Always the right scale

For their calculations, climate modellers portray the planet using grids. The smaller the grid’s scale, the higher the model’s resolution – and the more computational power is needed. Mathematicians at the AWI can now cover the entire globe with a variable-scale net. As a result, higher resolution can be selected for especially interesting regions without producing a major increase in required computational power.

It all starts with a grid – no matter whether the goal is to find out how much the planet is warming due to climate change, whether the Gulf Stream is likely to grow weaker, or if the Arctic will soon be completely free of sea ice in the summer. Practically nothing can be accomplished without grids – at least when it comes to climate modellers, who use powerful computer programs in an attempt to predict the planet’s future. The reason: the Earth’s climate and weather phenomena are so complex that they can only be analysed bit by bit. In response, modellers cover the globe with a net composed of square grids – the grid boxes. In global climate models, a single grid box usually has sides measuring 100 kilometres. As a result, thousands of individual grid boxes are required for the entire globe. And for each one, the climate model calculates a range of physical parameters like temperature or sunlight – using formulas that e.g. describe how wind flows between high-pressure and low-pressure areas. Millions of individual steps are needed to calculate all of the grid boxes. As such, it’s hardly surprising that climate models can only be run on supercomputers – and today, even they aren’t always up to the task.

A resolution of 100 kilometres isn’t good enough

Dr Sergey Danilov knows why. “In many cases, a resolu­tion of 100 kilometres isn’t fine enough to depict climate phenomena in detail,” he says. The reason: there can be significant climate differences in the course of 100 kilometres. Germany’s Harz Mountains offer a good example. The Western Harz is damp because it ­catches a good deal of rainfall. Yet the Eastern Harz, only 50 kilometres away, is much dryer, because it lies on the lee side of the mountains and receives much less pre­cipi­tation. A 100-kilometre-wide grid box can’t reflect these differences.

Danilov then cites a further example: many climate models have a hard time realistically portraying the course of the Gulf Stream. It originates in the Gulf of Mexico, heads north along the coast of Florida, and then turns east, heading toward ­Europe. Yet many models can’t show this turn at its proper location; they show the stream continuing much farther north. “Among other reasons, this is because the Gulf of Mexico is home to many circular flows – we call them eddies – in which water masses move past one another or become mixed,” Danilov explains. “If grid boxes are too coarse, they can’t accurately reflect these phenomena.”

The ideal solution would be a global grid box with a scale of ten kilometres or less. But that would exponentially increase the number of individual calculations, and a supercomputer would need weeks to complete climate simulations that only cover a few years. As a result, research would grind to a halt. Making matters worse, researchers have to reserve supercomputing time for their calculations, and the time doesn’t come cheap.


Prof Dr Sergey Danilov

As flexible as a string shopping bag

Accordingly, for the time being, an extremely fine-scale grid on a global scale is still just wishful thinking. But Sergey Danilov and his colleagues have found a good compromise: they have applied a mathematical method that allows them to weave together grid boxes with different scales, which means they can select higher resolutions for certain regions without having to change the entire net. The approach is a bit like a filled string shopping bag: in spots near heavy groceries like melons, the mesh is stretched out; in spots with lighter items like a bag of crisps, it’s more compact. Applied to climate models and the global grids, that means they can explore complex regions like the Gulf Stream with a much more precise grid box, while a coarser resolution suffices for the rest of the Atlantic.

A net for the entire ocean

To create such a flexible mesh, modellers have to say good­bye to the classical square grid boxes. “When working in a net, it’s extremely difficult to merge square grid boxes with different sizes or resolutions,” Danilov explains, “because this requires seriously deforming the boxes to include gradual transitions when calculating climate parameters.”

To overcome this problem, they use a mesh composed of small triangles that are flexible and malle­able, providing the same types of transitions we see in the string shopping bag. Modellers refer to these grids, which use triangles or other geometric figures, as ‘unstructured grids‘. In connection with the ocean, they were first used by Dutch coastal engineers in an effort to map the currents along coastlines, and for dykes, sluices and dams. “We’re the first researchers to apply unstructured grids to the ocean as a whole, so as to model climate processes or related phenomena in specific regions,” says Danilov.

Danilov himself rarely engages in extensive climate modelling. Instead, he’s the mathematical ‘brains’, and provides his colleagues with the tools they need. One such colleague is climate modeller Dr Helge Gößling: “For some time now, we’ve been working on forecasting changes in Arctic sea-ice cover for periods ranging from weeks to decades, and regional phenomena like the warm water influx through the Fram Strait between Greenland and Svalbard are important aspects.” Gößling now hopes to more accurately model them with the help of unstructured grids.

Nearly as fast as classical models

After several years of development, AWI climate modellers seem to have found a very promising approach. Granted, running the calculations for the unstructured grids takes longer than for the classical square grids. But they’re catching up; they continue to refine their algorithms, and the calculating time for standard climate simulations is now roughly twice as long as with conventional methods. “That’s remarkable, since just a few years ago we needed several times as much time,” says Danilov. As such, the unstructured grids are becoming a real alternative. The researchers have already successfully demonstrated that they can precisely simulate the Gulf Stream. And the unstructured grids can also accurately portray changes in the surface temperature of the Antarctic Ocean – the latest calculations are impressively close to the actual measurements.

A tool for the whole world

In the meantime, this extraordinary model, named FESOM, has already been used in a global comparison of climate models – the Coupled Model Intercomparison Project – the results of which will be used in the next IPCC Assessment Report. Sergey Danilov, Helge Gößling and their colleagues at the AWI are eager to see how their calculations match with those produced by other models. The more realistic depiction of key ocean regions, made possible by the unstructured grids, may prove to offer wholly new insights into what the future holds. The AWI team now wants to make its simulation tool available to other researchers online – as a knitting pattern of sorts, with which climate modellers around the world can reweave their grid nets


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