Speaker: Dr. Matt Covington, Associate Professor, Department of Geosciences
Date: Wednesday, April 14, 2021, 4:00 PM – 5:00 PM
Title: What can we learn from a toy model of subglacial hydrology?
Abstract: Mass loss from the Greenland Ice Sheet currently produces the largest meltwater contribution to ongoing global sea level rise. Mass is lost from the ice sheet via two mechanisms, direct melt and sliding. However, most of the melt water flows to moulins, which are holes in the ice that deliver the water to the base of the ice, after which it flows out to the margins via subglacial conduits. Both modeling and field work have demonstrated complex feedback mechanisms that act between melt water and ice sliding, whereby delivery of additional meltwater to the bed can accelerate, or decelerate, sliding. Models of such processes are currently poorly constrained by data. Here we develop a simple, “toy” model of subglacial drainage and storage of water within a moulin. This model approximates the behavior of more complex models, albeit with fewer unknown parameters. Due to its simplicity, it also lends itself to a variety of analytical techniques. For example, we demonstrate that, for much of the parameter space, the model has a stable critical point. However, a Hopf bifurcation also leads to a stable limit cycle, where water levels continuously oscillate within the moulin rather than reaching an equilibrium state. Near the stable critical point, the system behaves as a non-linear damped harmonic oscillator. However, a linearized solution provides a reasonable approximation of system dynamics for much of the parameter space, enabling an analytical estimation of the timescale of system evolution following a perturbation. Numerical solutions of the model equations were compared against field observations of the amplitude of daily summer water level oscillations within two moulins. Analysis of the parameter space of the model suggested that matching the observed water level amplitude required immense storage space within the moulins, a prediction that we initially deemed implausible. However, later direct observations within moulins illustrated that such volumes do indeed exist (Covington et al. 2020). In more recent work, we have begun developing a model that tracks the evolution of moulin volumes over time. Preliminary results from this model suggest another explanation for the low levels of water level variation, bringing us full circle to our question: “What can we learn from a toy model of subglacial hydrology?”
Bio: Matt Covington received undergraduate degrees in physics (BS) and philosophy (BA) from the University of Arkansas – Fayetteville and a PhD in theoretical astrophysics at the University of California – Santa Cruz, where he studied galaxy formation. During his education, he pursued a second life as an expedition caver, spending a month or more on caving expeditions every year in remote corners of the world, and helping to explore and map some of the deepest cave systems in the world. Upon completing his PhD in physics, Covington decided to merge his career and his passion for caves, and pursued research on the mathematical modeling of processes within caves and karst. He was supported as an NSF Earth Sciences Postdoc at the University of Minnesota, and then as a NSF International Postdoctoral Fellow at the Karst Research Institute in Slovenia. He then returned to the University of Arkansas – Fayetteville, where he is now an associate professor in the Department of Geosciences. His research applies a combination of mathematical modeling and field work in the fields of hydrogeology and geomorphology, with a particular focus on karst and glacial systems.
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