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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.
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.
Biomass allometries and coarse root biomass distribution of mountain birch in southern Iceland
(2014)
Root systems are an important pool of biomass and carbon in forest ecosystems. However, most allometric studies on forest trees focus only on the aboveground components. When estimated, root biomass has most often been calculated by using a fixed conversion factor from aboveground biomass. In order to study the size-related development of the root system of native mountain birch (Betula pubescens Ehrh. ssp. czerepanovii), we collected the coarse root system of 25 different aged birch trees (stem diameter at 50 cm length between 0.2 and 14.1 cm) and characterized them by penetration depth (< 1 m) and root thickness. Based on this dataset, allometric functions for coarse roots (> 5 mm and > 2 mm), root stock, total belowground biomass and aboveground biomass components were calculated by a nonlinear and a linear fitting approach. The study showed that coarse root biomass of mountain birch was almost exclusively (> 95 weight-%) located in the top 30 cm, even in a natural old-growth woodland. By using a cross-validation approach, we found that the nonlinear fitting procedure performed better than the linear approach with respect to predictive power. In addition, our results underscore that general assumptions of fixed conversion factors lead to an underestimation of the belowground biomass. Thus, our results provide allometric functions for a more accurate root biomass estimation to be utilized in inventory reports and ecological studies.
Bumps in river profiles
(2017)
The analysis of longitudinal river profiles is an important tool for studying landscape evolution. However, characterizing river profiles based on digital elevation models (DEMs) suffers from errors and artifacts that particularly prevail along valley bottoms. The aim of this study is to characterize uncertainties that arise from the analysis of river profiles derived from different, near-globally available DEMs. We devised new algorithms quantile carving and the CRS algorithm - that rely on quantile regression to enable hydrological correction and the uncertainty quantification of river profiles. We find that globally available DEMs commonly overestimate river elevations in steep topography. The distributions of elevation errors become increasingly wider and right skewed if adjacent hillslope gradients are steep. Our analysis indicates that the AW3D DEM has the highest precision and lowest bias for the analysis of river profiles in mountainous topography. The new 12m resolution TanDEM-X DEM has a very low precision, most likely due to the combined effect of steep valley walls and the presence of water surfaces in valley bottoms. Compared to the conventional approaches of carving and filling, we find that our new approach is able to reduce the elevation bias and errors in longitudinal river profiles.
Bumps in river profiles: uncertainty assessment and smoothing using quantile regression techniques
(2017)
The analysis of longitudinal river profiles is an important tool for studying landscape evolution. However, characterizing river profiles based on digital elevation models (DEMs) suffers from errors and artifacts that particularly prevail along valley bottoms. The aim of this study is to characterize uncertainties that arise from the analysis of river profiles derived from different, near-globally available DEMs. We devised new algorithms quantile carving and the CRS algorithm - that rely on quantile regression to enable hydrological correction and the uncertainty quantification of river profiles. We find that globally available DEMs commonly overestimate river elevations in steep topography. The distributions of elevation errors become increasingly wider and right skewed if adjacent hillslope gradients are steep. Our analysis indicates that the AW3D DEM has the highest precision and lowest bias for the analysis of river profiles in mountainous topography. The new 12m resolution TanDEM-X DEM has a very low precision, most likely due to the combined effect of steep valley walls and the presence of water surfaces in valley bottoms. Compared to the conventional approaches of carving and filling, we find that our new approach is able to reduce the elevation bias and errors in longitudinal river profiles.
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.
Remote sensing technology serves as a powerful tool for analyzing geospatial characteristics of flood inundation events at various scales. However, the performance of remote sensing methods depends heavily on the flood characteristics and landscape settings. Difficulties might be encountered in mapping the extent of localized flooding with shallow water on riverine floodplain areas, where patches of herbaceous vegetation are interspersed with open water surfaces. To address the difficulties in mapping inundation on areas with complex water and vegetation compositions, a high spatial resolution dataset has to be used to reduce the problem of mixed pixels. The main objective of our study was to investigate the possibilities of using a single date WorldView-2 image of very high spatial resolution and supporting data to analyze spatial patterns of localized flooding on a riverine floodplain. We used a decision tree algorithm with various combinations of input variables including spectral bands of the WorldView-2 image, selected spectral indices dedicated to mapping water surfaces and vegetation, and topographic data. The overall accuracies of the twelve flood extent maps derived with the decision tree method and performed on both pixels and image objects ranged between 77% and 95%. The highest mapping overall accuracy was achieved with a method that utilized all available input data and the object-based image analysis. Our study demonstrates the possibility of using single date WorldView-2 data for analyzing flooding events at high spatial detail despite the absence of spectral bands from the short-waveform region that are frequently used in water related studies. Our study also highlights the importance of topographic data in inundation analyses. The greatest difficulties were met in mapping water surfaces under dense canopy herbaceous vegetation, due to limited water surface exposure and the dominance of vegetation reflectance.
