Sonya KuokkanenBeverly MacLeodLaura RobinsonProject 2

Contour Lines: IntroductionObjective: By the end of this lesson the students should understand what a contour line is and how to use it.

Methodology:

1. What is a Contour? Define as a line that connects similar data points or intervals.

Give the following example: For intervals of ten units, this example has four contour lines.

70 85 63 73 82 90

65 79 76 82 95 62 71 81

2. Explain that contour lines never intersect other contour lines. Give the following example:

70 85 63 73 82 90

79 66 67 82 95 62 71 64 81

3. Give Worksheet #1. Point out that each problem has different intervals and remind them not to cross their lines.

4. Brainstorm areas where this type of map can be applied. Show and discuss different maps. Develop a word bank that can be used to describe these uses.

5. Give Worksheet #2. Have students use the word bank to help them describe what type of data the map is illustrating. Also have them try to work out the intervals being used.

Further Study of Contours:Lesson Plan: Weather and the Contours Associated With ItLesson Plan: Making Contours for Middle SchoolLesson Plan: Contours and Water BasinsLesson Plan: Military Uses For Contours

Worksheet 1: Determining contour lines based on intervals

Draw the contour lines by the given interval

1. Interval 15 units ( 0 –15, 16 –30 ,etc) 100 55 70 63 74

114 60 75 31 58

90 44 110 87 48 76 40 80 50

2. Interval 50 units ( 0 –50, 51 –100 ,etc)

52 50 105 64

100 48 90 110 120 125 73 80 30

3. Interval 125 units ( 0 –125, 126 –250 ,etc)

78 160 230 165

160 147 256 63 182

285 300 150 50 200 10

4. Interval 25 units ( 0 –25, 26 –50 ,etc)

132 165

145 150 200

100 55 170 90 62 153 56 95 43 73 162

Worksheet 2: What information is the map describing?

1.

2.

3.

4.

Lesson Plan: Weather and the Contours Associated With It

Objectives: To continue to explore contours and how they are use in real life applications.To explore the math associated with weather contours.

Overview: There are a number of contours associated with weather. In the following lesson (which is designed to be taught over approximately 2 84-minute block periods, but can be expanded to cover more time due to the vast amount of information available on this topic) students will explore, in detail, three of these contours. The three contours of choice will be the contours associated with pressure (isobars), temperature (isotherms), and precipitation accumulation (isohyets). Students will learn to map the contours for each type of data and then explore the conclusions they might draw from looking at contour maps for each type. It is anticipated that student curiosity will be piqued about associated topics and a natural extension for this lesson will be individual or small group projects in which they can research and present answers to questions that came up during the lesson.

Grade Level: 7-10

The Lesson

Discussion: What are weather contours? As was discussed earlier, contours are lines of equal values and weather contours show equal values of whatever parameter you are studying. The general term for weather contours is isopleth (Greek, iso – equal; pleth – value). The following table shows 12 common isopleths:

  Isobar PressureIsotherm TemperatureIsotach Wind SpeedIsogon Wind DirectionIsoshear Wind ShearIsodrosotherm Dew pointIsohyet Precipitation AccumulationIsohaline SalinityIsopycnic DensityIsohume HumidityIsoneph CloudinessIsohel Sunshine

We will be focusing in on isobars, isotherms, and isohyets, but before we start, let’s figure out why and how weather contour maps are useful.To understand atmospheric and oceanic circulations, you must be able to understand how variables (temperature, pressure, winds, humidity, clouds, salinity) are changing in time and how they are changing with respect to one another.  The weather map is a tool that aids this understanding. Various kinds of maps, or charts, are used to graphically depict these variables. A good map allows you to quickly  identify patterns. For example, a weather map of forecasted high temperatures typically available in newspapers indicates the location of warm and cold regions of the country. From these maps you can quickly gage the predicted high temperature for your town.

Maps depicting weather and ocean conditions are drawn based on simultaneous observations made at many places throughout the world. Accurate portrayal of these observations is the key to a correct interpretation of the data.  Meteorologists and oceanographers use a technique called contour analysis to visually explain the information the data is providing.  Contouring data represents an elementary step in data analysis.  Ability to correctly and confidently analyze data is critical to interpreting conditions.  For example, contouring is vital in:

1. finding the location of atmospheric and oceanic fronts, 2. locating potential regions of severe thunderstorms, 3. tracking hurricanes, 4. tracking the movement of pollutants. 5. tracing water movement in the oceans

These are just a few of they many ways that contours are used. As you explore isobars, isotherms, and isohyets, you’ll be discovering some of these.

