Like most Britons, many Danes have also known only one queen throughout their lifetime: one that was extremely popular, known for her sense of responsibility, propriety, and commitment to her duties.

On Sunday, the Danish queen, Margrethe, said that she would step down this month. That paves for the way for her son Prince Frederik, 55, to ascend to the throne.

Like King Charles III of Britain, who took over after the death of his mother, Elizabeth, Frederik is part of a younger generation of royals who have had their lives relentlessly documented in the media and who have embraced contemporary stances, chiefly the fight against climate change.

While Queen Margrethe once upset scientists for saying she was not convinced that climate change was directly caused by humans, her son is known for his preoccupation with environmental issues.

Prince Frederik has described how a trip to the Arctic permanently changed his perspective on the climate crisis, convincing him that it was his personal duty to speak out. He has attended United Nations climate summits and has given countless speeches and interviews on environmental matters, underlining the urgency to act and pressuring investors to use their capital in ways that address global warming.

Pernille Almlund, a communication professor at Roskilde University in Denmark, said that, like most businesses, a modern royal family could not refrain from being involved in climate issues. “They also have a brand,” she said.

But Prince Frederik’s commitment to the environment has also raised some doubts among those who say that having royal family members call for emissions reductions while living in castles and traveling on private planes could backfire.

“The crown prince must strike a balance,” Marie Ronde, a Danish reporter who covers the royals, said in an article on the website of the broadcaster TV2. “There is a discrepancy between being climate-friendly and showing grandeur and splendor.”

The recent coronation of Charles came as polls showed that Britons, particularly the young, feel a growing fatigue with the hoary rituals and elaborate trappings of the monarchy.

But royal watchers in Denmark say that Prince Frederik has shown a propensity for modernizing the monarchy, at least in its tone. Lars Hovbakke Sorensen, an expert on the Danish royal family, said that Prince Fredrik was known for speaking with an open mind, without placing much emphasis on formality and titles.

“When different Danes have met him and spoken with him, afterward they always felt that they have just spoken with Frederik,” Mr. Hovbakke Sorensen said. “And that is something that fits well with the time and the importance of the royal house renewing itself and gradually becoming more informal.”

Mr. Hovbakke Sorensen added that the Danish monarchy had already evolved much more quickly than the British crown and become less traditional. It was also much less sumptuous: Prince Frederik’s coronation on Jan. 14 will not be an hourslong pageantry with a gold-trimmed stage coach and acrobatic jets — as was the case with Charles’s elevation — but will involve a simple proclamation by the prime minister at the Christiansborg Palace in Copenhagen.

The monarchy in Denmark is also less galvanizing. Debates around the royals occasionally flare up in the news media but the Danish monarchy does not face the same level of scandal, scrutiny and criticism as its British counterpart. More than 75 percent of the Danish population supports a form of government with a royal head. In comparison, about 62 percent of Britons support retaining the monarchy, according to a recent YouGov poll.

Still, the news media has watched the royals’ lives up close. In 1988, Danish reporters extensively covered a car accident that Prince Frederik was involved in while in France after his younger brother lost control of their small Peugeot. Four years later, the prince was a passenger when the police stopped a car his girlfriend was driving; she was subsequently fined for driving while intoxicated and for not having a license.

In a biography of the prince written by Jens Andersen, Frederik was quoted as saying that in his youth, the prospect of becoming king was “a drawback” that made him insecure, shy and awkward.

Over the years though, the prince would earn a degree from Aarhus University in Denmark and embark on an extensive military career, serving in the army, the air force and the navy, where he was part of the maritime elite unit, the Frogman Corps.

As he became more familiar with his royal responsibilities, he said, the prospect of becoming a king “has shifted from a certain form of fear to awe.”

Prince Frederik has also come to be known for his dedication to fitness, having run marathons and completed an Ironman competition, and he has publicly promoted healthy living and personal well-being.

On Monday night, Denmark’s prime minister, Mette Frederiksen, made a last-minute change to the topic of her New Year speech to focus on the royal succession.

“The queen has said it in her own way: ‘I have a son whom I have great confidence in,’” Ms. Frederiksen said.

“I can add that we also have that confidence,” she added. “Because we know our future king.”

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