Homework #5
Due Friday November 17, 2000
The following table shows seven-day forecasts made by the local TV stations on November 2 for the following week. Each station forecasted the day’s high temperature, low temperature, and the chance for precipitation. The final column shows what actually occurred at Will Rogers Airport.
|
|
|
KFOR-4 |
KOCO-5 |
KWTV-9 |
actual |
|
Day 1 |
High |
68 |
68 |
66 |
73 |
|
(11/2) |
Low |
46 |
46 |
49 |
46 |
|
|
Precip |
0 |
0 |
0 |
0 |
|
Day 2 |
High |
59 |
56 |
58 |
58 |
|
(11/3) |
Low |
46 |
48 |
48 |
51 |
|
|
Precip |
30% |
30% |
0 |
0.38" |
|
Day 3 |
High |
60 |
59 |
60 |
55 |
|
(11/4) |
Low |
45 |
46 |
48 |
51 |
|
|
Precip |
40% |
chance |
20% |
0.01" |
|
Day 4 |
High |
60 |
61 |
66 |
62 |
|
(11/5) |
Low |
49 |
49 |
52 |
55 |
|
|
Precip |
80% |
chance |
40% |
0.01" |
|
Day 5 |
High |
62 |
62 |
48 |
59 |
|
(11/6) |
Low |
50 |
49 |
42 |
38 |
|
|
Precip |
40% |
chance |
30% |
0.35" |
|
Day 6 |
High |
53 |
52 |
46 |
38 |
|
(11/7) |
Low |
39 |
41 |
32 |
34 |
|
|
Precip |
20% |
0 |
0 |
0.06" |
|
Day 7 |
High |
51 |
53 |
53 |
36 |
|
(11/8) |
Low |
35 |
36 |
30 |
31 |
|
|
Precip |
20% |
0 |
0 |
0.72" |
In order to determine how well a forecast performs, meteorologists look at error. The error is the forecast minus the observation. So Channel 4’s error for the high on Day 1 would be 68-73 = -5 or 5 degrees cooler than the actual temperature. The closer the error is to zero, the better the forecast.
To find out how each station performed for the week’s highs, we look at the Mean Absolute Error. For each station, find the error by comparing it to the day’s actual high. Then drop any negative signs that the error has (take the absolute value). Add all the week’s absolute error values for each station. The divide each sum by 7. The lowest score indicates the best forecasts for the week. Which station had the lowest score for the high temperatures?
Now, do the same thing for the low temperatures. Which station had the lowest error score for the lows?
How well did the stations do when forecasting precipitation on Day 1? How well did they do on Day 2?
Were the forecasts for each station better on Day 1 or Day 7? Why do you think that the accuracy of the forecasts changed over time?