Stream Power Incision Research Articles

Graphically interpreting how incision thresholds influence topographic and scaling properties of modeled landscapes

Abstract. We examine the influence of incision thresholds on topographic and scaling properties of landscapes that follow a landscape evolution model (LEM) with terms for stream-power incision, linear diffusion, and uniform uplift. Our analysis uses three main tools. First, we examine the graphical behavior of theoretical relationships between curvature and the steepness index (which depends on drainage area and slope). These relationships plot as straight lines for the case of steady-state landscapes that follow the LEM. These lines have slopes and intercepts that provide estimates of landscape characteristic scales. Such lines can be viewed as counterparts of slope–area relationships, which follow power laws in detachment-limited landscapes but not in landscapes with diffusion. We illustrate the response of these curvature–steepness index lines to changes in the values of parameters. Second, we define a Péclet number that quantifies the competition between incision and diffusion, while taking the incision threshold into account. We examine how this Péclet number captures the influence of the incision threshold on the degree of landscape dissection. Third, we characterize the influence of the incision threshold using a ratio between it and the steepness index. This ratio is a dimensionless number in the case of the LEM that we use and reflects the fraction by which the incision rate is reduced due to the incision threshold; in this way, it quantifies the relative influence of the incision threshold across a landscape. These three tools can be used together to graphically illustrate how topography and process competition respond to incision thresholds.

GIS and DEM based analysis of incision and drainage reorganization of the Buyuan River basin in the upper Lancang-Mekong of China since the Late Pleistocene

River incision and drainage reorganization have an important impact on the site selection of many major projects including city, road and others, and are the key issues of Quaternary environmental changes. Studies of river incision and river-network adjustment have traditionally been based on extensive field evidence, such as sediment age and beheaded river system. The Buyuan River basin is a large sub-basin of the upper Lancang-Mekong, with high mountains and extremely active erosion. The latter affects the preservation of the Quaternary period sediments leading to difficulties in understanding the main evolution characteristics of the basin. This study investigates differences in the equilibrium state of the longitudinal profile, infers incision rates, and evaluates drainage divide migration timelines using the stream-power incision model, the latest morphological dating, and Chi-plots (χ-z) based on digital elevation models (DEMs) on the GIS software platform. The final results show that two significant erosion base-level decreases occurred in the Late Pleistocene at least. The incision rate of the mainstream might have been 0–2.99 mm/yr since 100 ka BP and 0–3.28 mm/yr since 46 ka BP. The Chi-values across the divides suggest that space limited (or constrained) river reorganization and that there is no severe reorganization in the basin; the imbalance of traceable erosion only exists in local areas. The main driving force for the geomorphologic evolution of the Buyuan River basin is likely climate fluctuations rather than strong tectonic uplift since the Late Pleistocene.

Dimensional analysis of a landscape evolution model with incision threshold

Abstract. The ability of erosional processes to incise into a topographic surface can be limited by a threshold. Incision thresholds affect the topography of landscapes and their scaling properties and can introduce nonlinear relations between climate and erosion with notable implications for long-term landscape evolution. Despite their potential importance, incision thresholds are often omitted from the incision terms of landscape evolution models (LEMs) to simplify analyses. Here, we present theoretical and numerical results from a dimensional analysis of an LEM that includes terms for threshold-limited stream-power incision, linear diffusion, and uplift. The LEM is parameterized by four parameters (incision coefficient and incision threshold, diffusion coefficient, and uplift rate). The LEM's governing equation can be greatly simplified by recasting it in a dimensionless form that depends on only one dimensionless parameter, the incision-threshold number Nθ. This dimensionless parameter is defined in terms of the incision threshold, the incision coefficient, and the uplift rate, and it quantifies the reduction in the rate of incision due to the incision threshold relative to the uplift rate. Being the only parameter in the dimensionless governing equation, Nθ is the only parameter controlling the evolution of landscapes in this LEM. Thus, landscapes with the same Nθ will evolve geometrically similarly, provided that their boundary and initial conditions are normalized according to appropriate scaling relationships, as we demonstrate using a numerical experiment. In contrast, landscapes with different Nθ values will be influenced to different degrees by their incision thresholds. Using results from a second set of numerical simulations, each with a different incision-threshold number, we qualitatively illustrate how the value of Nθ influences the topography, and we show that relief scales with the quantity Nθ+1 (except where the incision threshold reduces the rate of incision to zero).

