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The influence of the shape of the upslope area in the slope length calculation. g is the grid size; A, B, C are the mean values from different shapes and upslope areas.
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Although many studies have investigated slope gradient uncertainty derived from Digital Elevation Models (DEMs), the research concerning slope length uncertainty is far from mature. This discrepancy affects the availability and accuracy of soil erosion as well as hydrological modeling. This study investigates the formation and distribution of exist...
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... λ denotes the slope length, which relates to two times the upslope area, and a is the coefficient. Moreover, the CSL value is the horizontal distance of a point to its water-flow origin along the flow path. Nevertheless, the SCA value is an indirect derivation based on the upslope area. In general, the value of SCA is larger than that of CSL. When the upslope area of one pixel is in an orthogonal rake, the slope lengths from both methods are nearly the same. Assuming the flow path is on an orthogonal line, the slope length from SCA should be approximately two times as that from CSL. If the cell’s arrangement is in any other patterns, the differences are enlarged (Figure 8). To a certain degree, the CSL value reveals the internal mechanisms of the surface flow process. When the water flow on the surface is in a gathering mode, the value from SCA should be larger than that from CSL. A rank of the maximum slope length and the R 2 for the three test sites are listed, i.e., loess tableland, loess ridge and loess gully hill, which shows a decreasing tendency of slope length with surface roughness. This section analyzes the hydrological slope length (runoff line length) and discuss its uncertainty in different landform types. The slope length is considered as the horizontal projection distance of the longest slope length from the point lengths at various test areas reveals the influence of resolution and terrain on slope length values. The cell count of each slope length class decreases with the increase of grid size in the three test areas. Similar variation tendencies and distribution patterns are found not only in the different test areas but also at the different resolutions. Some fluctuations occur at nearly the same slope length class for all test areas. Although an approximate decreasing tendency of both the total slope length and the total grid count with the increase in grid size at all test sites is shown in Figure 10, Figure 11 reveals that the mean slope length, as a ratio of total slope length to total grid count, increases with grid size. It could be graphics are built along with a series of regression analyses. The mean slope length moved into a stable state when the DEM resolution reached 85 m. The linear regression analysis reveals the effect of resolution on the mean slope length in all terrain areas. All correlation coefficients are greater than 0.89, and the correlations are significant at the 0.001 level (n=9). Figure 11 also shows the changes of mean slope length with terrain complexity. The regression model for the loess terrace (TA-5) lies at the top, and that for loess gully hill (TA-2) at the bottom. The mean slope length in a rough terrain area is smaller than that in a smooth one. Upon rearranging the regression expressions, a group of equations is obtained (Equation 11): Y 1 =0.9446 X +54.771, R 2 =0.9282 Y 2 =0.6140 X +41.980, R 2 =0.9286 Y 3 =0.5774 X +46.535, R 2 =0.8994 Y 4 =0.3421 X +57.501, R 2 =0.9225 Y 5 =1.1129 X +84.320, R 2 =0.9616 Y 6 =1.0778 X +69.196, R 2 =0.9143 where X is the DEM resolution, the value of X is less than 85 m and Y is the mean slope length. For each regression, n equals nine. The regression models of the different test areas could be generalized ...
Citations
... Resampling can create a continuous sequence of DEMs, allowing for controlled changes in resolution while keeping other variables constant, making it particularly useful in studies investigating the uncertainties brought about by DEM resolution (Zhu et al., 2014). ...
Terrain parameters describe the morphological characteristics of a surface and are an important part of the application of geoscience. At present, there is still a lack of scientific and systematic research on the associations among terrain parameters. In this article, 14 representative terrain parameters are selected to explore their spatial association relationships by using the quantification methods of linear correlation degree, distribution similarity and influence degree. Then, we discuss the effects of the digital elevation model (DEM) cell size and landform region on the associations among terrain parameters. Furthermore, the mechanism of the association relationships among terrain parameters is also analyzed to achieve a better understanding of terrain analysis. This study revealed that the similarity in calculation methods, the derivation of terrain parameters from other parameters, the geographic significance of representations, and the characteristics and appearances of landforms are significant factors contributing to the associations of terrain parameters. The terrain parameters with strong associations remained stable with changes in cell size and landform region. However, terrain parameters with weak associations significantly respond to this variety of factors. We quantify the associations among terrain parameters, provide a new perspective for examining the associations among terrain parameters, and provide guidance for the selection of terrain parameters in geoscience research.
