Washington, D.C. (December 7, 2010) -- 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 ozone hole," Froyland says.
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.
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: http://link.
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CAPTION: These two images show that the most "coherent set," the most nondispersive transport time from September 1 to September 14, is in fact the vortex itself over this domain -- demonstrating that the new technique very accurately pinpoints the polar vortex at specific times.
Chaos is an interdisciplinary journal of non-linear science. The journal is published quarterly by the American Institute of Physics and is devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines. Special focus issues are published periodically each year and cover topics as diverse as the complex behavior of the human heart to chaotic fluid flow problems. See: http://chaos.
The American Institute of Physics is a federation of 10 physical science societies representing more than 135,000 scientists, engineers, and educators and is one of the world's largest publishers of scientific information in the physical sciences. Offering partnership solutions for scientific societies and for similar organizations in science and engineering, AIP is a leader in the field of electronic publishing of scholarly journals. AIP publishes 12 journals (some of which are the most highly cited in their respective fields), two magazines, including its flagship publication Physics Today; and the AIP Conference Proceedings series. Its online publishing platform Scitation hosts nearly two million articles from more than 185 scholarly journals and other publications of 28 learned society publishers.