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A coast's rate of retreat is distance over years, a building's years left are its distance over that rate, and communities defend, nourish or move back.
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By the end of this lesson you will be able to measure a coast's rate of retreat, project when buildings are at risk, and compare ways of managing a retreating coast.
You know how waves erode cliffs and move sand along the shore. This lesson measures how fast a coast retreats, works out what that means for the buildings near its edge, and compares the ways people respond.
| Term | What it means |
|---|---|
| Rate of retreat | How far a cliff edge or shoreline moves inland each year, on average. |
| Seawall | A wall built along the shore to take the force of the waves. |
| Riprap | Large rocks piled along a shore to absorb wave energy. |
| Groin | A low barrier built across a beach to trap sand moved by longshore drift. |
| Beach nourishment | Adding sand to an eroding beach, usually dredged from offshore. |
| Managed retreat | Deliberately moving buildings and roads back from an eroding coast. |
A coast's retreat can be measured and projected:
$$\text{rate} = \dfrac{\text{distance moved}}{\text{years}}, \qquad \text{years left} = \dfrac{\text{distance to the edge}}{\text{rate}}.$$
Every choice has costs, and some move the problem along the coast.
Another way: picture
Picture two aerial photos of the same stretch of cliff, taken thirty years apart. In the second, a field's edge has vanished, a path now ends in midair, and a barn that stood well back is near the brink. Measuring the gap between the two cliff lines, and dividing by thirty, gives the rate.
Another way: steps
A coastal retreat rate measured across past dates is a description, not a promise of steady future motion. Sea level, storm sequences, sediment supply and engineering can change it. Distinguish reducing greenhouse-gas emissions, which mitigates a cause of climate change, from moving buildings or restoring dunes, which adapts to coastal impacts. One plan may do both, but the mechanisms must be stated separately.
A fictional town compares a seawall, dune restoration and a setback for new construction. A wall may protect a particular frontage but alter beach access and sediment movement; dunes can store sand and reduce some storm impacts but need space and maintenance; a setback reduces new exposure while limiting where construction occurs. None makes the whole coast permanently safe.
Evaluate local and downstream effects under more than one scenario. A plan that works with abundant river sediment may perform differently after a dam traps that supply. A higher sea-level scenario may change the benefit of protection. Name the households affected by relocation, the cost of maintaining a structure and who retains access to the shore. A defensible recommendation explains these trade-offs and says what observations would trigger a revision.
On a cliff retreating $1.5$ m a year, three houses have very different futures.
| House | Distance from edge | Years left |
|---|---|---|
| nearest | 12 m | 8 |
| middle | 30 m | 20 |
| farthest | 45 m | 30 |
These are averages. A single winter storm can take several years' worth of cliff in one night, so owners and towns plan with a safety margin.
Coasts made of soft clay, sand or loose glacial deposits wear back fastest, sometimes several meters a year. Hard rock coasts may retreat only a few centimeters a year.
Retreat is also faster where waves are big, where the beach is too narrow to protect the cliff's foot, where water seeps out of the cliff and loosens it, and where rising seas let waves reach higher.
Seawalls, riprap and bulkheads armor the shore, taking the waves' force so the land behind them stays put. Groins trap drifting sand to widen a beach. Jetties keep harbor inlets open.
These structures work for what is directly behind them, but they are expensive, and they have side effects. Waves reflected off a seawall can scour away the beach in front of it, and a groin that traps sand starves the beaches down-drift.
Beach nourishment pumps sand dredged from offshore onto an eroding beach, making it wider so it absorbs the waves before they reach dunes and buildings. Dune restoration plants grasses and builds fences that trap blowing sand.
These measures look natural and do not starve neighboring beaches, but the sea keeps taking the sand, so nourishment must be repeated every few years, at a cost each time.
Sometimes the best choice is to move back. Towns buy out homes at the edge, move roads inland and ban new building near the shore. Individual buildings can be moved.
Managed retreat accepts that the coast will keep moving and gets people out of the way. It avoids repeated costs, but it asks owners to give up land and homes, which is hard, especially where families have lived for generations.
