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Journal of Geographical Sciences >

2015 , Vol. 25 >Issue 12: 1452 - 1466

DOI: https://doi.org/10.1007/s11442-015-1245-0

Research Articles

Slope spectrum critical area and its spatial variation in the Loess Plateau of China

  • TANG Guoan 1, 2, 3 ,
  • SONG Xiaodong 4 ,
  • LI Fayuan 1, 2, 3 ,
  • ZHANG Yong 5 ,
  • XIONG Liyang 1, 2, 3
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  • 1. Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China
  • 2. State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China
  • 3. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China
  • 4. State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, CAS, Nanjing 210008, China
  • 5. Key Laboratory of Radiometric Calibration and Validation for Environmental Satellites, National Satellite Meteorological Center, China Meteorological Administration, Beijing 100081, China;

Received date: 2015-04-01

  Accepted date: 2015-06-18

  Online published: 2015-12-31

Supported by

National Natural Science Foundation of China, No.41171299, No.41171320, No.41401237

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Journal of Geographical Sciences, All Rights Reserved
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Abstract

Slope spectrum has been proved to be a significant methodology in revealing geomorphological features in the study of Chinese loess terrain. The determination of critical areas in deriving slope spectra is an indispensable task. Along with the increase in the size of the study area, the derived spectra are becoming more and more alike, such that their differences can be ignored in favor of a standard. Subsequently, the test size is defined as the Slope Spectrum Critical Area (SSCA). SSCA is not only the foundation of the slope spectrum calculation but also, to some extent, a reflection of geomorphological development of loess relief. High resolution DEMs are important in extracting the slope spectrum. A set of 48 DEMs with different landform areas of the Loess Plateau in northern Shaanxi province was selected for the experiment. The spatial distribution of SSCA is investigated with a geo-statistical analysis method, resulting in values ranging from 6.18 km2 to 35.1 km2. Primary experimental results show that the spatial distribution of SSCA is correlated with the spatial distribution of the soil erosion intensity, to a certain extent reflecting the terrain complexity. The critical area of the slope spectrum presents a spatial variation trend of weak-strong-weak from north to south. Four terrain parameters, gully density, slope skewness, terrain driving force (Td) and slope of slope (SOS), were chosen as indicators. There exists a good exponential function relationship between SSCA and gully density, terrain driving force (Td) and SOS and a logarithmic function relationship between SSCA and slope skewness. Slope skewness increases, and gully density, terrain driving force and SOS decrease with increasing SSCA. SSCA can be utilized as a discriminating factor to identify loess landforms, in that spatial distributions of SSCA and the evolution of loess landforms are correlative. Following the evolution of a loess landform from tableland to gully-hilly region, this also proves that SSCA can represent the development degree of local landforms. The critical stable regions of the Loess Plateau represent the degree of development of loess landforms. Its chief significance is that the perception of stable areas can be used to determine the minimal geographical unit.

Key words： digital elevation model; slope spectrum; critical area; spatial variation; independent geomorphological unit; Loess Plateau

Cite this article

TANG Guoan , SONG Xiaodong , LI Fayuan , ZHANG Yong , XIONG Liyang . Slope spectrum critical area and its spatial variation in the Loess Plateau of China[J]. Journal of Geographical Sciences, 2015 , 25(12) : 1452 -1466 . DOI: 10.1007/s11442-015-1245-0

1 Introduction

The Loess Plateau of China has attracted much attention in the field of geoscience due to its specific loess landforms as well as for having the most severe soil erosion in the world (Shi et al., 2000; Hessel et al., 2003). A great deal of research has arisen since the 1950s from attempts to interpret various aspects of the landforms, such as the geological structure (Liang et al., 2004), soil and water conservation (Jing, 1986; He et al., 2003; Chen et al., 2007) and the geomorphological characteristics (McBride et al., 2007; Yang et al., 2011; Xiong et al., 2014a, 2014b), but has ignored the basic methodology for establishing a quantitative landform evolution model of the Loess Plateau (Rowbotham, 1998; Hughes et al., 2010). However, it is a crucial problem in correctly explaining the classification and topographic regions of the Loess Plateau (Luo, 1956). From a qualitative and quantitative research perspective, Luo (1956) analyzed and divided the loess landform into morphological and genetic types. Zhou et al. (2011) studied the characteristics of landform combinations and their regional distribution using proposed quantitative research methods. Recently, more attentions have been paid to geomorphological surveying by means of land surface parameters in digital elevation models (DEMs) (Iwahashi et al., 2001; Xu et al., 2009; Matsushi et al., 2010; Cheng et al., 2014; Tong et al., 2014).
It is widely accepted that slope is a primary land surface parameter that affects the formation and intensity of soil erosion in areas with serried gullies and fragmented landforms (Yamada, 1999; Shi et al., 2000; Hessel et al., 2003; Ayalew et al., 2004). Slope can be calculated from DEMs without further knowledge of the represented area (Shary et al., 2002; Tang et al., 2003; Zhou et al., 2006a). It is an interesting discovery that different loess landforms possess a stable frequency distribution histogram, which could be used as an effective indicator in discriminating loess landform types. Tang et al. (2008) defined such a histogram as a slope spectrum and the method as the slope spectrum method, a new methodology to quantitatively study the landforms of the Loess Plateau. This methodology also represents the spatial distribution of loess landforms and can be adapted to investigate the variability of terrain features in different evolutionary phases of loess landforms.
From a geomorphological perspective, each landform type has certain similarities both in its topographic structures and geomorphological features (Davis, 1899). Such similarities have been used as a quantitative representation via the slope spectrum as well as in the regional slope stability model (Rowbotham, 1998; Vanacker et al., 2003). However, the existence of the slope spectrum has an essential condition, namely, the histogram should remain consistent in various test areas. Therefore, it is essential that with the increase in test areas, the derived histogram becomes more and more stable in its distribution. The area of the stable histogram is defined as the slope spectrum critical area (SSCA). SSCA is not only the basis for a corrective slope spectrum derivative but may also be a potentially valuable clue in revealing the phases of geomorphological evolution.
This paper focuses mainly on the method of extracting SSCA based on grid DEMs, as well as the spatial distribution pattern of the SSCA in the Loess Plateau area. Furthermore, a deeper discussion explores the geographical significance of SSCA.