Geomorphic evidence for northeastward expansion of the eastern Qilian Shan, northeastern Tibetan Plateau

The eastern Qilian Shan is a tectonically-active region consisting of a series of faults with bounded intermountain basins and is located within the transition zone between the mainland Tibetan Plateau and the Alax Block. Active deformation affecting the topography in this region can be quantified based on geomorphic indices. Therefore, we applied the geomorphic indices (hypsometry and stream-power incision model) to evaluate the tectonic deformation pattern of the eastern Qilian Shan. Hypsometric curves and S-A plots of the selected seven rivers were determined. HI values of every single sub-basins were also calculated. The results show that the local topographic evolution of the eastern Qilian Shan is in pre-steady state and will soon reach its equilibrium state. According to the analysis of regional climate condition (e.g., rainfall and glaciers distribution) and fault characteristics, it is suggested that abundant glacial snowmelt water sustains fluvial incision, and tectonic deformation from sustained northeastward expansion of the Tibetan Plateau is the main reason for the landscape growth. Combining the research of the deep electric structure beneath the Gulang Boundary Zone, we claimed that the eastern Qilian Shan (even the northeastern Tibet) has been growing and expanding northeastward since the middle Miocene, and its leading edge now is the Hexibao-Sidaoshan Fault. On the premise of synthetically considering the western and middle parts of the Qilian Shan, it is suggested that the Hexibao-Sidaoshan Fault area will rise into a mountain in 1–2 Ma.

Scaling and similarity of a stream-power incision and linear diffusion landscape evolution model

Abstract. The scaling and similarity of fluvial landscapes can reveal fundamental aspects of the physics driving their evolution. Here, we perform a dimensional analysis of the governing equation of a widely used landscape evolution model (LEM) that combines stream-power incision and linear diffusion laws. Our analysis assumes that length and height are conceptually distinct dimensions and uses characteristic scales that depend only on the model parameters (incision coefficient, diffusion coefficient, and uplift rate) rather than on the size of the domain or of landscape features. We use previously defined characteristic scales of length, height, and time, but, for the first time, we combine all three in a single analysis. Using these characteristic scales, we non-dimensionalize the LEM such that it includes only dimensionless variables and no parameters. This significantly simplifies the LEM by removing all parameter-related degrees of freedom. The only remaining degrees of freedom are in the boundary and initial conditions. Thus, for any given set of dimensionless boundary and initial conditions, all simulations, regardless of parameters, are just rescaled copies of each other, both in steady state and throughout their evolution. Therefore, the entire model parameter space can be explored by temporally and spatially rescaling a single simulation. This is orders of magnitude faster than performing multiple simulations to span multidimensional parameter spaces. The characteristic scales of length, height and time are geomorphologically interpretable; they define relationships between topography and the relative strengths of landscape-forming processes. The characteristic height scale specifies how drainage areas and slopes must be related to curvatures for a landscape to be in steady state and leads to methods for defining valleys, estimating model parameters, and testing whether real topography follows the LEM. The characteristic length scale is roughly equal to the scale of the transition from diffusion-dominated to advection-dominated propagation of topographic perturbations (e.g., knickpoints). We introduce a modified definition of the landscape Péclet number, which quantifies the relative influence of advective versus diffusive propagation of perturbations. Our Péclet number definition can account for the scaling of basin length with basin area, which depends on topographic convergence versus divergence.

How concave are river channels?

