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Effects of DEM resolution on the accuracy of gully maps in loess hilly areas
Catena 177 (2019) 114–125
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Effects of DEM resolution on the accuracy of gully maps in loess hilly areas a,b,d
a,b,d,⁎
Wen Dai , Xin Yang Xiaoli Huangd
b
b
a,c
d
T
d
, Jiaming Na , Jingwei Li , Dick Brus , Liyang Xiong , Guoan Tang ,
a
Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, Nanjing 210023, China State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China Biometris, Wageningen University and Research, PO Box 16, 6700 AA Wageningen, the Netherlands d Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Gully mapping DEM resolution Uncertainty The Loess Plateau of China Accuracy assessment
Gully maps are important prerequisites for the study of gully erosion and land degradation. Many digital elevation model (DEM)-based methods have been proposed to enable automated gully mapping. However, the accuracy of a gully map derived from a DEM is inevitably affected by the DEM resolution. This study investigates the effects of DEM resolution on the accuracy of gully maps. A series of DEMs with resolutions of 0.1–10 m is employed to map gully areas. The effects of DEM resolution on the error in the mapped gully area and on the position error are described by regression models. The results from two catchments in hilly areas of the Loess Plateau in China are as follows. DEMs with resolutions of 0.5–2 m are the most suitable for gully mapping. Very high-resolution DEMs increase local position errors and over-predict the extents of gullies, whereas DEMs with coarser resolutions cause the downward migration of mapped gully boundaries, resulting in the under-prediction of gully areas. However, the effects of DEM resolution on gully maps are not constant but vary in space. The spatial disparities of the resolution effects are related to the gully morphology. The resolution effects on the gully maps in V-shaped gullies are stronger than those in U-shaped gullies. The findings of this study can be used to select a suitable DEM resolution for gully mapping in loess hilly areas and contribute to understanding the characterization of gullies by using DEMs.
1. Introduction Gully erosion, which widely threatens farmland and the environment, is the most serious type of water erosion (Valentin et al., 2005; Castillo and Gómez, 2016; Poesen et al., 2003). Gully maps are important prerequisites for studying gully erosion and land degradation. Consequently, many researchers have focused on gully surveying and mapping to determine the distribution, magnitude, and topographical properties of gullies (Taruvinga, 2009; Martínez-Casasnovas, 2003; Casalí et al., 2006; Zabihi et al., 2018; Wu and Cheng, 2005), the results of which can be used for agricultural management, soil and water conservation, and ecological planning. Field assessment and visual interpretation of imagery have been the most traditional and popular methods used to obtain gully information for decades (Daba et al., 2003; Fadul et al., 1999; Mararakanye and Le Roux, 2012; Perroy et al., 2010; Hansen and Law, 2007). However, while these methods are easy to implement and provide results with high accuracy, the substantial amount of manual work associated with these methods restricts their application on a large scale (Wang et al., ⁎
2014). With the launch of numerous Earth observation satellites, many researchers have proposed automatic gully mapping methods based on satellite imagery. These automatic methods can be categorized into two types: pixel-based and object-based methods. The unit of analysis in pixel-based methods is a single pixel, and the rules are applied to each pixel separately to achieve the final result (Seutloali et al., 2016; Vrieling et al., 2007; Knight et al., 2007). However, pixel-based methods consider only spectral information, thereby restricting their application. Alternatively, object-based methods, which have been utilized widely over the last decade, are superior to traditional pixelbased methods because the unit of analysis is any meaningful object (Shruthi et al., 2011; Shruthi et al., 2012; Shruthi et al., 2015; Kai et al., 2017; d'Oleire-Oltmanns et al., 2014; Blaschke, 2001). The three-dimensional features of gullies, such as their depth and volume, are not directly observable or measurable, although gully shapes can be acquired from imagery and used to improve the accuracy of a map. Therefore, to measure the three-dimensional properties of gullies, methods have been developed based on digital elevation models
Corresponding author at: School of Geographic Science, Nanjing Normal University, No. 1 Wenyuan Road, Qixia District, Nanjing, China. E-mail address: [email protected] (X. Yang).
https://doi.org/10.1016/j.catena.2019.02.010 Received 7 May 2018; Received in revised form 4 February 2019; Accepted 15 February 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Gullies on the Loess Plateau: (a) gully types; (b) gully map; and (c) field survey photo of gullies (gully area is marked by red line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2015; Hsu et al., 2016; Ariza-Villaverde et al., 2015; McMaster, 2002; Chaplot et al., 2000). A conclusion drawn from these studies is that the most suitable resolution exists and depends on the application. For example, Tang et al. (2003) proposed that a 5 m DEM is suitable for representing slopes in loess areas when the DEMs are produced by digitizing the contours of 1:10,000 scale topographical maps. Chaplot et al. (2000) reported that 10 m and 30 m DEMs can predict the elevations above the stream bank, downslope gradient and upslope contributing areas when using linear regression and co-kriging to predict the soil hydromorphy. López-Vicente and Álvarez (2018) proposed an optimum DEM resolution (0.2 m) to improve the results of modeling the structural hydrological connectivity in woody crop areas. Tan et al. (2018) found that better monthly streamflow simulations are obtained between 20 m and 60 m resolution DEMs with the smallest area threshold (1000 ha). Clearly, selecting an appropriate DEM resolution is important for studying soil erosion processes (Lu et al., 2017). Zhang et al. (2008) noted that the hydrological attributes extracted from DEMs with different resolutions exhibit different properties that influence the results predicted by soil erosion models. Lucà et al. (2011) discussed the influence of DEM resolution on maps depicting the susceptibility for gully erosion; they found that a coarser DEM resolution reduces both the extents of the most susceptible classes and the accuracy of the map. Gómez-Gutiérrez et al. (2015) reported that the finest resolution is not necessarily the best for mapping susceptibility of gully erosion. Garosi et al. (2018) found that the DEM with 10 m resolution resulted in the highest kappa coefficient of the map depicting the susceptibility for gully erosion. DEM resolution is also a critical factor that affects gully mapping
(DEMs). These methods can be categorized into three types: terrain morphological feature identification, image gradation detection, and terrain visibility analysis. Terrain morphological feature identification detects the locations of gullies by analyzing changes in terrain parameters, such as the slope, aspect, curvature, flow accumulation and positive-negative terrain index (P-N) (Lu, 1998; Tang et al., 2007b; Zhu et al., 2003; H. Liu et al., 2016; Zhou et al., 2010a; Zhou et al., 2010b; Chen et al., 2012; Li et al., 2008). In contrast, image gradation detection regards the DEM as a grayscale image and employs image processing algorithms, such as the edge detection operator (Yan et al., 2011) and snake model (Yan et al., 2014; Zhou and Tang, 2013; Song et al., 2013). Finally, terrain visibility analysis methods, such as the terrain openness method (Wang et al., 2015) and hill-shading method (Yang et al., 2017b; Na et al., 2018), obtain gully boundaries based on viewshed analysis or shade relief simulation. Among these DEM-based methods, the hill-shading method significantly improves the gully map accuracy for high-resolution DEMs (Yang et al., 2017b). Although DEM-based methodologies for gully mapping have been enriched, challenges still persist. DEM resolution, as a key factor, determines the potential of a DEM for characterizing the terrain surface. The uncertainty in terrain analysis and geomorphological feature mapping is inevitably related to this resolution. Consequently, many studies have focused on the importance of the DEM resolution for terrain analysis. These studies ranged from the derivation of terrain attributes (Tang et al., 2003; Zhou and Liu, 2004; Liu et al., 2009; Thompson et al., 2001; Sørensen and Seibert, 2007) and geo-analysis modeling (Wu et al., 2005; Chaubey et al., 2005; Zhang et al., 2008; López-Vicente and Álvarez, 2018; Tan et al., 2018) to the mapping of geomorphological features (Saksena and Merwade, 115
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elevations ranging from 1348 to 1556 m. The main channel of the catchment is oriented from east to west spanning a length of 700 m with a depth of 208 m. The Qiaogou catchment (Fig. 2b) (37°34′2′′ N, 110°16′48′′ E) is located in northern Suide County, Shaanxi Province, and has an area of 0.19 km2 with elevations ranging from 900 to 1017 m. The main channel of the catchment is oriented from southwest to northeast spanning a length of 550 m with a depth of 117 m.
(Castillo et al., 2012). DEMs with a 5 m resolution have generally been used in most previous gully mapping methods (H. Liu et al., 2016; Zhou et al., 2010a; Zhou et al., 2010b; Chen et al., 2012; Yan et al., 2011; Yan et al., 2014; Zhou and Tang, 2013; Song et al., 2013; Li et al., 2008; Wang et al., 2015); nevertheless, the suitability of 5 m DEMs for mapping gullies remains unclear. To the best of our knowledge, no publications are available that have compared the accuracies of gully maps obtained with different resolutions. Currently, with the ongoing development of data acquisition technologies, such as unmanned aerial vehicle (UAV) photogrammetry and light detection and ranging (LIDAR), high-resolution DEMs are becoming more available and convenient to obtain. However, whether high-resolution DEM data can achieve high mapping accuracy remains unknown. Accordingly, this study explores the effects of DEM resolution on the accuracy of gully maps by using a series of 0.1–10 m DEMs. This work specifically aims to 1) model the relationships between accuracy indices of gully maps and the DEM resolutions, 2) find a suitable DEM resolution for gully mapping, and 3) analyze the spatial disparities of the effect of DEM resolution on the accuracy of gully maps.
