Prasicek Günther, Herman Frédéric, Robl Jörg, Braun Jean
Institute of Earth Surface Dynamics University of Lausanne Lausanne Switzerland.
Department of Geography and Geology University of Salzburg Salzburg Austria.
J Geophys Res Earth Surf. 2018 Jun;123(6):1344-1362. doi: 10.1029/2017JF004559. Epub 2018 Jun 19.
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.
冰川和河流是山地侵蚀的主要营力。在河流领域，经验关系及其数学描述，如河流功率定律，增进了人们对地貌演化基本控制因素的理解，但在冰川地貌方面，简单的约束条件和主导的尺度关系却普遍缺乏。我们给出了一个耦合系统中沿侵蚀冰川纵向剖面的稳态解，该系统包括构造作用和气候因素。我们结合浅冰近似和冰川侵蚀规则，根据规定的冰川物质平衡梯度和岩石隆升速率来计算冰面和冰床地形。我们的方法受到用于描述河流稳态的河流功率定律经典应用的启发，但显著的不同之处在于，在冰川领域，冰川物质平衡作为一个随海拔变化的变量被加入其中。通过我们的分析发现，冰面坡度和冰川起伏与隆升速率呈比例关系，比例指数表明，与大多数河流地貌中的起伏相比，冰川起伏对隆升速率的敏感度较低。由底部滑动或内部变形控制的基本尺度关系遵循幂律，其指数取决于冰川侵蚀规则和格伦流动定律的指数。在滑动和变形的混合情况下，会出现具有可变指数的复杂尺度关系。此外，冰川物质平衡的截断或高海拔地区的冷冰会导致比例指数大幅增大，这可能为高纬度地区的高起伏提供一种解释。
