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Risk-reduction choices are compared by expected annual loss, losses avoided, benefit-cost ratio and payback, weighed against who benefits and the levee effect.
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By the end of this lesson you will be able to compare risk-reduction options with expected losses, benefit-cost ratios and payback periods, and name their trade-offs.
You can separate a disaster into hazard, exposure, vulnerability and capacity, and you know that a one-in-T-year event has a one-in-T chance each year. This lesson asks what a community can do before a hazard strikes, and how to compare the options with numbers and with judgment.
| Term | What it means |
|---|---|
| Mitigation | Action taken before a hazard to reduce the harm it can do, such as building codes or levees. |
| Preparedness | Plans, drills, warnings and supplies that ready people to respond. |
| Expected annual loss | The average yearly loss from a hazard: its yearly chance times the damage it would do. |
| Benefit-cost ratio | The losses a measure avoids over its life divided by what it costs. |
| Payback period | The years a measure takes to avoid losses equal to its cost. |
| Levee effect | The tendency for protection to draw new building into the protected area, raising the loss if the protection fails. |
Choosing how to reduce risk means comparing what a measure costs with what it saves:
$$\text{expected annual loss} = \text{yearly chance} \times \text{damage}.$$
The numbers guide the choice but do not settle it: who benefits, who pays, and whether the measure changes where people build all matter too.
Another way: picture
Picture a town on a river that floods badly about once in twenty-five years. Most years nothing happens, so spending on protection feels like waste. But averaged over many years, the flood costs the town a steady amount every year, and a measure that cuts that amount can pay for itself many times over.
Another way: steps
A network intervention changes access and risk together. Suppose a fictional flood-prone bridge connects farms to a market. A detour costs two additional hours; a raised replacement bridge costs more to build but stays open in a wider range of floods. To compare proposals, specify which floods interrupt each route, which goods spoil, who pays the construction cost and which settlements are bypassed.
Do not assume that a faster route benefits everyone equally. A direct highway may reduce regional freight time while removing customers from roadside shops or separating residents from a school. A second route can improve redundancy, but only if it does not share the first route's vulnerable floodplain. Map common failure points. Then compare ordinary operation and disruption conditions separately, retaining uncertainty about flood likelihood and traffic demand.
Emergency managers describe a cycle with four stages. Mitigation reduces harm before a hazard: stronger buildings, levees, moving homes out of floodplains. Preparedness readies people: warnings, plans, drills and supplies.
Response acts during and just after the event: rescue, shelter and medical care. Recovery rebuilds. Money spent on the first two stages often saves far more in the last two, which is why this lesson focuses on them.
A flood that would do $5$ million dollars of damage and has a $2$ percent chance each year costs, on average, $0.02 \times 5$ million, or $100$ thousand dollars a year. That average is the expected annual loss.
In most years the loss is zero; in a flood year it is the whole $5$ million. The expected annual loss is what the flood costs spread evenly over many years, which is the figure a measure's yearly savings are compared with.
A measure lowers the expected annual loss, either by making the hazard less likely to cause damage or by making the damage smaller. The difference between the expected loss before and after is the loss avoided each year.
A levee that cuts a flood's chance from $4$ percent to $1$ percent, where the damage would be $5$ million, lowers the expected loss from $200$ to $50$ thousand dollars a year, avoiding $150$ thousand.
The benefit-cost ratio divides the losses a measure avoids over its whole life by its cost. A project costing $3$ million that avoids $150$ thousand a year for fifty years saves $7.5$ million, a ratio of $2.5$.
A ratio above one means the measure saves more than it costs. Studies by the National Institute of Building Sciences found that federal mitigation grants save about six dollars for every dollar spent, and that modern building codes save even more.
The payback period divides the cost by the loss avoided each year. A measure costing $1.5$ million that avoids $150$ thousand a year pays for itself in ten years, on average.
The word average matters. If the flood comes in the first year, the measure pays for itself at once; if it does not come for decades, it takes longer. A payback period much shorter than the measure's life is a good sign.
Structural measures change the physical world: levees, flood walls, dams, seawalls, stronger buildings and safe rooms. They can protect many people at once and are easy to see, which makes them popular.
But they are expensive, need maintenance, and can fail when a hazard exceeds their design. The levees of New Orleans were built to hold back the storms engineers expected, and Hurricane Katrina showed what happened when they did not.
In 1942 the geographer Gilbert White wrote that floods are acts of nature, but flood losses are largely acts of people. He noticed that after levees were built, towns and farms spread onto the protected land, so each flood that overtopped a levee did more damage than before.
This is the levee effect: protection lowers the chance of a flood but raises exposure, and the expected loss can end up higher. A risk comparison that ignores where people will build next can mislead.