2.2. Data The data consisted of LIDAR point clouds and 0.05 m digital orthophoto maps (DOMs). The point clouds of the two areas were acquired by terrestrial LIDAR technology with a Riegl VZ400 terrestrial laser scanner (Riegl Laser Measurement Systems GmbH, Horn, Austria) in August 2014. The total number of points in the Madigou catchment exceeded 60 million with an average density of 2600 points per square meter, whereas the total number of points in the Qiaogou catchment was 20 million with an average density of 1200 points per square meter. A series of DEMs with different resolutions was generated by the point clouds (see Section 3.2). The DOMs were simultaneously generated by UAV photogrammetry with a Matrice 600 (SZ DJI Technology Co., Ltd., Shenzhen, China). Through visual interpretation of the DOMs for both study areas, gully maps were derived. These maps served as ground truth and as reference maps. The gully maps derived from the DEMs are compared with the reference maps to assess the errors in the gully maps derived from the DEMs (see Section 3.4.1).
2. Gully types, study areas, and data 2.1. Gully types and study areas The Loess Plateau of China exhibits one of the most severe rates of gully erosion worldwide (M. Li et al., 2017). This region contains three main gully types, namely, valley, bank, and ephemeral gullies (Yang et al., 2017a) (Fig. 1a). Valley and bank gullies constitute the main sediment yield sources and threaten the inter-valley land quality (Z. Li et al., 2017). Erosion caused by these two types of gullies accounts for more than 60% of all soil erosion in the watersheds of the hill-gully subregion and more than 80% in the high loess plain characterized by deeply incised gullies (Zheng and Wang, 2014). Generally, in the Loess Plateau, bank gullies, developing in both side slopes of valley gullies, form an integral part of the whole gully-affected area (Fig. 1c). This characteristic can be readily used for mapping the gully-affected area using DEMs. Accordingly, gully mapping is often referred to as mapping the gully-affected area (Fig. 1b) (Kai et al., 2017; Kai et al., 2016). Two catchments (Fig. 2), Madigou and Qiaogou, situated in the loess hilly areas of the northern Loess Plateau were selected. These study areas are characterized by typical loess gullies and hills. Many gullies with intense erosion have developed in these areas; these gullyaffected areas cover more than 60% of the region. The Madigou catchment (Fig. 2a) (37°28′59′′ N, 108°48′2′′ E) is located in northern Jingbian County, Shaanxi Province, and has an area of 0.23 km2 with
3. Methodology 3.1. Overview of the analyses To accomplish the objectives stated in the Introduction, we employed the following workflow (Fig. 3): i) Preprocessing of the point clouds to generate DEMs with different resolutions; ii) Mapping gullies by using the multidirectional hill-shading method; iii) Generating reference data by visual interpretation of the DOMs and then assessing the accuracies of the gully maps derived from the DEMs; iv) Modeling relationships between the DEM resolutions and accuracy indices; v) Investigating the spatial disparities of the effects of the DEM resolution on gully mapping.
Fig. 2. Study areas: (a) DOM of the Madigou catchment; (b) DOM of the Qiaogou catchment. 116
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Fig. 3. Workflow of this study.
are two parameters: the azimuth and the altitude of the light source. Yang et al. (2017b) demonstrated that six pairs of light azimuths are sufficient for gully mapping in the hilly Loess Plateau. Meanwhile, the light altitude can be detected by sampling transverse profiles across the gully boundaries and calculating the average median slope. The method is implemented in ArcGIS 10.2 for this study.
3.2. Generating a series of DEMs LIDAR elevation data sets provide flexibility for producing DEMs with multiple horizontal resolutions from the same data source. A series of DEMs was generated by inverse distance weighted (IDW) interpolation of the LIDAR point clouds. The resolutions of the generated DEMs ranged from 0.1 m to 10 m. DEMs with resolutions exceeding 10 m were excluded given that the ability to characterize the gully morphology becomes very poor (Tang et al., 2007b).
3.4. Accuracy assessment method 3.4.1. Reference data The visual interpretation of high-resolution images is widely used for ground truth to assess the accuracy of gully maps (d'OleireOltmanns et al., 2014; Kai et al., 2017; Shruthi et al., 2011). This approach provides a high position accuracy that meets the requirements of gully erosion research (Li et al., 2014). The features and boundaries of gullies are clearly observable in high-resolution DOMs and are readily recognized through field surveying (Fig. 1c). Thus, the reference maps were digitized manually based on DOMs and fieldwork knowledge.
3.3. Gully mapping To select an appropriate method for DEM-based gully mapping, the method should meet the following requirements. First, the method should be applicable to high-resolution DEMs because most DEM-based methods are based on a resolution of 5 m, and thus, they fail on DEMs with a higher resolution. For example, the slope segmentation method is unable to generate a satisfactory gully map using a DEM with a 1 m resolution (Yang et al., 2017b). Second, the parameters used in the candidate method should avoid the use of subjective experience as much as possible. The P-N method (Zhou et al., 2010a; Zhou et al., 2010b; Chen et al., 2012) relies on the appropriateness of the size of the neighboring windows, whereas the slope segmentation (Zhu et al., 2003) and terrain openness methods (Wang et al., 2015) rely on the appropriateness of slope segmentation thresholds and openness angles, respectively. In contrast, the multidirectional hill-shading method employs local terrain attributes as the input parameter instead of subjective experience to generate the results (Yang et al., 2017b). Hence, this method can achieve high accuracy and efficiency on DEMs with a 1 m resolution. Given these advantages, the multidirectional hillshading method was selected for gully mapping in this study. Fig. 4 shows the basic principles of the selected method. Simulations of shadows on shady slopes can be obtained when the gully surface is illuminated by light rays with a certain altitude and azimuth (Fig. 4a), and the shadows on the other side can be acquired when the light rays are reversed. Therefore, the gully-affected area can be determined by merging both sides of the shadows (Fig. 4b). The keys to this method
3.4.2. Accuracy indices The gully map accuracy is usually assessed by two aspects, namely, the position accuracy and the area accuracy. The position accuracy is usually assessed either by buffer-based or contour-matching difference (CMD) methods. The former method assesses the position accuracy by estimating the percentage of the total length of the representation that is within a specified distance of the reference data (Goodchild and Hunter, 1997; Yan et al., 2014; W. Liu et al., 2016), whereas the latter method describes the matching degree between two polyline features (i.e., the mapping results and reference data) by an area ratio of intersecting polygons to buffer zones of the reference data (Tang et al., 2007a; Yan et al., 2011). However, these methods reflect only the global error of the gully boundary and fail to describe the local error. As an alternative, this study proposes a novel index, namely, di (i = 1, 2, 3, …, n), which is defined as the minimum distance from the ith vertex of the mapped gully boundary to the reference data (Fig. 5). The index di is positive when the vertex is located upslope above the
Fig. 4. Sketches illustrating the principles of the multidirectional hill-shading method (Yang et al., 2017b). 117
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Fig. 5. Definition of the index di for the position accuracy.
reference line and negative when the vertex is located downslope below the reference line. Individual values of di describe the local error, while the global position accuracy is described by summary statistics of the frequency distribution of di. Another key index, the gully area, is widely used to determine the erosion magnitude in gully erosion research (Li et al., 2003; Burkard and Kostaschuk, 1997, 1995; Betts and DeRose, 1999). To assess the area accuracy, this study uses the relative error in the mapped gully area, Ar, which is defined as the ratio of the area difference (i.e., the mapped area minus the reference gully area) to the reference gully area (Eq. (1)):
Ar =
Amap − Areal Areal
× 100%
(1)
where Amap is the mapped gully area (derived from a DEM) and Areal is the gully area on the reference map. Fig. 6. Sketch of gully morphology.
3.5. Relationship modeling Once the gully maps for all DEMs were obtained, overlays of these maps and the shaded relief maps were made, thereby revealing the details of the local terrain surface. Then, in addition to conducting an accuracy assessment, quantitative relationships between the accuracy indices and the DEM resolution were established. To accomplish these tasks, summary statistics of the index di and the area accuracy Ar were regressed against the DEM resolution. Linear regression models were fitted by an ordinary least squares approach in which we assumed that the accuracy indices obtained with the different DEM resolutions were independent.
