Effects of nonlinear rheology, temperature and anisotropy on the relationship between age and depth at ice divides

C Martín,G H Gudmundsson

doi:10.5194/tc-6-1221-2012

Abstract

Abstract. Ice flow in divide areas is strongly anisotropic. The evolution of ice fabric, from the onset of divide flow towards steady state with a fully developed fabric, has been shown to profoundly affect both the stratigraphy and surface topography of ice divides. Here, we investigate the effects of ice flow on the age-versus-depth relationship at ice divides by using a full Stokes thermomechanical model with a non-linear anisotropic constitutive relation between stress and strain rates. We compare our results with analytical approximations commonly employed in age–depth predictions, such as the Dansgaard and Lliboutry approximations. We show that these approximations systematically underestimate the age of ice at fully developed divides by as much as one order of magnitude. We also show that divides with fully developed fabric are ideal locations for ice-core extraction because ice under them can be up to one order of magnitude older than ice at the same depth at the flanks. In addition, these divides have a distinctive morphological structure that allows them to be clearly identified from satellite imagery or ground-penetrating radar data.

Highlights

Ice cores contain a record of Earth’s climate, and are used, for example, to understand how recently observed changes in climate fit within a long history of natural climatic variability
An ice-core timeline is obtained by counting annual accumulation cycles or seasonal variations in its chemical constituents, but because of cumulative effects of vertical compression and ice flow distortion these techniques can often not be used in the lowermost sections of an ice core
Initial conditions are a flat surface over the whole model domain; ice fabric varying linearly from isotropic at the surface to vertically-aligned single-maximum fabric at the base; temperature following the Robin (1955) analytical approximation; and, for the age of ice, we use the steady state solution for anisotropic shallow ice approximation (SIA)

Summary

Introduction

Ice cores contain a record of Earth’s climate, and are used, for example, to understand how recently observed changes in climate fit within a long history of natural climatic variability. The underlying difficulty in using flow models to determine the age of ice cores is the complex nature of ice flow. For a nonNewtonian fluid such as ice, the effective viscosity is a function of the deviatoric stress state For ice divides this implies that close to the bedrock, where deviatoric stresses tend to be small, the ice will be harder to deform than in the surrounding areas that are characterized by, in comparison, larger deviatoric stresses. Beneath ice divides this non-linear effect gives rise to the well-known Raymond bump (Raymond, 1983), i.e. an anticline of the internal isochrones. The range of models used, includes stationary models with fixed geometry and fabric (e.g. Mangeney et al, 1996), models where fabric is not induced by flow (e.g. Pettit et al, 2007, 2011), models that

Results

Discussion

Conclusion