Abstract. For over a century, geomorphologists have attempted to unravel information about landscape evolution, and processes that drive it, using river profiles. Many studies have combined new topographic datasets with theoretical models of channel incision to infer erosion rates, identify rock types with different resistance to erosion, and detect potential regions of tectonic activity. The most common metric used to analyse river profile geometry is channel steepness, or ks. However, the calculation of channel steepness requires the normalisation of channel gradient by drainage area. This normalisation requires a power law exponent that is referred to as the channel concavity index. Despite the concavity index being crucial in determining channel steepness, it is challenging to constrain. In this contribution, we compare both slope–area methods for calculating the concavity index and methods based on integrating drainage area along the length of the channel, using so-called “chi” (χ) analysis. We present a new χ-based method which directly compares χ values of tributary nodes to those on the main stem; this method allows us to constrain the concavity index in transient landscapes without assuming a linear relationship between χ and elevation. Patterns of the concavity index have been linked to the ratio of the area and slope exponents of the stream power incision model (m∕n); we therefore construct simple numerical models obeying detachment-limited stream power and test the different methods against simulations with imposed m and n. We find that χ-based methods are better than slope–area methods at reproducing imposed m∕n ratios when our numerical landscapes are subject to either transient uplift or spatially varying uplift and fluvial erodibility. We also test our methods on several real landscapes, including sites with both lithological and structural heterogeneity, to provide examples of the methods' performance and limitations. These methods are made available in a new software package so that other workers can explore how the concavity index varies across diverse landscapes, with the aim to improve our understanding of the physics behind bedrock channel incision.

Geomorphic indices of rivers and drainage in China’s Longmen Shan Fault zone and their implications for regional tectonic activity

Theoretical models suggest that active tectonic deformation can impose a primary control on the patterns and styles of channels. The Longmen Shan Fault zone, which is located on the eastern margin of the Tibetan Plateau, has experienced strong tectonic activity, including uplift and strike-slip phases of tectonic movements. Here, we adopt ASTER-GDEM2 data and utilise a stream-power incision model to extract information on the spatial characteristics of differential tectonic movements. Analysis of the patterns and styles of 37 channels exhibits systematic differences in the channel steepness indices and the river sinuosity values along the strike of the Longmen Shan Fault zone. Our primary results demonstrate that the normalised channel steepness indices in the southern part of the Longmen Shan Fault zone are much higher than those in the northern part, where the river sinuosity values are much lower. Comparisons between the five drainage basins reveal that the river systems in the middle southern part of the fault zone are mainly controlled by tectonic uplift and thrusting, whereas the river systems in the middle northern part of the fault zone are mostly attributed to right-lateral strike-slip movement.

Very long-term incision dynamics of big rivers

Constraining large-scale incision dynamics of shield and post-rift margin domains is key to understanding the sediment routing system over the overwhelming part of the continental surface. Based on dated and regionally correlated incision markers from West Africa, we reconstruct for the first time the entire paleo-long profiles of big rivers such as the Niger at ca. 24, 11 and 6 Ma, as well as the Eocene topography those rivers have dissected. The results provide boundary conditions and calibration for surface process models and paleodrainage dynamics. Though spatially and temporally variable, incision remained mostly below 10m/my with a mean around 5m/my. The spatial stability of both the river outlets and divides imposed maintenance or increasing concavity of the river long profiles through time, resulting from spatially contrasted adjustment of river segments bounded by recurrent lithogenic knickzones that persisted since 24 Ma. Drainages evolved preferentially by very slow slope decrease or uniform incision in between the stationary knickzones of evolving amplitude, with apparently no relation to base level change. Therefore, knickzone height or position may not simply reflect the transient response of big rivers to base level fall as predicted by stream-power incision river models. This may also challenge uplift histories of deep continental interiors retrieved from river long profiles inversion relying on such models. Very slow incision allowed amplification of the Hoggar hot spot swell and flexural uplift of the continental margin to be recorded by river long profiles, emphasizing the potential of big non-orogenic rivers as gauges of dynamic topography.

