In 1909, a group of Virginia developers placed an ad in The Norfolk Ledger-Dispatch announcing the creation of a subdivision that — because it was built on a pair of peninsulas where the Lafayette and Elizabeth Rivers poured into Chesapeake Bay — came to be known as Larchmont-Edgewater. The developers set up private jitney service to downtown and advertised the area as “Norfolk’s only high-class suburb.” People flocked to live by the water’s edge.

Today the neighborhood is known for the venerable crepe myrtles that line its streets, for its fine houses and schools and water views and for the frequency with which it is not just edged by, but inundated with, water. Melting ice and warming water are raising sea levels everywhere. But because the land in the Hampton Roads area of Virginia (which includes Norfolk) is also sinking, relative sea levels there are rising faster than anywhere on the Atlantic coast. Water levels are already as much as 18 inches higher than they were when the developers created Larchmont-Edgewater a century ago, and they are still rising. As a result, it’s much easier for winds, storms and tides to push flood water into streets, yards and homes that once stood high and dry.

When Elisa Staton found a small house a block from the water in Larchmont-Edgewater in 2005, she was thinking of the neighborhood’s grand trees and Tudor-style houses, of the elementary school she hoped to send her kids to, once she had them. She wasn’t thinking much about flooding, though she knew the house was in a hundred-year flood zone, which meant that to get a federally backed mortgage, she was required to pay for flood insurance through the National Flood Insurance Program (N.F.I.P.), a government-subsidized system overseen by the Federal Emergency Management Agency. The insurance was reasonable, and there was no record of the house ever being flooded before. She bought it for $320,000.

A “hundred-year flood” sounds like a factor of time, as if the land were expected to flood only once every 100 years, but what it’s really meant to express is risk — the land has a 1 percent chance of flooding each year. As waters rise, though, flooding in low-lying places without sea walls, like Larchmont-Edgewater, will become more and more common until the presence of water is less about chance and more about certainty. And few insurers are willing to bet against a certainty.

Ten years later, Staton’s rec room had been flooded twice, and her insurance premiums, like those of many coastal property owners, had skyrocketed. She was seeing the effects not only of those local floods but also of rising waters elsewhere. As storm damage becomes more costly, it has left the N.F.I.P. tens of billions of dollars in debt and federal officials scrambling to bridge the divide between the rapidly growing expense of insuring these properties and the comparatively tiny, taxpayer-subsidized premiums that support it.

In 2012 and 2014, Congress responded to the N.F.I.P.’s troubles with bills known, thanks to the accidental aptness of their sponsors’ names, as Biggert-Waters and Grimm-Waters. The first law cut subsidies and phased out grandfathered rates so that premiums would start to reflect the true risk that properties like Staton’s face — reaching what the N.F.I.P. calls “actuarial soundness.” The second tried to slow the rate of those increases when it became clear how hard they would hit property owners.

Staton married and left Norfolk, renting out her house as she followed her husband’s job in the military. But eventually she was paying nearly $6,000 in flood premiums on top of her mortgage every year, nearly always more than she could make in rent. “I decided to cut my losses and get out,” she said. “The flood insurance kept going up, and I was drowning in it.” A real estate agent she consulted told her that she’d be lucky to sell the house for $180,000, barely more than half of what she paid for it and significantly less than what she still owed on the mortgage. Everyone looking at places near the river, the agent said, asked about flood insurance first. It wasn’t the risk of high waters that spooked buyers; it was the certainty of high premiums.

Staton lay awake at night wondering what to do. “I hate that house — that house has been my nightmare for 10 years,” she said last month, on a day when the dogwood and quince were bursting into flower in the front yard and the sun was sparkling off the calm, tidal river biding its time a block away. “I never got to get my head back above water.”

Insurance serves as a bulwark, both financial and mental, against the fact that we live in a fundamentally uncertain and dangerous world. “The revolutionary idea that defines the boundary between modern times and the past,” the financial historian Peter L. Bernstein wrote in his 1996 book, “Against the Gods,” “is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature.” Calamity can come for us all, but by bundling enough separate peril together we manage to form a general stability, a collective hedge against helplessness. As climate insecurity mounts, though, that math will get harder.

