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Most people believe that a single Category 3 hurricane, Katrina, devastated New Orleans on Aug. 29 of last year. The flood protection system for the New Orleans area was designed to protect the city from a direct hit by a fast-moving Category 3 storm.

Yet Hurricane Katrina, a Category 4 storm that did not strike the city directly, overwhelmed systems in dozens of places and cost more than 1,500 lives and billions in property damage.

Why? In part, say experts who studied the disaster, because the hurricane was more like four storms — at least — that battered the area in different ways. They say the system in New Orleans was flawed from the start because the model storm it was designed to stop was simplistic, and led to an inadequate network of levees, flood walls, storm gates and pumps.

The 2006 hurricane season begins Thursday, with four to six major storms predicted for this year by the National Oceanic and Atmospheric Administration. And experts say that understanding the failings is essential in planning the next generation of flood protection for a rebuilt New Orleans, and for systems nationwide.

"This is a national issue," said Raymond Seed, a professor of engineering at the University of California, Berkeley, and an author of a stinging report released last week. That report has identified flaws in design, construction and maintenance of the levees that contributed to the failures. But underlying it all, the report stated, were the problems with the initial model used to determine how strong the system should be.

With the right hurricane protection, he said, the result of Hurricane Katrina would have been different: "we call it 'wet ankles.' "

The flood protection system was first authorized by Congress after Hurricane Betsy flooded the city in 1965, and it was supposed to protect the area from the kind of storm that would come only once in two centuries. It was expected to take about 13 years to complete and cost about $85 million, according to a history by the Government Accountability Office.

When Hurricane Katrina hit New Orleans 40 years later, the system was still not finished, and it had already cost $738 million. In the eight months since the storm, the Corps of Engineers has spent some $800 million in direct costs to repair the system — $62 million more than it had cost in the first place.

The main tool used to design the system was a fiction — a hypothetical storm called the "standard project hurricane." The corps began developing the model with the Weather Bureau in 1959. The idea, as the corps has put it , was that the model would represent "the most severe storm that is considered reasonably characteristic of a region."

The corps based its model on data from previous storms, with some relatively straightforward calculations to estimate the surge and waves at various points. Maj. Gen. Don T. Riley, the director of civil works for the corps, said in an interview that the levee system "was built at the standard of the time."

In hindsight, however, it was a rough and inadequate tool. This month, Dr. David Daniel, the chairman of a panel reviewing the corps' investigation, said in an interview, "It was not a terribly sophisticated or detailed analysis by today's standards."

The report by Professor Seed's group found that the creators of the standard project hurricane, in an attempt to find a representative storm, actually excluded the fiercest storms from the database.

Storms like Hurricane Camille in 1969 were taken out of the data set as lying too far out of the norm; the Berkeley researchers noted that "excluding outlier data is not appropriate in the context of dealing with extreme hazards." Also, the calculations of the cost-benefit ratio did not take into account the costs of failure, both economic and social, far greater in an urban area like New Orleans than a rural one.

Once the standard project hurricane was completed, characterizing it was difficult. The standard was developed before the Saffir-Simpson hurricane scale came into use, and the features of the storm fit poorly with the scale. The wind speed for the project hurricane was just 100 miles per hour, which falls into Category 2; other features more closely resemble a much more severe Category 4. The corps generally calls it the equivalent of a fast-moving Category 3.

The standard project hurricane became enshrined within the corps, wrote the Berkeley group, and the corps saw little need to go back and reanalyze "the true risks of catastrophic flooding" in New Orleans. Even when the National Oceanic and Atmospheric Administration, the successor agency to the Weather Bureau, recommended increasing the strength of the model, the corps did not change its construction plans.

A report released this month by the Senate Committee on Homeland Security and Government Affairs said that calling the standard hurricane project storm a Category 3 was "at best a rough estimate, and at worst, simply inaccurate," and gave New Orleanians a false sense of security. In the report, Al Naomi, the senior project manager for the corps on the system, admitted to a simplification borne of convenience — or, as he put it to the Senate investigators, "What am I going to tell the Rotary Club?"

What the Rotary Club experienced last August was not what New Orleans was prepared for. The first stage of Hurricane Katrina touched Louisiana as it passed south of the city in the Plaquemines Parish town of Buras with winds of more than 125 miles per hour pushing a storm surge. The wind and water overwhelmed the local hurricane defenses: levees built to withstand 13 feet of water were overwhelmed by more than 17 feet of surge, damaging levees and scattering homes and boats across the thinly populated parish like toys.

As the hurricane moved across Lake Borgne to the east, the effect was quite different: the second storm sent strong waves and a surge estimated at 18 feet or more back across the lake to the levees bordering St. Bernard Parish. The long levees there had been designed to handle 13 feet of water. The assault washed over Chalmette and other communities with floodwaters exceeding 14 feet in some areas. A similar pounding took out the southeastern levee of the development known as New Orleans East.

In its third incarnation, the storm sent the water up a funnel formed at the northwest corner of Lake Borgne and into the city's Inner Harbor Navigation Canal, where the water rose and churned with exceptional force, said Hassan Mashriqui, a researcher with the Louisiana State University Hurricane Center. Those waters shattered flood walls in several places and destroyed the city's Lower Ninth Ward.

As the storm pushed into Mississippi, it sent a final surge toward New Orleans across Lake Pontchartrain, north of the city. As the water stacked up against the south shore of the lake, it rose against the walls of the three main drainage canals that run from the center of the city. Though the surge was weaker than the others and the water did not reach the tops of the flood walls, the 17th Street Canal and the London Avenue Canal suffered breaches that caused the lake's waters to spill into the center of the city.

Other parts of the area, like the West Bank communities, fared comparatively well. "If you were sitting over on the West Bank, you didn't think it was such a big deal," said Edward Link, an engineering professor at the University of Maryland, who is a leader of the corps investigation of the disaster.

Had the storm taken a westerly course instead, the effect would have been radically different, he said, and even a weak storm can, if it sits in one spot, cause profound flood damage. The lesson is that "a single storm cannot be equated to a single set of forces, or a single wave or surge environment," he said.

Dr. Daniel, who is reviewing the corps inquiry, said that today's engineers based their designs for buildings in areas prone to hazards like floods and earthquakes on statistical analyses that run through all probable conditions and produce estimates that more closely characterize the risks.

The Netherlands has built flood protection to withstand surges that might be expected every 10,000 years. Jurjen Battjes, a flood expert there who is working with Dr. Daniel's group, said his nation began embracing the statistical approach in the 1930's and got a wake-up call with floods in the 1950's. The Dutch planners extrapolated conditions far greater than anything seen in history but still possible, he said, and estimated the costs of protection, including the economic and social costs of failure, and boiled it down to a cost-benefit curve. The ultimate decision, he said, is less technical than political: "How much money do we want to spend now for protection in the future?"

In New Orleans, the hurricane protection system has now been restored to the strength it was intended to have before the storm, and it will be further improved. Congress has told the corps to study ways to improve protection for southern Louisiana. And this time, said Daniel Hitchings, director of the corps task force in charge of overall hurricane recovery for the Gulf Coast, it will be done right, with the probabilistic approach that experts have called for and a greater willingness to take new data into account.

"If we don't get the wake-up call now," he said, "we never will."