Costs are easier to compare per year. Pumping 500,000 cubic meters of sand at $20$ dollars a cubic meter costs $10$ million dollars; if it lasts five years, that is $2$ million a year.
A seawall may cost more at first but last decades, though it needs repairs and can cost the town its beach. A buyout costs once. Comparing yearly costs, and what each choice protects, helps a town decide.
As sea level rises, waves reach farther up beaches and cliffs, and storm surges push inland farther than before. Coasts that were stable begin to retreat, and retreating coasts retreat faster.
Rates measured over the past may underestimate the future. Planners increasingly use projected sea levels, not only past rates, when deciding how far back to build.
Checking an answer. The nearest building must have the fewest years left. A rate should be far smaller than the total distance moved over many years.
Dividing distance by years to get a rate is allowed because it gives the average retreat each year over the surveyed period. Dividing a building's distance by that rate is allowed as long as the rate holds, which is why the answer is an estimate.
Spreading a project's cost over its life is allowed because it lets options that last different lengths of time be compared fairly.
North Carolina's Outer Banks are a chain of barrier islands about 200 miles long. Storms wash sand over them from the ocean side to the sound side, so the islands are slowly moving landward, and parts of the ocean shore retreat many feet a year.
Towns there use all three approaches: nourishing beaches, rebuilding dunes, and in places letting houses go, or moving them back from the surf.
Choosing how to respond to a retreating coast is a public decision as much as an engineering one. Beach nourishment is often paid for partly by federal and state taxpayers, so people far from the coast help protect homes on it.
Buyouts and managed retreat ask the owners nearest the edge to move, sometimes with public help. Fair decisions weigh the costs to owners, to neighbors down the coast and to the public, not only the cost per year of each option.
The most common slip is reading the total distance moved as the yearly rate. Another is dividing the years by the distance, turning the rate upside down.
A third is assuming a seawall protects the whole coast, when it can speed erosion of the beach in front and beside it. A fourth is treating nourishment as permanent, when the sand must be replaced.
The Cape Hatteras Lighthouse on North Carolina's Outer Banks is the tallest brick lighthouse in the United States. When it was lit in 1870, it stood about 1,500 feet from the ocean. By 1999 the shoreline had retreated to within about 120 feet of its base, and storms threatened to topple it.
Engineers had tried groins and sandbags to hold the shore. Instead, the National Park Service chose managed retreat: in the summer of 1999, the lighthouse was lifted onto steel tracks and rolled 2,900 feet inland over twenty-three days, one of the largest moves of a structure ever attempted.
The average retreat since 1870 was about ten feet a year. At that rate, the move bought the lighthouse roughly two to three centuries. The decision shows the logic of managed retreat: rather than fight a moving coast forever, move what matters out of its way.
In the 1970s, the beach in front of Miami Beach's hotels had nearly vanished, eroded by storms and cut off from its sand supply by development and jetties. From 1976 to 1981, the U.S. Army Corps of Engineers pumped millions of cubic yards of sand onshore, building a beach about 300 feet wide along miles of the city's shore.
The new beach protected hotels from storm waves and drew tourists back. But the sea keeps carrying the sand away, so the beach has needed renourishing again and again, and as nearby offshore sand ran short, new sand has had to come from farther away, at rising cost.
Miami Beach shows both sides of soft engineering: it works, and it looks natural, but it is a subscription, not a purchase. Every few years the bill comes due again.
It is natural to think that building a seawall or groin protects the coast. It protects what stands directly behind it, but waves bouncing off a wall can strip the beach in front, and a groin that traps sand starves the beaches beyond it, which then retreat faster.
Every response moves costs somewhere: to neighbors, to the town's budget every few years, or to owners who must move. Judge each one by what it protects and whom it affects.
A cliff edge moved $84$ m inland between $1982$ and $2024$. Find the years.
$2024 - 1982 = 42$
Between surveys.
Find the rate.
$\dfrac{84}{42} = 2\ \text{m a year}$
Distance over years.
A barn stands $30$ m from the edge. Find its years left.
$\dfrac{30}{2} = 15$
Distance over rate.
Say what the owner should do.
$\text{plan to move well before}$
Edges become unsafe first.
