#### Science and Technology – Content Standard E

• Developing student abilities and understandings
• straightforward activity with only a few well-defined ways to solve the problems involved
• only one or two science ideas involved in the task
• Implement a proposed design
• Understandings about science and technology

#### History and Nature of Science – Content Standard G

• Science as a human endeavor
• Nature of science

#### Coordination of Science and Mathematics – Program Standard C

• Use estimations
• Identify and use functional relationships
• Develop and use tables, graphs and rules to describe situations
• Use statistical methods to describe, analyze, evaluate and make decisions

Source: National Science Education Standards, 1996, National Academy Press, Washington, DC, 262 pp., www.nas.edu.