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Lesson plan Grade 8 Science

Coldspar Reservoir Sediment: Storage Loss and Delta Volume

A grade 8 science lesson tracing rock from a fictional watershed into reservoir sediment, with survey math on storage loss and a cone-volume estimate of the delta.

Objectives

  1. Students will calculate the annual rate of reservoir storage loss from two survey volumes taken decades apart.
  2. Students will use the cone volume formula to estimate the volume of a sediment delta and convert it to acre-feet.
  3. Students will explain how weathering, transport, and deposition move rock from a headwater slope into a reservoir.

Vocabulary

Acre-foot
The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.
Deposition
Deposition is when water vapor in the air turns directly into ice without ever becoming liquid first, the way frost forms on a cold window. It is the opposite of sublimation, where ice turns straight into vapor.
Dead pool
A reservoir level so low that water can no longer flow out through the dam on its own. It is the worst-case marker in a long drought.

Also: sediment, delta, reservoir survey, weathering

Teacher overview

Every reservoir behind a dam is also a settling basin, because the river slows where the lake begins and drops the sand and silt it was carrying. In this lesson students work with two survey volumes for the fictional Coldspar Reservoir, taken forty years apart, and calculate how fast the storage is disappearing and how long the remaining storage will last. They also estimate the volume of the sediment delta at the river mouth using the cone formula. Students often assume that sediment spreads evenly across the whole reservoir floor; the coarse material actually piles up in a delta where the river enters, while only the finest clay reaches the dam, which is why the reservoir loses usable depth at the upstream end first.

Procedure

Hook (6 min): Tilt a shallow tray of sand and pour water down the slope into a flat pool at the low end. Ask students to watch where the sand stops moving. Point out the small fan that forms at the edge of the pool and tell them it has the same shape as the delta they will measure in the fictional reservoir today.

Direct instruction (12 min): Define an acre-foot as the volume covering one acre to a depth of one foot, and note that one acre-foot equals 43,560 cubic feet. Explain what a reservoir survey does: a boat runs sonar lines across the lake and the results are converted to a storage volume at a given water surface elevation. Model the subtraction and division for finding an annual loss rate using a different reservoir than the handout, such as one that fell from 5,000 to 4,600 acre-feet in 20 years. Review the cone volume formula and remind students that the base diameter must be halved before squaring.

Guided practice (12 min): Pairs complete handout items 1 through 4. Circulate and check the division in item 2 and the subtraction in item 4, where students often use the original capacity rather than the current storage as the starting point. Ask one pair to state what the phrase "40 acre-feet per year" means in plain words.

Independent practice (18 min): Students complete handout items 5 through 8 individually. Item 7 rewards students who notice that spreading a fixed volume over a stated area is a division problem, not a new formula.

Closure and exit ticket (7 min): Collect the handout. Read item 8 aloud and ask three students to each name one step in the sequence from mountain rock to reservoir mud, in order. If the class cannot assemble the three steps without prompting, reteach the sequence with the sand tray before the next lesson.

Coldspar Reservoir Sediment: Storage Loss and Delta Volume — Grade 8 Science
Name: ____________________________ Date: ______________

Student Handout

The fictional town of Castleford built Coldspar Dam on the Thrushwood River. Its records give the numbers below. Use 3.14 for pi, and use 43,560 cubic feet per acre-foot.

Measurement Value
Storage when the dam was finished 12,000 acre-feet
Storage measured in the survey 40 years later 10,400 acre-feet
Delta base diameter 400 feet
Delta height 12 feet
  1. How many acre-feet of storage did Coldspar Reservoir lose between the two measurements?
  2. What was the average storage loss per year over those 40 years?
  3. What percent of the original storage was lost in those 40 years? Round to the nearest tenth of a percent.
  4. If storage keeps falling at the rate you found in item 2, how many more years will pass before storage drops to 9,000 acre-feet?
  5. The sediment delta where the Thrushwood River enters the reservoir is shaped roughly like a cone with a base diameter of 400 feet and a height of 12 feet. Find its volume in cubic feet.
  6. Convert your answer to item 5 into acre-feet, using 43,560 cubic feet per acre-foot. Round to the nearest tenth.
  7. Suppose crews dredged that same delta volume and spread it evenly across a flat field measuring 200 feet by 300 feet. How deep would the layer be, to the nearest tenth of a foot?
  8. Describe the sequence of events that turns solid rock on a Thrushwood headwater slope into mud resting behind Coldspar Dam. Name at least three steps in order.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 1,600 acre-feet.
    Subtracting the survey volume from the original volume gives 12,000 minus 10,400, which equals 1,600 acre-feet of lost storage.
  2. Answer: 40 acre-feet per year.
    Dividing the loss by the elapsed time gives 1,600 divided by 40, which equals 40 acre-feet per year.
  3. Answer: 13.3 percent.
    Dividing 1,600 by 12,000 gives 0.13333, which is 13.3 percent to the nearest tenth.
  4. Answer: 35 years.
    Storage must fall from 10,400 to 9,000, a drop of 1,400 acre-feet. At 40 acre-feet per year, 1,400 divided by 40 equals 35 years.
  5. Answer: 502,400 cubic feet.
    The radius is half the diameter, so 400 divided by 2 equals 200 feet. The cone volume is one third times 3.14 times 200 squared times 12. That is one third of 3.14 times 40,000 times 12, or one third of 1,507,200, which equals 502,400 cubic feet.
  6. Answer: 11.5 acre-feet.
    Dividing 502,400 by 43,560 gives 11.534, which rounds to 11.5 acre-feet. The delta alone holds only a small share of the 1,600 acre-feet the fictional reservoir has lost, because sediment also settles across the lake bottom.
  7. Answer: 8.4 feet.
    The field area is 200 times 300, or 60,000 square feet. Dividing 502,400 by 60,000 gives 8.373, which rounds to 8.4 feet deep.
  8. Answer: Weathering breaks the rock, running water carries the pieces, and the slowing river deposits them in the reservoir.
    Accept any ordered account with three or more steps. A full response notes that freezing water, plant roots, and chemical change break bedrock into loose grains; that rain and streamflow carry those grains downhill, with faster water carrying larger pieces; and that the current slows where the river meets the still reservoir, so the coarsest material drops first at the delta and the finest clay settles farther out.

Differentiation

Support

Give these students items 1 through 4 with the operation named for each, such as "subtract" or "divide," and supply the radius of 200 feet directly in item 5 so the cone work starts at the formula. Provide a worked example of a cone volume with different numbers taped inside the folder.

Extension

Ask students to find the year the fictional reservoir would reach a dead pool of 3,000 acre-feet at the same loss rate, then write a short paragraph on why a utility would rather dredge early than wait, considering both cost and the shrinking margin during drought.

ELL supports

Pre-teach "sediment," "delta," "survey," and "acre-foot" using the sand tray and a labeled diagram of the reservoir in cross section, with the delta drawn at the upstream end. Provide sentence frames for item 8: "First, the rock ___. Next, the water ___. Finally, the sediment ___."

Extensions

Students compare two fictional watersheds that feed similar reservoirs, one forested and one recently logged, and predict which reservoir loses storage faster and why. This leads naturally into a discussion of why utilities pay attention to land use far upstream of the intake they own.