Non-structural measures change where and how people live rather than the hazard. They include building codes, zoning that keeps homes out of floodplains, buyouts of repeatedly flooded homes, warnings, insurance and education.
They are often cheaper and cannot fail the way a levee can. After the great Midwest floods of 1993, the town of Valmeyer, Illinois, moved to the bluffs above the Mississippi rather than rebuild behind a levee.
Checking an answer. An expected annual loss is always less than the damage of one event. A payback period is the cost over the yearly saving, so a bigger saving means a shorter payback.
Multiplying the chance by the damage is allowed because, over many years, the event happens in about that share of them, so the average yearly loss is that share of the damage.
Comparing a one-time cost with yearly savings is allowed as long as the savings are counted over the same span, the measure's life. Economists also discount future savings, counting a dollar saved in forty years as worth less than one saved today, which lowers the ratio somewhat.
Some of the most effective measures cost little. The National Weather Service's tornado warnings give many communities several minutes to take shelter, and hurricane forecasts give days to evacuate.
Warnings work only when people hear them, understand them and can act. So warning systems include sirens, phone alerts, practice drills, and plans for people who cannot leave on their own, such as hospital patients and residents without cars.
The numbers count a dollar of loss avoided the same wherever it falls. But a levee protecting expensive homes can have a better benefit-cost ratio than one protecting a poorer neighborhood, simply because there is more property to lose.
So a fair comparison also asks who is protected and who is left out. Federal programs have begun counting benefits to vulnerable residents, not only to property, so that the poorest neighborhoods are not always last in line.
Expected losses assume the hazard's chances stay the same. With rising seas and heavier rainstorms, a one-in-a-hundred-year flood today may become more frequent, which raises the expected loss a measure avoids.
Planners increasingly design for the hazard expected over a measure's life rather than the one recorded in the past. The next lessons, on climate, explain why those chances are changing.
Most communities combine measures rather than choosing one. A coastal town might restore marshes that absorb storm surge, raise its most exposed homes, strengthen its building code, and run evacuation drills.
Each measure reduces a different part of the risk: the hazard's reach, exposure, vulnerability or capacity. Together they leave less room for a single failure to turn a hazard into a disaster.
The most common slip is forgetting to divide a percent by one hundred when finding an expected loss, which gives a figure a hundred times too large. Another is counting the whole damage as if it happened every year.
A third is turning the benefit-cost ratio upside down. A fourth is judging a measure by its numbers alone, without asking whether it will draw more building into harm's way.
On May 20, 2013, a tornado rated EF5, the strongest category, tore through Moore, Oklahoma, killing twenty-four people. Seven of them were children at Plaza Towers Elementary School, which had no reinforced shelter. Another school hit that day also lacked one.
Afterward, Moore voters approved a bond to build tornado safe rooms, reinforced concrete spaces designed to withstand the strongest winds, in every school, and the city strengthened its building code for new homes to resist higher winds. FEMA helps pay for safe rooms across Tornado Alley because their cost per person sheltered is modest compared with the lives they can save.
The choice shows how risk reduction is weighed. Safe rooms do not change the tornado or who lives in its path; they lower vulnerability and raise capacity. Their value depends on where they are, how many people they hold and whether people can reach them in the minutes a warning gives.
The Mississippi and Missouri River floods of 1993 broke or overtopped hundreds of levees across the Midwest and caused billions of dollars of damage. Rather than rebuild every levee and every home as before, the federal government funded buyouts of thousands of flood-prone properties, turning the land into parks and open space that could flood without harm.
Some whole towns moved. Valmeyer, Illinois, rebuilt on the bluffs above its old site, and Pattonsburg, Missouri, moved to higher ground too. When later floods came, those former homes were empty fields, and the losses that would have been counted there never happened.
Buyouts illustrate Gilbert White's argument that flood losses are largely human choices. They reduce exposure directly, cost less over time than repeated rebuilding, and avoid the levee effect. But they ask families to leave homes and neighbors, a cost that no benefit-cost ratio fully captures.
It is natural to think the surest way to reduce risk is to build the largest levee or seawall possible. But structures are expensive, can fail when a hazard exceeds their design, and draw new homes and businesses into the land they protect, which raises the loss when they fail.
Moving homes out of floodplains, stronger building codes and good warnings often save more per dollar and cannot fail all at once. Compare options by the losses they avoid for their cost, and ask how each will change where people build.
A storm that would do $6$ million dollars of damage has a $5$ percent chance each year. Write the chance as a fraction.
$\dfrac{5}{100} = 0.05$
Out of one hundred.
Multiply by the damage.