2 Test area and data

Forty-eight sites, randomly distributed in Northern Shaanxi, the core region of the Loess Plateau, were selected as key test areas (Figure 1). Each site consisted of specific loess landforms and had an area of approximately 100 km2. The corresponding DEMs were prepared with a grid size of 5 m, produced from the contours of topographic maps.
The loess cover thickness of this area gradually increases from north to south, with a range of approximately 50 to 200 m. 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 (Zhou et al., 2011).
To investigate the spatial distribution pattern of SSCA in the Loess Plateau, eight representative test areas in northern Shaanxi, forming a longitudinal section from north to south, were selected as key test areas in which many small watersheds will be delineated to verify the stability of the slope spectrum (Table 1).
Figure 1 Location of the study area and distribution of test sites. The eight test areas are labeled in black corresponding numbers with white background: (I) Shenmu, (II) Yulin, (III) Suide, (IV) Yanchuan, (V) Yanan, (VI) Ganquan, (VII) Yijun and (VIII) Chunhua
Table 1 Parameters of elevation data on experimental plots
Site Area name 1: 10,000 DEM
Minimum (m) Maximum (m) Mean (m) Standard deviation (m)
I Shenmu 1005 1322 1197.92 49.95
II Yulin 1110 1310 1212.20 37.27
III Suide 814 1188 995.35 62.10
IV Yanchuan 922 1251 1088.92 61.14
V Yanan 990 1404 1196.86 79.45
VI Ganquan 1151 1432 1296.00 55.87
VII Yijun 761 1158 986.09 73.08
VIII Chunhua 768 1188 1044.75 75.27

3 Methodology

3.1 Test area

As illustrated above, the SSCA can be described as the area in which the slope spectrum becomes stable. Hence, along with an increase in the test area, the changing shape of slope spectrum or a specific parameter would continue to be measured until the rate of change of the spectrum is below a specific value. This value is SSCA, as influenced by the extraction method.
There are two types of extraction method to determine SSCA proposed in literatures (Figure 2). The first method is based on an N by N neighborhood statistic window. As the window increases, the spectrum from an N by N slope matrix dataset of DEMs gradually approaches its final stable status. Although this method is quick and easy to implement, such an artificial rectangle cannot describe the practical distribution of the surface, especially for anisotropic terrain.
Figure 2 Two different test areas in extracting SSCA
Another method for extracting SSCA is based on catchment units, which are natural geomorphological units. As the catchment class or the catchment area increases, the corresponding flow-accumulation threshold would also increase. In this process, the distribution of the slope histogram has a tendency to stabilize. When the variation in the slope spectrum drops to a relatively low level, its quantitative value can be recorded and defined as the critical value for the existing slope spectrum. Because this method uses natural catchment as an analysis window, it is a proper way to extract SSCA and may represent the inherent association between SSCA and the minimal geographical unit. Hence, this method is adopted in this paper for the discussion of the minimal geographical unit.

3.2 Extraction procedure

The procedure for extracting SSCA based on drainage networks is shown in Figure 3. At the beginning of this process, drainage networks should first be extracted from a DEM. The general procedures for drainage extraction from DEM data include: (1) pit filling, (2) flow direction calculation, and (3) computing the contributing area draining to each grid cell. The flow accumulation grid can be used to delineate drainage networks based on a threshold for accumulation value, one of the first and simplest flow-related quantities computed from a DEM. This layer, which contains numerous watersheds, is a drainage network extracted by the D8 model in the DEM. In this step, watersheds of various shapes and sizes will be extracted by different accumulation values. The larger threshold value input, the larger each watershed area will be.
Figure 3 The procedure for the extraction of SSCA
Afterwards, the slope matrix based on the original DEM is calculated; meanwhile, each slope spectrum within a specific catchment can be obtained using an overlap calculation. Slope gradient is calculated using grid-based algorithm developed by Zevenbergen and Thorne (1987). In the next step, the degree of stability of these slope spectra (hereafter referred to as the “current spectrum”) will be evaluated by its similarity to a reference slope spectrum. Here, the reference is defined as a slope spectrum extracted from a certain landform area with adequate acreage (approximately 100 km2) (Tang et al., 2008).
In generating a slope spectrum, a 3° equal interval slope classification is frequently adopted, which has proven to be suitable for the loess area (Wang, 2005; Tang et al., 2008). Some quantitative indicators of similarity are proposed for the comparison between the reference and current slope spectra. The area percentage is defined as the quotient of the slope amount divided by area as follows:
Pi = Count/S(1)
where count is the slope amount with the same classification of slope spectrum, and S is the size of the test area. The indicator of the maximum is the difference between the maximum value of the current and referenced slope spectra, and the function takes the form:
where Pri and Pci are percentages representing the reference and current slope spectra, respectively, Max( ) is a function to compute the maximum value, and Abs( ) is the absolute value of a given variable. Another indicator of slope spectrum has the form:
δ<a, δs<b (4)
The procedure for judgment of stability can be summarized as follows: all parameters extracted from all small watersheds and the entire test region meet the condition of Eq. (4).
This procedure reflects the similarity of adjacent landforms and is based on the extension of watershed units. In this paper, we set parameters a=0.001, b=0.001 and n=30. Under these limitations, the SSCA is suitable and accurate, as the slope spectrum in neighboring windows has a similarity of 99% when the test area is larger than SSCA (Li, 2007).
Figure 4 Spatial distribution of SSCA in northern Shaanxi
In addition, eight areas with typical loess landforms were selected to verify the existence of SSCA in watersheds. Standard techniques for DEM preparation include pit filling; the calculation of flow direction, which is computed with the D8 algorithm (O’ Callaghan et al., 1984); and flow accumulation grids. After inputting the proper threshold of accumulation, plenty of small watersheds might be seen as independent natural landscape units that could be extracted by the accumulations. Meanwhile, the mean slope within each unit has been calculated. Thus, thousands of statistical samples from each test area have been extracted to correctly investigate the trend of the mean slope on a large scale.
Figure 5 The trend of SSCA variation in northern Shaanxi loess area