At the cross-section scale, the magnitude of the DEM resolution effect is defined as the difference of di (DOD) between the maps with the lowest and highest accuracy (maximum and minimum DEM effects) (Eq. (3)):
3.6. Spatial disparity analysis
4. Results
The effect of DEM resolution on the accuracy of gully maps is not constant but varies in space. We analyzed whether this spatial variation in the resolution effect on the accuracy of gully maps is related to gully morphology. Cross-section analysis was performed in this study to determine the gully morphology (Vanmaercke et al., 2016; Z. Li et al., 2017; Caraballo-Arias et al., 2016; Castillo et al., 2012). Generally, the gully slope is obviously different from the inter-gully hillslope. According to the morphology of the gully profile (Fig. 6), the profile in the inter-gully area has negative curvature (the normal vector is perpendicular to the ground and upward), whereas the profile in the gully area has positive curvature (Yan et al., 2011). Hence, a slope variation point exists at the junction of positive curvature and negative curvature. Most DEM-based gully mapping methods depend on the slope variation between the gully slope and the inter-gully hillslope to map gullies (Yang et al., 2017b; Wang et al., 2015; Zhu et al., 2003). Accordingly, the slope variation (Sv) in each cross-section is used to describe gully morphology (Eq. (2)):
4.1. Gully maps
Sv = Sg − Si
DOD = di (a) − di (b)
(3)
where di (a) and di (b) are the di of the lowest and highest accuracy maps, respectively. Then, the Sv is regressed against the DOD to validate whether a correlation exists between them.
Fig. 7 shows the maps for the Madigou catchment obtained with the different DEMs. As shown in the shaded relief maps, the local details of rugged and rough surfaces are captured with the 0.1 and 0.2 m resolution DEMs (Fig. 7a and b). In these two DEMs, a large number of pixels reflect microscopic terrain fluctuations. These pixels represent noise irrelevant to both valley and bank gullies and cause errors in the gully mapping. For example, a trail located above the gully boundary exhibited obvious terrain fluctuations and was mistakenly mapped as a gully boundary (region I in Fig. 7a). Furthermore, some areas above the gully boundary with relatively large fluctuations and surface roughnesses were incorrectly included within the gully area (region II in Fig. 7a). Fig. 7 also shows that the derived terrain surface becomes smoother and the noise begins to diminish as the resolution coarsens; meanwhile, the gully boundary, which represents a division exhibiting a remarkable contrast between gully and inter-gully areas, becomes more distinct. The gully maps from 0.5 m to 2 m DEMs match well with the reference data (Fig. 7c–e). However, when the DEM resolution becomes coarser, the gully boundary becomes more ambiguous (Fig. 7f and g). Finally, the gully map from the 10 m DEM is clearly different from the reference
(2)
where Sg and Si are the average slope in the gully slope and inter-gully hillslope, respectively. 118
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Fig. 7. Gully maps in the Madigou catchment: (a)–(g) results from DEMs with successive resolutions of 0.1, 0.2, 0.5, 1, 2, 5, and 10 m; the backgrounds are the corresponding shaded relief maps.
data (Fig. 7g). Thus, the most suitable DEM resolution for gully mapping should constitute a balance between the removal of noise and the desired gully characterization. The experiment was duplicated in the Qiaogou catchment, which is also located in the loess hilly areas of the northern Loess Plateau in China. However, the gully morphology of the Qiaogou catchment differs from that of the Madigou catchment in terms of the gully size, direction, and depth. Fig. 8 shows the maps with specific DEM resolutions; the mapped gully area decreases as the DEM resolution becomes coarser. This finding is consistent with the results from the Madigou catchment. Evidently, the gully maps from very fine- (i.e., 0.1 and 0.2 m) and very coarse-resolution (i.e., 5 and 10 m) DEMs do not perform well.
are obviously affected by the DEM resolution in both study areas. First, the medians of both distributions are approximately zero with DEM resolutions of 0.5 and 1 m. When the DEM resolution becomes finer than 0.5 m, more positive errors exist than negative errors; when the DEM resolution becomes coarser than 1 m, the opposite is true. Second, the median values of di are rather stable with DEM resolutions of 0.1–2 m, whereas the median values become negative and rapidly decrease with DEM resolutions of 2–10 m. Various summary statistics of di are computed (Table 1): the mean and median, the maximum and minimum and the standard deviation. The relationships between these summary statistics and the DEM resolution are developed (Fig. 10) as well as the relationship between the relative area error, Ar, and the resolution. The statistics of di are affected by the DEM resolution differently, but the same trends in statistics are observed in both catchments. The mean has a strongly negative linear relationship with the DEM resolution (Fig. 10b); the mean is close to 0 when the DEM resolution is nearly 0.5 m in the Madigou catchment and 2 m in the Qiaogou catchment. In other words, the gully boundaries derived from coarser-resolution DEMs (2–10 m) are on average downslope from the reference gully
4.2. The relationships between the accuracy indices and DEM resolutions The abovementioned accuracy indices are computed to quantitatively analyze the effect of the DEM resolution on the gully map. The distributions of the position accuracy index (di) with each DEM resolution are displayed in the box plots in Fig. 9. The distributions of di 119
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Fig. 8. Gully mapping in the Qiaogou catchment: (a)–(g) results from DEMs with successive resolutions of 0.1, 0.2, 0.5, 1, 2, 5, and 10 m; the backgrounds are the corresponding shaded relief maps.
of di (the most negative error) suggests a linear relationship with the DEM resolution (Fig. 10e); the finer the DEM resolution, the smaller the minimum value is, which indicates that a finer resolution is beneficial for reducing the most negative error. The standard deviation has a weak correlation with the DEM resolution (Fig. 10f); thus, finding a trend is difficult. A strong negative linear relationship is observed between Ar and the DEM resolution (Fig. 10a), suggesting that DEMs with coarse resolution (2–10 m) under-predict the gully area, while DEMs with very fine resolution (0.1–0.5 m) over-predict the gully area. This result is consistent with the variations in the mean of di.
boundary, whereas boundaries derived from very high-resolution DEMs (0.1–0.5 m) are on average upslope of the reference gully boundary. Moreover, the median has a strongly negative secondary polynomial relationship with the DEM resolution (Fig. 10c), indicating that a very high resolution has little effect on the median, while a coarser resolution strongly affects the median. The fitting between the maximum value of di (the most positive error) and DEM resolution suggests a power law relationship (Y = aXb) (Fig. 10d). This relationship shows that the most positive error increases rapidly when the DEM resolution becomes very high; in contrast, when the DEM resolution becomes coarser than 4 m, the DEM resolution has little effect on the maximum value. The minimum value
Fig. 9. Box plots: (a) di distribution in the Madigou catchment; (b) di distribution in the Qiaogou catchment. 120
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The gully morphologies can be summarized as two typical gully shapes, namely, V-shaped gullies and U-shaped gullies (Fig. 13). A gully with a small slope variation between the inter-gully hillslope and the gully slope is called a V-shaped gully, whereas a gully with a large slope variation is called a U-shaped gully. According to the relationship between Sv and DOD, the resolution effects on the gully maps in V-shaped gullies are stronger than those in U-shaped gullies. The Ar and the mean of di decrease more quickly in the Qiaogou catchment than in the Madigou catchment (Fig. 10), which agrees with the fact that the spatial disparities of the DEM resolution effect are related to the difference in gully morphology. More bank gullies develop on both sides of valley gullies in the Qiaogou catchment; thus, the gullies are more V-shaped than the gullies in the Madigou catchment. According to the relationship between Sv and DOD, the accuracy indices decrease more quickly as the DEM resolution becomes coarser.
Table 1 Accuracy indices. Resolution (m)
Position accuracy
Area accuracy
Mean
Med
Max
Min
Std
Ar
Madigou 0.1 0.2 0.5 1 2 3 4 5 6 7 8 9 10
4.11 3.41 −0.06 −0.64 −1.70 −3.37 −4.03 −4.17 −5.06 −5.96 −5.72 −8.17 −8.83
0.80 0.40 −0.09 −0.22 −0.53 −1.47 −1.89 −2.20 −2.83 −3.42 −4.08 −4.43 −8.49
47.99 43.52 14.12 10.32 7.83 4.16 6.66 6.69 6.54 6.55 4.58 5.26 8.61
−7.68 −9.47 −8.65 −13.78 −24.52 −24.05 −37.61 −39.76 −36.44 −37.53 −38.31 −41.00 −34.51
8.72 8.41 2.00 2.04 4.02 5.10 6.26 6.21 7.80 8.33 7.38 10.59 8.79
17.57% 3.99% −0.43% −1.50% −3.40% −5.40% −8.28% −13.84% −17.97% −17.87% −22.54% −25.06% −32.45%
Qiaogou 0.1 0.2 0.5 1 2 3 4 5 6 7 8 9 10
4.80 3.96 2.44 2.60 0.21 −3.02 −3.49 −4.51 −7.04 −8.17 −9.27 −11.91 −13.94
0.97 0.39 −0.04 −0.03 −0.34 −1.14 −1.46 −2.47 −4.53 −4.81 −6.06 −11.47 −14.75
38.43 40.72 38.55 37.94 38.91 25.73 11.36 4.12 2.81 3.87 3.51 4.67 3.14
−8.29 −6.85 −20.63 −16.47 −26.79 −24.82 −22.20 −26.10 −30.56 −33.47 −29.21 −33.11 −34.27
7.91 8.27 8.27 8.82 11.06 6.84 5.99 6.38 8.05 8.98 9.24 9.39 9.73
7.49% 5.48% 2.67% 1.98% −3.75% −16.04% −18.75% −22.39% −33.67% −37.71% −43.22% −51.38% −56.78%
5. Discussion 5.1. The optimum DEM resolution for gully mapping The results of our experiment show that the gully as a major terrain feature is not mapped well when using DEMs with very high resolutions (such as 0.1 and 0.2 m) because the substantial amount of noise included at a very high resolution induces an increase in the local error. In contrast, DEMs with coarser resolutions lose information for gully characterization. The most suitable DEM resolution for gully mapping should constitute a balance between the removal of noise and the desired gully characterization. As Section 4.3 shows, the effects of DEM resolution on gully maps are not constant but vary spatially, preventing the application of a single optimum resolution. However, a suitable range of resolutions can be found according to the trends of indices in different areas. Resolutions of 0.1–0.5 m cause sharp increases in the local errors, whereas the mapped gully boundaries on 2–10 m DEMs deviate systematically from the reference data toward the downslope area. Thus, this study suggests that 0.5–2 m DEMs are the most suitable for gully mapping in the hilly areas of the Loess Plateau in China. This finding is in agreement with Hengl (2006), who proposed that no ideal grid resolution exists for output maps; rather, a range of suitable resolutions exists. A problem of this study is the ground truth. This study adopts gullies generated by visually interpreting very high-resolution DOMs for ground truth. The accuracy of visual interpretation is inevitably affected by subjective experience (Svatonova, 2016). However, the visual interpretation of a very high-resolution image is widely used for studying gully erosion and mapping (d'Oleire-Oltmanns et al., 2014; Kai et al., 2017; Shruthi et al., 2011) because this approach can meet the requirements of gully erosion research (Li et al., 2014) and relatively high-accuracy reference data are sufficient for conducting an accuracy assessment. Therefore, the general principle that gully maps vary with the DEM resolution is reliable in this study. A very high resolution does not ensure high accuracy and could increase local errors, whereas a coarser resolution causes a downward migration of the mapped gully boundary, resulting in a decrease in the gully area.