Frank Nutter, president of the Reinsurance Association of America, put it in more direct terms: “Constant risk — that’s not what insurance is about.”

Flooding is the most common, and most expensive, natural disaster in the United States. Private insurers have long declined to cover it, leaving the government on the hook for disaster assistance after floods. (Hence the famous lawsuits after Hurricane Katrina, when people who came home to empty slabs were asked to prove that their losses were a result of wind and not waves.) Congress created the N.F.I.P. in the late 1960s in response to a series of expensive floods caused by hurricanes and overflowing rivers. It offers insurance coverage, some of it subsidized, to communities that meet floodplain-management requirements; requires people who want loans to buy houses in dangerous places to buy it; and also provides grants for mitigation projects meant to reduce flooding damage, like elevating houses or buying out the owners of flood-prone homes. Private insurers including Farmers, Allstate and 68 other companies also sell and administer the policy on the government’s behalf — and take a sizable cut of the premium. If floods do come, though, it’s still the government that’s on the hook.

The N.F.I.P. was meant to encourage safer building practices. Critics argue that instead it created a perverse incentive — a moral hazard — to build, and to stay, in flood-prone areas by bailing people out repeatedly and by spreading, and in that way hiding, the true costs of risk. (In 1998, “repetitive-loss properties,” buildings that flood over and over, accounted for 2 percent of N.F.I.P.’s insured properties but 40 percent of its losses; since then, such losses have only increased.) As Larry Filer, an economist at the Center for Economic Analysis and Policy at Norfolk’s Old Dominion University, explains, “Somebody on a mountain in Colorado is helping the person in Virginia Beach live on the waterfront.”

And then came Hurricanes Katrina, Wilma and Rita, which in 2005 left the N.F.I.P. with claims six times higher than it had seen in any previous year. To cover them, it borrowed $17.3 billion from the Treasury. Hurricane Sandy in 2012 meant another $6.25 billion in debt, along with allegations that insurance companies distributing FEMA funds were shorting policyholders; 2016, when there were floods in Louisiana, Texas, Virginia and elsewhere, managed to be the third-most-expensive year in the N.F.I.P.’s history even with no single standout catastrophe, deepening the hole further. Servicing the debt is expensive, but FEMA sees no way to repay it, Roy Wright, the N.F.I.P. administrator, told Congress last month.

More losses loom. A single major storm-and-flooding event could cause $10 billion in damage in Hampton Roads alone, according to one planning report. AIR Worldwide, which models the risks of catastrophic events for insurance companies and governments, found that $1.1 trillion in property assets along the Eastern Seaboard lie within the path of a hundred-year storm surge. “That’s a very staggering number,” says AIR’s chief research officer, Jayanta Guin — and it represents only the risk on that coast, and only under current sea levels. By the 2030s, according to a 2008 analysis by Risk Management Solutions (R.M.S.) and Lloyd’s of London, annual losses from storm surges in coastal areas around the world could double.

In 2015, the N.F.I.P. asked R.M.S. and AIR Worldwide to update its modeling by running thousands of computer simulations to show what possible storms might mean for the properties it insures, helping it to quantify its financial exposure across the country. In 2016 and 2017, the N.F.I.P. — in a first-of-its-kind action for a federal program — transferred some of its risk to large, private companies known as reinsurers, which pool risk on gigantic scales: insurance for insurance companies.

Although Katrina and Sandy “felt like once-in-a-lifetime events,” Wright wrote in a recent blog post explaining the decision, “there is actually a 50 percent chance within a 10-year period the N.F.I.P. will once again experience Hurricane Sandy-size losses.” Removing subsidies is one partial solution, he told me — “There is no greater risk-communication tool than a pricing system” — but more hard decisions are coming. The N.F.I.P. is up for a reauthorization vote in September, its first since Biggert-Waters was passed; Wright believes the time has come to start limiting coverage for properties that are flooded over and over, a significant shift from the past. Multiple losses, he told me, “should force us to shift our position where we make an offer of mitigation to a homeowner, and if they do not choose to take it, we don’t renew their policy.”

After Biggert-Waters, some private insurers began showing an interest in covering flood insurance for the first time. A major factor is the end of subsidized coverage: As premiums increase, private insurers have a greater incentive to compete. Another, Guin says, is that risk analysis can be much more accurate than even a few years ago, thanks to powerful computers able to run more simulations that include more variables. Making money on insurance, after all, is a game of timing, and most policies are rewritten each year.

