Student Packet
5
Probabilistic Decision-Making and Weather Assessment
Use contents of this packet as you feel appropriate. You are free to copy and use any of the material in
this lesson plan.
Packet Contents
Assessment One - Science Concepts
Weather Map
Matching Questions
Multiple Choice Questions
Assessment Two - One-Day Ahead Forecasts
Assessment Three - Long-Range Forecasts
Assessment Four - Probabilistic Decision Making
Probabilistic Decision Making –Long-Range Forecasts
Probabilistic Decision Making –One-Day Ahead Forecasts
Blank Decision Making Tree
Name ___________________________Date______________________Class_______________
Weather Map Symbols
Place the correct symbol on a weather map for the following components of weather for January 25th.
1. Place a high-pressure system over the
northwestern U.S.
4. Put a warm front that extends from
southeastern U.S. into the Atlantic Ocean.
2. Place a low-pressure system in the eastern
U.S. near the State of New York.
5. Put a stationary front that extends across the
northwest U.S. in front of the high-pressure.
3. Put a cold front that extends from the Great
Lakes to the southwestern U.S.
6. Note that it will rain in front of the warm
front.
7. Note that is will snow in front of the cold
front in the Midwest.
Name ___________________________Date______________________Class_______________
Matching Questions
Put the correct letter of the definition in front of the term / phrase.
1. Air Mass
A. Heating caused by having an atmosphere
2. Symbol for Cold Front
B. The weight of air surrounding an object
3. Air Pressure
C. Transfer of heat energy in a fluid
4. Symbol for Warm Front
D. Measures wind speed
5. Convection
E.
6. Thermometer
F. A relatively narrow band of strong wind in the upper
levels of the atmosphere.
7. Jet Stream
G.
8. Symbol for Stationary Front
H. The transfer of heat energy from one substance to
another substance
9. Conduction
I.
10. Source Region
J. Large body of air with uniform temperature
humidity.
11. Rain Gauge
K. Measures air pressure
12. Barometer
L. How most of the energy from the sun reaches the
earth
13. Radiation
M. Instrument used to measure precipitation
14. Greenhouse Effect
N. Measures wind direction
15. Wind Vane
O. Area from which an air mass originates
16. Anemometer
P. Measure the temperature of an object
17. Pressure Gradient
Q. The difference in pressure between a high and low
pressure system
Name ___________________________Date______________________Class_______________
Multiple Choice Questions
Directions: Choose the best answer for the following questions.
___ 1. In any given area, how long can air masses control the weather?
A.
B.
C.
D.
Four days
Days to Months
Six weeks
One Month
___ 2. Why are fronts important when talking about weather change?
A.
B.
C.
D.
Most weather changes mostly occur along fronts.
Fronts have nothing to do with weather change.
Fronts indicate when the weather will be warmer.
Cold fronts indicate warmer air is replacing cold air
___ 3. In what part of a front do most weather changes occur?
A.
B.
C.
D.
In the middle of a front
On the side of a front
Along the boundary of a front
Weather changes do not occur on fronts
___ 4. What is a cold front?
A. Cold air replacing warm air
B. Warm air replacing cold air
C. A front that is not moving
D. A front undercutting another front
___ 5. What is a warm front?
A. Cold air replacing warm air
B. Warm air replacing cold air
C. A front that is not moving
D. A front undercutting another front
___ 6. What is a stationary front?
A. Cold air replacing warm air
B. Warm air replacing cold air
C. A front that is not moving
D. A front undercutting another front
Name ___________________________Date______________________Class_______________
___ 7. What is an occluded front?
A. Cold air replacing warm air
B. Warm air replacing cold air
C. A front that is not moving
D. A front undercutting another front
___ 8. Which of the following is a form of precipitation?
A.
B.
C.
D.
Rain
Tornado
Wind
Thunder
___ 9. Which of the following is an effective way for clouds to form?
A.
B.
C.
D.
Horizontal winds moving moisture to the east
A high pressure air mass remaining in place for several days
Winds blowing from land to the ocean
Forcing air to rise near fronts or low pressure systems
___10. What often determines the type of precipitation (rain, snow, sleet) during the winter?
A.
B.
C.
D.
Horizontal distribution of temperature
North / south distribution of temperature
East / west distribution of temperature
Vertical distribution of temperature
___11. What type of weather is associated with a high-pressure system?
A. Fair weather
B. Stormy weather
C. Change in the weather
___12. What type of weather is associated with a low-pressure system?
A. Fair weather
B. Stormy weather
C. Change in the weather
___13. Why does the air pressure decrease the higher one goes up a mountain side?
A.
B.
C.
D.