Mean – mean value of di; Med – median value of di; Max – maximum value of di; Min – minimum value of di; Std – standard deviation of di; Ar – area accuracy.
4.3. The spatial disparities of the DEM resolution effects The effect of DEM resolution on the gully map is not constant but varies in space. As the DEM resolution becomes coarser, the mapped gully area in the southern hillslope decreases more distinctly than that in the northern hillslope of the Madigou catchment (Fig. 7), and the variability of the maps with the DEM resolution in the Qiaogou catchment is greater than the variability of those in the Madigou catchment (Fig. 10a, b and c). As noted in Section 3.6, the Sv and DOD were designed to validate whether this spatial variation is related to gully morphology. According to the area accuracy assessment (Fig. 10a), the highest and lowest accuracy maps are from 0.5 and 10 m DEMs, respectively. Then, Eq. (3) is rewritten as Eq. (4):
DOD = di (10) − di (0.5)
(4)
where di (10) and di (0.5) are the di of the maps derived from 10 and 0.5 m DEMs, respectively. Hence, many cross-sections are selected randomly to calculate these indices in both study areas (Fig. 11). However, given the difference existing between the two sides of a gully, Sv and DOD are calculated on each side of a cross-section (Table 2). The linear regression models between the Sv and DOD in the Madigou and Qiaogou catchments fit well (Fig. 12). The similarity of the trends in the DOD in the two areas suggests that the two subgroups can be combined. Therefore, all data from the two areas are used to establish the relationship between Sv and DOD, revealing a positive linear relationship between Sv and DOD (Fig. 12) (R2 = 0.63). The smaller the Sv, the more negative the DOD is. Thus, it is reasonable that the spatial variation of DEM resolution effects is related to the difference in gully morphologies. However, the relationship also suggests that the maps in a gully with a small Sv are more severely affected by the DEM resolution than those in a gully with a large Sv.
5.2. Characterizing the gully morphology by a DEM Thompson et al. (2001) proposed that the terrain slopes extracted from areas with steep slopes decrease as the DEM resolution becomes coarser, whereas the terrain slopes from areas with relatively gentle slopes increase, resulting in a smoother surface. The variability of the gully morphology with the DEM resolution can be explained by the terrain slope changes. The slope variation points near actual gully boundaries become more ambiguous or even disappear when the DEM resolution becomes coarser. Meanwhile, a new slope variation point is generated by the terrain slope changes because a difference always exists between the gully slope and the inter-gully hillslope. Fig. 14 121
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Fig. 10. Relationships between the accuracy indices and DEM resolutions: (a) Ar; (b) mean of di; (c) median of di; (d) maximum of di; (e) minimum of di; and (f) standard deviation of di.
Thus, we conclude that in addition to DEM resolution, the potential of a DEM for characterizing a terrain feature relies on the terrain feature itself. This finding is confirmed by other studies: Gómez-Gutiérrez et al. (2015) reported that the size of the landform is important and must be considered for mapping susceptibility of gully erosion rather than the finest DEM resolution; Saksena and Merwade (2015) proposed that the channel slope and the shape of valley determine the extent to which DEM resampling affects the inundation results.
shows several cross-sectional profiles in the two study areas. The extracted slope variation points vary with the DEM resolution. However, predicting the sites where the slope variation points are developed is difficult in the study of Thompson et al. (2001). According to our study, the new site of the extracted slope variation point is related to the gully morphology. The more V-shaped the gully morphology is, the greater the downward movement of the extracted slope variation point when the DEM resolution is coarser, whereas the more U-shaped the gully morphology is, the smaller the downward, or even upward movement, of the extracted slope variation point (Fig. 12). 122
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Fig. 11. Cross-section analysis: (a) and (b) locations of cross-sections in Madigou and Qiaogou. Table 2 Slope variation and DOD on both gully sides of all cross-sections. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Side
North South North South North South North South North South North South North South North South North South North South North South North South North South North South North South North South
Madigou
Qiaogou
Sv (°)
DOD (m)
Sv (°)
DOD (m)
23.2553 20.9373 27.54 15.3808 29.665 12.981 30.2458 16.7119 25.2776 21.6208 32.0021 23.51 26.8962 20.1363 29.3499 18.266 34.4947 22.8543 34.6524 21.4782 38.9916 22.4089 40.6368 38.0521 36.3468 14.692 36.9594 17.1037 29.79 18.64 34.0543 35.9251
−5.03 −35.71 −6.11 −39.25 −6.73 −36.73 −3.61 −25.22 −3.73 −11.49 −6.52 −9.96 −5.03 −12.45 −7.48 −16.63 2.15 −29.79 −5.64 −26.49 6.66 −34.33 1.88 2.16 11.13 −17.74 2.38 −14.62 −11.13 −33.45 −9.94 −3.05
21.23 15.4851 25.0874 17.6366 28.6715 16.9673 12.7569 5.7368 14.6348 29.5805 22.8009 13.6003 29.4192 21.4883 31.0562 15.1844 29.3821 22.8911 27.2598 24.9409 24.5734 23.3268 30.1995 20.4488
−10.65 −53.08 −24.58 −24.87 −12.55 −33.95 −34.23 −46.55 −26.78 −13.19 −3.37 −16.48 6.25 −16.66 −3.33 −34.61 0.78 −34.51 0.41 −17.92 0.87 −16.13 −5.25 −17.53
Fig. 12. Modeling the relationship between the Sv and DOD.
boundaries, resulting in the under-prediction of gully areas. However, the effects of DEM resolution on the accuracy of gully maps are not constant but vary in space. The spatial disparities of the resolution effects are related to the gully morphology. The resolution effects on the gully maps in V-shaped gullies are stronger than those in U-shaped gullies. This finding suggests that a suitable DEM resolution for mapping V-shaped gullies is more urgently needed than one for mapping U-shaped gullies.
Acknowledgements We are grateful for the financial support provided by the National Natural Science Foundation of China (grant numbers 41771415, 41671389, 41571383, 41571398) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (number 164320H116). The authors express their gratitude to the journal editor and reviewers, whose thoughtful suggestions played an important role in improving the quality of this paper. Many thanks are also given to LI Jilong, HUANG Nan and DAI Ziyang for their helpful comments on the manuscript. DAI Wen also gives special thanks to WANG Jing for her support in his study life.
6. Conclusion In this study, we investigate the effect of DEM resolution on the accuracy of gully maps. The position and area accuracies are employed to quantitatively analyze this effect, and relationships between these accuracy indices and the DEM resolution are established. The findings indicate that 0.5–2 m resolution DEMs are more suitable for gully mapping than DEMs with very fine or relatively coarse resolutions in loess hilly areas. Very high-resolution DEMs increase local position errors and over-predict the extents of gullies, whereas DEMs with coarser resolutions cause the downward migration of mapped gully 123
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Fig. 13. Typical gully shapes: (a) V-shaped gully and (b) U-shaped gully.