Evan Hecht, chief executive of the Flood Insurance Agency, based in Florida, read the details of Biggert-Waters and decided to expand his business. He had sold N.F.I.P. policies for years, but in 2013 he and his wife, Tiara, went out on their own, seeking private underwriting from Lloyd’s of London and an A.I.G. subsidiary. The vast majority of their policies — now totaling 19,000 in 37 states, including some in the Norfolk area, according to Hecht — are on properties that require flood coverage because of their locations, and on which FEMA is raising rates. On average, he estimates, premiums from the Flood Insurance Agency cost 30 to 35 percent less than those bought through FEMA. And the agency plans to offer further discounts for properties with waterproof alternatives to easily damaged materials like wood floors and Sheetrock.

At a congressional hearing on flood insurance reform in March, Hecht asked lawmakers to approve legislation that makes it simpler for private flood insurance to satisfy mortgage requirements. FEMA supports this move as a way of spreading out risk — the bottom line, Wright says, is that “we need more people covered for their flood peril” — but also cautions that it could make things worse for taxpayers if, with the help of better data, private insurers are willing to cover only lower-risk properties, or purposefully price themselves out of high-risk ones, leaving FEMA with an even more dangerous portfolio than it started with.

Hecht believes his company’s interest in policies FEMA considers underpriced for their risk is evidence that such an outcome won’t occur. But private insurance, he noted in the hearings, is “of course” not interested in covering severe-repetitive-loss properties or buildings whose exposure is higher than what can be recouped in premiums. What will happen, I asked him, to houses that flood too often? “Insurance policies aren’t written for 100 years,” he replied, “so we’ll react as it happens.” He described a driver who has had so many speeding tickets and accidents that his auto insurance skyrockets: “Those houses will not exist, just like that driver will no longer have a car. There’s no magic answer.”

Elisa Staton still owns the house in Larchmont-Edgewater. After delivering the painful estimate of the house’s new value, Staton’s real estate agent suggested she call a man named Mike Vernon, an insurance agent in Hampton Roads who brands himself as “the Flood Insurance Guy.” His specialty is finding clever ways to reduce flood premiums. When Vernon visited Staton’s house, he saw a solution right away: The rec room, once a garage, sat lower than the first floor, lowering the minimum elevation level of livable space inside the house, which FEMA uses to calculate premiums. By converting it back to “low-value storage space,” lifting the electrical system to a higher elevation and adding flood vents, Staton could get her premiums close to $800 a year. She paid for the work, Vernon updated her policy and she put the house on the market for $100,000 more than the agent first advised — but it has yet to sell.

“We’re often actually making the building worse to bring down premiums,” Vernon told me: filling in basements, or preparing a house to let water flow through it instead of keeping it out (yes, the house may be damaged by moisture, but at least it won’t be pushed off its foundation). “Or we’re eliminating something good, like a sunroom on a slab.”

Vernon’s business is flourishing. A former consultant, he got the idea for his own venture after advising a flood-vent inventor around the time federal flood premiums began to increase: “Biggert-Waters passed, and I’m seeing dollar signs.” He’s hardly alone in looking for the financial silver linings of rising seas — local universities and the city itself are pointing to their growing expertise in flood mitigation and adaptation as a source of future revenue. Vernon gets most of his business from referrals from real estate agents, whose clients, unable to sell their houses, often come to him in tears. “People are getting killed,” he said. “To an appraiser it’s still worth $300,000, but to the real world it ain’t worth nothing, because it’s not going to sell.”

On a recent Wednesday morning, Vernon, seeking new business, described his work in the packed beige meeting room of a Hampton Roads real estate agency. He showed the agents a slide that listed the threats facing the area: changing weather patterns; bigger, stronger storms; rising sea levels; long-term erosion; sinking land mass; and poor building decisions. He got a laugh with a line about the absurdity of building houses with basements in Norfolk. “Was it a bad building decision back in 1900?” he continued. “Probably not, but it has turned into one.”