4 Results

4.1 Spatial distribution of slope spectrum critical area

The value of SSCA in each test area can be achieved by aforementioned method, and its spatial distribution in the northern Shaanxi Loess Plateau area is shown in Figure 4. As seen in this figure, the values of SSCA for different landforms present a specific spatial distribution pattern. The maximum appears near site VIII with a value of 35.1 km2 and the minimum at site III with a value of 6.18 km2. Across northern Shaanxi from north to south, the landform types include loess meadow-basin, loess-low-hill, loess deep incision gorge-hill, loss ridge-low-mountain, loess hill-ridge, loess tableland-ridge, loess tableland, loess middle-low mountain, and loess platform-tableland, indicating the variation in the landform from flat to fragmental to flat again. SSCA presents a trend of high-low-high, coinciding with the terrain fluctuation. This tendency might suggest an interesting finding that SSCA shows a strong correspondence with the evaluation of loess terrain. Namely, in the primary stage of loess landform evaluation, the existence and development of a loess gully is usually determined by disorder, i.e., a gully on the surface of loess tableland. Nevertheless, in the middle stage, the loess terrain possesses rather high similarity, and SSCA appears relatively low in this region, i.e., in the area of site III.
The variation of SSCA in different directions was investigated via the geo-statistical tool in ArcGIS 10. As shown in Figure 5, the SSCA for northern Shaanxi shows a “U-shaped” trend from north to south and an inverted “U-shaped” trend from east to west. The erosion intensity of the loess surface shows a regular weak-strong-weak pattern from north to south in northern Shaanxi, which leads to various physiographies, as well as various slope gradient compositions for each landform (Zhou et al., 2011). The rougher the surface is, the lower SSCA will be.

4.2 Existence of geomorphological units

The formation of a watershed is determined by unified features of the physical processes. An independent watershed is a combination of river and slope (Vanacker et al., 2003; Zhou et al., 2006b). Hence, there exist certain interrelations and mutual restraints between the landscape elements in any basin. Thousands of small watersheds of different sizes are selected as the basic units for the study of landform development on the basis of independent geomorphological units. We calculate eight typical scatter plots, including the mean slopes of geomorphological units, to compare the stability of the slope spectrum with SSCA for a large number of independent geomorphological units. It is noted that there are at least 10,000 statistical samples in each test area. Then, the mathematical relationships of the areas of the independent geomorphological units and mean slope values can be achieved.
Figure 6 Scatter plot of every area of independent natural landscape unit and its mean slope
Figure 6 shows the scatter plots of independent natural landscape units with their mean slopes, where the straight line on each scatter plot is the mean value of all units in a test area. As seen in this figure, the mean slope values of watersheds in the test areas gradually shrink to a certain value. The mean slope of the independent units in the desert-loess transitional area (site I), southern loess ridge-low-mountain (site VII) and loess tableland-ridge (site VIII) are discrete. The main reason for this phenomenon is that these test areas are flat and unbroken. In other words, these independent physiographic units do not include all types of relief within a basin; when the coverage areas of each relief type are significantly random, a geographical unit may only contain loess interfluves or gully-slope lands. Therefore, the mean slopes in these independent units do not show any trends. As area increases, independent geographical units will likely still include a few instances of relief. These synthetic results may cause the mean slopes to not obviously converge.
It can also be seen that in the center of northern Shaanxi, some test areas, such as sites III, IV, V and VI, which are loess hill-ridges, show an obvious trend in which the mean slopes converge toward the mean slope value of all units with increasing independent geographical units. The main reason might be that terrain in these areas is complicated, with many gullies. Each unit includes complex relief and relatively unbroken small watersheds.
The existence of SSCA could be proved by the tendency of the mean slope based on the statistics of small watersheds. This uncertainty in the slope spectrum leads to the instability of the mean slope, reflecting the variable curve fluctuation of the slope spectrum. Hence, the slope spectrum may also have various features under different landforms. In addition, the size of the stable development area of each landform could be determined using this method.
Thus, the larger the landscape test area a unit has, the more stable slope spectrum information we can ascertain. Through the analysis of these diagrams, we can be sure that SSCA could be used as an efficient indicator to determine the minimum size of the physiographic unit.

