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Will the Gulf Stream become stronger or weaker? Erwin Lambert uses a simple model to investigate a complicated problem. Photo: Martin van Drongelen

The entire ocean in three boxes

Sometimes things are so complicated that you're forced to think simple. Erwin Lambert is an expert at that. With a few, plain boxes he tries to calculate how a rainy future will influence Atlantic currents.


In the deep sea, the water barely moved. Ocean currents were driven by the wind blowing over the sea surface, and no matter how strong the wind was, only the upper layers of the sea were affected. Even though theories of deep ocean currents had been debated as early as in the 1870s, text books in the middle of the 20th Century still told a story of the quiet deep. In 1961, the American oceanographer Henry Stommel reduced the ocean to a few equations and showed that people were wrong.

With Stommel's model, the North Atlantic can be split into a warm part in the south and the cold Nordic Seas in the north – a thought experiment of two boxes, without coastlines, islands or underwater ridges. The Nordic Seas consist of the Norwegian Sea, the Icelandic Sea and the Greenland Sea. By calculating how warm and how salty the water is in each box, and how much water that moves between the boxes at the surface and at the bottom, you have a simple model of the Atlantic Ocean, a complete circulation regardless of the wind.

In the North Atlantic, water flows northward at the surface, before sinking to the bottom in the Nordic Seas and flowing back southward in the deep ocean. The surface current flowing north is what we think of as the Gulf Stream. Stommel's description of how water circulates between warm and cold regions like this, was entirely theoretical, and it was the Finnish oceanographer Clas Rooth who applied it to the Atlantic in 1982.

Stommel's model
The circulation in the Atlantic Ocean. In the Atlantic, water flows northward at the surface (red arrow), cools and sinks in the Nordic Seas, before flowing back south in the deep ocean (purple arrow). The surface current flowing north is the Gulf Stream and its extension into the Norwegian Sea. All illustrations: Ellen Viste

Stommel's and Rooth's calculations showed that the circulation is not only forced by the wind, but also by changes in the density of the water. The saltier and colder, the denser and heavier water is. When the salty and warm Atlantic water from the south flows northward, it gets denser as it cools. As a result, it sinks, and more water flows in from the south to replace the sinking water. It's this sinking that is the main driver of the circulation.

Simple answers to difficult questions

Stommel's model is simple. It does not represent all factors in the real world, but still made it possible to answer a big question. You can neglect the wind, and there will be circulation in the North Atlantic. As long as water sinks in the north, the Gulf Stream will continue to flow north.

– The beauty of such a model is that we can understand the full behavior of its circulation, says Erwin Lambert.

Lambert is a PhD candidate at the Geophysical Institute at the University of Bergen and the Bjerknes Centre, and works with a box model that builds on Stommel's model. He remarks that both theoretical models, like his, and the large and more detailed circulation models used for weather forecasting and climate projections, only represent the real world to a limited extent.

– The benefit of a theoretical model is that we know, and actually choose, what these limitations will be.

Climate change makes it complicated

Simple models make it easier to pin-point the effect of changes. Like Stommel, Lambert kan choose to let the water in the north be less salty and calculate how the ocean current will react to more freshwater in the Nordic Seas. A fresher north is exactly what is expected with global warming.

In a warmer world, there will be more rain and snow in the northern regions, meltwater from glaciers and sea ice will pour into the ocean, and together this will make the water in the Nordic Seas less salty. The salty Atlantic water that flows in from the south will mix with water that is fresher than it used to, and the mix will be less dense. As a result, water entering the Nordic Seas will not sink as efficiently as it has done in the past. According to Stommel's model, this would reduce the circulation in the Atlantic Ocean. This is the background for theories that global warming may weaken the Gulf Stream.

Stommels modell under klimaendring
Global warming causes more precipitation in the north, with more freshwater in the Nordic Seas. The extra freshwater will mix with the salty Atlantic water entering from the south, and as it gets less salty, it gets lighter. As a result, there will be less sinking, and this can contribute to reducing the Gulf Stream.

But after all, the world is not that simple.

– This is two thirds of the water, but only half of the story, says Erwin Lambert.

We're missing a box.

No blind alley in the Nordic Seas

Two thirds of the water that enters the Nordic Seas flow back south in the deep ocean. The remaining one third continues on the north-bound route and enters the Arctic Ocean. This water is not included in Stommel's model, and when calculating the effect of climate change, it must be. The old model consists of one box for the southern part of the North Atlantic and one for the Nordic Seas. Now, we need one more box: the Arctic Ocean.

Mighty rivers like Jenisej, Lena, Ob and Mackenzie bring enormous amounts of freshwater into the Arctic Ocean. Because the water is fresh, it's light and stays near the surface as it flows southward along the east coast of Greenland and into the Atlantic. The flow of freshwater to the south carries a surplus of water from the Arctic Ocean. It tries to regain the balance, and if this had been all, not much more would happen. But the freshwater current near the surface drags some of the saltier water below with it, removing more than just the extra water that came with the rivers. This shifts the balance in the other direction, and as a result, more water has to flow in from the Atlantic. In this way, the transport of freshwater out from the Arctic Ocean and the Nordic Seas also works to increase the flow of water into the Nordic Seas from the south.

Stommel's model extended with the Arctic Ocean
Freshwater from precipitation and run-off to the Arctic Ocean flows south near the surface along the east coast of Greenland, through the Nordic Seas and into the Atlantic Ocean (blue arrow). This current also drags some of the water below with it, and more water must flow in from the Atlantic to regain the balance (purple arrow). The flow of freshwater out of the Arctic Ocean thus enhances the circulation in the Atlantic Ocean.

A question of where rain will increase the most

With more rain and snow in the north, there will be more water in the large rivers, and there will be more freshwater in the Arctic Ocean. This may enhance the circulation in the North Atlantic and make the Gulf Stream and its extension along the Norwegian coast stronger. 

Stommels modell utvidet med Polhavet under klimaendring
When more precipitation increases the flow of freshwater out of the Arctic Ocean, more water will also have to flow in from the south to replace water that is driven out. This may increase the circulation in the Atlantic Ocean.

But the Arctic Ocean is not the only basin to get more freshwater with climate change. There will be more rain, snow, run-off and ice melt in the entire northern region, including the Nordic Seas. And freshwater there works the other way. With more light freshwater in the Nordic Seas, less of the water entering from the south will sink, and in Stommel's model, this sinking is the driver of the circulation in the Atlantic Ocean.

The question is which effect will be the largest. Will more freshwater in the Arctic Ocean strengthen the current more than it weakens as the Nordic Seas also become fresher?

– It's more important to know where precipitation will increase the most than exactly how much it will rain, Erwin Lambert concludes. – If more than 30 percent of the extra freshwater ends up in the Nordic Seas, the model shows that the circulation in the North Atlantic may become unstable.

Gulf Stream more stable than previously believed

The third box – the Arctic Ocean – stabilizes the circulation in the Atlantic Ocean. When you include the effect of more freshwater in the Arctic Ocean, the current will be less reduced than in Stommel's model with only two boxes. This makes Erwin Lambert think that increasing precipitation in the north may be less important for the circulation in the Atlantic than previously believed.

He admits that it's still an open question of how well such simple box models represent reality. For example, wind – which the Stommel model does not consider – is a vital driver of the Gulf Stream near the surface. But Lambert maintains that simple models still make it possible to study major processes in the ocean.

– It’s amazing how much knowledge can be gained from a model that consists of merely five equations.