NOAA Grant Curriculum



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

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.

2. Place a low-pressure system in the eastern U.S. near the State of New York.

3. Put a cold front that extends from the Great Lakes to the southwestern U.S.

4. Put a warm front that extends from southeastern U.S. into the Atlantic Ocean.

5. Put a stationary front that extends across the northwest U.S. in front of the high-pressure.

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.

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. [pic] |

| |6. Thermometer | |F. A relatively narrow band of strong wind in the upper levels of the |

| | | |atmosphere. |

| |7. Jet Stream | |G. [pic] |

| |8. Symbol for Stationary Front | |H. The transfer of heat energy from one substance to another substance |

| |9. Conduction | |I. [pic] |

| |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 |

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. Four days

B. Days to Months

C. Six weeks

D. One Month

___ 2. Why are fronts important when talking about weather change?

A. Most weather changes mostly occur along fronts.

B. Fronts have nothing to do with weather change.

C. Fronts indicate when the weather will be warmer.

D. Cold fronts indicate warmer air is replacing cold air

___ 3. In what part of a front do most weather changes occur?

A. In the middle of a front

B. On the side of a front

C. Along the boundary of a front

D. 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

___ 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. Rain

B. Tornado

C. Wind

D. Thunder

___ 9. Which of the following is an effective way for clouds to form?

A. Horizontal winds moving moisture to the east

B. A high pressure air mass remaining in place for several days

C. Winds blowing from land to the ocean

D. 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. Horizontal distribution of temperature

B. North / south distribution of temperature

C. East / west distribution of temperature

D. 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. Air pressure does not change as one goes up a mountain side

B. More air is present, therefore the weight is less

C. Low pressure systems are associated with mountain tops

D. Less air is present, therefore the weight is less

___14. What happens to most of the solar (sun’s) energy that reaches the earth’s surface?

A. It warms the earth surface

B. It cools the earth surface so the surface is not too hot to live on

C. Heating by conduction occurs

D. It is radiated back into the atmosphere to become heat energy

___15. How can heat transfer in the atmosphere cause wind?

A. Raising hot air is replaced by surrounding cooler air

B. Raising cool air is replaced by surrounding warm air

C. Heat transfer can not cause wind, wind is air movement

D. Sinking hot air is replaced by surrounding cooler air

___16. Why are nights cooler when there are no clouds?

A. There are no clouds to trap heat energy from the earth’s surface

B. Clouds trap the heat energy from the earth’s surface leading to warming nights

C. Heat transfer at night causes wind, which changes the temperature

D. Clear and cloudy nights are the same temperature if the daytime temperatures are the same

___17. What can cause clouds to form?

A. Air cools to its dew point

B. Air reaches its saturation point

C. Air with little moisture content

D. A and B

__18. Why does rising warm air become cool?

A. As air rising, air pressure increases cause the air to cool

B. Raising air expands causing it to lose heat

C. Raising air has more moisture content

D. 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. They hold the same amount of water vapor

B. Cold air

C. Warm air

D. Temperature has nothing to do with holding water vapor

__21. What is the greenhouse effect?

A. Heat energy generated by power plants

B. Cloudy night tend to warmer than clear nights

C. Heating effect caused by having an atmosphere

D. Clear nights tent to warmer than cloudy nights

___22. In which season are jet streams the strongest?

A. Fall

B. Spring

C. Summer

D. 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. Particles

B. Molecules

C. Atoms and Molecules

D. Atoms

___ 25. In which of the following ways can heat be transferred?

A. Radiation

B. Conduction

C. Convection

D. All of the above

Making a Rainfall Forecast for One-Day Ahead

Directions

Use your knowledge of probabilities and science concepts to develop day-ahead rainfall forecasts by answering the following questions.

In the following historical data tables, the weather map was observed one day before the rainfall amounts were observed. You will use the data and forecast map to create rainfall forecasts for one-day ahead.

The rainfall data is for Waco Texas.

Data Table 1 Map 1 – Cold Front in Colorado / North Texas

|Observation |Rain |

|1 |0.01 |

|2 |0.00 |

|3 |0.93 |

|4 |0.00 |

|5 |0.00 |

|6 |0.18 |

|7 |0.00 |

|8 |0.00 |

|9 |0.26 |

|10 |0.00 |

[pic]

1. For data table and map 1, what is the probability that it will rain the next day?

Hint: the formula to calculate the probability [pic].

3. What is your forecasted probability for rain tomorrow given data table and map 1?

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 [pic].