4.3 SSCA of typical landforms

Six sample sites were selected in Shaanxi Province in China, which contains typical landforms (Table 2). With finer resolution, DEM could reflect more topographic information, showing minute fluctuations of micro surfaces. Furthermore, the tendency of the landscape evolution might be determined by this fluctuation. The SSCAs of the loess hill and loess hill-ridge are smaller than those of the loess tableland, in which the undulations of relief are gentle, and most parts in the middle of these areas are flat. With the gentle undulations, the erosion intensity is increasing slowly. Hence, the SSCA of site VIII is affected most obviously by the relief and has the highest value among these test areas, whose terrain fluctuations are gentler than those of others. Even if the SSCAs of different landforms are extremely diverse, adjacent areas with the same landscape have approximately the same SSCAs.
Table 2 Statistics of SSCA of typical landforms
Site Area name SSCA (km2) 1:10,000 Landform types
I Shenmu 13.29 Loess deep incision gorge-hill
III Suide 8.21 Loess hill-ridge
IV Yanchuan 10.08 Loess hill-ridge
VI Ganquan 10.60 Loess ridge-low-mountain
VII Yijun 13.21 Loess tableland
VIII Chunhua 35.01 Loess middle-low mountain, loess platform-tableland

5 Discussion

It is noted that slope spectrum is a fundamental representation of loess landscape evolution and could be applied to determine the stage of the geographical cycle. By extending the study area, the homogeneous textures are enhanced. According to the first law of geography, the same landform should possess the same or approximately the same slope composition (i.e., slope spectrum). It has been proven that slope spectrum can be employed for the interpretation of loess landscape, as well as to evaluate the landform evolution of the Loess Plateau (Tang et al., 2008). Nevertheless, the experiments in this paper show that SSCA could be another valuable index for revealing the mechanism of loess landforms in the plateau.
Scores of terrain variables were used in the study to investigate the main factors affecting the intensity and spatial distribution of SSCA. By comprehensively considering the mechanism, dependency and algorithm etc., four indices, gully density, skewness of the slope spectrum (S), terrain dynamic force (Td) and slope of slope (SOS), have been chosen to quantitatively depict the relationships between geomorphological properties and SSCA.
Table 3 Algorithms for slope spectrum indices
Indicators Algorithms Units Significance
Gully density
ΣL: The gully distance in watershed
A:The area of watershed 		km/km2 Reflecting the fragmentation of the surface
Skewness of the
slope spectrum (S)
:Mean frequency
σ: Standard deviation 		Unitless Reflecting the distribution of slope gradient combination
Terrain dynamic
force (Td)
Pi: Frequency of each slope class
aij: Slope gradient of grid ij
j: Number of grid for slope class i 		Unitless Reflecting the erosional potential by the terrain
Slope of slope (SOS)
fx: The variation rate of slope along x axis
fy: The variation rate of slope along y axis 		Unitless Reflecting the complexity of the surface
Gully density is usually an indicator that reveals the development stage of a loess watershed (Jing, 1986; Zhang et al., 1998; Tucker et al., 2001). Slope spectrum, the histogram of slope grades, is proven to be an effective method for representing the combination of loess surfaces. As a key index, the skewness of slope spectrum mainly statistically and macroscopically reveals the steepness. Td is a ratio of the sum of the horizontal component force of gravities to the area of the watershed, which could represent the contribution of the terrain to erosion (Li et al., 2006, Li et al., 2007; Tang et al., 2008). SOS means slope of slope, representing the variation in slope gradient, and its statistical values can reveal the complexity and roughness of the surface to some extent. Table 3 shows the algorithms for calculating these indices.
The correlations between SSCA and gully density, S, Td and SOS are given in Figure 7. There exists a good exponential relationship between SSCA and gully density, Td and SOS, and a logarithmic relationship between SSCA and S. The relationship between SSCA and gully density is negative. SSCA shows a good logarithmic function with S and will increase with an increase in S values. The highest determination coefficient is 0.7782, which is achieved between gully density and SSCA, followed by Td and SSCA with a value of 0.6288. It is suggested that all of these indices have a significant correlation with SSCA and thus could be employed to reveal its geographical indication.
Figure 7 Plots of SSCA vs. gully density, S, Td and SOS in the Loess Plateau (R2 denotes the coefficient of determination)
The spatial variations of auxiliary indices described in Table 4 are also given in Figure 8. Generally, the landform types of the Loess Plateau vary in a sequence from north to south, i.e., loess low-hill, loess-hill, loess hill-ridge, loess ridge-hill and loess tableland. The gully density, Td and SOS change from low to high, then to low again, showing a similar variation trend with terrain roughness, in spite of the inverse skewness. Figure 8b shows that the range of skewness is from 0.196 to 0.057 in the northern Shaanxi test areas, and its mean value is 1.256, approaching a normal distribution pattern (Li, 2007). The relatively high values appear mainly in the southern loess tableland and loess meadow-basin, where surfaces are smooth, with the slope gradient ranging from 0° to 12°, showing a positive skewness in the slope spectrum.
Figure 8 Spatial distribution of the slope spectrum indices in northern Shaanxi
From north to south, the high values of Td mainly appear in the middle of northern Shaanxi. It is this area that produces the major sediment load for the lower reaches of the Yellow River via a few tributaries, including the Kuye River, Tuwei River, etc. The maximum values exist in sites III and IV, as shown in Figure 8c. The maximum values of SOS are located in the triangular region where the vertex is Ansai, i.e., sites III and IV, where landforms are dominated by loess hill-ridge. Analyzed together with Figure 8a, it is suggested that the terrains of these areas are complicated and suffer from serious and wide gully erosion. This is indirect evidence in support of Jiang’s (1966) result.
Simultaneously, landform evolution of the Loess Plateau and soil erosion are interrelated as cause and effect. The process of landform evolution can be classified into the following stages: inheritance, reformation and late evolution (Ma, 1996), which are greatly affected by the intensity of erosion. These four indicators are directly related to the spatial distribution of loess landforms, including loess tableland, loess ridge, loess hill and so on, and could depict terrain relief as well as erosion intensity from a geomorphological viewpoint. The similar spatial fluctuation of these indicators from south to north also shows an obvious spatial variation of surface roughness in this area. Combining Figures 4 and 8, we can conclude that the SSCA could be used to represent the spatial variation of terrain relief, as the spatial variation of gully density, SOS and Td are significantly correlated with SSCA. This is of great significance in describing the surface roughness and geomorphological evolution. It provides a theoretical basis for loess landform classification based on SSCA that is related to these indicators.
With the aggravation of soil erosion and the sharp undulation of loess terrain, the values of gully density, Td and SOS are increasing in the southern part of the test area. Along with the development of loess landforms, the loess tablelands will be gradually eroded to tattered loess tableland, loess ridges, and typical loess hills. In general, the changing trend is that the soil loss aggregates with the increase of slope gradient, even though there is a slight disparity in soil loss under the same topographic condition (Xu et al., 2009). A comprehensive analysis of the above discussion concluded that SSCA could be accepted as a discriminating factor in identifying loess landforms. Furthermore, SSCA represents, to some extent, the degree of landform development. SSCA values achieve a maximum in the early stages of loess landform development, i.e., loess tableland in the south of northern Shaanxi, and reach their bottom values in the middle stage of loess terrain evolution, i.e., loess hilly-gullied terrain, located mainly in the center of the study area.