... The LS-factor can be acquired from digital elevation models (DEMs) at regional scales 12,13 , which can be obtained through ground surveys, existing topographic maps, or remote sensing images 14,15 . With technological advances, remote sensing platforms (satellites, space shuttles, etc.) are increasingly used to acquire high-quality surface elevation data 16,17 , ranging from localized super high-resolution DEMs (i.e., LiDAR DEMs) to high-resolution global DEMs (GDEMs) 18 . ...
... These metrics can be obtained by Eqs. (12) and (13), respectively: where N is the number of grid cells, LS a is the LS-WPC calculation result, and LS b is the LS-PCS calculation result. ...
Topography is an important factor affecting soil erosion and is measured as a combination of the slope length and slope steepness (LS-factor) in erosion models, like the Chinese Soil Loss Equation. However, global high-resolution LS-factor datasets have rarely been published. Challenges arise when attempting to extract the LS-factor on a global scale. Furthermore, existing LS-factor estimation methods necessitate projecting data from a spherical trapezoidal grid to a planar rectangle, resulting in grid size errors and high time complexity. Here, we present a global 1-arcsec resolution LS-factor dataset (DS-LS-GS1) with an improved method for estimating the LS-factor without projection conversion (LS-WPC), and we integrate it into a software tool (LS-TOOL). Validation of the Himmelblau–Orlandini mathematical surface shows that errors are less than 1%. We assess the LS-WPC method on 20 regions encompassing 5 landform types, and R ² of LS-factor are 0.82, 0.82, 0.83, 0.83, and 0.84. Moreover, the computational efficiency can be enhanced by up to 25.52%. DS-LS-GS1 can be used as high-quality input data for global soil erosion assessment.
... The SDR model applied the algorithm developed by Desmet and Govers [57] to calculate the LS factor from DEM. Although Zhu et al. [58] pointed out the sensitivity of this algorithm to the resolution of DEM, it performed well at a resolution of 30 m [59]. Therefore, DEM data with a spatial resolution of 30 m were used and obtained from the USGS web portal (https://earthexplorer.usgs.gov/, ...
The construction of large-scale water reservoir facilities in transboundary river basins always arouses intense concern and controversy. The Grand Ethiopian Renaissance Dam (GERD) under construction in Ethiopia is perceived to affect water security in Egypt and Sudan. Therefore, this study investigated the water and sediment balance of the Blue Nile River (BNR) basin and identified the spatio-temporal variation in sediment and water yields along with the construction of GERD using Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST) sediment and water yield models. The BNR basin experienced increasing water and sediment yields between 1992 and 2020 and has shown a growth trend since 2020. The lion’s share of water and sediment yields come from upstream of the GERD. Taken together, these results imply that the construction of the GERD will serve as a water storage and silt trap for Sudan and Egypt.
... A s for each grid is obtained by dividing the upstream accumulated area by the effective contour length of the cell (Costa-Cabral and Burges, 1994). The UCA method is thus further deduced to calculate the cumulative slope length for each cell (Zhang et al., 2013;Zhu et al., 2014;Yang, 2015). An integrated tool (LS-TOOL) was designed in a recent model to improve the UCA method and calculate the distributed watershed erosion slope length (DWESL) (Zhang et al., 2013;, in which the cutoff factors caused by deposition (i.e. ...
The Universal Soil Loss Equation (USLE) and the Revised Universal Soil Loss Equation (RUSLE) have been widely used for predicting average soil loss. Slope length is an important topographical parameter of the L factor in USLE/RUSLE. Among the widely studied GIS procedures for extracting slope length, the distributed watershed erosion slope length (DWESL) based on the unit contributing area estimation method, which considers two-dimensional runoff process and cutoff factors, is a relatively complete model for calculating slope length. Slope length in the DWESL model is primarily calculated using conventional flow direction algorithms such as D8, Dinf, MS and MFD-md. However, DWESL outputs require further improvement due to the errors in the usual estimates of the uphill contributing area and the effective contour length of discrete elements. Combined with a theoretical differential equation of specific catchment area on hillsides, the calculation of the DWESL model was optimized without estimating the uphill contributing area or the effective contour length for each cell. The proposed integration method based on the topographical features slope line, contour curvature and cutoff factors (ITF method) was used to extract slope length from the raster digital elevation. Slope length extracted using the ITF method had the smallest error in verification of mathematical surfaces (average RRMSE = 0.0573), and its spatial distribution was more consistent with the structure of the terrain surface for all test data, relative to the conventional flow direction algorithms in the original DWESL model. The proposed ITF method could provide a reference for predicting soil erosion using the USLE/RUSLE model.
