Skip to main content

Applying Math to Shrinking Arctic Ice and the Search for Planets

September 27, 2016

Sahil Agarwal (Applied Mathematics) studies changes in the Arctic sea ice, even though he’s not an environmental scientist. He also searches for exoplanets (those that orbit stars outside our solar system), but he’s not an astronomer, either. He’s a mathematician, and he uses mathematics to research patterns in both the ocean and outer space.

There is a deep set of general mathematical principles that underlie complex geophysical processes and astrophysical phenomena. These principles are not always the basis from which traditional approaches are launched, but in applied mathematics, we actually begin with these principles,” Agarwal explains.

He recently won two highly competitive awards: a summer fellowship at Woods Hole and a prize that has taken him to the University of Cambridge in England.

Born in Agra, India, Agarwal began studying sea ice as an undergraduate. After his second year at the Indian Institute of Technology, Guwahati, he was awarded a visiting student research fellowship at the Oxford Center for Collaborative Applied Mathematics (OCCAM) in England. There he met his current adviser, John Wettlaufer, the A.M. Bateman Professor of Geophysics and Physics and professor of Mathematics and Applied Mathematics at Yale, who was then on a Guggenheim Fellowship. At OCCAM, Agarwal was working on “simple models of dynamical systems and chaos,” and together they began to look at sea ice as a mathematical dynamical system.

Arctic sea ice has been a bellwether for climate change,” he points out. “Because sea ice is white and the surrounding ocean is dark, the ocean absorbs more solar radiation than the ice. As the ice thins, it gets darker, absorbs more incoming solar radiation and thins out even more.” This is called “the ice-albedo feedback,” and it is largely responsible for the more rapid increase in temperature in the Arctic than in rest of the world.

Agarwal enrolled in the Applied Mathematics PhD program at Yale in 2012. He now uses both satellite observations and geophysical processes (e.g., sea ice motion, ocean currents, and atmospheric winds) to determine how they influence the Arctic sea ice. “We have built simple stochastic models to explain this dependence of ice extent on these processes and to understand its variability on multiple time scales,” he says.

This past summer he was one of ten Fellows invited to participate in the Geophysical Fluid Dynamics program at Woods Hole Oceanographic Institution (WHOI), the theme of which was “Fluid-Structure Interaction in the Living Environment.” Agarwal, with Cambridge University Professor Grae Worster, built “simple thermodynamic models to study the interactions of sea ice exiting the Fram Strait on the northeast coast of Greenland and the warm and salty Atlantic Ocean currents entering the Arctic near Svalbard. We showed that the relative velocity between ice and ocean currents was a major driver in determining the sea ice edge in the North Atlantic.”

Agarwal is currently at Cambridge on a David Crighton Fellowship. Every year, four students of fluid mechanics, acoustics, waves, and vibration are invited to spend a few months in the Department of Applied Mathematics and Theoretical Physics. He and Worster are continuing the work they started at Woods Hole.

Agarwal recently began to turn his gaze to the heavens, applying the mathematical concept of “temporal multifractality” to the field of astrophysics.

In the past few months, we have been able to develop a new method to detect exoplanets by analyzing the raw observations,” he says. The stellar evolution models commonly used today “are fit to the data to see if there is an exoplanet or any other stellar feature.” This approach requires the removal of “noise” from various sources: instrumental noise, convection on the stellar surface, light contamination from nearby stars, and other astrophysical phenomena.

“The noise reduction can lead to spurious signals in the filtered data, causing the false detection of an exoplanet. In contrast, we use the time scales obtained from the unfiltered data related to orbital motion of the planet around its star and simple geometry to calculate the physical parameters of the system (such as the ratio of the size of the planet to its star, the latitude it is transiting its parent star as viewed from Earth, etc.). Our method considers noise as a source of information, rather than something to be filtered out.”  

When not hard at work, Agarwal likes to play squash and field hockey, but his main sport is table tennis. He has won prizes on campus and represented Yale at the National Collegiate Table Tennis Association’s New York City Downtown Division. He is also a serious amateur photographer (see the Hindu Life at Yale website) and an avid reader, especially of science fiction and fantasy.