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Channel steepness index, k(s), is a metric derived from the stream power model that, under certain conditions, scales with relative rock uplift rate. Channel steepness index is a property of rivers, which can be relatively easily extracted from digital elevation models (DEMs). As DEM data sets are widely available for Earth and are becoming more readily available for other planetary bodies, channel steepness index represents a powerful tool for interpreting tectonic processes. However, multiple approaches to calculate channel steepness index exist. From this several important questions arise; does choice of approach change the values of channel steepness index, can values be so different that choice of approach can influence the findings of a study, and are certain approaches better than others? With the aid of a synthetic river profile and a case study from the Sierra Nevada, California, we show that values of channel steepness index vary over orders of magnitude according to the methodology used in the calculation. We explore the limitations, advantages and disadvantages of the key approaches to calculating channel steepness index, and find that choosing an appropriate approach relies on the context of a study. Given these observations, it is important that authors acknowledge the methodology used to calculate channel steepness index, to ensure that results can be contextualised and reproduced.
We propose a novel way to measure and analyze networks of drainage divides from digital elevation models. We developed an algorithm that extracts drainage divides based on the drainage basin boundaries defined by a stream network. In contrast to streams, there is no straightforward approach to order and classify divides, although it is intuitive that some divides are more important than others. A meaningful way of ordering divides is the average distance one would have to travel down on either side of a divide to reach a common stream location. However, because measuring these distances is computationally expensive and prone to edge effects, we instead sort divide segments based on their tree-like network structure, starting from endpoints at river confluences. The sorted nature of the network allows for assigning distances to points along the divides, which can be shown to scale with the average distance downslope to the common stream location. Furthermore, because divide segments tend to have characteristic lengths, an ordering scheme in which divide orders increase by 1 at junctions mimics these distances. We applied our new algorithm to the Big Tujunga catchment in the San Gabriel Mountains of southern California and studied the morphology of the drainage divide network. Our results show that topographic metrics, like the downstream flow distance to a stream and hillslope relief, attain characteristic values that depend on the drainage area threshold used to derive the stream network. Portions along the divide network that have lower than average relief or are closer than average to streams are often distinctly asymmetric in shape, suggesting that these divides are unstable. Our new and automated approach thus helps to objectively extract and analyze divide networks from digital elevation models.
The efficiency of sediment routing from land to the ocean depends on the position of submarine canyon heads with regard to terrestrial sediment sources. We aim to identify the main controls on whether a submarine canyon head remains connected to terrestrial sediment input during Holocene sea-level rise. Globally, we identified 798 canyon heads that are currently located at the 120m-depth contour (the Last Glacial Maximum shoreline) and 183 canyon heads that are connected to the shore (within a distance of 6 km) during the present-day highstand. Regional hotspots of shore-connected canyons are the Mediterranean active margin and the Pacific coast of Central and South America. We used 34 terrestrial and marine predictor variables to predict shore-connected canyon occurrence using Bayesian regression. Our analysis shows that steep and narrow shelves facilitate canyon-head connectivity to the shore. Moreover, shore-connected canyons occur preferentially along active margins characterized by resistant bedrock and high river-water discharge.
Knickpoints in longitudinal river profiles are proxies for the climatic and tectonic history of active mountains. The analysis of river profiles commonly relies on the assumption that drainage network configurations are stable. Here, we show that this assumption must be made cautiously if changes in contributing area are fast relative to knickpoint migration rates. We studied the Parachute Creek basin in the Roan Plateau, Colorado, United States, where knickpoint retreat occurs in horizontally uniform lithology so that drainage area is the sole governing variable. In this basin, we identified an anomalous catchment in the degree to which a stream power-based model predicted knickpoint locations. The catchment is experiencing area loss as the plateau edge is eroded by cliff migration in proximity to the Colorado River. Model predictions improve if the plateau edge is assumed to have migrated over the time scale of knickpoint retreat. Finally, a Lagrangian model of knickpoint migration enabled us to study the kinematic links between drainage area loss and knickpoint migration and offered constraints on the temporal aspects of area loss. Modeled onset and amount of area loss are consistent with cliff retreat rates along the margin of the Roan Plateau inferred from the incisional history of the upper Colorado River.
Drainage divide networks
(2020)
Drainage divides are organized into tree-like networks that may record information about drainage divide mobility. However, views diverge about how to best assess divide mobility. Here, we apply a new approach of automatically extracting and ordering drainage divide networks from digital elevation models to results from landscape evolution model experiments. We compared landscapes perturbed by strike-slip faulting and spatiotemporal variations in erodibility to a reference model to assess which topographic metrics (hillslope relief, flow distance, and chi) are diagnostic of divide mobility. Results show that divide segments that are a minimum distance of similar to 5 km from river confluences strive to attain constant values of hillslope relief and flow distance to the nearest stream. Disruptions of such patterns can be related to mobile divides that are lower than stable divides, closer to streams, and often asymmetric in shape. In general, we observe that drainage divides high up in the network, i.e., at great distances from river confluences, are more susceptible to disruptions than divides closer to these confluences and are thus more likely to record disturbance for a longer time period. We found that across-divide differences in hillslope relief proved more useful for assessing divide migration than other tested metrics. However, even stable drainage divide networks exhibit across-divide differences in any of the studied topographic metrics. Finally, we propose a new metric to quantify the connectivity of divide junctions.
