Karens Minde Park is one of them. Formerly a semi-marshy land area shunned by local residents, it has been renovated and transformed into a rainwater management area.
Because for the Danish capital, built on the Øresund coast, the biggest threat is water.
The city could be submerged both by rainwater (the local meteorological institute predicts an increase in precipitation of 30 to 70% by 2100), as well as by rising sea waters (42 cm on average by the end of the century), and by rising groundwater levels.
"All of Copenhagen is, in a way, in negotiation with the water cycle, because it is a wetland that has been drained," Anna Aslaug Lund, lecturer in architecture at the University of Copenhagen, sums up for AFP.
In Karens Minde Park, only a trained eye can guess the specificity of the place.
At the bend in a stone path there are three drain mouths: this is where the rain collected in the vicinity arrives, then flows to an artificial lake, a few hundred meters away.
The water "will be treated through the drainage area, then we can store it and finally we will discharge it into the port," describes Ditte Reinholdt Jensen, spokesperson for Hofor, the water and electricity supplier of the Danish capital, which designed the park with the municipal services.
Around the artificial lake, nature flourishes.
Virtuous effects
"The aim is to create synergies between stormwater management on the one hand and all the other benefits we want to bring to the city on the other," explains Aslaug Lund.
There is no shortage of ambitions.
"Improving biodiversity, combating heat islands, urban warming, offering citizens a meeting place, a green space to gather," lists Jan Rasmussen, one of Copenhagen's climate adaptation managers.
The city began its work in 2008 by identifying its weaknesses, primarily flooding.
"The biggest challenge is that we don't have a manual, no method to follow to do this," Rasmussen admits.
Depending on the neighborhood, the solutions differ.
Rain "Highways"
In more than a decade, the topography of the capital, which has 650.000 inhabitants within its walls, has been significantly modified, and not just on the surface.
After the torrential rains of July 2, 2011 (135,4 mm in two hours causing damages of more than a million euros), the city undertook to develop a network of tunnels.
These act as underground rain "highways" in neighborhoods where urbanization does not allow for direct water management.
"When we are short on space, we use pipes to distribute water out of the city," Rasmussen said.
Some projects, such as the construction of an artificial island intended in particular as a dam against rising waters, are very controversial.
But the city's dynamism in terms of adaptation is generally praised.
"At least the initiatives are there, they are really trying," notes researcher Isabel Froes, lecturer at the Copenhagen Business School, who welcomes the collaboration "with researchers and the public to raise awareness of the city's development."
A guiding principle for future construction projects as the population grows - and ages - is to avoid building in the city's many basins.
The Copenhagen model has a special feature, says Froes: it is built on trust.
"I call Denmark a prototype country," she says. "It's a great place to test new measures, to involve citizens around them, and also because it's a trusting society."