The future is Nye: an extension of the perfect plastic approximation to tidewater glaciers

Abstract

ABSTRACT. Accurate modeling of calving glaciers relies on knowledge of many processes (ice flow, surface/submarine melting, calving, mélange interaction) and glacier-specific factors (air temperature, ocean circulation, precipitation rate, glacier geometry) that remain challenging to assess. Iceberg calving, especially, is important to glacier mass loss and difficult to resolve in currently-available models. Given these challenges facing even the most sophisticated models, there is value in simple, computationally-efficient models that can capture first-order effects. In this study we derive a simple model, extending Nye's perfect plastic approximation to include a yield surface at the calving front. With one climate-related input-either an upstream glacier thinning rate or glacier-wide accumulation-this model is able to simulate the advance and retreat of marine-terminating glaciers on annual to decadal scales. Our model requires knowledge of only two glacier-specific factors: glacier bed topography and basal shear strength, both reasonably constrained by laboratory and field observations. We apply the model to a case study of Columbia Glacier, Alaska and show that, despite its simplicity, the model succeeds in reproducing observed centerline profiles and rates of terminus retreat up to 2007.

Glacier Calving in Greenland

“…In turn, this means that calving laws also need to be simple and easy to implement. The calving laws currently in use either predict calving location based on theoretical crevasse penetration depths or yield criteria [74][75][76][77][78] or predict calving rates from empirical functions (e.g. [28,29]).…”

“…Similar models were used by Lea et al [80] to simulate the historical behaviour of Kangiata Nunaata Sermia (KNS) and by Enderlin et al [27] to explore topographic controls on glacier behaviour using synthetic geometries representative of Greenland glaciers. In contrast, Ultee and Bassis [13,78] used physical considerations to define simple calving criteria that have proved very effective at reproducing observed patterns of glacier terminus advance and retreat, including Jakobshavn Isbrae and Helheim Glacier.…”

“…[78]). The advent of discrete element models such as HiDEM [81] and efficient calving routines in Elmer/Ice [30] has opened up the possibility of simulating the full range of frontal ablation processes in unprecedented detail.…”

A Plastic Network Approach to Model Calving Glacier Advance and Retreat

“…In Ultee and Bassis (2016), we extended the perfect plastic approximation of Nye (1951Nye ( , 1952Nye ( , 1953) to a centerline model of tidewater glaciers that self-consistently predicts terminus advance and retreat forced with upstream elevation change. We now generalize this model to account for the intersection of networks of tributaries.…”

“…Moreover, in recent decades Columbia and Jakobshavn have been undergoing sustained retreat (Krimmel, 2001;Joughin et al, 2004Joughin et al, , 2012Joughin et al, , 2014O'Neel et al, 2005;McNabb et al, 2012), Hubbard has been advancing (Trabant et al, 2003;Ritchie et al, 2008) and Helheim has experienced both advance and retreat episodes (Howat et al, 2005(Howat et al, , 2010Murray et al, 2010), providing tests of our model's ability to resolve calving dynamics in a range of environments. Further, with the case studies selected here we go beyond the work of Ultee and Bassis (2016) to show that the model can reproduce patterns of retreat and advance in both Greenland and Alaska and that the model can be used to analyze glaciers with more than one branch.…”