Fig. 14. Cross-sectional profiles: (a), (c) and (e) cross-section Nos. 2, 5, and 15, respectively, in the Madigou catchment; (b), (d) and (f) cross-section Nos. 4, 7, and 11, respectively, in the Qiaogou catchment. The red and blue lines represent the gully profiles determined with 0.1 and 10 m DEMs, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Catena journal homepage: www.elsevier.com/locate/catena
Effects of DEM resolution on the accuracy of gully maps in loess hilly areas a,b,d
a,b,d,⁎
Wen Dai , Xin Yang Xiaoli Huangd
b
b
a,c
d
T
d
, Jiaming Na , Jingwei Li , Dick Brus , Liyang Xiong , Guoan Tang ,
a
Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, Nanjing 210023, China State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China Biometris, Wageningen University and Research, PO Box 16, 6700 AA Wageningen, the Netherlands d Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China b c
A R T I C LE I N FO
A B S T R A C T
Keywords: Gully mapping DEM resolution Uncertainty The Loess Plateau of China Accuracy assessment
Gully maps are important prerequisites for the study of gully erosion and land degradation. Many digital elevation model (DEM)-based methods have been proposed to enable automated gully mapping. However, the accuracy of a gully map derived from a DEM is inevitably affected by the DEM resolution. This study investigates the effects of DEM resolution on the accuracy of gully maps. A series of DEMs with resolutions of 0.1–10 m is employed to map gully areas. The effects of DEM resolution on the error in the mapped gully area and on the position error are described by regression models. The results from two catchments in hilly areas of the Loess Plateau in China are as follows. DEMs with resolutions of 0.5–2 m are the most suitable for gully mapping. Very high-resolution DEMs increase local position errors and over-predict the extents of gullies, whereas DEMs with coarser resolutions cause the downward migration of mapped gully boundaries, resulting in the under-prediction of gully areas. However, the effects of DEM resolution on gully maps are not constant but vary in space. The spatial disparities of the resolution effects are related to the gully morphology. The resolution effects on the gully maps in V-shaped gullies are stronger than those in U-shaped gullies. The findings of this study can be used to select a suitable DEM resolution for gully mapping in loess hilly areas and contribute to understanding the characterization of gullies by using DEMs.
1. Introduction Gully erosion, which widely threatens farmland and the environment, is the most serious type of water erosion (Valentin et al., 2005; Castillo and Gómez, 2016; Poesen et al., 2003). Gully maps are important prerequisites for studying gully erosion and land degradation. Consequently, many researchers have focused on gully surveying and mapping to determine the distribution, magnitude, and topographical properties of gullies (Taruvinga, 2009; Martínez-Casasnovas, 2003; Casalí et al., 2006; Zabihi et al., 2018; Wu and Cheng, 2005), the results of which can be used for agricultural management, soil and water conservation, and ecological planning. Field assessment and visual interpretation of imagery have been the most traditional and popular methods used to obtain gully information for decades (Daba et al., 2003; Fadul et al., 1999; Mararakanye and Le Roux, 2012; Perroy et al., 2010; Hansen and Law, 2007). However, while these methods are easy to implement and provide results with high accuracy, the substantial amount of manual work associated with these methods restricts their application on a large scale (Wang et al., ⁎
2014). With the launch of numerous Earth observation satellites, many researchers have proposed automatic gully mapping methods based on satellite imagery. These automatic methods can be categorized into two types: pixel-based and object-based methods. The unit of analysis in pixel-based methods is a single pixel, and the rules are applied to each pixel separately to achieve the final result (Seutloali et al., 2016; Vrieling et al., 2007; Knight et al., 2007). However, pixel-based methods consider only spectral information, thereby restricting their application. Alternatively, object-based methods, which have been utilized widely over the last decade, are superior to traditional pixelbased methods because the unit of analysis is any meaningful object (Shruthi et al., 2011; Shruthi et al., 2012; Shruthi et al., 2015; Kai et al., 2017; d'Oleire-Oltmanns et al., 2014; Blaschke, 2001). The three-dimensional features of gullies, such as their depth and volume, are not directly observable or measurable, although gully shapes can be acquired from imagery and used to improve the accuracy of a map. Therefore, to measure the three-dimensional properties of gullies, methods have been developed based on digital elevation models
Corresponding author at: School of Geographic Science, Nanjing Normal University, No. 1 Wenyuan Road, Qixia District, Nanjing, China. E-mail address: [email protected] (X. Yang).
https://doi.org/10.1016/j.catena.2019.02.010 Received 7 May 2018; Received in revised form 4 February 2019; Accepted 15 February 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Gullies on the Loess Plateau: (a) gully types; (b) gully map; and (c) field survey photo of gullies (gully area is marked by red line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2015; Hsu et al., 2016; Ariza-Villaverde et al., 2015; McMaster, 2002; Chaplot et al., 2000). A conclusion drawn from these studies is that the most suitable resolution exists and depends on the application. For example, Tang et al. (2003) proposed that a 5 m DEM is suitable for representing slopes in loess areas when the DEMs are produced by digitizing the contours of 1:10,000 scale topographical maps. Chaplot et al. (2000) reported that 10 m and 30 m DEMs can predict the elevations above the stream bank, downslope gradient and upslope contributing areas when using linear regression and co-kriging to predict the soil hydromorphy. López-Vicente and Álvarez (2018) proposed an optimum DEM resolution (0.2 m) to improve the results of modeling the structural hydrological connectivity in woody crop areas. Tan et al. (2018) found that better monthly streamflow simulations are obtained between 20 m and 60 m resolution DEMs with the smallest area threshold (1000 ha). Clearly, selecting an appropriate DEM resolution is important for studying soil erosion processes (Lu et al., 2017). Zhang et al. (2008) noted that the hydrological attributes extracted from DEMs with different resolutions exhibit different properties that influence the results predicted by soil erosion models. Lucà et al. (2011) discussed the influence of DEM resolution on maps depicting the susceptibility for gully erosion; they found that a coarser DEM resolution reduces both the extents of the most susceptible classes and the accuracy of the map. Gómez-Gutiérrez et al. (2015) reported that the finest resolution is not necessarily the best for mapping susceptibility of gully erosion. Garosi et al. (2018) found that the DEM with 10 m resolution resulted in the highest kappa coefficient of the map depicting the susceptibility for gully erosion. DEM resolution is also a critical factor that affects gully mapping
(DEMs). These methods can be categorized into three types: terrain morphological feature identification, image gradation detection, and terrain visibility analysis. Terrain morphological feature identification detects the locations of gullies by analyzing changes in terrain parameters, such as the slope, aspect, curvature, flow accumulation and positive-negative terrain index (P-N) (Lu, 1998; Tang et al., 2007b; Zhu et al., 2003; H. Liu et al., 2016; Zhou et al., 2010a; Zhou et al., 2010b; Chen et al., 2012; Li et al., 2008). In contrast, image gradation detection regards the DEM as a grayscale image and employs image processing algorithms, such as the edge detection operator (Yan et al., 2011) and snake model (Yan et al., 2014; Zhou and Tang, 2013; Song et al., 2013). Finally, terrain visibility analysis methods, such as the terrain openness method (Wang et al., 2015) and hill-shading method (Yang et al., 2017b; Na et al., 2018), obtain gully boundaries based on viewshed analysis or shade relief simulation. Among these DEM-based methods, the hill-shading method significantly improves the gully map accuracy for high-resolution DEMs (Yang et al., 2017b). Although DEM-based methodologies for gully mapping have been enriched, challenges still persist. DEM resolution, as a key factor, determines the potential of a DEM for characterizing the terrain surface. The uncertainty in terrain analysis and geomorphological feature mapping is inevitably related to this resolution. Consequently, many studies have focused on the importance of the DEM resolution for terrain analysis. These studies ranged from the derivation of terrain attributes (Tang et al., 2003; Zhou and Liu, 2004; Liu et al., 2009; Thompson et al., 2001; Sørensen and Seibert, 2007) and geo-analysis modeling (Wu et al., 2005; Chaubey et al., 2005; Zhang et al., 2008; López-Vicente and Álvarez, 2018; Tan et al., 2018) to the mapping of geomorphological features (Saksena and Merwade, 115
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elevations ranging from 1348 to 1556 m. The main channel of the catchment is oriented from east to west spanning a length of 700 m with a depth of 208 m. The Qiaogou catchment (Fig. 2b) (37°34′2′′ N, 110°16′48′′ E) is located in northern Suide County, Shaanxi Province, and has an area of 0.19 km2 with elevations ranging from 900 to 1017 m. The main channel of the catchment is oriented from southwest to northeast spanning a length of 550 m with a depth of 117 m.
(Castillo et al., 2012). DEMs with a 5 m resolution have generally been used in most previous gully mapping methods (H. Liu et al., 2016; Zhou et al., 2010a; Zhou et al., 2010b; Chen et al., 2012; Yan et al., 2011; Yan et al., 2014; Zhou and Tang, 2013; Song et al., 2013; Li et al., 2008; Wang et al., 2015); nevertheless, the suitability of 5 m DEMs for mapping gullies remains unclear. To the best of our knowledge, no publications are available that have compared the accuracies of gully maps obtained with different resolutions. Currently, with the ongoing development of data acquisition technologies, such as unmanned aerial vehicle (UAV) photogrammetry and light detection and ranging (LIDAR), high-resolution DEMs are becoming more available and convenient to obtain. However, whether high-resolution DEM data can achieve high mapping accuracy remains unknown. Accordingly, this study explores the effects of DEM resolution on the accuracy of gully maps by using a series of 0.1–10 m DEMs. This work specifically aims to 1) model the relationships between accuracy indices of gully maps and the DEM resolutions, 2) find a suitable DEM resolution for gully mapping, and 3) analyze the spatial disparities of the effect of DEM resolution on the accuracy of gully maps.