Initiation and recession of the fluvial knickpoints: A case study from the Yalu River-Wangtian’e volcanic region, northeastern China

Initiation and recession of the knickpoints are significant boundary condition for processes of fluvial system. The distribution and recession rates of knickpoints contain information that provides a fundamental understanding of geomorphic processes. In the Yalu River-Wangtian’e volcanic region of northeastern China, broadly distributed flat lava terrain provides an ideal site to study the recession of fluvial knickpoints because knickpoints and waterfalls are well preserved here. Here we describe the distribution of knickpoints in the Yalu River-Wangtian’e volcanic region by combining DEM analysis and numerical modeling. Furthermore, we present a knickpoint celerity model, derived from stream-power incision model, to relate knickpoint recession rate to drainage area. We calibrate important empirical coefficients with our knickpoint celerity model; the best fit erosion coefficient (K) is 1.32×10−8, and the best fit drainage area exponent (m) is 0.69. Error analysis indicates a close correspondence between synthetic and real knickpoints. Finally, we show that knickpoint recession rates in the Yalu River-Wangtian’e volcanic region are ∼1–10 mm/a during the early stages of transient incision, and that the present rates are ∼1–6 mm/a. Our recession rate results are in good agreement with previous findings from the Aso Volcano and volcanoes near Boso Peninsula (Japan), which have a similar geologic history to the Yalu River-Wangtian’e volcanic region. Our present effort provides new insight into landscape evolution in the Yalu River-Wangtian’e volcanic region in northeastern China.

Stream-power incision model in non-steady-state mountain ranges: An empirical approach

Stream-power incision model has always been applied to detecting the steady-state situation of ranges. Oblique arc-continent collision occurring during the period of Penglai Orogeny caused the Taiwan mountain belt to develop landscape of three evolution stages, namely stages of pre-steady-state (growing ranges in southern Taiwan), steady-state (ranges in central Taiwan) and post-steady-state (decaying ranges in northern Taiwan). In the analysis on streams of the Taiwan mountain belt made by exploring the relationship between the slope of bedrock channel (S) and the catchment area (A), the topographic features of the ranges at these three stages are acquired. The S-A plot of the steady-state ranges is in a linear form, revealing that the riverbed height of bedrock channel does not change over time (dz/dt = 0). The slope and intercept of the straight line S-A are related to evolution time of steady-state topography and tectonic uplift rate respectively. The S-A plots of the southern and northern ranges of Taiwan mountain belt appear to be in convex and concave forms respectively, implying that the riverbed height of bedrock channel at the two ranges rises (dz/dt > 0) and falls (dz/dt < 0) over time respectively. Their tangent intercept can still reflect the tectonic uplift rate. This study develops an empirical stream-power erosion model of pre-steady-state and post-steady-state topography.

Fluvial Landscape Response Time: How Plausible Is Steady-State Denudation?

Whether or not steady-state topography and denudation are probable states depends on the timescale of system response to tectonic and climatic perturbations relative to the frequency of those perturbations. This paper presents analytical derivations of algebraic relations for the response time of detachment-limited fluvial bedrock channel systems both to tectonic and climatic perturbations. Detachmentlimited fluvial erosion is described by the stream-power incision model, and the derivations are limited to the applicability of that model. All factors likely to influence system response time that are not adequately captured by the stream-power incision model will tend to increase the response time. The calculations presented thus provide minimum estimates of landscape response time and therefore over-predict the probability of attaining and sustaining steady-state topography and denudation. The Central Range of Taiwan is used as a case study to estimate response times in a landscape often argued to be in steady state. Model parameters are fit to modern stream profiles by assuming that the topography represents a quasi-steady-state form. Estimated response times generally range from 0.25 to 2.5 Ma, depending on the non-linearity of the incision rule and the magnitude and type of perturbation. Thus it may be reasonably argued that steady-state topography and denudation are likely to prevail during periods of climatic stability (response time is sufficiently short compared with plate tectonic timescales). However, rapid climatic fluctuation in the Quaternary appears to preclude the attainment of steady-state conditions in modern orogens.