We’ve all heard stories of islands of floating rubbish in the middle of the oceans, but it’s the trillions of barely visible microscopic fragments that are set to be the world’s next ecological emergency.

I just sat next to a coral reef and watched the sharks go by,” says Céline Cousteau. The filmmaker is talking about a recent dive in Australia, when for once she left her camera behind. “There’s a certain grace when a massive tiger shark acknowledges your presence but just swings by. It doesn’t have time for you.” But then Cousteau is more comfortable in the ocean than most of us, as you might expect from the daughter of environmentalist Jean-Michel and granddaughter of Jacques, whose films first brought the deep to the surface.

Increasingly Cousteau finds herself battling to preserve not just the family legacy but the ocean itself. A member of the World Economic Forum Council on Oceans, she has spent the past few days at Davos pushing to move ocean issues up the global agenda. “My grandfather said: ‘People protect what they love.’ And my father followed with: ‘How can you protect what you don’t understand?’ I see my role as explaining to people why the health of oceans matters.”

In particular, it will be difficult to explain to future generations how and why humanity decided to use the planet’s oceans as a dustbin for plastic, a material known for its durability. Perhaps we thought it magically evaporated. Trillions of pieces are now swirling around the planet’s great oceanic gyres. Gyres occur when airflows moving from the tropics to the polar regions create a clockwise rotating air mass, which then drives oceanic surface currents in the same direction. It is here, where winds are light, that the plastic debris of our throwaway lives is dramatically visible.

Scientists and explorers are also drawn to the gyres, especially the so-called Eastern Garbage Patch in the north Pacific, the largest of the five major examples. Indeed, the trend threatens to displace the destruction of the Amazon rainforest as the ecological cause célèbre. Global adventurers (including David de Rothschild on a boat, Plastiki, made of plastic bottles) have headed to the Eastern Garbage Patch to raise public awareness, monitor the flux of plastic and to vlog for National Geographic.

While these swashbucklers have made an important contribution, however, they do not tell the full story. Richard Thompson, professor of marine biology at Plymouth University, wants to solve a huge mystery: rather than being stunned by the amount of plastic swirling around in the ocean, he has always wondered why there isn’t more.

It first occurred to him that something was missing when, as a PhD student, he co-ordinated beach clean-ups for the Marine Conservation Society. “Everyone collected the more exciting pieces, running to get a tyre or fishing net but trampling over thousands of bits of fragmented plastic,” he says. Once he started teaching his own students, he challenged them to find the smallest bits of plastic possible. They came back with sand samples and “from the start we saw pieces that didn’t look natural”. Rather than fancy field trips, he spent (and still spends) a good bit of time out in all weathers in the English Channel, just up from Plymouth’s Tamar estuary, with a trawl net.

Sieving the ocean is a thankless task. There are hundreds of variations of plastic polymers, and the natural world also throws up decoys: two tiny fragments in a test tube look to my eyes like so-called “mermaid’s tears”, small pellets which are a raw material in the manufacture of plastic that have spilled into the environment. More than 250bn are produced each year. “Actually,” says Thompson, “those are squid eyes.” In the ocean they’d naturally biodegrade.

In Lost at Sea: Where is All the Plastic?, a landmark study published in Science in 2004, Thompson and his team were able to demonstrate to the world that plastic litter seen in the gyres was only the start of the problem. The study coined the term microplastics (now commonly used) to describe tiny pieces of plastic under 5mm in diameter. Using the samples he had collected around Plymouth he showed microscopic plastic fragments to be abundant in the water column. He also used a cache of plankton samples dating back to the 1960s, collected on stretches of sea between Aberdeen and the Shetlands and between Sule Skerry and Iceland, very far from the subtropical gyres. Again these revealed microplastics but also proved that they had increased substantially since the 1960s, alongside our production and consumption of plastic. Thompson had his proof that microscopic pieces of plastic are potentially presenting a huge threat to the oceans.

After the 2004 study, he continued his plastic detection, doggedly crunching the numbers. Even taking into account microplastics on the ocean’s surface as well as all the more obvious junk monitored in the gyres, it didn’t add up. Each year globally we manufacture, at the very least, 300m tonnes of plastic, and the “flux” of plastic to the world’s oceans is suggested to be at least 0.1% of all plastic. Thompson added in “legacy plastic”, the results of six decades of producing plastic waste. But still there was a deficit. Where on earth was it?

Every detective needs a breakthrough moment. Thompson and his team had two. The first was in 2014, when they came across samples of sea ice from remote Arctic locations and tested it for microplastics. The results were extraordinary. Thompson found in some cases that the Arctic ice contained concentrations of microplastics greater even than in the Pacific gyre. What became apparent was that as it formed, sea ice concentrated natural particulates from the water column, drawing in a high level of microplastics.

I always imagined that this would be the point when scientists high-five each other and whoop for joy. But the discovery of a proportion of the missing plastics was cold comfort to a conservationist like Thompson. Not only did it illustrate the extensive reach of manmade plastics, but it also raised a second issue: if Arctic ice continues to melt at its current rate, then more than one trillion pieces of microplastic could be released. The toxicological and long-term environmental effects of this are unknown. Besides, Thompson’s figure still came up short even if he factored in the plastic residing in the bellies of seabirds.

The next breakthrough came from 3,000 metres below the ocean surface. Thompson received a call from Dr Lucy Woodall of the Natural History Museum, who had been surveying the deep seabed and found mystery particles. Far from bobbing around on the surface of the five gyres, an abundance of microplastics were likely to have accumulated at the bottom of the sea. Seemingly buoyant particles sank as they weathered, were colonised by organisms or caught up in storms. Another huge sink had been uncovered.

And there we might end, if this was just an eco whodunit. The bad news is that plastic contamination stretches from the seabed to Arctic ice and shorelines as far south as Punta Arenas, Chile. As Thompson puts it: “Everywhere we’ve looked so far for plastic contamination, we’ve found it.” But what is the impact of all this plastic, which can be ingested by almost every species and stored in their tissue? Now that Thompson has begun to work out where the plastic goes, he needs to quantify its impact.

“Plastic itself isn’t the problem,” he says. “It’s the way we use it that turns this wondrous material into a major waste problem.” The question remains: can we change our habits in time? It will take more than the efforts of the Plymouth University marine science department and a few dedicated environmentalists to make a difference.

Céline Cousteau, meanwhile, remains contemplative about the aquatic universe of which her family has done so much to raise awareness. If he were alive today, it’s hard not to think that her grandfather Jacques would be devoting his energies to raising awareness of the plastic pandemic. “It’s a privilege to have access to an underwater world,” Céline says. “Down there it’s sort of quiet, but loud at the same time.”