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Lesson plan Grade 11 Science

Ketteridge Basin's Snowpack: Albedo Feedback and Runoff Timing

A grade 11 lesson tracing the snow-albedo feedback, then using rates of change and a runoff table to show how earlier melt shifts a city's summer water supply.

Objectives

  1. Students will describe the snow-albedo feedback as a sequence of causes and effects.
  2. Students will calculate average rates of change from a snow water equivalent record and compare two intervals.
  3. Students will explain how a shift in runoff timing changes what a reservoir must store.

Vocabulary

Key words: albedo, feedback, snow water equivalent, runoff timing, usable storage

Teacher overview

A mountain basin stores much of a city's summer water as snow, and the date that snow melts matters as much as the amount. This lesson uses the fictional Ketteridge Basin and the city of Tarrowby downstream to connect one physical mechanism, the snow-albedo feedback, to two things a water utility can measure: a declining April snowpack and a runoff peak that arrives a month earlier than it once did. The misconception to correct at the start is the assumption that a warming basin must be receiving less precipitation. Ketteridge's annual runoff totals barely change between the two periods in the handout, while the form of the precipitation and the timing of its release change a great deal, and that timing is what forces the reservoir operator's hand.

Procedure

Hook (5 min): Describe two June photographs of the same slope in Ketteridge Basin, one from the earlier period showing continuous snow above the tree line and one from the recent period showing bare rock with snow only in gullies. Ask students to predict which slope will be warmer at midday and to give a reason. Record predictions without confirming them.

Direct instruction, albedo and the feedback (12 min): Define albedo as the fraction of incoming sunlight a surface reflects. Fresh snow reflects most of what reaches it, while bare rock and soil reflect very little, so the same sunlight delivers far more energy to a bare slope. Build the loop on the board one arrow at a time: warmer spring, earlier melt at the snowline, more bare ground exposed, more sunlight absorbed, warmer surface, faster melt of the snow that remains, which exposes still more ground. Name this a positive feedback, and be explicit that positive means self-reinforcing rather than beneficial. Ask what would break the loop, and steer toward a heavy late-season snowfall resetting the surface.

Guided practice, rate of change (10 min): Model one average rate of change on the board using values students will not reuse. Suppose a different snow course measured 40.0 inches of snow water equivalent in 1970 and 29.0 inches in 2010. The average rate of change is (29.0 - 40.0) / (2010 - 1970) = -11.0 / 40 = -0.275 inches per year, or -2.75 inches per decade. Emphasize that the sign carries meaning and that per-decade units make long records easier to compare.

Independent practice (22 min): Students complete the Student Handout, which uses Ketteridge Basin's own snow course record, an absorption comparison, and a two-period runoff table. Circulate and watch for students who divide by the number of readings rather than the number of years.

Discussion, what the reservoir operator does (4 min): Ask two or three students to state, using their handout answers, why an earlier runoff peak forces Tarrowby to hold water in the reservoir that the snowpack used to hold for free. Draw out the flood-control tension: holding more water in May leaves less room for a late storm.

Closure and exit ticket (2 min): On an index card, students answer: "Name one step in the snow-albedo feedback and the step it causes next." Collect and confirm that at least three-quarters of the class produces a correct cause-and-effect pair before moving on.

Ketteridge Basin's Snowpack: Albedo Feedback and Runoff Timing — Grade 11 Science
Name: ____________________________ Date: ______________

Student Handout

All questions describe the Ketteridge Basin and the city of Tarrowby, both fictional. The basin's snow course has been measured on April 1 for decades.

Year April 1 snow water equivalent (inches)
1965 34.0
1975 32.2
1985 30.8
1995 28.6
2005 26.9
2015 24.1

Runoff from the basin, in thousands of acre-feet:

