“If he had got the forecast wrong,” Peter Stagg said from his home an hour from Bordeaux, “I could have been sitting in German France — not France France.”

Mr. Stagg was speaking about the pivotal role his father, Group Capt. James Stagg, played in liberating France from Nazi occupation.

The elder Mr. Stagg was not a general or a foot soldier, but in the final hours before one of the most consequential moments of World War II, he was the man everyone was waiting on.

On June 6, 1944, Gen. Dwight D. Eisenhower ordered more than 150,000 Allied troops to storm the beaches of Normandy in one of the largest seaborne invasions in history. But hours before, Eisenhower’s eyes were fixed not on the battlefield, but on the skies. More precisely, on the weather report laid out before him. And the meteorologist who had created it, described by his son as “a dour irascible Scot,” had to get it right.

“The weather forecast was a go or no-go,” said Dr. Catherine Ross, a library and archive manager at the Met Office, the weather service for the United Kingdom. “Everything else was ready.”

Success demanded a very specific set of conditions:

• Before the landings, the weather needed to be calm for 48 hours.

• For the three days following, the wind needed to stay below Beaufort Force 4, equivalent to a moderate breeze.

• Parachutists and other air support needed less than 30 percent cloud cover below 8,000 feet, with a cloud base no lower than 2,500 feet and visibility of over three miles.

• A low tide at dawn was needed to expose German defenses.

• The invasion had to occur one day before or four days after a full moon for nighttime operations.

• Furthermore, the invasion had to align with the Soviet summer offensive in the East, to maximize pressure on German forces.

The Allies identified a window: between June 5 and June 7.

The odds were daunting. According to Dr. Ross, the likelihood of all the desired weather conditions aligning was 13 to 1 — and roughly triple that once the full moon was added to the equation.

Making matters worse, the beginning of June brought a spell of highly unsettled weather.

“There was a succession of low pressures and fronts coming across the Channel, and the challenge was trying to find a gap,” she said. “Not just to allow them to invade, but to be able to get enough backup troops and supplies across.”

The fifth “was the ideal day,” Eisenhower recalled in an interview 20 years later. But the date was subject to last-minute revision in the event of bad weather.

The man tasked with delivering that all-important forecast was Group Captain Stagg, the chief meteorological adviser to Eisenhower from the British Meteorological Office. He was responsible for producing a unified forecast based on input from three independent groups, two British and one American.

Peter Stagg, who was a toddler in 1944, said his father upheld strict discipline at home and rarely smiled. Yet he also had a lighter side.

“He had a sense of humor,” Mr. Stagg said. “If we had visitors to the house, they’d all say, ‘Oh, what a wonderful host.’ And he was charming with it, and plying them with whiskey and everything else.”

In the days leading up to D-Day, that charm was tested under enormous pressure.

“He did go through, obviously, tremendous stress — not just because it was his responsibility to get the decision right, but he was working with Americans as well as Brits,” Mr. Stagg said.

‘It was very much an evolving science.’

There was no unified approach to forecasting in 1944. The American team, part of the newly formed U.S. Strategic Air Forces based near Eisenhower’s headquarters in southwest London, employed analogue forecasting, a method that compared current conditions to historical weather patterns. The British teams relied on hand-drawn charts, observational data and newer understandings of upper-atmosphere patterns. These approaches often clashed.

“At the time, it was very much an evolving science that evolved in different ways in different countries,” said Dan Suri, a meteorologist at the Met Office.

Mr. Suri said that some of these methods remain in use today, albeit digitally.

“Aspects of what they did still feature, and the D-Day forecasters would recognize aspects of what they did in what we do today,” he said.

Group Captain Stagg’s job was not just scientific, but diplomatic — a delicate act of balancing contrasting forecasts from the American and British teams, and shaping them into a coherent narrative with a single decisive recommendation for Eisenhower.

“That wasn’t always entirely possible,” Mr. Suri said. “He had quite a difficult job, really.”

Ahead of the invasion, tensions rose between the forecasting teams. Transcripts from the daily telephone discussions between Group Captain Stagg, the general and the three forecasting teams revealed a strong difference of opinions between the groups.

Mr. Stagg remembered his father telling him how he had to navigate the growing tensions.

“The American guy was pushing all the time to give Eisenhower the good news, or what he felt was the good news,” he said. “Whereas my father had to somehow get over to Eisenhower that that wasn’t the right answer.

“My father was saying, the British weather is not like that. It’s not predictable in that sort of way,” he continued. “It’s one of the most difficult weathers in the world to predict, because it is so changeable.”

The American meteorologists believed that June 5 or 6 would offer suitable weather. The British, however, opposed June 5.

“He had to make the decision of which side he was going to go with,” Dr. Ross said, “and take that to Eisenhower.”

According to Professor Julian Hunt in his book “D-Day: The Role of the Met Office,” a high-pressure system over the Atlantic Ocean and a strong storm near northern Scotland were expected to cause rough seas and excessive cloud cover in the English Channel on June 5. Group Captain Stagg delivered his decision: Gales would sweep through Normandy, making landings impossible.

“He gave us the worst report you ever saw,” Eisenhower later recalled. Convoys that had already set off were ordered to turn back.

But by June 4, forecasts indicated that the storm system would shift northeast, giving way to a brief period of calmer conditions on June 6.

Still, Group Captain Stagg was uncertain. His diary reveals his doubt: “I am now getting rather stunned — it is all a nightmare.”

Dr. Ross said the decision to go ahead was a compromise. “It was a question of, will the sixth be good enough? And the call was, yes, it will be good enough. But it was a challenge.”

Eventually, the American and British meteorologists moved toward consensus for June 6. On the evening of June 4, Group Captain Stagg returned with the more optimistic forecast. Eisenhower later described a “little grin on his face.”

“We hoped that with this break, we could do it,” Eisenhower later said. After a brief moment of contemplation — “about 45 seconds,” he recalled — he gave the order that would change the course of history: “OK, we’ll go.”

The invasion went ahead on June 6, 1944, but the forecast turned out to be off the mark.

Mr. Suri said that, instead of moving northeast, the storm over northern Scotland shifted southward into the North Sea, weakening as it did. This unexpected change allowed winds to ease slightly, and visibility improved as the front over northern France moved away.

“That’s why things got better,” Mr. Suri said. “So they were right for the wrong reasons.”

But conditions were windy and the seas remained rough.

Many of the first troops to cross the English Channel had “considerable seasickness,” The Associated Press wrote, and the strong winds whipped up whitecaps, making the journey to the beaches even more punishing.

But the marginal weather may have given the Allies a vital edge.

The German forecasts were similar to those of the Allies, but they had not expected an invasion under such adverse conditions. On June 4, the chief meteorologist of the third German Air Fleet reported to Field Marshal Rommel that the weather in the Channel would be so poor that there could be no landing attempts until June 10.

“The Germans assumed high tide, cover of darkness and better cloud, wind and visibility conditions than the Allies actually needed,” Mr. Suri said. When the Allied forces struck, the Germans were unprepared.

In the aftermath of the invasion, as the weight of its success came into focus, the full significance of the meteorological gamble became clear.

In a memorandum accompanying an official report to Eisenhower, Group Captain Stagg reflected on just how close they had come to disaster. Had the invasion been postponed to the next suitable tides, the troops would have faced the Channel’s worst storm in 20 years.

“Thanks,” Eisenhower wrote in response. “And thank the Gods of war we went when we did.”

Remembering D-Day