Landform equations fitted to contour maps

Abstract

It has long been recognized that various land forms have characteristic shapes. The problem here considered is how to describe these shapes with three-dimensional equations. The shapes of specific land forms such as alluvial cones and pediments are con sidered describable; areas including two or more land forms must be subdivided. The basic equation used is Z = P + SR + LR® in which Z represents the elevation at any point, P is the elevation at the center of the figure described by the equation, S is the slope gradient of the surface at that center, L is half the rate of change of the slope gradient with radial distance, and R is radial distance from the center of the figure. Landform features that can be readily obtained from such equations are the slope gradient and the curvature of both the slope profile and the contour lines. Solution of the equations is based upon measurements along radial lines constructed on contour maps. The algebraic signs of the slope gradient and of the coefficient L provide a basis for classifying the concavity and convexity of surfaces. Graphs of these two parameters are significant relative to rates of runoff and to soil drainage.