6 Conclusions

Slope spectra have been widely utilized as indicators of terrain roughness and the relief of loess landforms. Based on the mean slope statistics in eight representative areas, this paper found that a necessary condition for the existence of slope spectrum is SSCA, namely, the critical area in which the slope histogram becomes stable. We argue strongly that this condition is necessary for four reasons:
(1) Generally, SSCA values are obviously different in areas of different loess landforms, such as loess tableland and loess hills. The more complex the loess terrain is, the lower SSCA values will be.
(2) Experimental results show that SSCA is significantly correlated with gully density, SOS, slope skewness and Td, four selected core terrain factors of loess landforms. SSCA may reflect the development stage of loess landform evolution; hence, it should be a novel and highlighted index in geomorphological studies.
(3) The stability area of slope spectrum is obviously dependent on the DEM scale and is reflected by topographic complexity. In the study plots, the size of the SSCA is closely related to the specific topography and the qualification of slope spectrum’s stability. Moreover, the SSCAs of different landform types, even some of the same landform types, are generally inconsistent. However, for the same landform region, when the test areas include enough information on landform features, we can always find the critical area of the stable slope spectrum.
(4) The spatial variation of SSCA is one of the main indications of water and soil erosion’s spatial performance. SSCA can reveal the objective laws of a river basin’s geomorphological evolution effectively, improving the qualitative description of the river basin’s geomorphological evolution and topographic elements by making it more quantitative.
More work is necessary to deeply and comprehensively investigate the geomorphological significance of SSCA, especially its universality in geographical and geomorphological research.

The authors have declared that no competing interests exist.

References

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1
Ayalew L, Yamagishi H, 2004. Slope failures in the Blue Nile basin, as seen from landscape evolution perspective.Geomorphology, 57(1/2): 95-116.ABSTRACT The Blue Nile basin is severely affected by slope failures, and the characteristics of its deep gorges and rugged valley walls called for a study on the relationships between topography and the process of landsliding and rock falling. Work was commenced with the conception of nine types of landforms on the basis of a one-to-one combination of lateral and vertical slope profiles and thence the determination of the effect of these landforms on the occurrence of slope failures. Observations showed that topographic surfaces with concave lateral profiles shelter mudflows and some retrogressive rotational slumps while slopes characterized by planar lateral profiles are sites mainly for translational slides. Landslides are rare in convex-shaped slopes but when they occur, they are big and deep-seated. As an effort to understand the significant contributions of landslides and rock falls to landscape development, direct and indirect methods are employed. Direct methods are based on quantitative relationships between the volume of material that had been removed from the area and the amount that could, in principle, be taken away based on available erosion rates. Indirect methods used the nature of river incision and the effect of the present-day landslides on the landscape. In general, discrepancy in calculated figures in the first, and the overall drop and form of the Abay River gorge coupled with the observed landslide-caused landform changes in the second, led us to deduce that slope failures were part of the mega-forces that shaped the entire Blue Nile basin, and in fact, played the dominant role in landscape evolution.

