Using chaos to model geophysical phenomena

Dec 07, 2010
These two images show that the most "coherent set," the most nondispersive transport time from Sept. 1 to Sept. 14, is in fact the vortex itself over this domain -- demonstrating that the new technique very accurately pinpoints the polar vortex at specific times. Credit: American Institute of Physics

Geophysical phenomena such as the dynamics of the atmosphere and ocean circulation are typically modeled mathematically by tracking the motion of air or water particles. These mathematical models define velocity fields that, given (i) a position in three-dimensional space and (ii) a time instant, provide a speed and direction for a particle at that position and time instant.

"Geophysical phenomena are still not fully understood, especially in turbulent regimes," explains Gary Froyland at the School of Mathematics and Statistics and the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS) at the University of New South Wales in Australia.

"Nevertheless, it is very important that scientists can quantify the 'transport' properties of these geophysical systems: Put very simply, how does a packet of air or water get from A to B, and how large are these packets? An example of one of these packets is the Antarctic polar vortex, a rotating mass of air in the stratosphere above Antarctica that traps chemicals such as ozone and chlorofluorocarbons (CFCs), exacerbating the effect of the CFCs on the ," Froyland says.

These two images show that the most "coherent set," the most nondispersive transport time from Sept. 1 to Sept. 14, is in fact the vortex itself over this domain -- demonstrating that the new technique very accurately pinpoints the polar vortex at specific times. Credit: American Institute of Physics

In the American Institute of Physics' journal CHAOS, Froyland and his research team, including colleague Adam Monahan from the School of Earth and Ocean Sciences at the University of Victoria in Canada, describe how they developed the first direct approach for identifying these packets, called "coherent sets" due to their nondispersive properties.

This technique is based on so-called "transfer operators," which represent a complete description of the ensemble evolution of the fluid. The transfer operator approach is very simple to implement, they say, requiring only singular vector computations of a matrix of transitions induced by the dynamics.

When tested using European Centre for Medium Range Weather Forecasting (ECMWF) data, they found that their new methodology was significantly better than existing technologies for identifying the location and transport properties of the vortex.

The transport operator methodology has myriad applications in atmospheric science and physical oceanography to discover the main transport pathways in the atmosphere and oceans, and to quantify the transport. "As atmosphere-ocean models continue to increase in resolution with improved computing power, the analysis and understanding of these models with techniques such as transfer operators must be undertaken beyond pure simulation," says Froyland.

Their next application will be the Agulhas rings off the South African coast, because the rings are responsible for a significant amount of transport of warm water and salt between the Indian and Atlantic Oceans.

Explore further: New method for non-invasive prostate cancer screening

More information: The article, "Transport in time-dependent dynamical systems: Finite-time coherent sets" by Gary Froyland, Naratip Santitissadeekorn, and Adam Monahan appears in the journal CHAOS. See: link.aip.org/link/chaoeh/v20/i4/p043116/s1

Provided by American Institute of Physics

not rated yet
add to favorites email to friend print save as pdf

Related Stories

2008 ozone hole larger than last year

Oct 07, 2008

The 2008 ozone hole – a thinning in the ozone layer over Antarctica – is larger both in size and ozone loss than 2007 but is not as large as 2006.

Study Finds Clock Ticking Slower On Ozone Hole Recovery

Jun 30, 2006

The Antarctic ozone hole's recovery is running late. According to a new NASA study, the full return of the protective ozone over the South Pole will take nearly 20 years longer than scientists previously expected.

Recommended for you

New method for non-invasive prostate cancer screening

16 hours ago

Cancer screening is a critical approach for preventing cancer deaths because cases caught early are often more treatable. But while there are already existing ways to screen for different types of cancer, ...

How bubble studies benefit science and engineering

17 hours ago

The image above shows a perfect bubble imploding in weightlessness. This bubble, and many like it, are produced by the researchers from the École Polytechnique Fédérale de Lausanne in Switzerland. What ...

Famous Feynman lectures put online with free access

18 hours ago

(Phys.org) —Back in the early sixties, physicist Richard Feynman gave a series of lectures on physics to first year students at Caltech—those lectures were subsequently put into print and made into text ...

Single laser stops molecular tumbling motion instantly

22 hours ago

In the quantum world, making the simple atom behave is one thing, but making the more complex molecule behave is another story. Now Northwestern University scientists have figured out an elegant way to stop a molecule from ...

User comments : 1

Adjust slider to filter visible comments by rank

Display comments: newest first

geokstr
3 / 5 (2) Dec 07, 2010
Geophysical phenomena are still not fully understood...

Lies, I tell you, lies.

The debate is over, the consensus has been reached, 100% of the evidence is in and it is totally undisputed by every intelligent human being not in thrall to Exxon and Cheney. There is no longer any doubt left whatsoever that we need to radically restructure and impoverish our civilization under the watchful and beneficent hand of St. Algore and his acolytes, or we suffer the fate of Venus by next Tuesday.

Gaia be with you.