GENERAL OVERVIEW: Golden’s research is focused on modeling sea ice and its role in the climate system, using a wide range of methods from mathematics and theoretical physics. His work is helping to advance how sea ice is represented in global climate models and improve projections of the fate of Earth’s sea ice packs and the marine ecosystems they support. Eighteen expeditions to conduct sea ice field experiments inform, validate, and guide development of his models, and have enabled him to observe firsthand the processes driving change in the polar regions. As a material sea ice is a polycrystalline composite of pure ice with brine inclusions. It shares similarities with many natural and high tech composites, and Golden’s mathematical sea ice work has also advanced other areas of science and engineering that may seem unrelated, but have the same underlying mathematics.
SCIENTIFIC SUMMARY: Polar sea ice is a critical component of Earth’s climate system. It exhibits complex composite structure over a wide range of length scales, from millimeter scale brine inclusions and centimeter scale polycrystalline structure, to the ice cover itself - a granular composite of ice floes, centimeters to tens of kilometers in horizontal extent, in a sea water host. A principal challenge in modeling sea ice and its role in climate is how to use information on smaller scale structure to find the effective or homogenized properties on larger scales relevant to coarse-grained climate models and process studies. That is, how do you predict macroscopic behavior from microscopic laws? Also of interest is the inverse problem of recovering parameters controlling small scale processes from large scale observations.Our research focuses on developing mathematical models of sea ice processes that are important to understanding the role of sea ice in the climate system and as a critical habitat in the polar marine ecosystem. Many of the models are inspired by statistical physics and theories of homogenization for composite materials. Processes of interest include fluid and electromagnetic transport through the brine and polycrystalline microstructure of sea ice, advection diffusion, waves on ice-covered seas, remote sensing, the evolution of melt ponds, and the dynamics of the sea ice concentration field. We also investigate how the microstructure of sea ice influences, and is influenced by, microbial communities living in the ice. Many fields of mathematics are used in our studies of sea ice and other composites, including percolation theory, partial differential equations, stochastic processes, functional analysis, spectral theory, complex analysis, fractal geometry, random matrix theory, Morse theory, topological data analysis, and machine learning.
FIELD EXPERIMENTS: Dr. Golden has conducted extensive field measurements and experiments on the fluid and electromagnetic transport properties of sea ice, its brine and polycrystalline microstructure, the growth and melting of sea ice, and other dynamic and thermodynamic processes, in both the Arctic (2007, 2011, 2012, 2013, 2014) and Antarctic (1994, 1999, 2007, 2010, 2012). Golden's field experiments are designed to help guide the development of the models, monitor microstructural transitions and track the state of the sea ice pack, provide data for comparison with theories of transport in sea ice that are critical to modeling climate and polar ecosystems, and help lay the groundwork for next generation sensors.
K. M. Golden, et al., Modeling sea ice, invited article for the Notices of the American Mathematical Society, Volume 67, Number 10, pages 1535-1555 (including issue cover), November 2020. PDF
K. M. Golden, Climate change and the mathematics of transport in sea ice, invited article for the Notices of the American Mathematical Society, Volume 56, Number 5, pages 562-584 (including issue cover), May 2009. PDF (Additional References, PDF)
K. M. Golden, Mathematics of sea ice, invited article for The Princeton Companion to Applied Mathematics, N. J. Higham (Ed.), M. R. Dennis, P. Glendinning, P. A. Martin, F. Santosa, and J. Tanner (Assoc. Eds.), Princeton University Press, pp. 694-705, September 2015. PDF
NSF Research Overview Video:
NSF Discoveries Video: On Golden's Melt Pond (Bringing Mathematics to Sea Ice Research)