$0.05 \times 6 = 0.3\ \text{million}$
Chance times damage.
Convert to thousands of dollars.
$300\ \text{thousand}$
The expected annual loss.
Say what the figure means.
$\text{the average yearly cost over many years}$
Not what any one year costs.
A flood doing $8$ million dollars of damage has a $5$ percent yearly chance. Find the expected loss.
$0.05 \times 8000 = 400$
Thousand dollars.
A levee cuts the chance to $1$ percent. Find the new expected loss.
$0.01 \times 8000 = 80$
Thousand dollars.
Find the loss avoided each year.
$400 - 80 = 320$
Thousand dollars.
The levee costs $6400$ thousand. Find the payback.
$\dfrac{6400}{320} = 20\ \text{years}$
Cost over yearly saving.
Name the risk the numbers miss.
$\text{new homes behind the levee}$
The levee effect.
Option A, a flood wall, costs $5000$ thousand and avoids $200$ thousand a year for $50$ years. Find its total benefit.
$200 \times 50 = 10000$
Thousand dollars.
Find A's benefit-cost ratio.
$\dfrac{10000}{5000} = 2$
Two dollars saved per dollar.
Option B, buying out the most flooded homes, costs $2000$ thousand and avoids $120$ thousand a year for $50$ years. Find its benefit.
$120 \times 50 = 6000$
Thousand dollars.
Find B's benefit-cost ratio.
$\dfrac{6000}{2000} = 3$
Three dollars saved per dollar.
Compare the two ratios.
$3 > 2$
B returns more per dollar.
Name what else to weigh.
$\text{families moved, and the levee effect}$
Numbers guide; they do not decide.
Write the payback as a fraction.
$\dfrac{2400}{160}$
Cost over yearly saving.
Evaluate the payback period.
$15\ \text{years}$
On average.
Say what would shorten it.
A flood that would do $1.5$ million dollars of damage to a town has a $4$ percent chance each year. What is the town's expected annual loss from it, in thousands of dollars?
Complete the worked solution: a flood that would do $12$ million dollars of damage has a $2$ percent chance each year. Raising the town's homes, at a cost of $2700$ thousand dollars, would cut the chance of damage to $0.5$ percent. Find the expected annual loss before and after, in thousands of dollars, and the payback period in years.
Find the expected loss before.
$\text{chance} \times \text{damage} =$ s
In thousands of dollars.
Find the expected loss after.
$\text{new chance} \times \text{damage} =$ t
In thousands of dollars.
Divide the cost by the yearly saving.
$\dfrac{\text{cost}}{\text{before} - \text{after}} =$ k
Years to pay for itself.
Compare it with the homes' expected life.
$\text{worth it if much shorter}$
The saving continues after payback.
Match each stage of disaster management to an example.
| a town adopts a stronger building code | families pack emergency kits and practice a plan | rescuers search damaged buildings after a tornado | a flooded school is repaired and reopened | |
|---|---|---|---|---|
| mitigation | ||||
| preparedness | ||||
| response | ||||
| recovery |
A flood that would do $4$ million dollars of damage has a $5$ percent chance each year. A proposed levee would cut that chance to $1$ percent. Fill in the expected annual loss before and after, and the loss avoided each year, all in thousands of dollars.
| value | |
|---|---|
| expected annual loss before (thousand dollars) | |
| expected annual loss after (thousand dollars) | |
| loss avoided each year (thousand dollars) |
A flood wall costs $4800$ thousand dollars to build and avoids an expected $240$ thousand dollars of losses each year. Write its net benefit, in thousands of dollars, as a function of the years $y$ since it was built.
Answer:
A mitigation project costs $2000$ thousand dollars and avoids an expected $160$ thousand dollars of losses each year for $50$ years. What is its benefit-cost ratio?
Answer:
Suppose a town in Alabama builds tornado safe rooms costing $1200$ thousand dollars that can shelter $1500$ people. What is the cost per person sheltered, in dollars?
Answer: dollars
An island exports food through one bridge, now closed by flooding. Route A restores a 20-minute crossing over the same low floodplain. Route B takes 9 more minutes over high ground. Mark every sentence supported in a route comparison, including the evidence still needed before a decision.
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 flood wall costs $2000$ thousand dollars to build and avoids an expected $160$ thousand dollars of losses each year. Write its net benefit, in thousands of dollars, as a function of the years $y$ since it was built.
Answer:
You can compare risk-reduction choices. Explain how building a levee can end up raising a town's flood losses.
27. Your turn: a measure costs $2400$ thousand dollars and avoids $160$ thousand dollars of losses a year. What is its payback period?, step 3
$\text{a larger yearly saving}$
Or a cheaper measure.