Topology of ridge patterns: Randomness and constraints
A simple model, in which ridge networks are simulated by forming minimum spanning trees of sets of N points (representing peaks), distributed randomly within an ellipse, provides good predictions for ridge topological class frequencies involving six peaks. When goodness-of-fit (measured by chi-square) is plotted against the elongation ratio of the ellipse, the shape of the plot indicates the degree of ridge anisotropy present within the topography. In areas of heterogeneous geology but without overt structural control, the curve shows approximately equal fit for all elongations between a circle and a 2:1 ellipse; beyond this point the fit rapidly becomes very poor. In contrast, areas of flat-lying, homogeneous geology show curves that decline noticeably as one goes from the circle to an optimum fit at an elongation of about 0.5. This indicates a significant within-network ridge anisotropy in these landscapes, which is attributed to local topographic control imposed by the major tributaries of master streams. The model also fits areas with overt structural control (ridge-and-valley topography), but with an optimum elongation ratio of about 0.1. The ridge model fits networks having from four to seven peaks, but the shapes of the goodness-of-fit plots indicate that degree of anisotropy varies with magnitude in some landscapes; this is a scale effect. It is difficult to relate the ridge topology research presented in this study to previous stream topology work; reasons for this difficulty are discussed.