POLYNOMIAL AND POWER FUNCTIONS FOR GLACIAL VALLEY CROSS-SECTION MORPHOLOGY

An empirical evaluation of glacial trough cross-section shape is perfo rmed on seven vertical cross-sections in three Sierra Nevada valleys g laciated during the late Quaternary. Power and second-order polynomial functions are fitted by statistical regression. Power functions are v ery sensitive to subtle valley-bottom topographic features and require precise specification of the valley-bottom-centre location. This depe ndency is problematic given under-representation of valley bottoms by conventional contour-sampling methods, and the common alteration of va lley-bottom morphology by non-glacial processes. Power function expone nts vary greatly in response to these and other non-genetic factors an d are not found to be reliable indicators of overall valley morphology . Second-order polynomials express overall valley shape in a single ro bust function. They are applied to both bedrock- and sediment-floored glacial valleys with negligible statistical bias except where side-slo pes are stepped or convex-upward or where valley form is asymmetrical. They can describe alluviated or severely eroded valleys, and can obje ctively identify individual components of polymorphic valleys, because valley bottom and centre locations need not be specified. Mathematica l expressions of parameters useful for geomorphic measurements and gla ciological modelling are analytically derived from the polynomials as functions of the three polynomial coefficients. These parameter equati ons provide estimates of valley side-slopes, mean and maximum depth, m idpoint location, width, area, boundary length, form ratio and symmetr y.