... The accuracy of calculated topographic factors depends not only on the grid sizes at which the elevation data is represented, but also the data sources and terrain complexity (Gertner et al., 2002;Liu et al., 2011;Mukherjee et al., 2013;Oliveira et al., 2013;Shan et al., 2019;Shi et al., 2012;Thomas et al., 2015;Thompson et al., 2015;Wang et al., 2001;Warren et al., 2004;Wolock and Mccabe, 2015;Wu et al., 2005;Zhou and Liu, 2004;Zhu et al., 2014). For instance, Fu et al. (2014) reported that as the DEM grid size increased, the slope steepness factor was underestimated and the slope length factor was overestimated. ...
The availability and precision of topographic data determines the reliability of the calculated slope length and slope gradient (LS) factor, which limits the use of the universal soil loss equation (USLE) and its adapted versions in region-scale soil erosion risk assessment. One of the common complications is the effectiveness of topographic data with different resolutions or the compatibility of topographic data originated from different sources. In this study, the topographic data from five common sources, 5-m digital elevation model (DEM) based on 1:10,000 topographic maps (5-m topo DEM of 1:10,000), 25-m DEM derived from 1:50,000 topographic maps (25-m topo DEM of 1:50,000), 30-m ASTER GDEM, 30-m and 90-m SRTM DEMs, were individually applied to calculate the LS factors of five catchments with distinct terrain characteristics. Our results show that the computation accuracy of the LS factors in the five study catchments decreased with greater grid sizes derived from the five topographic data sources. Compared to the most precision 5-m topo DEM of 1:10,000, the relative computation error of the mean LS factors was less than 10% when calculated from the 25-m topo DEM of 1:50,000, and that was less than 25% from the 30-m ASTER and 30-m SRTM DEMs. For scenarios in gently rolling areas, the 90-m SRTM DEM with the relative computation error less than 15% could be recommended when there are noises on the open sources DEMs surface. Therefore, depending on the requirements of data accuracy, different data sources can be applied individually or in combined to obtain the optimal predictions of the LS factors. However, such recommendations on data sources proposed in this study appeared to be more applicable for regions with complex terrains. Further studies over a range of terrain features and spatial scales are required to validate the effectiveness of different topographic data sources in calculating the LS factor.
... Normally, the result of extracted gullies relies on the threshold of drainage area with the flow accumulation matrix (Zhu et al., 2014), which would further affect the result of the gully evolution index. Thus, to quantitatively analyze the stability of gully evolution index and the relationship between gully extraction threshold and gully evolution index, we selected 50, 100,150,200,250,300,350,400,450, and 500 as the threshold values and extracted the GPC on the basis of these gully extraction thresholds. ...
The expression of gully landforms can be regarded as an indicator of the evolutionary process of gullies. Most existing studies on the expression of gully landforms focus on plane characteristics. However, the vertical characteristics of a gully should be given considerable attention because gullies have mainly eroded the surface in the vertical direction. Current studies on vertical characteristics of gullies mainly focused on a single gully or rarely a few gullies, thereby failing to express the entire gully landform in a certain area. In this study, gully profile combination (GPC) was proposed to investigate the morphology and reveal the evolution of gully landforms. It was defined as the combination of vertical projection of all gully profiles in the entire drainage basin. Then, a gully evolution index and its statistic values were used to reveal the evolution of gully landforms based on GPC. The proposed method was applied and validated in three typical loess gully landform areas (i.e., loess tableland, ridge, and hill) in the Loess Plateau of China. Results show that GPC can effectively express gully landforms. The specific geomorphological feature (monoclinic loess tableland) can also be identified using GPC. The gully evolution index results also demonstrate different magnitudes of gully evolutionary stages in a certain area, which reflect the diversity of gullies. The average and median values of the gully evolution index increase in the three typical loess gully landforms. From loess tableland, loess ridge, and loess hill, the average values are 0.653, 0.703, and 0.763, and the median values are 0.661, 0.719, and 0.783, respectively. This method is also found to be stable with gully extraction thresholds for distinguishing different loess gully landforms. Accordingly, the evolution magnitudes of loess gully are obtained.
