Slope distributions, threshold hillslopes, and steady-state topography

Digital elevation models of two "steady-state" mountain ranges, the Olympic Mountains (OM) and Oregon Coast Range (OCR), are used to examine relationships between slope distributions, the development of threshold hillslopes, and steady-state topography. Plots of drainage area versus slope for these mountain ranges exhibit substantial scatter that complicates comparison of range form to analytical theories and landscape evolution models. Contour plots of the density of such data reveal an attractor at the scale of the transition from hillslope processes to channel processes, and log-bin averaging reveals trends that parallel predictions of steady-state erosion laws but with different rate laws for five distinct process domains: hillslopes, valley heads, and colluvial, bedrock, and alluvial valley segments. Slope histograms computed for 100 km(2) areas (defined by a 10 X 10 km grid) throughout the OM exhibit approximately normal or exponential distributions in areas of active rock uplift and depositional topography, respectively. Local slope distributions in the OCR also tend to be normally distributed, but some are left-skewed in areas with gentler slopes. Mean slopes determined both over the above referenced grid and a 10-km diam moving window are relatively invariant in the core of the OM in spite of strong contrasts in bedrock erodibility and gradients in long-term rock uplift rates. In contrast, the mean slopes in the OCR parallel latitudinal gradients in rock uplift rates and bedrock erodibility. Hence, the slope distributions in the OM and OCR reflect distinct relationships between development of threshold bedrock and soil-mantled hillslopes and steady-state topography.