By her own admission, Diana Balmori is a bit of a dreamer, although she prefers to call it thinking in the theoretical. Consider this, for example. She has a vision for the mostly drab, post-industrial landscape of Long Island City, just across the East River from Manhattan, where every flat roof, car park and available unused open space – even the beds of rail tracks – would be covered with plants.

But when Balmori has an idea, she doesn’t just discard it. She follows it through, using computer graphics to create a virtual mock-up of what it would be like. In this case, the results were beyond even what she had imagined. Thus transformed, Long Island City would offer no less than 270 hectares of brand-new green space – the size of Prospect Park in Brooklyn. “You can’t seriously think of making a new Prospect Park,” she says. “But you can create a new Prospect Park in bits and pieces. It’s an incredible possibility.”

Incredible indeed. But Balmori is no crackpot eco-idealist: she heads her own urban design company, Balmori Associates, which is ready to put such proposals into practice whenever people listen. Occupying a loft-like floor of a building (which it shares with such singular tenants as the painter Jasper Johns and Ian Schrager, the hotel developer) in the West Village of Manhattan, it finds itself in the vanguard of the suddenly burgeoning global green-space industry.

The industry is still extremely young and largely experimental. Balmori found-ed her company in New Haven, Connecticut in 1990, focusing on landscape design as we used to understand it. But in 2000 she moved it to Manhattan and the timing was serendipitous. At that moment planners in the US, lagging a little behind Europe, were beginning to latch on to commissioning far more audacious new green landscapes in urban settings with an emphasis on public recreation but also ecological reward. The green-roof revolution followed soon after.

“Urban environmentalists in the US started to think in bigger chunks in the early 2000s,” she explains. “Riverfronts became a big deal, which meant approaching things on a much larger scale rather than plot by plot. It is where this fusion of landscape and urban design works really well. European cities did this much earlier. We’re behind, but we’re catching up, if a bit slowly.”

The seeds of the Long Island City project have already been sown. In 2006 the owners of two buildings who had heard about it hired Balmori to install green roofs for them. Drive across the Queensboro Bridge from Manhattan today and you will see them. One is on top of the Silvercup television studios, where the TV serial The Sopranos was made.

Balmori’s motivation for the project is at least as much aesthetic as ecological. “We are interested in it as art,” she says, “not as a bureaucratic endeavour or a planting endeavour. The search for form is the name of the game. Yes, they work as an ecological function but we are more interested in them as a new kind of public space. That’s the big agenda that we have. For the moment most of the roofs are being built as ecological machines cleaning the air and cleaning water but the longer term idea for us is the invention of public space where it wasn’t one before.”

She achieved some of this fusion at the Solaire, a new residential building in Battery Park City, lower Manhattan, that has been certified as New York’s first truly ecological apartment block. Its green roof has paths running through it for residents. So-called “grey water” from the apartments – from sinks, not toilets – is cleaned by the soil and root systems and used again to water the whole green expanse.

Some of the Balmori proposals may still be ahead of their time. It has developed detailed renderings, for example, for the building of floating and movable islands of green space and even beaches that would be anchored in the waters around New York. Each summer, they would be moved to benefit a different borough or neighbourhood.

The city has not bought into that just yet. Nor, meanwhile, is the company without its competitors, all of which have appeared in the past few years. When Balmori joined up with the London-based architect Zaha Hadid to pitch for New York’s much vaunted High Line project, which will turn a 2.4km stretch of elevated and abandoned railway track on its west side into a raised park, they came in second. “I don’t care, we had fun with that,” Balmori says. Yet, the company has recently won competitions for two other civic projects as vast as they are startling. Planning approval is under way for the company to create new public spaces in a neglected waterfront area between the massive Gateway Arch that identifies St Louis and the Mississippi river. It will consist of a series of ramps and terraces down to the river’s edge.

And here the floating island concept will come to life. Connected to the shore by pontoons that will rise and fall with the river (the variation is as much as 12m), the islands will include parkland, a restaurant and a large pool that will become an ice rink in winter.

More dazzling still is the role recently awarded to Balmori Associates in developing an entire new town of administrative buildings for the government of South Korea about an hour and a half’s drive from Seoul. The company’s vision, which beat competition from other international bidders, is of a whole series of interconnected office buildings only six floors high, all of which will be covered with green, ecological roofs. It will be the world’s first zero-waste city. Fly over it when it is completed and you will think you are looking at fields.

“It’s a very exciting project,” Balmori says. “It’s colossal.” With projects such as this it is easy to forget that the green roof movement is still in its infancy – this is because, says Balmori, most developers still have trouble computing the cost of creating them with the longer term ecological and economic benefits. Yet that too is changing, she says, as “the public is suddenly clamouring for something ecological. The developers are beginning to see the writing in the sand.” Maybe we can dare to imagine that one day in the not too distant future Balmori’s dream for a green-roofed Long Island City will come true.

But wait, look carefully at the company’s renderings and you see something even more surprising – the one sky-scraper in the neighbourhood does not have a green roof, but one entirely green façade, from pavement to pinnacle. Now that is dreaming. Or is it?

On 5 June, Seoul Mayor Oh Se-hoon and Skylan Development broke ground on a €1.5bn property project. Designed by Richard Rogers, its name hints at the desirability of its location: Parc1. Once notorious as Asia’s greyest capital, Seoul has over the past decade invested €560m splashing its city with green.

Two elements are behind this: a recognition that lifestyle is critical to Seoul’s competitiveness as a business destination, and falling security risks. Ten years ago Parc1’s frontage was a concrete plaza, previously used for mass parades by the then authoritarian governments and designed as a helicopter evacuation zone for the nearby parliament in the event of a North Korean attack. Today it is the 230,000 sq m Yeouido Park, a swathe of low hills, streams, ponds, pavilions and reflexology footpaths.

More followed. Just before 2002’s World Cup the bioengineering of the world’s largest rubbish landfill – 3.4 million sq m of Nanj-Do – was completed. The trash mountains are now flat-topped hills, planted with trees and grasses. In the same year Seonyudo Island in the Han River, formerly the city’s waterworks, was reborn as a 110,000 sq m park.

In 2005, under the direction of then Mayor Lee Myung-bak, Seoul rejuvenated Cheonggye Stream, the city’s historic watercourse, after demolishing the expressway that had hidden it for 50 years. The stream, complete with carp and installation art, now winds through the city. The same year, Seoul Forest – a 1.15 million sq m nature reserve opened on the banks of the Han.

And this spring, President Roh Moo-hyun reopened hiking trails on the mountain behind his official residence. The trails were closed off in 1968, after North Korean commandos rendezvoused there before launching a suicide attack on the residence.