Three-Dimensional Numerical Modeling of Glacier Flow and U-Shaped Valley Evolution in Subtropical Taiwan
Abstract
Glacial erosion plays a critical role in shaping alpine topography,yet the coupled effects of ice deformation, basal sliding, andbedrock erosion on millennial-scale valley morphodynamics remainchallenging to quantify. This study presents three-dimensionalsimulations of glacier dynamics and bed evolution in Xue MountainGlacial Cirque No.~2, Taiwan, over an effective glaciation timescaleof 9~ka. The nonlinear Stokes equations with Glen's flow law aresolved using a stabilized equal-order Galerkin least-squares (GLS)finite element method coupled with a basal sliding law, an empiricalerosion law, and an Arbitrary Lagrangian--Eulerian (ALE) moving-meshformulation. Numerical experiments evaluate how ice thickness andthe basal sliding constant govern long-term bed lowering and valleydevelopment. Spatially concentrated basal erosion along the valleyaxis progressively deepens and widens an initially V-shaped valley,producing a characteristic U-shaped cross-section. Sensitivityanalyses reveal nonlinear coupled effects of ice thickness and thebasal sliding constant on bed-normal lowering distance, as increasingice thickness enhances basal sliding velocity and, consequently,subglacial erosion rates. Using the present-day valley-floor elevationas a geomorphic constraint yields a physically plausible reconstructionof former glacier conditions. After 9 ka, the reconstructed bed profilereproduces the smooth U-shaped morphology, with a minimum elevationof 3716.6 m, only 0.6 m above the present-day valley-floor elevationof 3716 m used as a constraint. These findings demonstrate howintegrated flow-sliding-erosion modeling provides quantitativeinsights into the long-term morphodynamic evolution of subtropicalalpine glacial landscapes.
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BibTeX
@misc{lee2026threedimensional,
title = {{Three-Dimensional Numerical Modeling of Glacier Flow and U-Shaped Valley Evolution in Subtropical Taiwan}},
author = {Hsueh-Chen Lee},
howpublished = {EarthArXiv},
year = {2026},
month = sep,
doi = {10.31223/x5fr4j},
url = {https://eartharxiv.org/repository/view/15154/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Three-Dimensional Numerical Modeling of Glacier Flow and U-Shaped Valley Evolution in Subtropical Taiwan
AU - Hsueh-Chen Lee
PY - 2026
DA - 2026/09/24
PB - EarthArXiv
DO - 10.31223/x5fr4j
UR - https://eartharxiv.org/repository/view/15154/
AB - Glacial erosion plays a critical role in shaping alpine topography,yet the coupled effects of ice deformation, basal sliding, andbedrock erosion on millennial-scale valley morphodynamics remainchallenging to quantify. This study presents three-dimensionalsimulations of glacier dynamics and bed evolution in Xue MountainGlacial Cirque No.~2, Taiwan, over an effective glaciation timescaleof 9~ka. The nonlinear Stokes equations with Glen's flow law aresolved using a stabilized equal-order Galerkin least-squares (GLS)finite element method coupled with a basal sliding law, an empiricalerosion law, and an Arbitrary Lagrangian--Eulerian (ALE) moving-meshformulation. Numerical experiments evaluate how ice thickness andthe basal sliding constant govern long-term bed lowering and valleydevelopment. Spatially concentrated basal erosion along the valleyaxis progressively deepens and widens an initially V-shaped valley,producing a characteristic U-shaped cross-section. Sensitivityanalyses reveal nonlinear coupled effects of ice thickness and thebasal sliding constant on bed-normal lowering distance, as increasingice thickness enhances basal sliding velocity and, consequently,subglacial erosion rates. Using the present-day valley-floor elevationas a geomorphic constraint yields a physically plausible reconstructionof former glacier conditions. After 9 ka, the reconstructed bed profilereproduces the smooth U-shaped morphology, with a minimum elevationof 3716.6 m, only 0.6 m above the present-day valley-floor elevationof 3716 m used as a constraint. These findings demonstrate howintegrated flow-sliding-erosion modeling provides quantitativeinsights into the long-term morphodynamic evolution of subtropicalalpine glacial landscapes.
ER -