IsobarsAn isobar is a line connecting locations of equal barometric pressure. Isobar maps show where pressures are relatively high and low, and show us where pressure changes are gradual or dramatic over a distance.

At the right is an example of a map of the US with the isobar contours drawn. The thick black lines are the isobars. They are typically placed at intervals of 4 millibars, the standard unit of measurement for atmospheric pressure used by the National Weather Service. One millibar is equivalent to 100 newtons per square meter. Standard surface pressure is 1,013.2 millibars.

(A newton is the unit of force giving a mass of about one kilogram (2.205 pounds) an acceleration of about one meter (1 yard) per second per second. )

It may be helpful for you to think of isobars like a topographic contour map.  On a contour map, higher values denote higher ground--it is just the same with pressure maps and temperature maps--the higher values represent higher pressures.

Some useful knowledge we can obtain from isobar maps:

The wind tends to flow parallel to the isobars with lowest pressures always to the LEFT.  You can also think of this in terms of high and low pressure centers:  the wind flows in a clockwise circulation around areas of high pressure, and in a counterclockwise circulation around areas of low pressure.

 

   

Wind speed is also a reflection of isobaric spacing. Isobars should be more or less be parallel to each other. How close or how far away they are can be correlated to the wind speed. The spacing of isobars is inversely proportional to the wind speed. In other words, the greater the wind speed, the smaller the spacing and vice versa. Isobars are spaced closer together in areas where the wind is strong and further apart where the wind is light. Wind information is of great importance to successful and accurate isobaric analysis. We can also think of this in terms of “flow.” Water flows from higher to lower regions, and flows at a faster rate down a steeper slope.  The same is true for the air--it could be said to "flow" at a faster rate "down" a steeper pressure slope.  Simply put, the closer the spacing of the isobars, the faster the wind will flow.

SO:  now, by looking at a map containing only isobars, you should be able to say a lot about the speed and direction of the wind!

IsothermsAn isotherm is a line connecting locations with equal temperatures. Isotherm maps show where temperatures are relatively high or low, and also where temperature changes are gradual or dramatic over a distance.

Looking a an isotherm map can help answer question such as, “What is the outdoor temperature? What clothes should we wear? What is the weather, including temperature, going to be? Should we go ahead with our planned outdoor activity? Should we make that trip today? Is it warmer or colder in other parts of the country?”

The map at the right shows an example of a weather map containing 60° and 70° isotherms. The large black lines are called isotherms. They are typically placed at intervals of 10 degrees Fahrenheit.

Isotherm maps are used for more than just to plan the day’s events. Temperature patterns (increasing or decreasing at various rates) indicate the movement of fronts into or from an area. Temperature patterns can help with predictions of weather types.

The contours associated with thermal advection (the horizontal transfer of heat in the atmosphere by the movement of air) are indicators of warm or cold air being moved slowly or quickly by the wind. This movement is an indication that weather systems are moving in a particular direction and at a particular speed.

Temperature also affects the type of precipitation an area will be receiving. The precipitation type can be estimated by surface temperatures: temperatures below 32 degrees most likely represents snow while temperatures above 32 degrees most likely represents rain. Temperatures that are fluctuating in this vicinity can produce some dangerous traveling situations.

Additionally, scientists track regional and global temperatures for a variety of reasons. For instance, global temperature gradients are directly related to global wind circulation. To keep long term temperatures stable, there must be an efficient transfer of heat from the regions with surplus heat to the regions with deficit. This global heat transfer is the cause of most of our weather. It is important to know how temperature patterns are changing.

IsohyetsIsohyets are lines of equal intensities drawn through geographic locations on a topographic map. Just as a contour line represents equal elevations on a topographic map, isohyets represent equal intensities of rainfall. Isohyets can be draw to represent rainfall for a particular storm or over a short period of time or they can be used to indicate rainfall amounts over a longer period of time, for instance, annual rainfall. It is important to indicate the period of time over which the rainfall is being recorded. For instance, when listening to a weather report, you may hear how much precipitation has fallen in a specified period of time, quite often the last 24 hours. This is the total amount of rain that fell. If it is stated that the total amount of rain that fell in the last 24 hours is 2 inches, you have no idea what the intensity, or rate of rainfall was. Did the rain fall evenly for 24 hours; in which case the rate would be approximately 0.083 in/hr (2 inches divided by 24 hours), or did the entire amount of rain fall in 30 minutes; in which case the intensity is 4 in/hr (2 inches divided by 0.5 hours). As you can see, the rate can make a big difference. In the first case, there was a nice, gentle rain, while in the second case, there was a real "gully washer." The gentle rain would cause little, if any, flooding; the heavy rain would probably cause severe ponding and flooding in some locations.