2.2. Data The data consisted of LIDAR point clouds and 0.05 m digital orthophoto maps (DOMs). The point clouds of the two areas were acquired by terrestrial LIDAR technology with a Riegl VZ400 terrestrial laser scanner (Riegl Laser Measurement Systems GmbH, Horn, Austria) in August 2014. The total number of points in the Madigou catchment exceeded 60 million with an average density of 2600 points per square meter, whereas the total number of points in the Qiaogou catchment was 20 million with an average density of 1200 points per square meter. A series of DEMs with different resolutions was generated by the point clouds (see Section 3.2). The DOMs were simultaneously generated by UAV photogrammetry with a Matrice 600 (SZ DJI Technology Co., Ltd., Shenzhen, China). Through visual interpretation of the DOMs for both study areas, gully maps were derived. These maps served as ground truth and as reference maps. The gully maps derived from the DEMs are compared with the reference maps to assess the errors in the gully maps derived from the DEMs (see Section 3.4.1).
2. Gully types, study areas, and data 2.1. Gully types and study areas The Loess Plateau of China exhibits one of the most severe rates of gully erosion worldwide (M. Li et al., 2017). This region contains three main gully types, namely, valley, bank, and ephemeral gullies (Yang et al., 2017a) (Fig. 1a). Valley and bank gullies constitute the main sediment yield sources and threaten the inter-valley land quality (Z. Li et al., 2017). Erosion caused by these two types of gullies accounts for more than 60% of all soil erosion in the watersheds of the hill-gully subregion and more than 80% in the high loess plain characterized by deeply incised gullies (Zheng and Wang, 2014). Generally, in the Loess Plateau, bank gullies, developing in both side slopes of valley gullies, form an integral part of the whole gully-affected area (Fig. 1c). This characteristic can be readily used for mapping the gully-affected area using DEMs. Accordingly, gully mapping is often referred to as mapping the gully-affected area (Fig. 1b) (Kai et al., 2017; Kai et al., 2016). Two catchments (Fig. 2), Madigou and Qiaogou, situated in the loess hilly areas of the northern Loess Plateau were selected. These study areas are characterized by typical loess gullies and hills. Many gullies with intense erosion have developed in these areas; these gullyaffected areas cover more than 60% of the region. The Madigou catchment (Fig. 2a) (37°28′59′′ N, 108°48′2′′ E) is located in northern Jingbian County, Shaanxi Province, and has an area of 0.23 km2 with
3. Methodology 3.1. Overview of the analyses To accomplish the objectives stated in the Introduction, we employed the following workflow (Fig. 3): i) Preprocessing of the point clouds to generate DEMs with different resolutions; ii) Mapping gullies by using the multidirectional hill-shading method; iii) Generating reference data by visual interpretation of the DOMs and then assessing the accuracies of the gully maps derived from the DEMs; iv) Modeling relationships between the DEM resolutions and accuracy indices; v) Investigating the spatial disparities of the effects of the DEM resolution on gully mapping.
Fig. 2. Study areas: (a) DOM of the Madigou catchment; (b) DOM of the Qiaogou catchment. 116
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Fig. 3. Workflow of this study.
are two parameters: the azimuth and the altitude of the light source. Yang et al. (2017b) demonstrated that six pairs of light azimuths are sufficient for gully mapping in the hilly Loess Plateau. Meanwhile, the light altitude can be detected by sampling transverse profiles across the gully boundaries and calculating the average median slope. The method is implemented in ArcGIS 10.2 for this study.
3.2. Generating a series of DEMs LIDAR elevation data sets provide flexibility for producing DEMs with multiple horizontal resolutions from the same data source. A series of DEMs was generated by inverse distance weighted (IDW) interpolation of the LIDAR point clouds. The resolutions of the generated DEMs ranged from 0.1 m to 10 m. DEMs with resolutions exceeding 10 m were excluded given that the ability to characterize the gully morphology becomes very poor (Tang et al., 2007b).
3.4. Accuracy assessment method 3.4.1. Reference data The visual interpretation of high-resolution images is widely used for ground truth to assess the accuracy of gully maps (d'OleireOltmanns et al., 2014; Kai et al., 2017; Shruthi et al., 2011). This approach provides a high position accuracy that meets the requirements of gully erosion research (Li et al., 2014). The features and boundaries of gullies are clearly observable in high-resolution DOMs and are readily recognized through field surveying (Fig. 1c). Thus, the reference maps were digitized manually based on DOMs and fieldwork knowledge.
3.3. Gully mapping To select an appropriate method for DEM-based gully mapping, the method should meet the following requirements. First, the method should be applicable to high-resolution DEMs because most DEM-based methods are based on a resolution of 5 m, and thus, they fail on DEMs with a higher resolution. For example, the slope segmentation method is unable to generate a satisfactory gully map using a DEM with a 1 m resolution (Yang et al., 2017b). Second, the parameters used in the candidate method should avoid the use of subjective experience as much as possible. The P-N method (Zhou et al., 2010a; Zhou et al., 2010b; Chen et al., 2012) relies on the appropriateness of the size of the neighboring windows, whereas the slope segmentation (Zhu et al., 2003) and terrain openness methods (Wang et al., 2015) rely on the appropriateness of slope segmentation thresholds and openness angles, respectively. In contrast, the multidirectional hill-shading method employs local terrain attributes as the input parameter instead of subjective experience to generate the results (Yang et al., 2017b). Hence, this method can achieve high accuracy and efficiency on DEMs with a 1 m resolution. Given these advantages, the multidirectional hillshading method was selected for gully mapping in this study. Fig. 4 shows the basic principles of the selected method. Simulations of shadows on shady slopes can be obtained when the gully surface is illuminated by light rays with a certain altitude and azimuth (Fig. 4a), and the shadows on the other side can be acquired when the light rays are reversed. Therefore, the gully-affected area can be determined by merging both sides of the shadows (Fig. 4b). The keys to this method
3.4.2. Accuracy indices The gully map accuracy is usually assessed by two aspects, namely, the position accuracy and the area accuracy. The position accuracy is usually assessed either by buffer-based or contour-matching difference (CMD) methods. The former method assesses the position accuracy by estimating the percentage of the total length of the representation that is within a specified distance of the reference data (Goodchild and Hunter, 1997; Yan et al., 2014; W. Liu et al., 2016), whereas the latter method describes the matching degree between two polyline features (i.e., the mapping results and reference data) by an area ratio of intersecting polygons to buffer zones of the reference data (Tang et al., 2007a; Yan et al., 2011). However, these methods reflect only the global error of the gully boundary and fail to describe the local error. As an alternative, this study proposes a novel index, namely, di (i = 1, 2, 3, …, n), which is defined as the minimum distance from the ith vertex of the mapped gully boundary to the reference data (Fig. 5). The index di is positive when the vertex is located upslope above the
Fig. 4. Sketches illustrating the principles of the multidirectional hill-shading method (Yang et al., 2017b). 117
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Fig. 5. Definition of the index di for the position accuracy.
reference line and negative when the vertex is located downslope below the reference line. Individual values of di describe the local error, while the global position accuracy is described by summary statistics of the frequency distribution of di. Another key index, the gully area, is widely used to determine the erosion magnitude in gully erosion research (Li et al., 2003; Burkard and Kostaschuk, 1997, 1995; Betts and DeRose, 1999). To assess the area accuracy, this study uses the relative error in the mapped gully area, Ar, which is defined as the ratio of the area difference (i.e., the mapped area minus the reference gully area) to the reference gully area (Eq. (1)):
Ar =
Amap − Areal Areal
× 100%
(1)
where Amap is the mapped gully area (derived from a DEM) and Areal is the gully area on the reference map. Fig. 6. Sketch of gully morphology.
3.5. Relationship modeling Once the gully maps for all DEMs were obtained, overlays of these maps and the shaded relief maps were made, thereby revealing the details of the local terrain surface. Then, in addition to conducting an accuracy assessment, quantitative relationships between the accuracy indices and the DEM resolution were established. To accomplish these tasks, summary statistics of the index di and the area accuracy Ar were regressed against the DEM resolution. Linear regression models were fitted by an ordinary least squares approach in which we assumed that the accuracy indices obtained with the different DEM resolutions were independent.
