Longitudinal variations in cross-section morphology along a glacial valley: A case-study from the Tien Shan, China

Abstract

A new model, the variable width/depth ratio (VWDR) model, is used to analyze longitudinal variations in cross-section morphology along glacial valleys. In the VWDR, the cross-sectional shape of a valley is expressed as a function of the width/depth ratio at various heights above the valley floor. Two parameters, m, a measure of the breadth of the valley floor, and n, a measure of the steepness of the valley sides, appear in the model. We have used the VWDR model to study morphological variations of cross-sections along glacial valleys in the middle Tien Shan mountains, China, and find that: (1) in valleys without tributaries, m increases (the valley floor becomes wider) and n becomes more negative (valley sides become steeper) from the head of the valley to the equilibrium line, and then m decreases and n becomes less negative to the end of the valley; (2) in valleys with tributaries, a similar pattern is observed, with an oscillating maximum in m and minimum in n in those sections where a tributary enters the main valley. These characteristics are believed to reflect a maximization of glacial erosion potential in the vicinity of the equilibrium line and in locations of confluence.