Remote sensing technology serves as a powerful tool for analyzing geospatial characteristics of flood inundation events at various scales. However, the performance of remote sensing methods depends heavily on the flood characteristics and landscape settings. Difficulties might be encountered in mapping the extent of localized flooding with shallow water on riverine floodplain areas, where patches of herbaceous vegetation are interspersed with open water surfaces. To address the difficulties in mapping inundation on areas with complex water and vegetation compositions, a high spatial resolution dataset has to be used to reduce the problem of mixed pixels. The main objective of our study was to investigate the possibilities of using a single date WorldView-2 image of very high spatial resolution and supporting data to analyze spatial patterns of localized flooding on a riverine floodplain. We used a decision tree algorithm with various combinations of input variables including spectral bands of the WorldView-2 image, selected spectral indices dedicated to mapping water surfaces and vegetation, and topographic data. The overall accuracies of the twelve flood extent maps derived with the decision tree method and performed on both pixels and image objects ranged between 77% and 95%. The highest mapping overall accuracy was achieved with a method that utilized all available input data and the object-based image analysis. Our study demonstrates the possibility of using single date WorldView-2 data for analyzing flooding events at high spatial detail despite the absence of spectral bands from the short-waveform region that are frequently used in water related studies. Our study also highlights the importance of topographic data in inundation analyses. The greatest difficulties were met in mapping water surfaces under dense canopy herbaceous vegetation, due to limited water surface exposure and the dominance of vegetation reflectance.
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.
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 Norwegian traffic network is impacted by about 2000 landslides, avalanches, and debris flows each year that incur high economic losses. Despite the urgent need to mitigate future losses, efforts to locate potential debris flow source areas have been rare at the regional scale. We tackle this research gap by exploring a minimal set of possible topographic predictors of debris flow initiation that we input to a Weights-of-Evidence (WofE) model for mapping the regional susceptibility to debris flows in western Norway. We use an inventory of 429 debris flows that were recorded between 1979 and 2008, and use the terrain variables of slope, total curvature, and contributing area (flow accumulation) to compute the posterior probabilities of local debris flow occurrence. The novelty of our approach is that we quantify the uncertainties in the WofE approach arising from different predictor classification schemes and data input, while estimating model accuracy and predictive performance from independent test data. Our results show that a percentile-based classification scheme excels over a manual classification of the predictor variables because differing abundances in manually defined bins reduce the reliability of the conditional independence tests, a key, and often neglected, prerequisite for the WofE method. The conditional dependence between total curvature and flow accumulation precludes their joint use in the model. Slope gradient has the highest true positive rate (88%), although the fraction of area classified as susceptible is very large (37%). The predictive performance, i.e. the reduction of false positives, is improved when combined with either total curvature or flow accumulation. Bootstrapping shows that the combination of slope and flow accumulation provides more reliable predictions than the combination of slope and total curvature, and helps refining the use of slope-area plots for identifying morphometric fingerprints of debris flow source areas, an approach used outside the field of landslide susceptibility assessments.
Purpose: Dry land vegetation is expected to respond sensitively to climate change and the projected variability of rainfall events. Rainfall as a water source is an obvious factor for the water supply of vegetation. However, the interaction of water and surface on rocky desert slopes with a patchy soil cover is also vital for vegetation in drylands. In particular, runoff on rocky surfaces and infiltration capacity of soil patches determine plant available water. Process-based studies into rock-soil interaction benefit from rainfall simulation, but require an approach accounting for the micro-scale heterogeneity of the slope surfaces. This study therefore aims at developing a suitable procedure for examining rock-soil interaction and the relevance of soil volume for storing plant available water in the northern Negev, Israel.
Materials and methods: To determine the amount of rainfall required to fill the available soil water storage capacity rainfall simulation experiments were conducted. The design of the rainfall-simulator and the selection of the plots aimed specifically at observing infiltration into small soil patches on a micro-scale relevant for the prevalent vegetation cover.
Results and discussion: The preliminary results of the study in the Negev Desert indicate that the ratio between soil volume and frequency of rainfall events determine the effect of climate change on plant available water and thus ultimately vegetation cover.
Conclusions: Based on the experiments examining runoff and soil moisture the qualitative understanding of hillslope ecohydrology in a rocky desert environment can be expanded into a quantitative assessment of the potential impact of varying rainfall conditions. The study also illustrates the contribution of rainfall simulation experiments for studies on the impact of climate change.
Digital flow networks derived from digital elevation models (DEMs) sensitively react to errors due to measurement, data processing and data representation. Since high-resolution DEMs are increasingly used in geomorphological and hydrological research, automated and semi-automated procedures to reduce the impact of such errors on flow networks are required. One such technique is stream-carving, a hydrological conditioning technique to ensure drainage connectivity in DEMs towards the DEM edges. Here we test and modify a state-of-the-art carving algorithm for flow network derivation in a low-relief, agricultural landscape characterized by a large number of spurious, topographic depressions. Our results show that the investigated algorithm reconstructs a benchmark network insufficiently in terms of carving energy, distance and a topological network measure. The modification to the algorithm that performed best, combines the least-cost auxiliary topography (LCAT) carving with a constrained breaching algorithm that explicitly takes automatically identified channel locations into account. We applied our methods to a low relief landscape, but the results can be transferred to flow network derivation of DEMs in moderate to mountainous relief in situations where the valley bottom is broad and flat and precise derivations of the flow networks are needed.
