| Abstract: | An empirical evaluation of glacial trough cross-section shape is performed on seven vertical cross-sections in three Sierra Nevada valleys glaciated during the late Quaternary. Power and second-order polynomial functions are fitted by statistical regression. Power functions are very sensitive to subtle valley-bottom topographic features and require precise specification of the valley-bottom-centre location. This dependency is problematic given under-representation of valley bottoms by conventional contour-sampling methods, and the common alteration of valley-bottom morphology by non-glacial processes. Power function exponents vary greatly in response to these and other non-genetic factors and are not found to be reliable indicators of overall valley morphology. Second-order polynomials express overall valley shape in a single robust function. They are applied to both bedrock- and sediment-floored glacial valleys with negligible statistical bias except where side-slopes are stepped or convex-upward or where valley form is asymmetrical. They can describe alluviated or severely eroded valleys, and can objectively identify indi-vidual components of polymorphic valleys, because valley bottom and centre locations need not be specified. Mathematical expressions of parameters useful for geomorphic measurements and glaciological modelling are analytically derived from the polynomials as functions of the three polynomial coefficients. These parameter equations provide estimates of valley side-slopes, mean and maximum depth, midpoint location, width, area, boundary length, form ratio and symmetry. |
