1. Outline for Today • Brief Lecture on weather forecasting • A comment on the upcoming Exam 4

2. Theoretical Models and Accuracy • As we discussed previously, one of the most useful ways of evaluating a theoretical model is to compare the predictions of the model against empirical data • Unfortunately, many industries do not provide you with information on the accuracy of their predictions • how many people improve after taking a drug • how many people actually lose weight by eating Subway sandwiches • how many horoscopes accurately predict the future • As a consequence, it is almost impossible for you, as a consumer, to evaluate the quality of the product

3. In general, weather forecasters make their predictions based on either mathematical models/simulations of weather systems, past weather conditions, intuitive judgments based on the movement of current weather systems, or “all of the above”

4. Unfortunately, weather forecasters do not tell us—the consumers—how accurate their forecasts are. We don’t know what the “track record” is for any weather/news team. (Moreover, they don’t keep records of past forecasts on their websites, thereby preventing consumers from investigating the matter themselves.)

5. A scientific analysis of the accuracy of weather forecasting • Students recorded the 5-day forecasts (on Sunday nights) for the following sources • ABC Ch. 7 Panagiota Sveronis • CBS Ch. 2 Lisa Carlisle • WGN Ch. 9 Debjit Sarkar • NBC Ch. 5 Mary-Jennelle Guevara • Fox Ch. 32 Greg Zykowski • Weather.com Allison Vadasz • Chicago Tribune Manuel Aponte • Chicago Sun Times Kelly Meehan-Coussee • I recorded the actual, end-of-the-day weather from an unrelated source: Weather Underground. • This allows us to compare the predictions made by the different teams with the actual weather.

6. Average temperature observed, as recorded by Weather Underground, Chicago 100 80 Actual temperature 60 40 2 4 6 8 10 Day

7. Predictions made by NBC, Channel 5, on Sunday nights Average absolute discrepancy: 4.7 degrees ~ not too bad, eh? ~

8. 12 Errors tended to get larger as more days passed between when the prediction was made (Sunday evenings) and the day in question. Five days later, the average prediction was off by about 10 degrees. (These numbers are based on averages across NBC, ABC, CBS, WGN, & Sun Times.) 10 Discrepancy between predicted and actual temperature 8 6 4 1 2 3 4 5 Number of days since prediction

9. NBC | Mean Discrepancy = 4.7 ABC | Mean Discrepancy = 11 CBS | Mean Discrepancy = 6.8 100 100 100 80 80 80 Actual temperature 60 60 60 40 40 40 40 60 80 100 40 60 80 100 40 60 80 100 Predicted temperature Predicted temperature Predicted temperature SUN TIMES | Mean Discrepancy = 5.5 WGN | Mean Discrepancy = 7.3 100 100 80 80 Actual temperature 60 60 40 40 40 60 80 100 40 60 80 100 Predicted temperature Predicted temperature

10. TRUE.TEM NBC.TEMP ABC.TEMP CBS.TEMP WGN.TEMP SUN.TEMP • TRUE.TEM 1.00 0.85 0.72 0.89 0.58 0.74 • NBC.TEMP 0.85 1.00 0.85 0.98 0.74 0.83 • ABC.TEMP 0.72 0.85 1.00 0.90 0.79 0.95 • CBS.TEMP 0.89 0.98 0.90 1.00 0.75 0.88 • WGN.TEMP 0.58 0.74 0.79 0.75 1.00 0.75 • SUN.TEMP 0.74 0.83 0.95 0.88 0.75 1.00

11. As an additional comparison, we can generate predictions in another way: based on “day before” temperature In this case, we’re assuming that the best bet for tomorrow’s temperature is today’s. Average discrepancy: 8.3

12. Day before method NBC 100 100 80 80 Actual temperature Actual temperature 60 60 40 40 40 60 80 100 40 60 80 100 DAY.BEFORE NBC.TEMP Average discrepancy: 11.8 degrees Average discrepancy: 4.7 degrees

13. What about broader weather conditions? • Broader weather conditions • (a) sunny/clear • (b) partly cloudy/mostly cloudy • (c) thunderstorm • (d) rain/showers • Accuracy in prediction • NBC 55% • ABC 34% • CBS 55% • WGN 34% • SUN 34% day before accuracy = 34%

14. Summary • It appears that the various weather teams do a pretty good job in predicting the temperature • They were only off by approximately 4.7 – 11 degrees. • Their ability to make accurate forecasts was lower for extended forecasts • In predicting weather conditions (e.g., rain, shine), the best outlets were only right half the time; the worst outlets were right 34% of the time—which is as accurate as simply guessing the weather today based on yesterday’s weather. • Nonetheless, you wouldn’t know how good they are without doing the research yourself.