... Determining the uncertainty in slope estimation, based on resolution, DTM uncertainty, analysis scale and computation algorithm, is an active area of research in terrain analysis and modeling. Dolan and Lucieer (2014) and Zhu et al. (2014) have shown uncertainties in slopes to reach up to 5°-6° when using a MBES-derived DTM. Furthermore, assumptions about the macro-relief of the surveyed seafloor at the spatial resolution of the backscatter samples are needed for an a priori estimate of slope uncertainty; for most MBES this cannot be assessed by using only the bathymetry available from the MBES. ...
Multibeam echosounders (MBES) have become a widely used acoustic remote sensing tool to map and study the seafloor, providing co-located bathymetry and seafloor backscatter. Although the uncertainty associated with MBES-derived bathymetric data has been studied extensively, the question of backscatter uncertainty has been addressed only minimally and hinders the quantitative use of MBES seafloor backscatter. This paper explores approaches to identifying uncertainty sources associated with MBES-derived backscatter measurements. The major sources of uncertainty are catalogued and the magnitudes of their relative contributions to the backscatter uncertainty budget are evaluated. These major uncertainty sources include seafloor insonified area (1–3 dB), absorption coefficient (up to > 6 dB), random fluctuations in echo level (5.5 dB for a Rayleigh distribution), and sonar calibration (device dependent). The magnitudes of these uncertainty sources vary based on how these effects are compensated for during data acquisition and processing. Various cases (no compensation, partial compensation and full compensation) for seafloor insonified area, transmission losses and random fluctuations were modeled to estimate their uncertainties in different scenarios. Uncertainty related to the seafloor insonified area can be reduced significantly by accounting for seafloor slope during backscatter processing while transmission losses can be constrained by collecting full water column absorption coefficient profiles (temperature and salinity profiles). To reduce random fluctuations to below 1 dB, at least 20 samples are recommended to be used while computing mean values. The estimation of uncertainty in backscatter measurements is constrained by the fact that not all instrumental components are characterized and documented sufficiently for commercially available MBES. Further involvement from manufacturers in providing this essential information is critically required.
... In arid and semi-arid loess plateau, although there are several challenges in obtaining suitable topographic factors in regional scale because the occurrence of landslides is closely related to the evolution of geography and geomorphology, the recent study works on the evolution of loess geomorphology have gained important achievements, such as quantitative calculation and precise interpretation of geomorphic evolution using geographic information systems (Ayalew et al.) and digital terrain analysis (DTA) technology. For example, DEM is mainly used to describe the morphology of the ground and has been applied to the characterization of geomorphology Liu et al. 2015;Song et al. 2013;Tang et al. 2015;Xiong et al. 2014;Zhu et al. 2014). Moreover, some studies have focused the extraction of other terrain parameters, such as extraction of valley shoulder line (Song et al. 2013), the research of topography and geomorphology of the loess plateau based on DEM and fractal technique (Lv et al. 1998) and the relationship between soil erosion and landform evolution in the loess plateau watershed (Cai et al. 1996). ...
Loess Plateau is one of the ecologically fragile regions in China. It is one of the slippery strata of which landslides often developed. The formation and development of landslides are mainly affected by various natural environments, triggering factors, the vulnerability of landslide-bearing bodies, and topography has a controlling effect on landslides and determines landslide distribution. As important environmental elements, the selection and reclassification of topographic factors are the basis for loess landslide vulnerability map. In this study, our research suggests an effective workflow to select and analyze the topographic factors in the loess landslides. Nine hazard-formative environmental factors [e.g., slope, aspect, slope shape (SS), slope of slope (SOS), slope of aspect (SOA), surface amplitude (SA), surface roughness (SR), incision depth (ID) and elevation variation coefficient (EVC)] are prepared for landslide suitability analysis. The models of certainty factor, sensitivity index and correlation coefficient are combined to select and analyze the suitability of these factors. Four topographic factors (i.e., slope, SOS, SS and SR) were ultimately selected to carry out the landslide vulnerability mapping with other factors. Our results showed that most of the landslides were located in medium and high classes and accounting for 75.3%, and these places also coincided with higher economies and intense human activities. Our research also suggested that in situ measurements are necessary to determine how to reclassify these topographic factors and how many grades these topographic factors divided, which would further improve the reliability of landslide vulnerability map for the decision makers to deal with the possible future landslides in terms of safety and human activities.
