Abstract
Glaciers and rivers are the main agents of mountain erosion. While in the fluvial realm empirical relationships and their mathematical description, such as the stream power law, improved the understanding of fundamental controls on landscape evolution, simple constraints on glacial topography and governing scaling relations are widely lacking. We present a steady state solution for longitudinal profiles along eroding glaciers in a coupled system that includes tectonics and climate. We combined the shallow ice approximation and a glacial erosion rule to calculate ice surface and bed topography from prescribed glacier mass balance gradient and rock uplift rate. Our approach is inspired by the classic application of the stream power law for describing a fluvial steady state but with the striking difference that, in the glacial realm, glacier mass balance is added as an altitude‐dependent variable. From our analyses we find that ice surface slope and glacial relief scale with uplift rate with scaling exponents indicating that glacial relief is less sensitive to uplift rate than relief in most fluvial landscapes. Basic scaling relations controlled by either basal sliding or internal deformation follow a power law with the exponent depending on the exponents for the glacial erosion rule and Glen's flow law. In a mixed scenario of sliding and deformation, complicated scaling relations with variable exponents emerge. Furthermore, a cutoff in glacier mass balance or cold ice in high elevations can lead to substantially larger scaling exponents which may provide an explanation for high relief in high latitudes.
Highlights
Glaciers shape major mountain landscapes worldwide and scour characteristic landforms such as cirques and overdeepened troughs (e.g., Davis, 1906; Ehlers & Gibbard, 2007; Penck, 1905)
Our approach extends the work of Headley et al (2012) by using a different method to solve the shallow ice approximation (SIA) at topographic equilibrium and, more importantly, by treating glacial landscapes as a coupled system in which glacial topography is the product of the different interactions between tectonic and climatic processes
Higher rock uplift rates can be expected to increase mountain height in both fluvial and glacial landscapes, but in the latter, the increase is reduced due to a resulting increase in glacier mass balance and ice flux, sliding velocity and glacial erosion, which counteracts the growth of relief
Summary
Glaciers shape major mountain landscapes worldwide and scour characteristic landforms such as cirques and overdeepened troughs (e.g., Davis, 1906; Ehlers & Gibbard, 2007; Penck, 1905). The time frame of the buzzsaw effect has not been clearly articulated It may describe the climate-induced rapid destruction of fluvial relief in an overall transient system state and a glacial steady state scenario where climate controls how rock uplift and erosion rates can balance each other. Our approach extends the work of Headley et al (2012) by using a different method to solve the SIA at topographic equilibrium and, more importantly, by treating glacial landscapes as a coupled system in which glacial topography is the product of the different interactions between tectonic and climatic processes This allows us to investigate the potential links and feedbacks between rock uplift rate and glacier mass balance. Our theoretical results help to put constraints on the nature of the glacial buzzsaw effect and to explain the observed dependencies of glacial relief on rock uplift rates, as well as the presence of high topography in high latitudes
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