At the cross-section scale, the magnitude of the DEM resolution effect is defined as the difference of di (DOD) between the maps with the lowest and highest accuracy (maximum and minimum DEM effects) (Eq. (3)):
3.6. Spatial disparity analysis
4. Results
The effect of DEM resolution on the accuracy of gully maps is not constant but varies in space. We analyzed whether this spatial variation in the resolution effect on the accuracy of gully maps is related to gully morphology. Cross-section analysis was performed in this study to determine the gully morphology (Vanmaercke et al., 2016; Z. Li et al., 2017; Caraballo-Arias et al., 2016; Castillo et al., 2012). Generally, the gully slope is obviously different from the inter-gully hillslope. According to the morphology of the gully profile (Fig. 6), the profile in the inter-gully area has negative curvature (the normal vector is perpendicular to the ground and upward), whereas the profile in the gully area has positive curvature (Yan et al., 2011). Hence, a slope variation point exists at the junction of positive curvature and negative curvature. Most DEM-based gully mapping methods depend on the slope variation between the gully slope and the inter-gully hillslope to map gullies (Yang et al., 2017b; Wang et al., 2015; Zhu et al., 2003). Accordingly, the slope variation (Sv) in each cross-section is used to describe gully morphology (Eq. (2)):
4.1. Gully maps
Sv = Sg − Si
DOD = di (a) − di (b)
(3)
where di (a) and di (b) are the di of the lowest and highest accuracy maps, respectively. Then, the Sv is regressed against the DOD to validate whether a correlation exists between them.
Fig. 7 shows the maps for the Madigou catchment obtained with the different DEMs. As shown in the shaded relief maps, the local details of rugged and rough surfaces are captured with the 0.1 and 0.2 m resolution DEMs (Fig. 7a and b). In these two DEMs, a large number of pixels reflect microscopic terrain fluctuations. These pixels represent noise irrelevant to both valley and bank gullies and cause errors in the gully mapping. For example, a trail located above the gully boundary exhibited obvious terrain fluctuations and was mistakenly mapped as a gully boundary (region I in Fig. 7a). Furthermore, some areas above the gully boundary with relatively large fluctuations and surface roughnesses were incorrectly included within the gully area (region II in Fig. 7a). Fig. 7 also shows that the derived terrain surface becomes smoother and the noise begins to diminish as the resolution coarsens; meanwhile, the gully boundary, which represents a division exhibiting a remarkable contrast between gully and inter-gully areas, becomes more distinct. The gully maps from 0.5 m to 2 m DEMs match well with the reference data (Fig. 7c–e). However, when the DEM resolution becomes coarser, the gully boundary becomes more ambiguous (Fig. 7f and g). Finally, the gully map from the 10 m DEM is clearly different from the reference
(2)
where Sg and Si are the average slope in the gully slope and inter-gully hillslope, respectively. 118
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Fig. 7. Gully maps in the Madigou catchment: (a)–(g) results from DEMs with successive resolutions of 0.1, 0.2, 0.5, 1, 2, 5, and 10 m; the backgrounds are the corresponding shaded relief maps.
data (Fig. 7g). Thus, the most suitable DEM resolution for gully mapping should constitute a balance between the removal of noise and the desired gully characterization. The experiment was duplicated in the Qiaogou catchment, which is also located in the loess hilly areas of the northern Loess Plateau in China. However, the gully morphology of the Qiaogou catchment differs from that of the Madigou catchment in terms of the gully size, direction, and depth. Fig. 8 shows the maps with specific DEM resolutions; the mapped gully area decreases as the DEM resolution becomes coarser. This finding is consistent with the results from the Madigou catchment. Evidently, the gully maps from very fine- (i.e., 0.1 and 0.2 m) and very coarse-resolution (i.e., 5 and 10 m) DEMs do not perform well.
are obviously affected by the DEM resolution in both study areas. First, the medians of both distributions are approximately zero with DEM resolutions of 0.5 and 1 m. When the DEM resolution becomes finer than 0.5 m, more positive errors exist than negative errors; when the DEM resolution becomes coarser than 1 m, the opposite is true. Second, the median values of di are rather stable with DEM resolutions of 0.1–2 m, whereas the median values become negative and rapidly decrease with DEM resolutions of 2–10 m. Various summary statistics of di are computed (Table 1): the mean and median, the maximum and minimum and the standard deviation. The relationships between these summary statistics and the DEM resolution are developed (Fig. 10) as well as the relationship between the relative area error, Ar, and the resolution. The statistics of di are affected by the DEM resolution differently, but the same trends in statistics are observed in both catchments. The mean has a strongly negative linear relationship with the DEM resolution (Fig. 10b); the mean is close to 0 when the DEM resolution is nearly 0.5 m in the Madigou catchment and 2 m in the Qiaogou catchment. In other words, the gully boundaries derived from coarser-resolution DEMs (2–10 m) are on average downslope from the reference gully
4.2. The relationships between the accuracy indices and DEM resolutions The abovementioned accuracy indices are computed to quantitatively analyze the effect of the DEM resolution on the gully map. The distributions of the position accuracy index (di) with each DEM resolution are displayed in the box plots in Fig. 9. The distributions of di 119
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Fig. 8. Gully mapping in the Qiaogou catchment: (a)–(g) results from DEMs with successive resolutions of 0.1, 0.2, 0.5, 1, 2, 5, and 10 m; the backgrounds are the corresponding shaded relief maps.
of di (the most negative error) suggests a linear relationship with the DEM resolution (Fig. 10e); the finer the DEM resolution, the smaller the minimum value is, which indicates that a finer resolution is beneficial for reducing the most negative error. The standard deviation has a weak correlation with the DEM resolution (Fig. 10f); thus, finding a trend is difficult. A strong negative linear relationship is observed between Ar and the DEM resolution (Fig. 10a), suggesting that DEMs with coarse resolution (2–10 m) under-predict the gully area, while DEMs with very fine resolution (0.1–0.5 m) over-predict the gully area. This result is consistent with the variations in the mean of di.
boundary, whereas boundaries derived from very high-resolution DEMs (0.1–0.5 m) are on average upslope of the reference gully boundary. Moreover, the median has a strongly negative secondary polynomial relationship with the DEM resolution (Fig. 10c), indicating that a very high resolution has little effect on the median, while a coarser resolution strongly affects the median. The fitting between the maximum value of di (the most positive error) and DEM resolution suggests a power law relationship (Y = aXb) (Fig. 10d). This relationship shows that the most positive error increases rapidly when the DEM resolution becomes very high; in contrast, when the DEM resolution becomes coarser than 4 m, the DEM resolution has little effect on the maximum value. The minimum value
Fig. 9. Box plots: (a) di distribution in the Madigou catchment; (b) di distribution in the Qiaogou catchment. 120
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The gully morphologies can be summarized as two typical gully shapes, namely, V-shaped gullies and U-shaped gullies (Fig. 13). A gully with a small slope variation between the inter-gully hillslope and the gully slope is called a V-shaped gully, whereas a gully with a large slope variation is called a U-shaped gully. According to the relationship between Sv and DOD, the resolution effects on the gully maps in V-shaped gullies are stronger than those in U-shaped gullies. The Ar and the mean of di decrease more quickly in the Qiaogou catchment than in the Madigou catchment (Fig. 10), which agrees with the fact that the spatial disparities of the DEM resolution effect are related to the difference in gully morphology. More bank gullies develop on both sides of valley gullies in the Qiaogou catchment; thus, the gullies are more V-shaped than the gullies in the Madigou catchment. According to the relationship between Sv and DOD, the accuracy indices decrease more quickly as the DEM resolution becomes coarser.
Table 1 Accuracy indices. Resolution (m)
Position accuracy
Area accuracy
Mean
Med
Max
Min
Std
Ar
Madigou 0.1 0.2 0.5 1 2 3 4 5 6 7 8 9 10
4.11 3.41 −0.06 −0.64 −1.70 −3.37 −4.03 −4.17 −5.06 −5.96 −5.72 −8.17 −8.83
0.80 0.40 −0.09 −0.22 −0.53 −1.47 −1.89 −2.20 −2.83 −3.42 −4.08 −4.43 −8.49
47.99 43.52 14.12 10.32 7.83 4.16 6.66 6.69 6.54 6.55 4.58 5.26 8.61
−7.68 −9.47 −8.65 −13.78 −24.52 −24.05 −37.61 −39.76 −36.44 −37.53 −38.31 −41.00 −34.51
8.72 8.41 2.00 2.04 4.02 5.10 6.26 6.21 7.80 8.33 7.38 10.59 8.79
17.57% 3.99% −0.43% −1.50% −3.40% −5.40% −8.28% −13.84% −17.97% −17.87% −22.54% −25.06% −32.45%
Qiaogou 0.1 0.2 0.5 1 2 3 4 5 6 7 8 9 10
4.80 3.96 2.44 2.60 0.21 −3.02 −3.49 −4.51 −7.04 −8.17 −9.27 −11.91 −13.94
0.97 0.39 −0.04 −0.03 −0.34 −1.14 −1.46 −2.47 −4.53 −4.81 −6.06 −11.47 −14.75
38.43 40.72 38.55 37.94 38.91 25.73 11.36 4.12 2.81 3.87 3.51 4.67 3.14
−8.29 −6.85 −20.63 −16.47 −26.79 −24.82 −22.20 −26.10 −30.56 −33.47 −29.21 −33.11 −34.27
7.91 8.27 8.27 8.82 11.06 6.84 5.99 6.38 8.05 8.98 9.24 9.39 9.73
7.49% 5.48% 2.67% 1.98% −3.75% −16.04% −18.75% −22.39% −33.67% −37.71% −43.22% −51.38% −56.78%
5. Discussion 5.1. The optimum DEM resolution for gully mapping The results of our experiment show that the gully as a major terrain feature is not mapped well when using DEMs with very high resolutions (such as 0.1 and 0.2 m) because the substantial amount of noise included at a very high resolution induces an increase in the local error. In contrast, DEMs with coarser resolutions lose information for gully characterization. The most suitable DEM resolution for gully mapping should constitute a balance between the removal of noise and the desired gully characterization. As Section 4.3 shows, the effects of DEM resolution on gully maps are not constant but vary spatially, preventing the application of a single optimum resolution. However, a suitable range of resolutions can be found according to the trends of indices in different areas. Resolutions of 0.1–0.5 m cause sharp increases in the local errors, whereas the mapped gully boundaries on 2–10 m DEMs deviate systematically from the reference data toward the downslope area. Thus, this study suggests that 0.5–2 m DEMs are the most suitable for gully mapping in the hilly areas of the Loess Plateau in China. This finding is in agreement with Hengl (2006), who proposed that no ideal grid resolution exists for output maps; rather, a range of suitable resolutions exists. A problem of this study is the ground truth. This study adopts gullies generated by visually interpreting very high-resolution DOMs for ground truth. The accuracy of visual interpretation is inevitably affected by subjective experience (Svatonova, 2016). However, the visual interpretation of a very high-resolution image is widely used for studying gully erosion and mapping (d'Oleire-Oltmanns et al., 2014; Kai et al., 2017; Shruthi et al., 2011) because this approach can meet the requirements of gully erosion research (Li et al., 2014) and relatively high-accuracy reference data are sufficient for conducting an accuracy assessment. Therefore, the general principle that gully maps vary with the DEM resolution is reliable in this study. A very high resolution does not ensure high accuracy and could increase local errors, whereas a coarser resolution causes a downward migration of the mapped gully boundary, resulting in a decrease in the gully area.
