Using Math to Track the Pacific Garbage Patch

By Ankit Dangi, CS Graduate Student, 2015

Take a flight from Boston to Tokyo and you’d witness great scoops of clouds, floating by like islands of ice cream; travel by the sea, and you would cherish your luxurious cruise. However, if you were to travel by submarine, you might see huge islands of garbage.

In 2006, a Greenpeace report on marine litter for the United Nations Environment Program titled Plastic Debris in the World’s Oceans announced that the scale of contamination of the marine environment by plastic debris is significant and widespread; plastic can now be found floating in all of the world’s oceans. This plastic is disturbing at least 267 known species by entanglement or ingestion, including seabirds, turtles, seals, sea lions, whales and fish. In a 2012 scientific research expedition, 38 scientists, sailors and students at the Sea Education Association (SEA) traveled 2597 nautical miles from San Diego, CA to Honolulu, HI with 118 net tows over 36 days. In their report, ‘Plastics at SEA: North Pacific Expedition,’ the team reported that they gathered a total of 69,566 plastic pieces over 36 days.

In a recent study of how well water mixes between different regions of the surface ocean, referring to the Ekman dynamics of ocean surface circulation, researchers in Australia have developed a mathematical model to understand the evolution of these large garbage patches spanning across the waters of the Pacific Ocean. The largest known of these patches is the Great Pacific Garbage Patch, also referred as the Pacific Trash Vortex. This gyre of marine debris particles is comprised of garbage rotating along oceanic currents with large wind movements into convergence zones, areas of high concentration that are determined by the National Oceanic and Atmospheric Administration (NOAA).

Pacific-garbage-patch-map_2010_noaamdp[1]

The curious mind may want to look-up this garbage patch in the North Pacific on Google Earth, and may question the visibility of floating garbage objects. It is important to understand that the accumulated plastic debris are not solid expanses of plastic which one could walk on. Rather, most of the debris is tiny shreds of plastic film known as microplastics, which float suspended beneath the surface waters of the ocean and are almost invisible to the naked eye.

The mathematical study of ocean surface waters, published in Chaos: An Interdisciplinary Journal of Nonlinear Science by the American Institute of Physics, focuses on analyzing the spatial discretion of flow dynamics using a probabilistic approach by a Markov chain model, a mathematical system that undergoes transitions from one state to another, as opposed to the traditional time-derivative approach. This mathematical model reads a set of short-run trajectories from a global ocean model and uses those to construct a transition probability matrix, thereby representing the dynamics as a Markov chain. This enables scientists to efficiently compute the evolution of densities and calculate surface upwelling and downwelling. These results are further combined with an eigenvector approach to partition the ocean into regions that interact minimally with other regions.

Transfer operator methods were then developed to reveal the locations of garbage patches and further adapted to decompose the surface ocean into almost-invariant sets in a forward-time and backward-time sense. The study facilitates interpretation of decompositions of the ocean’s surface into basins of attraction of the major garbage patches. The mathematical model permits for probabilistic statements about the flow in such an open dynamical system; in particular, towards defining the probability of eventual absorption into an attracting region, in which water, biomass, and pollutants become trapped ‘forever.’ It also helps to determine the probability as to when any garbage particle at any given location will eventually leave the computational domain of the mathematical model. Eventually, when such mixtures of ocean surface water are studied with man-made garbage as a regressor, one could potentially form the basis of a geography demarcation of the world’s oceans where the boundaries between water basins could be determined by their circulation, rather than traditional geographical demarcations.

There have also been other varied attempts, using pervasive computing, to track trash within the US. In 2013, resident volunteers in Seattle attached small, smart, location-aware micro-electromechanical tags to 3000 trash objects. These ‘trash tags’ periodically measured the location of 3000 trash objects as the trash object moved from one place to another, and reported it to a server via triangulated cellular networks. This study was performed as part of the TrashTrack project by MIT SENSEable City Lab in order to investigate the ‘removal chain’ of consumable products as opposed to their supply chain.The results from the study, upon visualization, were awarded first place in NSF’s 2010 International Science & Engineering Visualization Challenge under the Non-interactive Multimedia category. One of the team leaders, Dietmar Offenhuber, now teaches at Northeastern’s MFA in Information Design and Visualization in the Art + Design and Public Policy department.

Using Math to Track the Pacific Garbage Patch

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