Air pressure does not change as one goes up a mountain side
More air is present, therefore the weight is less
Low pressure systems are associated with mountain tops
Less air is present, therefore the weight is less
Name ___________________________Date______________________Class_______________
___14. What happens to most of the solar (sun’s) energy that reaches the earth’s surface?
A.
B.
C.
D.
It warms the earth surface
It cools the earth surface so the surface is not too hot to live on
Heating by conduction occurs
It is radiated back into the atmosphere to become heat energy
___15. How can heat transfer in the atmosphere cause wind?
A.
B.
C.
D.
Raising hot air is replaced by surrounding cooler air
Raising cool air is replaced by surrounding warm air
Heat transfer can not cause wind, wind is air movement
Sinking hot air is replaced by surrounding cooler air
___16. Why are nights cooler when there are no clouds?
A.
B.
C.
D.
There are no clouds to trap heat energy from the earth’s surface
Clouds trap the heat energy from the earth’s surface leading to warming nights
Heat transfer at night causes wind, which changes the temperature
Clear and cloudy nights are the same temperature if the daytime temperatures are the same
___17. What can cause clouds to form?
A.
B.
C.
D.
Air cools to its dew point
Air reaches its saturation point
Air with little moisture content
A and B
__18. Why does rising warm air become cool?
A.
B.
C.
D.
As air rising, air pressure increases cause the air to cool
Raising air expands causing it to lose heat
Raising air has more moisture content
Raising does not cool
__19. Why does sinking air result in fair weather?
A. As air sinks it cools, causing evaporation of clouds
B. Sinking air is not associated with fair weather, but rather stormy weather
C. As air sinks it warms up, causing evaporation of clouds
D. As air sinks it warms up, causing clouds to form
__20. Which holds more water vapor, cold or warm air?
A.
B.
C.
D.
They hold the same amount of water vapor
Cold air
Warm air
Temperature has nothing to do with holding water vapor
Name ___________________________Date______________________Class_______________
__21. What is the greenhouse effect?
A.
B.
C.
D.
Heat energy generated by power plants
Cloudy night tend to warmer than clear nights
Heating effect caused by having an atmosphere
Clear nights tent to warmer than cloudy nights
___22. In which season are jet streams the strongest?
A.
B.
C.
D.
Fall
Spring
Summer
Winter
___23. In what general direction do the winds blow in a jet stream?
A. North to South
B. South to North
C. East to West
D. West to East
___24. What makes up the air we breathe?
A.
B.
C.
D.
Particles
Molecules
Atoms and Molecules
Atoms
___ 25. In which of the following ways can heat be transferred?
A.
B.
C.
D.
Radiation
Conduction
Convection
All of the above
Name ___________________________Date______________________Class_______________
Making a Rainfall Forecast for One-Day Ahead
rainfall amounts were observed. You will use
the data and forecast map to create rainfall
forecasts for one-day ahead.
Directions
Use your knowledge of probabilities and science
concepts to develop day-ahead rainfall forecasts
by answering the following questions.
The rainfall data is for Waco Texas.
In the following historical data tables, the
weather map was observed one day before the
Map 1 – Cold Front in Colorado / North Texas
Data Table 1
Observation
1
2
3
4
5
6
7
8
9
10
Rain
0.01
0.00
0.93
0.00
0.00
0.18
0.00
0.00
0.26
0.00
1. For data table and map 1, what is the
probability that it will rain the next day?
2. For data table and map 1, what is the
probability that it will not rain the next day?
Hint: the formula to calculate the probability
Hint: the formula to calculate the probability
number of days it rained
=
× 100 .
total number of days
=
number of days it did not rained
× 100 .
total number of days
Hint: your probabilities for rain plus no rain
must sum to 100.
3. What is your forecasted probability for rain
tomorrow given data table and map 1?
4. What is your forecasted probability that it
will not rain tomorrow given data table and
map 1?
Name ___________________________Date______________________Class_______________
Data Table 2
Observation
1
2
3
4
5
6
7
8
9
10
Map 2 High pressure over the central Rockies
Rain
0.00
0.00
0.00
0.26
0.00
0.00
0.00
0.00
0.00
0.00
5. For data table and map 2, what is the
probability that it will rain the next day?
8. What is your forecasted probability that it
will not rain tomorrow given data table and
map 2?
Hint: the formula to calculate the probability
=
number of days it rained
× 100 .
total number of days
9. Look at the maps and your calculated
probabilities of rain. Which map and data
has the highest probability of rain (circle
your answer)?
6. What is your forecasted probability for rain
tomorrow given data table and map 2?
7. For data table and map 2, what is the
probability that it will not rain the next day?
