How long is a hillslope?

Hillslope length is a fundamental attribute of landscapes, intrinsically linked to drainage density, landslide hazard, biogeochemical cycling and hillslope sediment transport. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density or identification of a break in slope–area scaling, where the hillslope domain transitions into the fluvial domain. Here we implement a technique which models flow from point sources on hilltops across pixels in a digital elevation model (DEM), based on flow directions calculated using pixel aspect, until reaching the channel network, defined using recently developed channel extraction algorithms. Through comparisons between these measurement techniques, we show that estimating hillslope length from plots of topographic slope versus drainage area, or by inverting measures of drainage density, systematically underestimates hillslope length. In addition, hillslope lengths estimated by slope–area scaling breaks show large variations between catchments of similar morphology and area. We then use hillslope length–relief structure of landscapes to explore nature of sediment flux operating on a landscape. Distinct topographic forms are predicted for end-member sediment flux laws which constrain sediment transport on hillslopes as being linearly or nonlinearly dependent on hillslope gradient. Because our method extracts hillslope profiles originating from every ridgetop pixel in a DEM, we show that the resulting population of hillslope length–relief measurements can be used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes. We find that across a broad range of sites across the continental United States, topography is consistent with a sediment flux law in which transport is nonlinearly proportional to topographic gradient

Global projection of lead-zinc supply from known resources

© 2018 by the authors. Lead and zinc are used extensively in the construction and automotive industries, and require sustainable supply. In order to understand the future availability of lead and zinc, we have projected global supplies on a country-by-country basis from a detailed global assessment of mineral resources for 2013. The model GeRS-DeMo was used to create projections of lead and zinc production from ores, as well as recycling for lead. Our modelling suggests that lead and zinc production from known resources is set to peak within 15 years (lead 2025, zinc 2031). For lead, the total supply declines relatively slowly post peak due to recycling. If additional resources are found, these peaks would shift further into the future. These results suggest that lead and zinc consumers will need to plan for the future, potentially by: seeking alternative supplies (e.g., mine tailings, smelter/refinery slags); obtaining additional value from critical metals contained in lead-zinc ore deposits to counter lower grade ores; identifying potential substitutes; redesigning their products; or by contributing to the development of recycling industries