What follows are two maps of isohyets. Both maps represent annual rainfalls and both are color-coded. The contours are still the lines between each of the differently colored areas and so represents a boundary of equal rainfall.

Critical precipitation boundaries in Midcontinent North America: the 40, 20 and 12 inch (approximately 250, 500 and 1000mm) isohyets. These isohyets correspond closely with three critical climate and ecosystem boundaries covered in this case: a) the forest/tallgrass prairie boundary, b) tallgrass prairie/shortgrass prairie boundary, and c) the shortgrass prairie or steppe/desert boundary.

The second map (above) was taken from a document regarding runoff from rainfall. Runoff can be a huge problem. For example, it carries debris into water sources (physical debris and pollutants) and erodes valuable land. Runoff is just one of the reasons that rainfall is studied. Precipitation also directly affects groundwater recharge and the water supply available to plants. Precipitation also causes wash-outs from the atmosphere and, as “infiltration water,” is the medium for transport of pollutants into the ground. Isohyetal maps are extremely important to people studying these problems as well as other problems such as flooding and desertification.

Activity: Drawing Weather Contours1. Students will be given a map of the United States. They will then collect data

using temperatures gathered from a weather source such as the National Weather Service (available online) Chart temperatures the map. Students will draw lines separating areas with varying temperature ranges and color accordingly. These lines are called isotherms.

2. The same activity can be repeated with pressure data and rainfall data.

3. Students should be able to some general analysis for each type of contour. After analyzing, a class discussion should be held to see what their ideas are, what conclusions they formed, and what evidence they have to support their conclusions.

Fig. 1: Precipitation in Germany (from a Geo Magazine Special Issue 1982)

Extensions: As was mentioned before, students should have a number of questions

regarding these weather topics and all the links from them. Individual or groups projects could be assigned so that they could research and answer some of their questions.

Resources

http://cimss.ssec.wisc.edu/wxwise/contour/contour1.html

http://vathena.arc.nasa.gov/curric/weather/hsweathr/isobar.html

http://www.w3.weather.com/glossary/

http://www.infodotinc.com/weather2/7-9.htm

http://marrella.meteor.wisc.edu/aos452/aos101/lect/lecture6.html

http://earthsci.org/weather/fundam/fundam.html#Global%20Effects

http://www.wiley.com/college/geocases/cases/case8/images/tour_1/1_3.html(first map of isohyets)

http://www.stadtentwicklung.berlin.de/umwelt/umweltatlas/e_text/ek408.doc(second map of isohyets and information on precipitation effects)

Williams, Jack. 1992. The Weather Book – An Easy-To-Understand Guide to the USA’s Weather. Random House, Inc. New York, NY. 209 pp.

Lesson Plan: Making Contours for Middle School

Students will make their own map by taking measurements of an island submerged in water that is hidden in a box or aquarium.

Materials:Aquarium covered with paper or a box- of aquarium, could add water to continue with island themeModel of a mountain (clay, wood, or rocks)Probe to take measurements (small dowel)RulerStudent graph worksheet

Procedure:

-The top of the box will be covered with graph paper with holes at each intersection, this is where students will take their measurements. Diagram of model

- Each team of students should be scheduled to spend 20 minutes taking probes.

- Students will probe at each hole, and write on their graph the measurement of how much of the probe is sticking out of the box. Remind students that we are taking measurements below sea level.

-Each student group will record their data on their graph and then draw in their contours. They should decide what the interval of contours should be.

- Then ask the students to draw what they think the underwater island looks like from each side.

-When all students are done, reveal what the actual underwater island looks like.

Lesson Plan: Watersheds

Objective: By the end of the lesson the students will understand how contour maps can be used to determine where in the US are major and minor water basins and why it is important to find these areas.

Methodology:Terms: major water basin, minor water basin, watershed, U.S. Army Corps. Of Engineers

1. Define with students what a water basin is.

2. Look at a map of the US and discuss what are the areas that they think would be water basins and why

3. Give out a blank map of the US and a list of places from around the country (cities, mountains, lakes, etc)

4. Have students work in pairs and find the elevation and location of the places and mark them on map.

5. Tell them to draw contour lines connecting areas of similar elevation. Remind them to pick an appropriate interval for their map

6. From their maps have them identify areas where they think water basins would be.

7. Discuss with them the idea of major and minor water basins. Have them find the difference in the lowest points and highest points on their map. Can they find where they think the major and minor water basins would be.

8. Talk about the idea of flooding and why they think it happens in some areas and not in others. How could they figure out what areas might be more susceptible to flooding. Try to find the slopes of some of the water basins and see if this could be a predictor.