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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.
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.
Beta diversity is a conceptual link between diversity at local and regional scales. Various additional methodologies of quantifying this and related phenomena have been applied. Among them, measures of pairwise (dis)similarity of sites are particularly popular. Undersampling, i.e. not recording all taxa present at a site, is a common situation in ecological data. Bias in many metrics related to beta diversity must be expected, but only few studies have explicitly investigated the properties of various measures under undersampling conditions. On the basis of an empirical data set, representing near-complete local inventories of the Lepidoptera from an isolated Pacific island, as well as simulated communities with varying properties, we mimicked different levels of undersampling. We used 14 different approaches to quantify beta diversity, among them dataset-wide multiplicative partitioning (i.e. true beta diversity') and pairwise site x site dissimilarities. We compared their values from incomplete samples to true results from the full data. We used these comparisons to quantify undersampling bias and we calculated correlations of the dissimilarity measures of undersampled data with complete data of sites. Almost all tested metrics showed bias and low correlations under moderate to severe undersampling conditions (as well as deteriorating precision, i.e. large chance effects on results). Measures that used only species incidence were very sensitive to undersampling, while abundance-based metrics with high dependency on the distribution of the most common taxa were particularly robust. Simulated data showed sensitivity of results to the abundance distribution, confirming that data sets of high evenness and/or the application of metrics that are strongly affected by rare species are particularly sensitive to undersampling. The class of beta measure to be used should depend on the research question being asked as different metrics can lead to quite different conclusions even without undersampling effects. For each class of metric, there is a trade-off between robustness to undersampling and sensitivity to rare species. In consequence, using incidence-based metrics carries a particular risk of false conclusions when undersampled data are involved. Developing bias corrections for such metrics would be desirable.
Badlands have long been considered as model landscapes due to their perceived close relationship between form and process. The often intense features of erosion have also attracted many geomorphologists because the associated high rates of erosion appeared to offer the opportunity for studying surface processes and the resulting forms. Recently, the perceived simplicity of badlands has been questioned because the expected relationships between driving forces for erosion and the resulting sediment yield could not be observed. Further, a high variability in erosion and sediment yield has been observed across scales. Finally, denudation based on currently observed erosion rates would have lead to the destruction of most badlands a long time ago. While the perceived simplicity of badlands has sparked a disproportional (compared to the land surface they cover) amount of research, our increasing amount of information has not necessarily increased our understanding of badlands in equal terms. Overall, badlands appear to be more complex than initially assumed. In this paper, we review 40 years of research in the Zin Valley Badlands in Israel to reconcile some of the conflicting results observed there and develop a perspective on the function of badlands as model landscapes. While the data collected in the Zin Valley clearly confirm that spatial and temporal patterns of geomorphic processes and their interaction with topography and surface properties have to be understood, we still conclude that the process of realizing complexity in the "simple" badlands has a model function both for our understanding as well as perspective on all landscape systems.
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.
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.
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.
TopoToolbox is a MATLAB program for the analysis of digital elevation models (DEMs). With the release of version 2, the software adopts an object-oriented programming (OOP) approach to work with gridded DEMs and derived data such as flow directions and stream networks. The introduction of a novel technique to store flow directions as topologically ordered vectors of indices enables calculation of flow-related attributes such as flow accumulation similar to 20 times faster than conventional algorithms while at the same time reducing memory overhead to 33% of that required by the previous version. Graphical user interfaces (GUIs) enable visual exploration and interaction with DEMs and derivatives and provide access to tools targeted at fluvial and tectonic geomorphologists. With its new release, TopoToolbox has become a more memory-efficient and faster tool for basic and advanced digital terrain analysis that can be used as a framework for building hydrological and geomorphological models in MATLAB.
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.
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.