Since 2004, there has been at least one catastrophic flood somewhere in the world every year, and flooding has become one of the most visible effects of global warming. The 2010 floods in Pakistan left 10m people homeless and the World Bank estimated the total cost of the disaster to be $9.7 billion. The price tag for the 2015 flood in Missouri, in the American Midwest, is estimated at $3 billion, while the flooding in Britain last winter came to £5 billion (just over $7 billion). As sea levels rise and the weather becomes more extreme, there is more to come.

Accordingly, architects are increasingly being asked to design buildings to resist deluges. Baca, an architectural practice in London, have become specialists in the field. The firm’s Amphibious House (below), completed earlier this year, was built on an island prone to frequent flooding near Marlow on the River Thames. Constructed in a purpose-built wet dock with a permeable base, it has buoyant foundations and can rise up to 2.5 metres above its normal position. The basement is fully waterproofed and habitable even when submerged. The terraced gardens, meanwhile, act as both a way of measuring a rise in the water level and as an early-warning system: when the first two terraces are submerged, the owners know that the Amphibious House should have begun to rise between its mooring posts. Since this project was completed, the firm has proposed a simpler, narrow pre-fab building that would float by the banks of canals, designed to help ease London’s shortage of affordable housing while leaving enough room for water traffic.

A similar problem lay behind a more grandiose project in the Netherlands, where around half the population lives below sea level and where there is a lack of suitable land on which to build. All 97 of the houses in the Ijburg district in Amsterdam have Styrofoam-filled bases that make them float. The simple, white-and-glass structures are connected by a series of jetties and provide relatively high-density, flood-resistant accommodation.

For cities on dry land that are at increased risk of flooding, such as Hamburg and Rotterdam, architects are moving away from traditional defences such as dykes, levees and dams, all of which work by holding water back but are sometimes overwhelmed in extreme conditions and are expensive to maintain. Instead, they are trying to make space for water in the urban fabric so that life can continue uninterrupted during flooding. Water plazas, which have been built in both cities, usually function as public spaces, but during floods they act as reservoirs until the water can drain away naturally. Buildings in the HafenCity district in Hamburg have been waterproofed, and entrances and walkways are elevated. In Britain, Baca have been working on large-scale city and town plans for Britain’s Department of Environment, Food and Rural Affairs, using an elegant, plank-fronted house that the firm built in Oxfordshire in 2015 as a template (pictured top). The whole structure is raised off the ground so that floodwater flows beneath it.

But floating architecture needn’t be grand and expensive. The Nigerian-born architect, Kunlé Adeyemi, captured the imaginations of designers around the world with a floating school for a slum in Lagos. The district of Makoko is home to around 100,000 people in a rapidly expanding city where the total population already exceeds 18m and where 2,000 new people arrive each day. The slum’s ramshackle houses teeter on stilts above the water, and are crowded and prone to collapsing. Adeyemi’s school seemed like an ingenious and cheap solution. The triangular, three-storey structure was made of timber off-cuts and bamboo, and buoyancy was provided by a platform of 250 recycled plastic barrels. Adeyemi’s biggest problem was making this simple assembly sufficiently strong. Earlier this year, a prototype collapsed during a heavy thunderstorm, sending a cascade of splintered wood into the lagoon and causing a squall of dismay in the local and architectural communities.

A second, sturdier version of the floating school, the MFSII, is currently moored in Venice (above) – another European city bedeviled by rising water. It won the Venice Beinnnale’s Silver Lion award days before the collapse of the first model. The design, Adeyemi says, is “a prototype for a new type of architecture and urbanism on the water.” Even if his structure has had mixed success so far, plenty of architects are thinking about what this new urbanism might look like. One Anglo-Chinese firm, AT Design Offices, even dreamt up an unlikely plan for a complex of partially submerged, rounded hexagonal towers, connected by passages and interspersed with green spaces, farms, and docks for ships and submarines. If it ever got off the ground it wouldn’t be simply a collection of floating buildings, but an entire floating city.