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 numerical simulations investigating glacier dynamics and bed evolution in Xue Mountain Glacial Cirque No.~2, Taiwan over a 9~ka time scale. The non-linear Stokes equations governed by Glen's flow law are solved using a stabilized equal-order Galerkin least-squares finite element method, fully coupled with a basal sliding relationship, an empirical erosion law, and an Arbitrary Lagrangian--Eulerian moving-mesh formulation. The computational experiments evaluate how variations in ice thickness and the basal sliding constant govern long-term bedrock lowering and valley development. Simulation results demonstrate that spatially concentrated basal erosion along the valley axis drives progressive deepening and widening of an initially V-shaped valley over 9~ka, evolving into a characteristic U-shaped cross-section. Sensitivity analyses further reveal that ice thickness and the basal sliding constant exert strong, non-linear coupling controls on bed-normal lowering distance, as ice thickness amplifies basal sliding velocity and, consequently, subglacial erosion rates. Constrained by the present-day valley cross-profile, the numerical framework yields a physically plausible reconstruction of former glacier conditions. The reconstructed bed profile reproduces the smooth U-shaped morphology with exceptional fidelity, yielding a minimum bed elevation after 9~ka that differs by merely 0.6~m from the present-day observed value. These findings highlight how integrated flow--sliding--erosion modeling can quantitatively elucidate the long-term morphodynamic evolution of subtropical alpine glacial landscapes.