Glacial valley cross-profile morphology, Tian Shan Mountains, China

The morphology of glacial valley cross-sections can be described in terms of power law (y=axb) or quadratic equations (y=a+bx+cx2) fitted to empirical data. The quadratic solution provides a more robust way of describing the morphology of glacial valley cross-sections, whereas the power law has more potential in understanding the cross-sectional shapes and their evolution. These two functions are used to study the cross-sectional morphology of glacial valleys in the middle and western Tian Shan Mountains and to discuss the comparison with fluvial channels. The major conclusions are: (1) Power law equation parameters (a and b) are sensitive to the origin selection with larger sensitivity in vertical and A (A=lna) values. Conversely, c values of the quadratic equation are more stable regardless of different origins selected. (2) Hirano and Aniya [Earth Surf. Processes Landforms 13 (1988) 707–716] suggested two characteristic patterns in the relationship between the power law exponent, b, and the valley form ratio, FR. However, glacial valleys in these areas do not fit the Rocky Mountain model for b–FR values described by Hirano and Aniya for alpine glacial valleys. This indicates that this Rocky Mountain model cannot be applied to all alpine glacial areas. (3) The c values of the quadratic equation represent a curvi-linear trend with its corresponding FRs. At the same time, power law parameters (A and b) fit a closed linear relationship both from these areas and others in the published literature. (4) The cross-sectional shapes of glacial valleys show clear differences with fluvial channels by comparing A–b values of glacial valleys with the hydraulic geometry of fluvial channels. This implies that the A–b relationship and the variation range of b values (commonly with 1.5–2.5) may be helpful to differentiate valleys formed by different processes.