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Chen Liding, Huang Zhilin, Gong Jieet al., 2007. The effect of land cover/vegetation on soil water dynamic in the hilly area of the Loess Plateau, China.Catena, 70(2): 200-208.<h2 class="secHeading" id="section_abstract">Abstract</h2><p id="">Severe soil and water loss has lead to widespread land degradation in China's loess plateau. During the past decades, a great deal of effort was made on vegetation restoration to reduce soil and water loss in the loess plateau. However, due to water shortage the efficiency of vegetation restoration was not as satisfactory as expected. As part of a vegetation restoration project, we conducted research aiming to understand the relationship between vegetation pattern and soil water dynamics. The goal was to find vegetation types appropriate for the loess plateau with scarce water resources. In 1986, fifteen plots of land were planted with five vegetation types: pine woodland, shrubland, sloping cropland, alfalfa and semi-natural grassland. Soil water content, runoff, soil erosion were measured for each plot. Environmental variables, such as rainfall, evaporation and temperature, were recorded simultaneously by an automated meteorological station. The relationship between land cover pattern and soil water dynamic was evaluated by using statistical models. We found that: (1) soil water loss occurred during the growing season, and it reached the maximum in the second half of July; (2) soil water was not fully replenished from rainfall during the rainy season; (3) pine woodland induced the largest water loss to surface runoff, followed by sloping cropland, alfalfa, semi-natural grassland and shrubland; the poor capability of pine woodland for water conservation may be attributed to soil compaction and poor ground coverage under the tree; (4) in most cases, soil water of the five vegetation types was low except for shrubland and semi-natural grassland where it was moderate-high during a few periods. These conditions inhibit sustainable vegetation growth in the semi-arid loess hilly area of the loess plateau, China.</p>

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Cheng Weiming, Zhou Chenghu, 2014. Methodology on hierarchical classification of multi-scale digital geomorphology.Progress in Geography, 33(1): 23-33. (in Chinese)In this paper, based on classification method and legend layout of published geomorphological maps of the nation at different levels and different scales and the hierarchical classification method for the digital geomorphology of China with a scale of 1:1000000, we proposed a hierarchical land classification system with the indicators in five major categories. The indicators include basic landform form, morphological characteristics of geomorphological types (including morphological assembly, micro-landform morphological entities, slope form characteristics of landform surface), basic genesis and main genetic action ways, materials and lithology, formation age or period of geomorphological types, which all combined are a comprehensive presentation of geomorphological characteristics. These indicators can be divided into three categories and nine levels: landform superclass (sub-superclass), landform class (sub-class) and landform type (sub-type), at the nine levels, such as macro morphology, terrain characteristics, main genetic condition, main genetic action ways, morphological assembly, micro-landform morphological entity, slope characteristics, material and lithology and landform formation age. The geomorphological characteristics can be expressed by means of not only continuous polygons addressing morpho-genetic types, but also discrete points, lines and polygons addressing morpho-structural types. The morpho-genetic and morpho-structural geomorphological types can be exchanged for each other based on mapping scales. Based on geomorphological characteristics, the indicators of former four grades can be mapped for 1: 4000000 geomorphological maps, and former five grades for 1:1000000 geomorphological maps, and former seven grades for 1:500000 geomorphological maps. As to 1:250000 and 1:50000 geomorphological maps, parts of morpho-structural geomorphological types can be converted to morpho-genetic geomorphological types, slope form characteristics, terrain slope position, material and lithology and formation age of micro-landforms can be highlighted in order to realize the expression for detailed geomorphological types. As to China's offshore and adjacent ocean topography and geomorphology, four hierarchical geomorphological types can be classified in terms of spatial position, water dynamic condition (ocean water depth and slope characteristics), and lithosphere types and depth change. Form-genetic types can be expressed by means of the former three classes and form-structural types can be expressed by means of fourth class.

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Davis W M, 1899. The geographical cycle.Geographical Journal, 14: 481-504.

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He Xiubin, Li Zhanbin, Hao Mingdeet al., 2003. Down-scale analysis for water scarcity in response to soil-water conservation on Loess Plateau of China. Agriculture, Ecosystems & Environment, 94(3): 355-361.ABSTRACT Water scarcity is one of the most prominent issues of discussion worldwide concerned with sustainable development, especially in the arid and semi-arid areas. On the Loess Plateau of China, population growth and fast-growing cities and industries have caused ever-increasing competition for water. The present paper shows a down-scale analysis on how the region wide mass action of soil&ndash;water conservation ecologically influenced regional water scarcity on the Loess Plateau, the Middle Reaches of the Yellow River of China. Result shows a great progress has been achieved in erosion control and food production since the 1980s. About 24% of erosion area has been controlled. Grain yield has increased greatly and sediment in the Yellow River has decreased by about 25%. However, various sources of evidence show that the soil&ndash;water conservation measures might have played a significant role on regional hydrocycles, leading to the depletion of deep soil water and reduced runoff in the Yellow River and consequently ecological problems. The study implies that cropland and forest plantations are increasingly suffering water stress. Advancing sustainable development further, or even maintaining the current situation, will be a great challenge given the burgeoning socio-economic development of the area combined with global climatic change.