The assessment of uncertainty is a major challenge in geomorphometry. Methods to quantify uncertainty in digital elevation models (DEM) are needed to assess and report derivatives such as drainage basins. While Monte-Carlo (MC) techniques have been developed and employed to assess the variability of second-order derivatives of DEMs, their application requires explicit error modeling and numerous simulations to reliably calculate error bounds. Here, we develop an analytical model to quantify and visualize uncertainty in drainage basin delineation in DEMs. The model is based on the assumption that multiple flow directions (MFD) represent a discrete probability distribution of non-diverging flow networks. The Shannon Index quantifies the uncertainty of each cell to drain into a specific drainage basin outlet. In addition, error bounds for drainage areas can be derived. An application of the model shows that it identifies areas in a DEM where drainage basin delineation is highly uncertain owing to flow dispersion on convex landforms such as alluvial fans. The model allows for a quantitative assessment of the magnitudes of expected drainage area variability and delivers constraints for observed volatile hydrological behavior in a palaeoenvironmental record of lake level change. Since the model cannot account for all uncertainties in drainage basin delineation we conclude that a joint application with MC techniques is promising for an efficient and comprehensive error assessment in the future.
Through their relevance for sediment budgets and the sensitivity of geomorphic systems, geomorphic coupling and (sediment) connectivity represent important topics in geomorphology. Since the introduction of the systems perspective to physical geography by Chorley and Kennedy (1971), a catchment has been perceived as consisting of landscape elements (e.g. landforms, subcatchments) that are coupled by geomorphic processes through sediment transport. In this study, we present a novel application of mathematical graph theory to explore the network structure of coarse sediment pathways in a central alpine catchment. Numerical simulation models for rockfall, debris flows, and (hillslope and channel) fluvial processes are used to establish a spatially explicit graph model of sediment sources, pathways and sinks. The raster cells of a digital elevation model form the nodes of this graph, and simulated sediment trajectories represent the corresponding edges. Model results are validated by visual comparison with the field situation and aerial photos. The interaction of sediment pathways, i.e. where the deposits of a geomorphic process form the sources of another process, forms sediment cascades, represented by paths (a succession of edges) in the graph model. We show how this graph can be used to explore upslope (contributing area) and downslope (source to sink) functional connectivity by analysing its nodes, edges and paths. The analysis of the spatial distribution, composition and frequency of sediment cascades yields information on the relative importance of geomorphic processes and their interaction (however regardless of their transport capacity). In the study area, the analysis stresses the importance of mass movements and their interaction, e.g. the linkage of large rockfall source areas to debris flows that potentially enter the channel network. Moreover, it is shown that only a small percentage of the study area is coupled to the channel network which itself is longitudinally disconnected by natural and anthropogenic barriers. Besides the case study, we discuss the methodological framework and alternatives for node and edge representations of graph models in geomorphology. We conclude that graph theory provides an excellent methodological framework for the analysis of geomorphic systems, especially for the exploration of quantitative approaches towards sediment connectivity.
The evaluation and verification of landscape evolution models (LEMs) has long been limited by a lack of suitable observational data and statistical measures which can fully capture the complexity of landscape changes. This lack of data limits the use of objective function based evaluation prolific in other modelling fields, and restricts the application of sensitivity analyses in the models and the consequent assessment of model uncertainties. To overcome this deficiency, a novel model function approach has been developed, with each model function representing an aspect of model behaviour, which allows for the application of sensitivity analyses. The model function approach is used to assess the relative sensitivity of the CAESAR-Lisflood LEM to a set of model parameters by applying the Morris method sensitivity analysis for two contrasting catchments. The test revealed that the model was most sensitive to the choice of the sediment transport formula for both catchments, and that each parameter influenced model behaviours differently, with model functions relating to internal geomorphic changes responding in a different way to those relating to the sediment yields from the catchment outlet. The model functions proved useful for providing a way of evaluating the sensitivity of LEMs in the absence of data and methods for an objective function approach.
The evaluation and verification of landscape evolution models (LEMs) has long been limited by a lack of suitable observational data and statistical measures which can fully capture the complexity of landscape changes. This lack of data limits the use of objective function based evaluation prolific in other modelling fields, and restricts the application of sensitivity analyses in the models and the consequent assessment of model uncertainties. To overcome this deficiency, a novel model function approach has been developed, with each model function representing an aspect of model behaviour, which allows for the application of sensitivity analyses. The model function approach is used to assess the relative sensitivity of the CAESAR-Lisflood LEM to a set of model parameters by applying the Morris method sensitivity analysis for two contrasting catchments. The test revealed that the model was most sensitive to the choice of the sediment transport formula for both catchments, and that each parameter influenced model behaviours differently, with model functions relating to internal geomorphic changes responding in a different way to those relating to the sediment yields from the catchment outlet. The model functions proved useful for providing a way of evaluating the sensitivity of LEMs in the absence of data and methods for an objective function approach.