Image Contains Modified Copernicus Sentinel Data (2019), Processed By ESA, CC BY SA 3.0 IGO

Your mission is to move a fractal, where do you start?

Yue Ying and his colleagues have proven that their new data assimilation method is able to reliably correct the position of vortices – swirls in water. They have high hopes for its use on features in sea ice like cracks and ridges, improving operational sea-ice forecasting.

You have probably noticed how a tree branch looks like a tiny version of a full-grown tree. Lightning bolts show a similar structure, branching out thinner and smaller. And the distinct shape of a fern leaf is made up of smaller leaves that are also made up of even smaller leaves, all looking like the big fern leaf. Trees, lightning, and ferns have something in common: They are fractals occurring in nature. A fractal is a shape or pattern that repeats itself at different scales.

Another example of a natural fractal are swirls in the ocean called eddies or vortices. In the ocean, a vortex is caused by winds or ocean currents, making the water spin in a circular motion. In the atmosphere, the same vortices create the weather you see every morning. And since vortices are fractals, such a vortex is always accompanied by smaller vortices around it, looking the same way and behaving the same way. And these smaller vortices have in turn even smaller vortices as travel companions.

Data such as from satellite images can tell us where in the ocean a vortex is. When we want to know where it will move, we can use mathematical (data assimilation) methods to make sure a forecast model stays as close to reality as possible. Knowing about the position can be useful for studying the ocean, or for example to adjust shipping routes to be more effective with respect to time and fuel use. The current data assimilation methods work well for correcting the position of a main vortex, but they struggle with getting the position of smaller vortices around it right, which are following a fractal pattern.

Yue Ying and colleagues from the National Center for Atmospheric Research (NCAR) in the USA and the Nansen Center developed an idea to address that issue. They originally focused on weather forecasts but found the method useful for other forecasts such as for the ocean or sea ice. Their new data assimilation method makes it possible to properly correct the position of a large feature, and consecutively the positions of its smaller and smaller companions following a fractal pattern. Ying and his colleagues showed that their method works well, using the example of vortices. It is better than traditional methods for aligning features like vortices of different sizes.

Currently, Ying and his colleagues are working on adapting their new method for sea-ice features like cracks, leads, and ridges. These features are lines, not circular like vortices, but they are also fractals, so Ying and his colleagues are hopeful to soon be able to show that their new method also works well for sea ice. They believe that this will make a big difference in operational sea-ice forecasting. Forecasting sea ice is beneficial for the safety of human activities in the Arctic such as shipping. And as sea ice is declining under global warming, accurate forecasts are even more crucial. Improving the quality of such forecasts is therefore of great value to society.


Monthly weather review:
“Improving vortex position accuracy with a new multiscale alignment ensemble filter”