A house is $60$ m from an edge retreating $2$ m a year. Write its distance.
$60 - 2t$
Today minus retreat.
Find its distance after $10$ years.
$60 - 2 \times 10 = 40\ \text{m}$
Substitute.
Find when it is $10$ m away, a common safety limit.
$60 - 2t = 10 \Rightarrow t = 25$
Years.
Find when the edge reaches it.
$\dfrac{60}{2} = 30\ \text{years}$
At zero.
Say what could shorten both.
$\text{bigger storms, rising seas}$
The rate may grow.
Nourishment: $400000$ cubic meters at $30$ dollars, lasting $4$ years. Find the whole cost.
$400000 \times 30 = 12000000$
Dollars.
Find its cost per year.
$\dfrac{12000000}{4} = 3000000$
Three million a year.
A seawall costs $45000000$ and lasts $30$ years. Find its cost per year.
$\dfrac{45000000}{30} = 1500000$
Before repairs.
Compare the two results.
$1.5 \text{ million} < 3 \text{ million}$
The wall is cheaper per year.
Name the wall's hidden cost.
$\text{the beach in front may vanish}$
Reflected waves scour it.
Say what else to weigh.
$\text{neighbors down the coast}$
Who pays for side effects.
Write distance over rate.
$\dfrac{50}{2.5}$
Years left.
Evaluate the expression.
$20\ \text{years}$
If the rate holds.
Say why to plan sooner.
Surveys show a cliff edge moved $27$ m inland between $2006$ and $2024$. What was its average rate of retreat, in meters a year?
Complete the worked solution: a cliff edge moved $100$ m inland over $50$ years. A house now stands $36$ m from the edge. Find the rate of retreat and the years the house has left, if the rate holds.
Find the rate of retreat.
$\dfrac{\text{distance moved}}{\text{years}} =$ r
Meters a year.
Find the years left.
$\dfrac{\text{house's distance}}{\text{rate}} =$ t
Until the edge arrives.
Say when to act.
$\text{well before that}$
A cliff edge becomes unstable first.
Name the choices.
$\text{defend, nourish or move back}$
Hard, soft or managed retreat.
Match each way of managing a retreating coast to how it works.
| a concrete wall that takes the waves' force at the shore | a low barrier across the beach that traps longshore drift | sand dredged offshore and pumped onto the beach | moving homes and roads back from the eroding edge | |
|---|---|---|---|---|
| a seawall | ||||
| a groin | ||||
| beach nourishment | ||||
| managed retreat |
A cliff retreats $0.5$ m a year. Three houses stand $10$ m, $25$ m and $40$ m from its edge. If the rate holds, fill in the years each has left.
| years left | |
|---|---|
| the first house (years) | |
| the second house (years) | |
| the third house (years) |
A house stands $40$ m from a cliff edge that retreats $1.5$ m a year. Write the house's distance from the edge, in meters, as a function of the years $t$ from now.
Answer:
A town pumps $600000$ cubic meters of sand onto its beach at $18$ dollars a cubic meter. The new sand lasts about $9$ years before storms and drift carry it away. What does the beach cost the town each year, in dollars?
Answer: dollars
When the Cape Hatteras Lighthouse in North Carolina was lit in 1870, it stood about $1500$ feet from the ocean. By 1999 the shoreline had retreated to about $120$ feet from its base. What was the average rate of retreat, in feet a year, to one decimal place?
Answer: feet a year
An invented coast has a measured retreat rate over 6 years. A proposal places new homes behind a wall, restores dunes elsewhere and cuts fossil-fuel use. Mark every supported sentence in an evaluation of these mechanisms and the limits of using the historical retreat record.
This task has no paper form; do it on a device.
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A house stands $80$ m from a cliff edge that retreats $2.5$ m a year. Write the house's distance from the edge, in meters, as a function of the years $t$ from now.
Answer:
You can measure and manage a retreating coast. Explain why a seawall can make erosion worse somewhere else.
24. Your turn: a cliff retreats $2.5$ m a year and a cottage stands $50$ m from the edge. How many years does it have?, step 3
$\text{storms can speed it}$
An average hides bad years.