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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.