Mean – mean value of di; Med – median value of di; Max – maximum value of di; Min – minimum value of di; Std – standard deviation of di; Ar – area accuracy.
4.3. The spatial disparities of the DEM resolution effects The effect of DEM resolution on the gully map is not constant but varies in space. As the DEM resolution becomes coarser, the mapped gully area in the southern hillslope decreases more distinctly than that in the northern hillslope of the Madigou catchment (Fig. 7), and the variability of the maps with the DEM resolution in the Qiaogou catchment is greater than the variability of those in the Madigou catchment (Fig. 10a, b and c). As noted in Section 3.6, the Sv and DOD were designed to validate whether this spatial variation is related to gully morphology. According to the area accuracy assessment (Fig. 10a), the highest and lowest accuracy maps are from 0.5 and 10 m DEMs, respectively. Then, Eq. (3) is rewritten as Eq. (4):
DOD = di (10) − di (0.5)
(4)
where di (10) and di (0.5) are the di of the maps derived from 10 and 0.5 m DEMs, respectively. Hence, many cross-sections are selected randomly to calculate these indices in both study areas (Fig. 11). However, given the difference existing between the two sides of a gully, Sv and DOD are calculated on each side of a cross-section (Table 2). The linear regression models between the Sv and DOD in the Madigou and Qiaogou catchments fit well (Fig. 12). The similarity of the trends in the DOD in the two areas suggests that the two subgroups can be combined. Therefore, all data from the two areas are used to establish the relationship between Sv and DOD, revealing a positive linear relationship between Sv and DOD (Fig. 12) (R2 = 0.63). The smaller the Sv, the more negative the DOD is. Thus, it is reasonable that the spatial variation of DEM resolution effects is related to the difference in gully morphologies. However, the relationship also suggests that the maps in a gully with a small Sv are more severely affected by the DEM resolution than those in a gully with a large Sv.
5.2. Characterizing the gully morphology by a DEM Thompson et al. (2001) proposed that the terrain slopes extracted from areas with steep slopes decrease as the DEM resolution becomes coarser, whereas the terrain slopes from areas with relatively gentle slopes increase, resulting in a smoother surface. The variability of the gully morphology with the DEM resolution can be explained by the terrain slope changes. The slope variation points near actual gully boundaries become more ambiguous or even disappear when the DEM resolution becomes coarser. Meanwhile, a new slope variation point is generated by the terrain slope changes because a difference always exists between the gully slope and the inter-gully hillslope. Fig. 14 121
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Fig. 10. Relationships between the accuracy indices and DEM resolutions: (a) Ar; (b) mean of di; (c) median of di; (d) maximum of di; (e) minimum of di; and (f) standard deviation of di.
Thus, we conclude that in addition to DEM resolution, the potential of a DEM for characterizing a terrain feature relies on the terrain feature itself. This finding is confirmed by other studies: Gómez-Gutiérrez et al. (2015) reported that the size of the landform is important and must be considered for mapping susceptibility of gully erosion rather than the finest DEM resolution; Saksena and Merwade (2015) proposed that the channel slope and the shape of valley determine the extent to which DEM resampling affects the inundation results.
shows several cross-sectional profiles in the two study areas. The extracted slope variation points vary with the DEM resolution. However, predicting the sites where the slope variation points are developed is difficult in the study of Thompson et al. (2001). According to our study, the new site of the extracted slope variation point is related to the gully morphology. The more V-shaped the gully morphology is, the greater the downward movement of the extracted slope variation point when the DEM resolution is coarser, whereas the more U-shaped the gully morphology is, the smaller the downward, or even upward movement, of the extracted slope variation point (Fig. 12). 122
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Fig. 11. Cross-section analysis: (a) and (b) locations of cross-sections in Madigou and Qiaogou. Table 2 Slope variation and DOD on both gully sides of all cross-sections. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Side
North South North South North South North South North South North South North South North South North South North South North South North South North South North South North South North South
Madigou
Qiaogou
Sv (°)
DOD (m)
Sv (°)
DOD (m)
23.2553 20.9373 27.54 15.3808 29.665 12.981 30.2458 16.7119 25.2776 21.6208 32.0021 23.51 26.8962 20.1363 29.3499 18.266 34.4947 22.8543 34.6524 21.4782 38.9916 22.4089 40.6368 38.0521 36.3468 14.692 36.9594 17.1037 29.79 18.64 34.0543 35.9251
−5.03 −35.71 −6.11 −39.25 −6.73 −36.73 −3.61 −25.22 −3.73 −11.49 −6.52 −9.96 −5.03 −12.45 −7.48 −16.63 2.15 −29.79 −5.64 −26.49 6.66 −34.33 1.88 2.16 11.13 −17.74 2.38 −14.62 −11.13 −33.45 −9.94 −3.05
21.23 15.4851 25.0874 17.6366 28.6715 16.9673 12.7569 5.7368 14.6348 29.5805 22.8009 13.6003 29.4192 21.4883 31.0562 15.1844 29.3821 22.8911 27.2598 24.9409 24.5734 23.3268 30.1995 20.4488
−10.65 −53.08 −24.58 −24.87 −12.55 −33.95 −34.23 −46.55 −26.78 −13.19 −3.37 −16.48 6.25 −16.66 −3.33 −34.61 0.78 −34.51 0.41 −17.92 0.87 −16.13 −5.25 −17.53
Fig. 12. Modeling the relationship between the Sv and DOD.
boundaries, resulting in the under-prediction of gully areas. However, the effects of DEM resolution on the accuracy of gully maps are not constant but vary in space. The spatial disparities of the resolution effects are related to the gully morphology. The resolution effects on the gully maps in V-shaped gullies are stronger than those in U-shaped gullies. This finding suggests that a suitable DEM resolution for mapping V-shaped gullies is more urgently needed than one for mapping U-shaped gullies.
Acknowledgements We are grateful for the financial support provided by the National Natural Science Foundation of China (grant numbers 41771415, 41671389, 41571383, 41571398) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (number 164320H116). The authors express their gratitude to the journal editor and reviewers, whose thoughtful suggestions played an important role in improving the quality of this paper. Many thanks are also given to LI Jilong, HUANG Nan and DAI Ziyang for their helpful comments on the manuscript. DAI Wen also gives special thanks to WANG Jing for her support in his study life.
6. Conclusion In this study, we investigate the effect of DEM resolution on the accuracy of gully maps. The position and area accuracies are employed to quantitatively analyze this effect, and relationships between these accuracy indices and the DEM resolution are established. The findings indicate that 0.5–2 m resolution DEMs are more suitable for gully mapping than DEMs with very fine or relatively coarse resolutions in loess hilly areas. Very high-resolution DEMs increase local position errors and over-predict the extents of gullies, whereas DEMs with coarser resolutions cause the downward migration of mapped gully 123
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Fig. 13. Typical gully shapes: (a) V-shaped gully and (b) U-shaped gully.
Fig. 14. Cross-sectional profiles: (a), (c) and (e) cross-section Nos. 2, 5, and 15, respectively, in the Madigou catchment; (b), (d) and (f) cross-section Nos. 4, 7, and 11, respectively, in the Qiaogou catchment. The red and blue lines represent the gully profiles determined with 0.1 and 10 m DEMs, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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