Functions in the Real World We’re now going to explore one of the countless areas in which scientists use functions, their graphs and their equations, to model data and make predictions that impact our lives in a significant way every day. Photo from Tropical Storm Allison Recovery Project

Diffusion in the Environment The area we are going to focus on is diffusion and its effects on the environment. Since these are numerous and far reaching, we need to limit our investigation further. What we’ll be concentrating on is diffusion’s impact on water quality when it rains – no - not just when it rains, but when it FLOODS! Photo from Tropical Storm Allison Recovery Project

Diffusion Let’s begin with some definitions, so everyone will understand exactly what is meant by the particular terms that we’ll be using. Diffusion is defined as the process where molecules move from a high concentration to a low concentration. Diffusion simulation Diffusion simulationDiffusion simulation For example, spray a squirt of cologne in a room. There will be a strong scent where you sprayed it, but it will diffuse and become a weaker scent as it moves from the area where it was first sprayed until it is the same concentration throughout the room. This movement of molecules in order to maintain an equilibrium is known as homeostasis.

Diffusion in Water Following a rain, runoff occurs. Runoff is water from rainfall which is not absorbed by the soil as it flows downhill, where it eventually drains into the local drainage system and ultimately into a creek, bayou, stream, river or other body of water. Photo from Tropical Storm Allison Recovery Project

Diffusion in Water Continued As the water flows downhill, it picks up insoluble material. This is material that will not dissolve in the water. Topsoil is an example. Even things like decomposing animals or oil that has spilled or leaked onto streets and highways can become part of the runoff. The runoff can also pick up contaminants like toxic chemical fertilizers and pesticides. The runoff can also pick up contaminants like toxic chemical fertilizers and pesticides. Photo from Tropical Storm Allison Recovery Project

Diffusion in Water Continued These contaminants may create serious water quality problems because they will diffuse, allowing the harmful substances to pollute all the bodies of water the runoff empties into as it flows. Photo from Allison Tropical Storm Allison Recovery Project

Significance of Diffusion in Runoff Therefore, it is extremely important to be able to predict the amount of runoff a particular area will experience during a storm, for this can help in the prevention of major water pollution problems. Therefore, it is extremely important to be able to predict the amount of runoff a particular area will experience during a storm, for this can help in the prevention of major water pollution problems. This is especially true in flood prone regions where high levels of contaminants exist. This is especially true in flood prone regions where high levels of contaminants exist. Photo from Tropical Storm Allison Recovery Project

Watersheds A watershed is the total of all the land area and smaller bodies of water whose rainfall ultimately drains into a specific body of water. Example: The total region of land, creeks and streams whose runoff flows into the Colorado River is called The Colorado River Watershed

Watersheds continued Later in our study, we will use a computer model to examine the amount of runoff in various watersheds in Harris County, Texas following Tropical Storm Allison which hit the Houston area June 5-9, Later in our study, we will use a computer model to examine the amount of runoff in various watersheds in Harris County, Texas following Tropical Storm Allison which hit the Houston area June 5-9, But before we can do that, we need some more information. But before we can do that, we need some more information.

Assignment Part I Go to Surface Water Runoff and click on Background Science. Go to Surface Water Runoff and click on Background Science.Surface Water RunoffSurface Water Runoff Read: Read: “Why is it important to model runoff water?” “Why is it important to model runoff water?” “How is surface water runoff determined?” “How is surface water runoff determined?” “What is a hydrologic soil group?”. “What is a hydrologic soil group?”. Answer the Part I questions given on the next slide on your own paper. When you have completed Part II of the assignment, you will turn in your work to your teacher. You may also choose to use Word to complete your assignment and your work to your teacher. Answer the Part I questions given on the next slide on your own paper. When you have completed Part II of the assignment, you will turn in your work to your teacher. You may also choose to use Word to complete your assignment and your work to your teacher.

Questions Part I 1. How does the addition of fertilizers affect the entire ecosystem of a body of water? 1. How does the addition of fertilizers affect the entire ecosystem of a body of water? 2. What is currently the most appropriate and authentic numerical model in use by soil scientists? 2. What is currently the most appropriate and authentic numerical model in use by soil scientists? 3. In the graph on Runoff Curves, 3. In the graph on Runoff Curves, a. Which axis is the independent variable and what does it represent? a. Which axis is the independent variable and what does it represent? b. Which axis is the dependent variable and what does it represent? b. Which axis is the dependent variable and what does it represent?

Questions Part I continued 4. What is a predictive model? 4. What is a predictive model? 5. The runoff curve number depends on what four factors? 5. The runoff curve number depends on what four factors? 6. How are soil groups classified? 6. How are soil groups classified? 7. Describe the four soil groups. 7. Describe the four soil groups. Tropical Storm Allison Recovery Project

Questions Part II Go to Surface Water Runoff and click on Mathematics. Read through this section. Go to Surface Water Runoff and click on Mathematics. Read through this section.Surface Water RunoffSurface Water Runoff Then answer the following questions on the same page as the responses to Questions Part I. Then answer the following questions on the same page as the responses to Questions Part I. Turn the completed assignment in to your teacher. Turn the completed assignment in to your teacher.

Questions Part II 1. Give the equation used to calculate runoff and identify each variable. 1. Give the equation used to calculate runoff and identify each variable. 2. Define initial abstraction and infiltration of the variables. 2. Define initial abstraction and infiltration of the variables. 3. What is the runoff curve number (CN) and its range of values? 3. What is the runoff curve number (CN) and its range of values? 4. Which equation that was specifically formulated through the use of data compiled from the study of many small watersheds? 4. Which equation that was specifically formulated through the use of data compiled from the study of many small watersheds?

Assignment Part II Continued  5. Fill in the missing step. a. b. ? ? ? ? ? ? ? ? ? ? ? c.

Questions Part II Continued 6. In the equation given above, 6. In the equation given above, a. Name the type of function. a. Name the type of function. b. Write the function in functional notation. b. Write the function in functional notation. c. Identify the independent variable. c. Identify the independent variable. d. Identify the dependent variable. d. Identify the dependent variable. e. What would be a reasonable domain? e. What would be a reasonable domain? f. What would be a reasonable range? f. What would be a reasonable range?