Hint: the formula to calculate the probability
=
number of days it did not rained
× 100 .
total number of days
Hint your probabilities for rain plus no rain
must sum to 100.
Map 1
Map 2
10. Use your knowledge of weather and your
Weatherman’s Backpack to explain why the
map you circled in question 5 has a higher
probability than the other map.
Name ___________________________Date______________________Class_______________
Making a Long-Range Forecast
Directions
Once the forecast is for approximately 7-14 days
into the future, current weather maps provide
little information for meteorologists to develop
forecasts. This is because of the uncertainty in
the ocean and atmosphere system. The use of
historical weather data for a particular day is the
Year
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
best way to create long-range weather forecasts.
Using the following temperature and rainfall
data for November 15 and March 15, answer the
following questions. In answering the questions,
you will create long-range forecasts.
Use the data table to answer question 1. Use the
data summary table to answer questions 2-10.
Historical Weather Data for Waco, TX
November 15
March 15
Maximum
Maximum
Temperature
Rainfall
Temperature
Rainfall
80
0.00
76
0.03
72
0.25
59
0.00
74
0.00
75
0.05
73
1.41
75
0.00
87
0.01
66
0.00
72
0.00
68
0.00
77
0.00
71
0.00
78
0.01
48
0.31
73
0.00
83
0.00
61
0.00
59
0.25
58
1.05
76
0.00
79
0.00
63
0.31
70
0.18
75
0.00
47
0.21
51
0.00
59
0.00
64
0.15
84
0.00
63
0.00
54
0.05
73
0.00
66
2.12
68
0.00
66
0.00
73
0.00
73
0.04
77
0.00
Name ___________________________Date______________________Class_______________
1. Fill in the following data summary table by counting the number of days in the Waco data table that
meet the statement. The first blank is filled in for you as an example.
Data Summary Table for Waco Texas.
Number of days the maximum temperature was greater than 65
Number of days with no rainfall
Number of days the maximum temperature was greater than 65 and
there was no rainfall – be sure the day meets both criteria
Total number (observations)
2. For November 15, what is the probability
that maximum temperature is higher than 65
degrees Fahrenheit?
Hint: the formula to calculate the probability
number of days temperature was greater than 65
=
× 100
total number of days
November 15
15
March 15
6. For November 15, what is the probability
that it will not rain?
Hint: the formula to calculate the probability
=
number of days without rainfall
× 100 .
total number of days
3. What is your forecasted probability for
temperature greater than 65 degrees on
November 15?
7. What is your forecasted probability for no
rain on November 15?
4. For March 15, what is the probability that
maximum temperature is higher than 65
degrees Fahrenheit?
Hint: the formula to calculate the probability
8. For March 15, what is the probability that it
will not rain?
Hint: the formula to calculate the probability
number of days temperature was greater than 65
=
× 100
total number of days
=
number of days without rainfall
× 100 .
total number of days
.
5. What is your forecasted probability for
temperature greater than 65 degrees on
March 15?
9. What is your forecasted probability for no
rain on November 15?
Name ___________________________Date______________________Class_______________
10. For November 15, what is the probability
that temperature is greater than 65 degrees
and it does not rain?
Hint: the formula to calculate the probability
=
number of days temperature > 65 and no rain
×100
total number of days
12. For March 15, what is the probability that
temperature is greater than 65 degrees and it
does not rain? Hint: the formula to
calculate the probability
=
number of days temperature > 65 and no rain
×100
total number of days
.
11. What is your forecasts probability of
temperature greater than 65 degrees and it
does not rain for November 15?
13. What is your forecasts probability of
temperature greater than 65 degrees and it
does not rain for November 15?
13. Provide a reason for the difference in the
short-range and long-range forecasting
procedure. Hint: think about the first
section.
Name ___________________________Date______________________Class_______________
Probabilistic Decision Making –Long-Range Forecasts
4. Considering only rainfall, which date do you
pick to hold P? (Circle your answer)
Directions
Read the problem statement and use your longrange forecasts to answer the following
questions.
November 15
March 15
Problem Statment
Today’s date is August 25 and you must get the
date for your fieldtrip to the zoo on the school
calendar. The school has given you the choice
of November 15 or March 15 to have your zoo
fieldtrip. Past experience suggests the students
have the most fun at the zoo if the maximum
temperature exceeds 65 degrees Fahrenheit and
it does not rain.
5. Which date November 15 or March 15 has
the highest probability of maximum
temperature
exceeding
65
degrees
Fahrenheit and no rainfall? (Circle your
answer)
November 15
1. Which date November 15 or March 15 has
the highest probability of maximum
temperature
exceeding
65
degrees
Fahrenheit? (Circle your answer)
November 15
March 15
6. Considering both temperature and rainfall,
which date do you pick to hold the zoo
fieldtrip? (Circle your answer)
March 15
November 15
March 15
2. Considering only temperature, which date
do you pick to hold the zoo fieldtrip?