Month Historical average Recent average
March 18 30
April 42 68
May 96 118
June 120 84
July 64 40
August 26 18
  1. April 1 snow water equivalent was 34.0 inches in 1965 and 24.1 inches in 2015. Calculate the average rate of change in inches per year, rounded to the nearest thousandth.
  2. Express your item 1 answer as inches per decade.
  3. April 1 snow water equivalent was 28.6 inches in 1995 and 24.1 inches in 2015. Calculate the average rate of change in inches per decade.
  4. Compare your item 2 and item 3 answers. State what the comparison says about how the rate of decline has changed, and give one reason the shorter interval is a less reliable guide to the future.
  5. Suppose fresh snow reflects 80 percent of the sunlight reaching it and bare ground reflects 15 percent. Calculate the percent of sunlight bare ground absorbs.
  6. Fresh snow absorbs 20 percent of the sunlight reaching it. Using your item 5 answer, calculate how many times more sunlight bare ground absorbs than fresh snow does.
  7. Using your item 6 answer, write the snow-albedo feedback as a sequence of at least four steps that begins with an earlier spring melt and returns to melting.
  8. Add the historical monthly runoff values to find the annual total, then identify the first month in which cumulative historical runoff passes half that total.
  9. Add the recent monthly runoff values to find the annual total, then identify the first month in which cumulative recent runoff passes half that total.
  10. Combined July and August runoff was 90 thousand acre-feet historically and 58 thousand acre-feet recently. Calculate the percent decrease, rounded to the nearest tenth of a percent.
  11. Tarrowby needs 84 thousand acre-feet of water during July and August, and recent runoff supplies 58 thousand acre-feet in those months. Calculate how much the reservoir must release from storage to cover the difference.
  12. Tarrowby's reservoir holds 60 thousand acre-feet of usable storage. Using your item 9 and item 11 answers, explain what the shift in runoff timing requires the operator to do differently in May and June, and name one risk that choice creates.

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: -0.198 inches per year.
    (24.1 - 34.0) / (2015 - 1965) = -9.9 / 50 = -0.198 inches per year.
  2. Answer: -1.98 inches per decade. -0.198 inches per year x 10 years = -1.98 inches per decade.
  3. Answer: -2.25 inches per decade.
    (24.1 - 28.6) / (2015 - 1995) = -4.5 / 20 = -0.225 inches per year, which is -2.25 inches per decade.
  4. Answer: The recent decline is steeper than the long-run decline.
    The last two decades lost 2.25 inches per decade against 1.98 inches per decade across the full record, so the decline has been faster lately. A twenty-year interval holds only three readings in this record, and a single heavy or thin snow year near an endpoint can swing a short-interval rate, so the longer record is the better guide.
  5. Answer: 85 percent.
    Bare ground reflects 15 percent, so it absorbs 100 - 15 = 85 percent of the sunlight that reaches it.
  6. Answer: 4.25 times.
    85 percent / 20 percent = 4.25, so bare ground absorbs about four and a quarter times the sunlight fresh snow absorbs.
  7. Answer: A four-step self-reinforcing loop.
    Accept any ordered sequence equivalent to this one: an earlier spring melt exposes bare ground at the snowline; bare ground absorbs 4.25 times the sunlight snow absorbs; the extra absorbed energy warms the surface and the air just above it; that warmth melts the neighboring snow faster, which exposes more bare ground and repeats the cycle. Full credit requires the return to melting that closes the loop.
  8. Answer: June.
    The historical total is 18 + 42 + 96 + 120 + 64 + 26 = 366 thousand acre-feet, and half is 183. Cumulative runoff reaches 18, then 60, then 156, then 276 by the end of June, so June is the first month past half.
  9. Answer: May.
    The recent total is 30 + 68 + 118 + 84 + 40 + 18 = 358 thousand acre-feet, and half is 179. Cumulative runoff reaches 30, then 98, then 216 by the end of May, so the halfway point now arrives a month earlier.
  10. Answer: 35.6 percent.
    (90 - 58) / 90 = 32 / 90 = 0.3556, a decrease of 35.6 percent in combined July and August runoff.
  11. Answer: 26 thousand acre-feet.
    84 - 58 = 26 thousand acre-feet must come out of reservoir storage during July and August.
  12. Answer: The operator must store the May peak instead of letting the snowpack hold it.
    Half the year's runoff now arrives by the end of May rather than the end of June, so water that used to stay frozen until midsummer arrives while demand is still low. To cover the 26 thousand acre-foot summer gap, the operator has to capture and hold more of that early runoff in the 60 thousand acre-feet of usable storage. The risk is flood control: a reservoir kept fuller in May has less room for a late spring storm, so the operator trades summer supply against storm capacity.

Differentiation

Support

Give students the two runoff column totals already computed so items 8 and 9 reduce to tracking a running sum against a stated halfway value. Provide a partially completed feedback diagram for item 7 with two of the four arrows labeled, and a worked rate-of-change example with a different pair of years directly above item 1.

Extension

Have students estimate the April 1 snow water equivalent for 2035 using each of the two rates they calculated, state how far apart the two projections are, and explain which they would report to Tarrowby's utility board and why. Ask them to name one physical limit that keeps a straight-line projection from holding indefinitely.

ELL supports

Pre-teach albedo, feedback, snow water equivalent, and runoff timing with a labeled diagram of a slope in two states, one snow-covered and one bare, with arrows for reflected and absorbed sunlight. Provide the item 7 sequence as a set of sentence strips students order and connect, and offer the frame "Because more sunlight is absorbed, the snow ___, which means ___."