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Hessel R, van Asch T, 2003. Modelling gully erosion for a small catchment on the Chinese Loess Plateau.Catena, 54(1/2): 131-146.The rolling hills region of the Chinese Loess Plateau is one of the areas with the highest erosion rates on earth. A striking feature of this area is the occurrence of many large, permanent gullies. A 3.5-km2 catchment was selected to study the processes of erosion and to adapt the storm-based Limburg Soil Erosion Model (LISEM) to the conditions prevailing on the Loess Plateau. Part of this work consisted of mapping and measuring the largest gully headcuts. The amount of loose soil material beneath the headcuts was also estimated. Observations suggest that gully headcuts are relatively stable (i.e., do not migrate rapidly), but that gullies can nevertheless produce significant amounts of sediment during overland flow events. Erosion of headcuts occurs mainly by soil falls in between storms. The loose soil material produced by these soil falls accumulates on the gully bottom. As the LISEM simulates storm erosion, the development of gullies over time can be ignored, and only the amount of material produced by them during runoff events needs to be studied. A digital elevation model (DEM) was used to estimate the position of existing gully heads by applying an adapted form of the Montgomery and Dietrich [Science 255 (1992) 826] index. Using the assumption that headcuts are vertical, it is possible to calculate headcut height from the slope angle map. A simple stability model, which assumes soil falls on gully headcuts to be a function of soil moisture content and headcut height, was applied. This daily-based model can then be used to simulate the accumulation of loose soil material below the headcut. The results show that while the DEM is not accurate enough to allow the detection of individual headcuts, this method can be used to produce a reasonable estimate of the amount of loose soil material available. A map showing the amount of loose soil material accumulated can then serve as input for a storm-based erosion model such as LISEM.

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Hughes M W, Almond P C, Roering J Jet al., 2010. Late Quaternary loess landscape evolution on an active tectonic margin, Charwell Basin, South Island, New Zealand.Geomorphology, 122(3/4): 294-308.Loess deposits constitute an important archive of aeolian deposition reflecting wider patterns of glacial atmospheric circulation, and more localised interactions between riverine source areas, loess trapping efficiency and geomorphic controls on erosion rate. Conceptual models have been formulated to explain the coeval evolution of loess mantles and associated landscapes (loess landscape model...

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Iwahashi J, Watanabeb S, Furuya T, 2001. Landform analysis of slope movements using DEM in Higashikubiki area, Japan.Computers & Geosciences, 27(7): 851-865.Land-form analysis of slope movements using DEM in Higashikubiki area, Japan IWAHASHI J. Computers & Geosciences 27, 851-865, 2001

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Jiang Deqi, Zhao Chengxin, Chen Zhanglin, 1966. Research on the sediment source in middle reaches of Yellow River.Acta Geographica Sinica, 31(1): 20-36. (in Chinese)

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Jing Ke, 1986. A study on gully erosion on the Loess Plateau.Scientia Geographica Sinica, 6(4): 340-347. (in Chinese)The Loesss Plateau is characterized by crisscross gullies. The developing degree, erosion type and distribution characteristics of gullies are influenced strongly by the height of erosion base level, the amount and intensity of rainfall, and the composition of ground materials in the basin. The gully density (Y) on the Loess Plateau has direct effects on erosion quantity (X). Their relation can be expressed as Y=2.4223+1.083X (r=0.7437) on the Loess Plateau the sediment comes mainly from gullies. The ratio of sediment yield coming from gullies to that from interfluves is nearly 6:4. If the hillslope runoff is intercepted, the sediment yield from gully erosion may reduce by 70%. The key factors reducing gully erosion are to increase the vegetation coverage on hillslopes and to lower the erosion base level.

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Li Fayuan, 2007. Research on the slope spectrum and its spatial distribution in the Loess Plateau [D]. Nanjing Normal University, 55-70. (in Chinese)

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Li Fayuan, Tang Guoan, 2006. DEM based research on the terrain driving force of soil erosion in the Loess Plateau. In: Geoinformatics 2006: Geospatial Information Science, Proc. of SPIE, 2006, 6420, Reston, Virginia, USA.ABSTRACT DEM data availability and GIS-assisted processing of the data have extended the usage of DEM to a great extent. Taking 5 m grid resolution DEMs of 48 test areas in the Loess Plateau in north Shaanxi as test data, this paper introduces the definition, calculation, extraction and stable threshold area of terrain driving force (Td) for soil erosion. Then, spatial distribution of Td is investigated with a method of geostatistics analysis. Results show that spatial distribution of Td is correlatable with spatial distribution of the soil erosion intensity and Td can be taken as a regional terrain factor of regional soil erosion in the Loess Plateau. But Td is not exact enough in evaluation processing of regional soil erosion, an integrated analysis combining the climate, vegetation cover, soil and water conservation management is demanded. Then, some problems existing in the research of regional soil erosion are analyzed and a preliminary model of regional soil erosion contained Td is proposed. Subsequent research is focused on data collection and integration of regional soil erosion and its applicability in the Loess Plateau.

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Li Fayuan, Tang Guoan, Wang Chun et al., 2007. Quantitative analysis and spatial distribution of slope spectrum: A case study in the Loess Plateau in north Shaanxi province. In: Chen J M, Pu Y X, eds. Proceedings or SPIE-Geoinformatics 2007: Geospatial In-formation Science. Bellingham: SPIE, 2007.