(Circle your answer)
November 15
March 15
3. Which date November 15 or March 15 has
the highest probability of no rainfall?
(Circle your answer)
November 15
March 15
Congratulations, you have just learned
another way of using probabilities to make
decisions. That is, you choose the decision
that either minimizes or maximizes the
probability of an event occurring. Another
example would be getting a newly developed
vaccine for a disease. There is some risk
associated with all vaccines and there are
obvious risks associated with getting sick with
the disease. Your decision is to get the new
vaccine or not. Your goal would be to
minimize the risk of getting sick. You would
choose the decision that minimized the
probability of getting sick.
Name ___________________________Date______________________Class_______________
Probabilistic Decision Making –One-Day Ahead Forecasts
the zoo. You will only buy a pass at the zoo if it
is raining.
Directions
Read the problem statement.
Use your
knowledge of decision-trees, probabilities,
expected values, and your one-day ahead
forecasts to answer the following questions.
Problem Statement
It is now one day before the zoo fieldtrip. You
now need to make a decision on if you should
buy a shelter pass or wait and buy the pass at the
zoo. A shelter pass allows you to eat under a
cover. If it is raining, you want to eat under the
shelter. If it is not raining, you will not need the
shelter. If you buy the pass today, it costs $1 per
person. Regardless of whether it rains or not,
the pass cost is nonrefundable. The cost of the
pass is $2 per person if you wait until you are at
Summary of the Decision – Cost of the
Shelter Pass per Person
Weather Conditions at the Zoo
Date Pass
Raining
Not Raining
Bought
Early
1
1
At zoo
2
0
1. Using your one-day ahead forecasts from
data table and map 1, develop the decision
tree for this shelter pass problem, assuming
your objective is to minimize the cost of
buying the pass. Hints: the probabilities are
from your forecasts, the outcomes are the
costs, and the decision is to buy the pass
today or wait until you are at the zoo.
Shelter Pass Decision Tree Using Forecast from Map 1
Decision
Chance of Rain
Goal: ____________________________________________
Outcome
Name ___________________________Date______________________Class_______________
2. Calculate the expected value for the decision
to buy the pass early using the following
equations.
Hint: the equations are very similar to those
used earlier, only changed to fit the problem.
Expected Cost of buying the pass at the zoo if no
rain
______%chanceof no rain x ______cost of thepass
=
100
100
Expected cost of buying the pass early if it rains
is
______%chanceof rain x ______cost of thepass
=
 ____
100
100
Total expected cost = expected if rains +
expected if no rain
_____ + ______ = _____
Expected cost of buying the pass early if no rain
______%chanceof no rain x ______cost of thepass
=
 ____
100
100
5. Why is the expected value different than the
actual cost of buying the pass at the zoo?
Total expected cost = expected if rains +
expected if no rain
_____ + ______ = _____
6. Given your objective to minimize expected
costs of the shelter pass, which decision do
you make, buy the pass early or wait and
buy the pass at the zoo?
3. Why is the expected value the same as the
cost of buying the pass early?
4. Calculate the expected value for the decision
to buy the pass at the zoo using the
following equations.
Expected Cost of buying the pass at the zoo if it
rains is
______%chanceof rain x ______cost of thepass
=
 ____
100
100
7. Given the low cost of buying the shelter pass
early, remember it only costs $1 per person,
why is this an important problem for your
school zoo fieldtrip? Hint: how many
people would go on such a fieldtrip?

____
Name ___________________________Date______________________Class_______________
8. Fill in the following table for the forecast
data table and map 1 forecast of rain
information in questions 1 -7, using the
letters given for the answers. One box is
completed for you.
a) Poor decision – expected value did not
support making this decision, weather
outcome resulted no need for the pass.
b) Good decision – expected value
supported making this decision, weather
outcome resulted no need for the pass.
c) Poor decision – expected value did not
support making this decision, however
weather outcome resulted in a need for the
pass.
d) Good decision – expected value
supported making this decision, weather
outcome resulted in a need for the pass.
Weather Outcome
Rain
Sunshine
Decision Made before Weather Outcome is Realized with a 40%
chance of Rain
Buy Pass Early
Buy Pass at Zoo
a
Name ___________________________Date______________________Class_______________
Decision Tree
Shelter Pass Decision Tree Using Forecast from Map 1
Decision
Chance of Rain
Goal: _____________________________________________
Outcome