Alternative coordinate systems for analyzing cross-section shapes of glaciated valleys: a case study from the Dalijia Mountains, China

Abstract

The morphometry of glaciated valleys has been of considerable significance in evaluating models and processes of valley form development, and is typically evaluated using a power law function fit to topographic data. Results of the power law method are sensitive to the location of the coordinate system origin, but most previous research has used a coordinate system centered on the valley midpoint and has not systematically assessed alternative approaches. Here, we test four options for selecting the coordinate system origin, using cross-section profiles from glacial, fluvial, and transitional valleys in the Dalijia Mountains, China: (A) the lowest elevation point, (B) the valley midpoint, (C) the lowest point on the valley side wall, and (D) the highest point on the valley side. Option A produces results that are most consistent with expected values and trends for shape parameters in the Dalijia Mountains. Over half of the values calculated using Option B overestimate key valley-shape parameters compared to Option A. Options C and D produce similar values to each other, but these values are very different from Option A and less useful for landform interpretation. In morphometric studies designed to evaluate impacts of glacial erosion using the power law approach, we recommend that alternate coordinate system origins be evaluated, including the lowest elevation point on a cross-profile.