Hint: your probabilities for rain plus no rain must sum to 100.

4. What is your forecasted probability that it will not rain tomorrow given data table and map 1?

Data Table 2 Map 2 High pressure over the central Rockies

|Observation |Rain |

|1 |0.00 |

|2 |0.00 |

| |0.00 |

|3 | |

|4 |0.26 |

|5 |0.00 |

|6 |0.00 |

|7 |0.00 |

|8 |0.00 |

|9 |0.00 |

|10 |0.00 |

[pic]

5. For data table and map 2, what is the probability that it will rain the next day?

Hint: the formula to calculate the probability [pic].

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 [pic].

Hint your probabilities for rain plus no rain must sum to 100.

8. What is your forecasted probability that it will not rain tomorrow given data table and map 2?

9. Look at the maps and your calculated probabilities of rain. Which map and data has the highest probability of rain (circle your answer)?

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.

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 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 Temperature | |Maximum Temperature | |

|Year | |Rainfall | |Rainfall |

|1984 |80 |0.00 |76 |0.03 |

|1985 |72 |0.25 |59 |0.00 |

|1986 |74 |0.00 |75 |0.05 |

|1987 |73 |1.41 |75 |0.00 |

|1988 |87 |0.01 |66 |0.00 |

|1989 |72 |0.00 |68 |0.00 |

|1990 |77 |0.00 |71 |0.00 |

|1991 |78 |0.01 |48 |0.31 |

|1992 |73 |0.00 |83 |0.00 |

|1993 |61 |0.00 |59 |0.25 |

|1994 |58 |1.05 |76 |0.00 |

|1995 |79 |0.00 |63 |0.31 |

|1996 |70 |0.18 |75 |0.00 |

|1997 |47 |0.21 |51 |0.00 |

|1998 |59 |0.00 |64 |0.15 |

|1999 |84 |0.00 |63 |0.00 |

|2000 |54 |0.05 |73 |0.00 |

|2001 |66 |2.12 |68 |0.00 |

|2002 |66 |0.00 |73 |0.00 |

|2003 |73 |0.04 |77 |0.00 |

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. |

| |November 15 |March 15 |

|Number of days the maximum temperature was greater than 65 |15 | |

|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 [pic]

3. What is your forecasted probability for temperature greater than 65 degrees 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 [pic].

5. What is your forecasted probability for temperature greater than 65 degrees on March 15?

6. For November 15, what is the probability that it will not rain?

Hint: the formula to calculate the probability [pic].

7. What is your forecasted probability for no rain on November 15?

8. For March 15, what is the probability that it will not rain?

Hint: the formula to calculate the probability [pic].

9. What is your forecasted probability for no rain on November 15?

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

[pic]

11. What is your forecasts probability of temperature greater than 65 degrees and it does not rain for November 15?

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

[pic].

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.

Probabilistic Decision Making –Long-Range Forecasts

Directions

Read the problem statement and use your long-range forecasts to answer the following questions.

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.

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

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

4. Considering only rainfall, which date do you pick to hold P? (Circle your answer)

November 15 March 15

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 March 15

6. Considering both temperature and rainfall, which date do you pick to hold the zoo fieldtrip? (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.

Probabilistic Decision Making –One-Day Ahead Forecasts

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 the zoo. You will only buy a pass at the zoo if it is raining.

|Summary of the Decision – Cost of the Shelter Pass per Person |

| |Weather Conditions at the Zoo |

|Date Pass Bought |Raining |Not Raining |

|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.

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 early if it rains is

[pic]

Expected cost of buying the pass early if no rain

[pic]

Total expected cost = expected if rains + expected if no rain

_____ + ______ = _____

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

[pic]

Expected Cost of buying the pass at the zoo if no rain

[pic]

Total expected cost = expected if rains + expected if no rain

_____ + ______ = _____

5. Why is the expected value different than the actual cost of buying the pass at the zoo?

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?

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?

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.

| |Decision Made before Weather Outcome is Realized with a 40% chance of Rain |

|Weather Outcome |Buy Pass Early |Buy Pass at Zoo |

|Rain | | |

|Sunshine |a | |

Decision Tree

-----------------------

5

Shelter Pass Decision Tree Using Forecast from Map 1

Decision Chance of Rain Outcome

Goal: ____________________________________________

[pic]

Student Packet

Shelter Pass Decision Tree Using Forecast from Map 1

Decision Chance of Rain Outcome

Goal: _____________________________________________

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