Vernon described which problems are fairly easy to remedy and which are not. Houses built directly on slabs, which are especially common in low-income neighborhoods, have the fewest alternatives: Basically, raise it up or raze it down. (“If you ever want to make an enemy, or get back at one,” he’ll tell agents, “just sell them a house on a slab in a required flood zone.”) With flood insurance, Vernon said, the agents should be prepared for the three Fs: frustration, fear and foreclosure. “I’ve seen people, they just walk the keys down to the bank and say, ‘You can have it.’ ”

The biggest reaction came when Vernon explained that, because of the effort to make the N.F.I.P. more financially sound, premiums are set to go up by 18 to 25 percent every year, and cited a study that found that each $500 annual increase in flood insurance lowers a home’s value by $10,000. The room filled with gasps and whistles. “What was that ratio again?” an agent named Carmon Pizzanello called out from the back. “In two years,” Vernon replied, “you’ve lost tens of thousands of dollars on your house.”

Pizzanello volunteered that she’d sent one of her clients, living in a below-flood-elevation house on a slab and paying $3,200 annually for N.F.I.P. coverage, to talk to Vernon. Short of options, they looked into private insurance. The lowest quote that came back was $22,000 a year. It was one of those raise-or-raze situations, Vernon told the gathering, saying, “Elevation certificates are literally about tenths of feet.”

Spend a few days talking about floods and real estate in Norfolk, and you’ll quickly learn the importance of even tiny inclines. Locals know where, on what appears to the uninitiated to be a flat street, to park their cars to keep them from flooding past the axles when the wind pushes the tide up. Landscapers build what are essentially decorative earthen dikes around houses. When I asked one man how close storm and tidal surges come to his front porch, he pointed at the bricks under my feet, which I had taken for the wall of a flower bed. “You’re actually standing on a bulkhead,” he said.

In the coming decades, these fine distinctions will mean little, as the risk of flooding becomes the certainty of it. The operative measurement for rising waters in Norfolk is not inches but feet — as many as six of them by the end of the century, according to the Army Corps of Engineers, though estimates vary. City planners are forthright that they’re preparing for a future in which parts of the city do not survive. “We absolutely cannot protect 200 miles of coastline,” George Homewood, Norfolk’s planning director, says. “We have to pick those areas we should armor, and the places where we’re going to let the water be.”

Norfolk now mandates that new construction be built three feet above current base flood elevation (as if the houses were boats, this distance from the waterline is called freeboard), and 18 inches above what Homewood says is “euphemistically known as the 500-year floodplain.” But Norfolk is an old, established city, where changing new construction can only get you so far. In 2008, the city hired a Dutch engineering firm, experienced with life below sea level, to help develop a plan for adaptation. The firm suggested $1 billion in changes, more than half of which would go to simply updating existing infrastructure.

Like insurers, residents are playing a game of risk and timing. “Adaptation is a range,” says Fred Brusso, a former city flood manager. “Do you need to just move your car? Do you have to put your washer and dryer on cinder blocks? Or do you need to get the heck out of town?” Sean Becketti, the chief economist for Freddie Mac, cautioned in a report last year that economists aren’t sure if coastal property values will decline gradually, as the life expectancy of homes shrinks, or precipitously, “the first time a lender refuses to make a mortgage on a nearby house or an insurer refuses to issue a homeowner’s policy.”

Skip Stiles, the executive director of the local nonprofit Wetlands Watch, took me on a tour of frequently flooded areas of Norfolk — when waters are down, Stiles uses rusty storm drains and marsh plants growing in yards and medians to show where they’ve been — and pointed out buildings that had been elevated. Often their awkwardness made them obvious: ordinary, colorful houses perched uncomfortably atop walls of bare concrete blocks. While FEMA does pay to elevate risky houses, it struggles to keep up with demand: Wetlands Watch compared the number of people on the FEMA waiting list in Norfolk with the number of houses raised in a year, and concluded that it would take 188 years to complete them all. By then, of course, waters would be far higher.

This is the hardest reality to discuss, Stiles said, and a reason flood insurance is serving as a kind of advance scout into a more difficult future. “When you go out to the end of the century, some of these neighborhoods don’t exist, so it’s hard to get community engagement,” he said. “Nobody wants to talk beyond where the dragons are on the map, into uncharted territory.”