Landscape evolution models (LEMs) allow the study of earth surface responses to changing climatic and tectonic forcings. While much effort has been devoted to the development of LEMs that simulate a wide range of processes, the numerical accuracy of these models has received less attention. Most LEMs use first-order accurate numerical methods that suffer from substantial numerical diffusion. Numerical diffusion particularly affects the solution of the advection equation and thus the simulation of retreating landforms such as cliffs and river knickpoints. This has potential consequences for the integrated response of the simulated landscape. Here we test a higher-order flux-limiting finite volume method that is total variation diminishing (TVD-FVM) to solve the partial differential equations of river incision and tectonic displacement. We show that using the TVD-FVM to simulate river incision significantly influences the evolution of simulated landscapes and the spatial and temporal variability of catchment-wide erosion rates. Furthermore, a two-dimensional TVD-FVM accurately simulates the evolution of landscapes affected by lateral tectonic displacement, a process whose simulation was hitherto largely limited to LEMs with flexible spatial discretization. We implement the scheme in TTLEM (TopoToolbox Landscape Evolution Model), a spatially explicit, raster-based LEM for the study of fluvially eroding landscapes in TopoToolbox 2.
The 2015 magnitude 7.8 Gorkha earthquake and its aftershocks weakened mountain slopes in Nepal. Co- and postseismic landsliding and the formation of landslide-dammed lakes along steeply dissected valleys were widespread, among them a landslide that dammed the Kali Gandaki River. Overtopping of the landslide dam resulted in a flash flood downstream, though casualties were prevented because of timely evacuation of low-lying areas. We hindcast the flood using the BREACH physically based dam-break model for upstream hydrograph generation, and compared the resulting maximum flow rate with those resulting from various empirical formulas and a simplified hydrograph based on published observations. Subsequent modeling of downstream flood propagation was compromised by a coarse-resolution digital elevation model with several artifacts. Thus, we used a digital-elevation-model preprocessing technique that combined carving and smoothing to derive topographic data. We then applied the 1-dimensional HEC-RAS model for downstream flood routing, and compared it to the 2-dimensional Delft-FLOW model. Simulations were validated using rectified frames of a video recorded by a resident during the flood in the village of Beni, allowing estimation of maximum flow depth and speed. Results show that hydrological smoothing is necessary when using coarse topographic data (such as SRTM or ASTER), as using raw topography underestimates flow depth and speed and overestimates flood wave arrival lag time. Results also show that the 2-dimensional model produces more accurate results than the 1-dimensional model but the 1-dimensional model generates a more conservative result and can be run in a much shorter time. Therefore, a 2-dimensional model is recommended for hazard assessment and planning, whereas a 1-dimensional model would facilitate real-time warning declaration.
Plain Language Summary The 2015 Gorkha earthquake in Nepal caused severe losses in the hydropower sector. The country temporarily lost similar to 20% of its hydropower capacity, and >30 hydropower projects were damaged. The projects hit hardest were those that were affected by earthquake-triggered landslides. We show that these projects are located along very steep rivers with towering sidewalls that are prone to become unstable during strong seismic ground shaking. A statistical classification based on a topographic metric that expresses river steepness and earthquake ground acceleration is able to approximately predict hydropower damage during future earthquakes, based on successful testing of past cases. Thus, our model enables us to estimate earthquake damages to hydropower projects in other parts of the Himalayas. We find that >10% of the Himalayan drainage network may be unsuitable for hydropower infrastructure given high probabilities of high earthquake damages.
Climate science is highly interdisciplinary by nature, so understanding interactions between Earth processes inherently warrants the use of analytical software that can operate across the disciplines of Earth science. Toward this end, we present the Climate Data Toolbox for MATLAB, which contains more than 100 functions that span the major climate-related disciplines of Earth science. The toolbox enables streamlined, entirely scriptable workflows that are intuitive to write and easy to share. Included are functions to evaluate uncertainty, perform matrix operations, calculate climate indices, and generate common data displays. Documentation is presented pedagogically, with thorough explanations of how each function works and tutorials showing how the toolbox can be used to replicate results of published studies. As a well-tested, well-documented platform for interdisciplinary collaborations, the Climate Data Toolbox for MATLAB aims to reduce time spent writing low-level code, let researchers focus on physics rather than coding and encourage more efficacious code sharing. Plain Language Summary This article describes a collection of computer code that has recently been released to help scientists analyze many types of Earth science data. The code in this toolbox makes it easy to investigate things like global warming, El Nino, or other major climate-related processes such as how winds affect ocean circulation. Although the toolbox was designed to be used by expert climate scientists, its instruction manual is well written, and beginners may be able to learn a great deal about coding and Earth science, simply by following along with the provided examples. The toolbox is intended to help scientists save time, help them ensure their analysis is accurate, and make it easy for other scientists to repeat the results of previous studies.