Three-Dimensional Numerical Modeling of Glacier Flow and U-Shaped Valley Evolution in Subtropical Taiwan

Hsueh-Chen Lee 

Glacial erosion plays a critical role in shaping alpine topography,
yet the coupled effects of ice deformation, basal sliding, and
bedrock erosion on millennial-scale valley morphodynamics remain
challenging to quantify. This study presents three-dimensional
simulations of glacier dynamics and bed evolution in Xue Mountain
Glacial Cirque No.~2, Taiwan, over an effective glaciation timescale
of 9~ka. The nonlinear Stokes equations with Glen's flow law are
solved using a stabilized equal-order Galerkin least-squares (GLS)
finite element method coupled with a basal sliding law, an empirical
erosion law, and an Arbitrary Lagrangian--Eulerian (ALE) moving-mesh
formulation. Numerical experiments evaluate how ice thickness and
the basal sliding constant govern long-term bed lowering and valley
development. Spatially concentrated basal erosion along the valley
axis progressively deepens and widens an initially V-shaped valley,
producing a characteristic U-shaped cross-section. Sensitivity
analyses reveal nonlinear coupled effects of ice thickness and the
basal sliding constant on bed-normal lowering distance, as increasing
ice thickness enhances basal sliding velocity and, consequently,
subglacial erosion rates. Using the present-day valley-floor elevation
as a geomorphic constraint yields a physically plausible reconstruction
of former glacier conditions. After 9 ka, the reconstructed bed profile
reproduces the smooth U-shaped morphology, with a minimum elevation
of 3716.6 m, only 0.6 m above the present-day valley-floor elevation
of 3716 m used as a constraint. These findings demonstrate how
integrated flow-sliding-erosion modeling provides quantitative
insights into the long-term morphodynamic evolution of subtropical
alpine glacial landscapes.