A glacial buzzsaw effect generated by efficient erosion of temperate glaciers in a steady state model

Highlights

• We introduce a new valley network parameter accounting for elevation-drainage area distribution.

• We develop a new 1D model for coupled glacial-fluvial topography in steady state.

• Tectonics and climate control the shape of both glacial and fluvial topography.

• Temperate glaciers erode more efficiently than rivers for typical parameter sets.

• The influence of tectonics and climate on glacial relief is compatible with the glacial buzzsaw.

Abstract

Studies on relief and hypsometry in glaciated mountain ranges have recognized the equilibrium line altitude of glaciers as a major control on mountain height. This has led to the belief that, in contrast to fluvial topography, glacial topography is limited by climate, with tectonics playing a secondary role. This concept is known as the glacial buzzsaw. However, the understanding of controls on glacial relief has remained mainly qualitative, in part because a reference scenario for glacial landscape evolution — a glacial topographic steady state linked to the base level by a fluvial topographic steady-state downstream of the glacier terminus - and its dependencies have not yet been defined. Here we define such a reference and compare steady state longitudinal profiles in a coupled system of glacial and fluvial erosion that involves both tectonics and climate. Our model is based on the stream power law for fluvial erosion, the shallow ice approximation in combination with a glacial erosion rule, and an empirically determined drainage area-flow length relationship for both rivers and glaciers. Further, we introduce a new approach to incorporate dendritic glacier network structures into the one-dimensional model. Modeling of coupled glacial-fluvial steady-state profiles with empirical glacial and fluvial erosion parameters shows that the difference between glacial and fluvial relief depends on climate, tectonics and the applied erosion laws. Our results imply that glacial erosion can typically balance tectonic uplift rates at lower relief and topographic slopes than fluvial erosion. This steady state equivalent of the glacial buzzsaw effect suggests that glaciers may indeed be more efficient erosional agents than rivers increasing erosion in a cooling climate.

Introduction

A key question for understanding the mechanisms behind long-term global climate change is whether a cooling climate, similar to an increase in tectonic mountain building, can lead to increased erosion. In this case, a feedback can develop where increased silicate weathering and burial of terrestrial organic carbon in the ocean leads to further climate cooling (Molnar and England, 1990; Raymo and Ruddiman, 1992; West et al., 2005; Von Blanckenburg, 2005). Global studies on long-term erosion have argued in favor (Herman et al., 2013; Zhang et al., 2001) and against (Willenbring and von Blanckenburg, 2010) a link between climate cooling and erosion. This debate is enriched by studies comparing topography (e.g. Brozović et al., 1997) and erosion rates (e.g. Harbor and Warburton, 1993; Koppes and Montgomery, 2009) in glacial and fluvial landscapes. While they provide information on erosion under different climate conditions, they do not necessarily enable us to draw conclusions on the erosional efficiency of glacial relative to fluvial processes. Present-day glacial topography is in a transient state, where it is unclear and highly variable how far the transition from a fluvial to a glacial mountain geometry (and back) has progressed (e.g. Brocklehurst and Whipple, 2004; Prasicek et al., 2015), and short-term erosion rates highly depend on local environmental conditions (e.g. Harbor and Warburton, 1993; Hallet et al., 1996), while long-term rates reflect tectonic activity rather than differences between different processes (e.g. Willett and Brandon, 2002). Here we present new insights into the efficiency of glacial and fluvial erosion based on a landscape evolution approach.

The evolutionary state of active mountain ranges must reflect the competition between tectonic and erosion processes. This allows the definition of a theoretical steady state, a reference state where uplift is balanced by erosion and topography is thus invariant over time everywhere in the landscape (e.g. Whipple and Tucker, 1999; Willett and Brandon, 2002). In such a reference state, tectonics controls the uplift and erosion rates, while both tectonics and climate control the height and steepness of topography. In this way, the steady state reference can be useful to learn about the competition of climate and tectonics and to understand the theoretical relations between the shape of topography and the underlying process rates. In the specific case examined here, the steady state reference can be used to infer the efficiency of glacial and fluvial erosion processes from the height and steepness of modeled topography.

Efficient glacial erosion is implied by the so-called ‘glacial buzzsaw’ effect. Several studies have found little to no variation in the height and steepness of glacial topography with tectonically-driven uplift and identified the equilibrium line altitude (ELA), and thus climate, as the governing or even the sole influence on mountain relief (e.g. Brozović et al., 1997; Egholm et al., 2009), while others link relief above the ELA to tectonic activity (Pedersen et al., 2010). Modeling of steady state topography can be employed to evaluate such relationships in a theoretical benchmark test. This has become a standard approach in fluvial landscape evolution modeling (e.g. Whipple and Tucker, 1999; Perron and Royden, 2013), and has recently been adopted for the glacial realm (Headley et al., 2012; Prasicek et al., 2018).

The glacier mass balance rate, the rate of ice production, is positive above the ELA (accumulation of ice) and negative below the ELA (ablation of ice). Its dependence on elevation exerts a major control on glacial steady state topography (Herman et al., 2018; Prasicek et al., 2018). Longitudinal profiles of eroding glaciers in topographic steady state have been defined with glacier mass balance depending on position along the glacier (Headley et al., 2012), and on elevation (Prasicek et al., 2018). These glacier-specific steady state models can inform about the role of glacier mass balance on the scaling of relief and topographic slope with rock uplift rate and climate. However, the reference point of these glacial models is at the intersection between the ice surface and the ELA, and a baselevel does not exist. A direct comparison between glacial and fluvial steady state profiles requires a modeling framework that couples glacial and fluvial processes, where at the glacier terminus glacial topography is linked to fluvial topography and thus to baselevel.

In this study, we build on the work of Prasicek et al. (2018) and develop a modeling framework for glacial steady state longitudinal profiles based on the shallow ice approximation (SIA) that is fully compatible with the stream power law (SPL) and can thus be used to directly combine glacial and fluvial profiles to compare topographic characteristics such as relief, slope and shape in the same tectonic scenarios. We constrain the roles of ELA and tectonic uplift in shaping the glacial steady state profile and controlling the ratio between glacial and fluvial relief.