Modeling oscillations in connected glacial lakes

• Published in: Journal of glaciology Vol. 65; no. 253; pp. 745 - 758
• Main Authors: Stubblefield, Aaron G., Creyts, Timothy T., Kingslake, Jonathan, Spiegelman, Marc
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.10.2019
• Subjects: Boundary conditions; Confluence; Cycles; Differential equations; Drainage systems; Dynamic systems theory; Finite element method; Glacial lakes; Glaciation; Glacier hydrology; Glaciers; Glaciohydrology; Hydraulics; Ice sheets; Ice streams; Jökulhlaups (GLOFs); Lake size; Lakes; Mathematical models; Meltwater; Mountain glaciers; Mountains; Ordinary differential equations; Oscillations; Partial differential equations; Qualitative analysis; Rheology; Streams; Subglacial lakes; subglacial processes; Water shortages; Antarctica; subglacial processes; Jökulhlaups (GLOFs); Glacier hydrology; subglacial lakes
• ISSN: 0022-1430; 1727-5652
• DOI: 10.1017/jog.2019.46

Mountain glaciers and ice sheets often host marginal and subglacial lakes that are hydraulically connected through subglacial drainage systems. These lakes exhibit complex dynamics that have been the subject of models for decades. Here we introduce and analyze a model for the evolution of glacial lakes connected by subglacial channels. Subglacial channel equations are supplied with effective pressure boundary conditions that are determined by a simple lake model. While the model can describe an arbitrary number of lakes, we solve it numerically with a finite element method for the case of two connected lakes. We examine the effect of relative lake size and spacing on the oscillations. Complex oscillations in the downstream lake are driven by discharge out of the upstream lake. These include multi-peaked and anti-phase filling–draining events. Similar filling–draining cycles have been observed on the Kennicott Glacier in Alaska and at the confluence of the Whillans and Mercer ice streams in West Antarctica. We further construct a simplified ordinary differential equation model that displays the same qualitative behavior as the full, spatially-dependent model. We analyze this model using dynamical systems theory to explain the appearance of filling–draining cycles as the meltwater supply varies.