Learning Scenario - Pan Water Cycle (Vensim)

Basic Model:

Description

This is a system model of the different physical processes that water can go through. The model consists of a pan and water. It tracks the percentage of water that is in the pan, on the cover of the pan, and in the air around the pan. The percentages fluctuate due to the physical processes of evaporation, condensation, and precipitation. Parameters in the model - the physical processes mentioned earlier - determine the percentage of water at each location over time. When the model is run a graph is produced depicting the change in percentage of water at each location over the progression of the pan water cycle.

Background Information

The water cycle is a topic that students encounter in all different levels of science classes. This model focuses on the chemistry and physics aspects. The model of the Pan Water Cycle is a subset of an SIR or disease model. An initial amount of water works its way through different states of water through precipitation, evaporation, and condensation. Depending on the temperature and constant values, the amount of water on different parts of the pan changes. This disease type of model is helpful to try and understand how different variables of disease interact with each other. In this case, it shows how water due to physical processes changes. In a larger view of these types of models, a vital part of these efforts involve the use of computational models that make quantitative predictions about how the disease will spread, based on measured data and scientific understanding of the biological and systematic processes involved. This model can be used to learn about these processes and how they interact to determine the affect of temperature on physical processes of water changes.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. At the beginning of the simulation there is a total population of water with water in the air, water on the cover, and water in the pan each being a separate value that you can adjust. After each time step you have the same total population, but the make up of the total population is different. You can look at the three types of water (cover, air, and pan water) and apply the fundamental principle to it. For example, for the water in pan, the new population of water in pan (HAVE) is equal to the old population of water in pan (HAD) plus the percentage of water on the cover that precipitated (CHANGE). With each time step, the following things happen:

1. Water in pan becomes water in air due to evaporation according to the player-set variable entitled spreading probability: evaporation - condensation - water vapor leak
2. Water in air becomes water on cover due to condensation: condensation - precipitation - water vapor leak
3. Water on cover becomes water in pan due to precipitation: precipitation - evaporation - water vapor leak
4. The water temperature is set to 100.
5. The amount of evaporation per degree is set to 0.05.
6. K1 is set to .5
7. K2 is set to .5
8. Total population is determined by the summation of all sub categories of the population: Total population = Water in pan + water in air + water on cover

Teaching Strategies

An effective way of introducing this model is to ask students to brainstorm the physical processes in which water can undergo and what that looks like. You can further challenge them to brainstorm other ideas that resemble this such as the change of physical states of water. Focusing specifically on water, students should be encouraged to discuss other factors that may impact the water cycle such as the total population itself, location of the population, or facts introduced to the population. Guiding questions may include:

1. How does water undergo physical processes? What does that look like?
2. What are the different states of water?
3. What are other variables that affect condensation, evaporation, and precipitation besides temperature?
4. How can we prevent these physical processes from occurring?

Implementation:

How to use the Model

This is a relatively simple system model with just a few parameters that can be changed. The important parameters are as follows:

1. The three different water parameters determine the number of each type of water location placed on the board at the start of the simulation.
2. The "water temperature" and "amount of evaporation per degree" parameters determine the system temperature and the percentage of water that will evaporate based upon that temperature respectively.

All of the aforementioned parameters are manipulated by clicking and dragging their respective sliders. The maximum, minimum, and step values for each parameter are pre-set. Any changes made to the sliders take effect immediately with the exception of the initial values, which take effect the next time the simulation is run. To run the simulation, click the "Run a Simulation" button. The results from the simulation are displayed immediately in graphical form. Below the model, a graph will depict the populations of pan, cover, and air water, as well as the total population. The graph allows for visual and quantitative analysis of how the population changes with the spread of the water. For more information on Vensim, reference the Vensim tutorial at: http://shodor.org/tutorials/VensimIntroduction/Preliminaries.

Learning Objectives:

1. Understand the relationship between condensation, precipitation, and evaporation
2. Understand the effect of each parameter on the populations over time

Objective 1

To accomplish this objective, have students run the simulation with the default parameters and observe the graph. They should specifically pay attention to how the populations fluctuate or change over time. Guiding questions may include:

1. From your observations, what happens to the numbers of cover water as time progresses? Air water? Pan water?
2. Do you notice any patterns between the three populations? Is so, what types of patterns are they?
3. What do you think would happen if you had more cover water to start off the simulation? Air water? Pan water?

Ask students to change the initial numbers of cover water, pan water, and then air water (one at a time). Do the answers to any of these questions change? Students should compare the hypotheses they made earlier to the results now and discuss any differences.

Objective 2

To accomplish this objective, have students change the parameters to see how they affect the graph. Students can do this by clicking and dragging on the parameter buttons on the model. Encourage the students to choose one parameter at a time at first. Guiding questions may include:

1. What changes do you notice in the graph if you change the initial numbers of water in pan? Are there any long-term behavior changes or does the graph look similar?
2. Which parameter causes the water on cover to develop the quickest? Is it a mixture of temperature and total water?
3. Can you cause the entire population to become air water? Why or why not? If you can, how can you accomplish that?
4. Can you create a constant population, or will they continue to change? Why or why not?

Extensions:

1. Explore the use of models for predicting outcomes before they occur
2. Think about the qualities this model still lacks when compared with the real world
3. Build a more complex model based off of Extension 2

Extension 1

Encourage the students to discuss the uses of disease models, such as the pan water cycle, in preparing for epidemics. Guiding questions can include:

1. How could you use a model similar to this to determine how to prevent the condensation of water, or more generally, a disease? What are some reasons why we may want to use a model for this?
2. How can this model be manipulated to represent different ideas, physical processes, or diseases?
3. What other types of situations could you use this model for? How would you change this one for those situations? How would the model be helpful for investigating those situations?

Extension 2

Have students consider the ways in which this model is accurate and then compare those to the ways it is inaccurate. Guiding questions can include:

1. What are the basic or main parts of a system where water undergoes physical processes? Does this model accurately include those parts? Why or why not?
2. Can you think of any factors in the real world that are left out of this model? What are some examples? How would you incorporate them into the model?
3. In the real world, models such as this one do not produce perfectly smooth curves like we see in our model's graph. What are some reasons why smooth curves would not exist? Explain how they would affect the curves.

Extension 3

Have students investigate Extension 2 question 2 by reviewing the Vensim tutorial found here: http://shodor.org/tutorials/VensimIntroduction/Preliminaries

1. How did the graphs change from when you ran the default model to your improved model?
2. Did the graphs change the way you expected? If not, how did it compare to your hypothesis?
3. What factors did you include and how did you include them?

Related Models

Disease Epidemic Model

This is the agent model version of a Vensim disease model created in NetLogo. It follows the same idea, but models a sickness with many more variables. This model also contains a graph showing the number of people who are healthy, sick, immune, and dead. Students can compare disease in this model to the rumors in the Vensim model. Students should discuss the pros and cons of this model as a way to predict the spread of disease in comparison to the Vensim model.

Supplemental Materials:

• Agent Modeling Discussion

Spread of Disease Model

This is a simpler agent model of disease spread that focuses on the longevity of the disease. This model is unique because the agents do not gain permanent immunity to the disease after they recover. Students should discuss the affect this has on the spread of disease and how this changes the methods used to prevent the disease.