... The size of the slope directly affects the surface material flow, energy conversion scale, and intensity. On the surface of the Moon, the slope of a certain point is the elevation variability on the lunar surface from the East-West direction to the North-South direction [34], [35]. A simplified difference formula is often used for gradient extraction, as shown below: ...
... where f x is the elevation change rate in the x-direction, and f y is the elevation change rate in the y-direction. Aspect is an important topographic factor influencing local site microclimate mainly because it determines the amount of solar radiation received [34], [35]. For a given point on the lunar surface, the direction of the maximum change of elevation value of this point is represented by ...
... In this paper, the section curvature is called the curvature kv, which is the change rate of the ground elevation along the maximum gradient, as shown in Formula (3). And the plane curvature kh describes the surface bending and changes along the horizontal direction, which is expressed by Formula (4) [34], [35] ...
Different land-surface parameters reflect the topographic features of the lunar surface from different aspects. Surface roughness is one of the basic land-surface parameters, and the analysis of correlations between surface roughness and other six land-surface parameters, i.e., slope, aspect, curvature, plane curvature, slope variability, and aspect ratio, is very important in scientific research. However, there are no transform functions or related algorithms defined among these parameters. Therefore, this study focuses upon the correlations between the lunar surface roughness and other six land-surface parameters. In the proposed scheme, the morphological roughness method is used to calculate the lunar surface roughness, and other related parameters are processed by their own corresponding formulas. In addition, the Lunar Orbiter Laser Altimeter Gridded Data Records are used as the sample data, and 14 areas on the Moon are selected as the study areas. For each selected area, a backpropagation neural network is presented to find the complex nonlinear correlations between surface roughness and other six land-surface parameters. The experimental results show that there are clear correlations between surface roughness and other six land-surface parameters in each selected area. More specifically, slope, surface curvature, and slope variability have much better correlations with the lunar surface roughness.
... In addition, rainstorms are concentrated in the summer season, and the main vegetation cover consists of shrubs, grass, and wood forests. Dry land, accelerated soil erosion, and high sediment yield are serious problems in this area Zhu et al. 2014). ...
The automatic recognition of landforms is regarded as one of the most important procedures to classify landforms and deepen the understanding on the morphology of the earth. However, landform types are rather complex and gradual changes often occur in these landforms, thus increasing the difficulty in automatically recognizing and classifying landforms. In this study, small-scale watersheds, which are regarded as natural geomorphological elements, were extracted and selected as basic analysis and recognition units based on the data of SRTM DEM. In addition, datasets integrated with terrain derivatives (e.g., average slope gradient, and elevation range) and texture derivatives (e.g., slope gradient contrast and elevation variance) were constructed to quantify the topographical characteristics of watersheds. Finally, Random Forest (RF) method was employed to automatically select features and classify landforms based on their topographical characteristics. The proposed method was applied and validated in seven case areas in the Northern Shaanxi Loess Plateau for its complex and gradual changed landforms. Experimental results show that the highest recognition accuracy based on the selected derivations is 92.06%. During the recognition procedure, the contributions of terrain derivations were higher than that of texture derivations within selected derivative datasets. Loess terrace and loess mid-mountain obtained the highest accuracy among the seven typical loess landforms. However, the recognition precision of loess hill, loess hill–ridge, and loess sloping ridge is relatively low. The experiment also shows that watershed-based strategy could achieve better results than object-based strategy, and the method of RF could effectively extract and recognize the feature of landforms. © 2017, Science Press, Institute of Mountain Hazards and Environment, CAS and Springer-Verlag Berlin Heidelberg.