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Liang Guanglin, Chen Hao, Cai Qiangguoet al., 2004. Research progress of modern topographic evolvement and landform erosion in Loess Plateau.Research of Soil and Water Conservation, 11(4): 131-137. (in Chinese)

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Luo Laixing, 1956. A tentative classification of landforms in the Loess Plateau.Acta Geographica Sinica, 22(3): 201-222. (in Chinese)Two distinctive groups of landforms may be recognised in the Loess Plateau, namely, the interfluves and the valleys. These two are considered here as the meso-forms, each being an independent of morphological unit. Parts of an in-dependent unit are considered as the micro-forms, and parts of the latter the minute forms. Each of these 3 grades of forms is classified into types, each of which is subdivided into varieties. Some types have sub types before further subdivision. For the meso forms, there are 2 forms and they are, as already mentioned, the interfluves and the valleys. For the interfluves, there are 2 subtypes and altogether 5 varieties; the same numbers are for the valleys. With regard to micro-forms, the interfluves are divided into water-divides and slopes. There are subtypes for the divides. 2 of which are with 2 varieties each, and 3 subtypes for the slopes. The valleys are divided into 5 types, 3 of which are with 4 subtypes, 1 with 5, and 1 with 3.Minute form may occur both in the interfluves and the valleys. There are 6 types, each with 2 or 3 subtypes. Of the subtypes, 6 have varieties, 2 or 3 each. Soil conservation measures are introduced respectively for (i) water divides' (ii) slopes, (iii) valley heads, (iv) undulating lands, and (v) river chan-nels. According 6 the morphological characteristics, as well as the different modes of erosion, a certain conbination of some of the following measures are suggested for each of the above 5 types of landforms; terracing, damming, reforestation, Pend-digging and dyke-building.

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Matsushi Y, Matsuzaki H, 2010. Denudation rates and threshold slope in a granitic watershed, central Japan. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 268(7/8): 1201-1204.ABSTRACT This study examines the relationship between long-term denudation rates and mean catchment slope in a mountainous watershed in central Japan. The denudation rates were determined from 26Al measurements for fluvial sediments obtained from the outlets of the whole basin and nine sub-catchments. The denudation rates ranged from 200 to 2000mmkyr611, increasing exponentially with increasing mean slope of the catchments, but declining abruptly for the catchments with mean slope above 38°. This result suggests that the basin topography is not in a morphometric steady-state, but is evolving dynamically.

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Ma Naixi, 1996. Relationship between loess geomorphic evolution and soil erosion.Bulletin of Soil and Water Conservation, 16(2): 6-10. (in Chinese)Based on the analysis of loess landforms division and its evolution,the law of addederosion is discussed.The result shows that the accelerated erosion power equals to the sum ofnatural erosion capacity and the added erosion ability. Then. the principles of controlling soil ero-sion are alsodiscussed.

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McBride R A, Taylor M J, Byrnes M R, 2007. Coastal morphodynamics and Chenier-Plain evolution in southwestern Louisiana, USA: A geomorphic model.Geomorphology, 88(3/4): 367-422.Using 28 topographic profiles, air-photo interpretation, and historical shoreline-change data, coastal processes were evaluated along the Chenier Plain to explain the occurrence, distribution, and geomorphic hierarchy of primary landforms, and existing hypotheses regarding Chenier-Plain evolution were reconsidered. The Chenier Plain of SW Louisiana, classified as a low-profile, microtidal, storm-dominated coast, is located west and downdrift of the Mississippi River deltaic plain. This Late-Holocene, marginal-deltaic environment is 200 km long and up to 30 km wide, and is composed primarily of mud deposits capped by marsh interspersed with thin sand- and shell-rich ridges (“cheniers”) that have elevations of up to 4 m.In this study, the term “ridge” is used as a morphologic term for a narrow, linear or curvilinear topographic high that consists of sand and shelly material accumulated by waves and other physical coastal processes. Thus, most ridges in the Chenier Plain represent relict open-Gulf shorelines. On the basis of past movement trends of individual shorelines, ridges may be further classified as transgressive, regressive, or laterally accreted. Geomorphic zones that contain two or more regressive, transgressive, or laterally accreted ridges are termed . Consequently, we further refine the Chenier-Plain definition by Otvos and Price [Otvos, E.G. and Price, W.A., 1979. Problems of chenier genesis and terminology—an overview. Marine Geology, 31: 251–263] and define as containing at least two or more chenier complexes. Based on these definitions, a geomorphic hierarchy of landforms was refined relative to dominant process for the Louisiana Chenier Plain. The Chenier Plain is defined as a first-order feature (5000 km) composed of three second-order features (30 to 300 km): chenier complex, beach-ridge complex, and spit complex. Individual ridges of each complex type were further separated into third-order features: chenier, beach ridge, and spit.To understand the long-term evolution of a coastal depositional system, primary process–response mechanisms and patterns found along the modern Chenier-Plain coast were first identified, especially tidal-inlet processes associated with the Sabine, Calcasieu, and Mermentau Rivers. Tidal prism () and quantity of littoral transport () are the most important factors controlling inlet stability. Greater discharge and/or tidal prism increase the ability of river and estuarine systems to interrupt longshore sediment transport, maintain and naturally stabilize tidal entrances, and promote updrift deposition. Thus, prior to human modification and stabilization efforts, the Mermentau River entrance would be classified as wave-dominated, Sabine Pass as tide-dominated, and Calcasieu Pass as tide-dominated to occasionally mixed.Hoyt [Hoyt, J.H., 1969. Chenier versus barrier, genetic and stratigraphic distinction. Am. Assoc. Petrol. Geol. Bull., 53: 299–306] presented the first detailed depositional model for chenier genesis and mudflat progradation, which he attributed to changes in Mississippi River flow direction (i.e., delta switching) caused by upstream channel avulsion. However, Hoyt's model oversimplifies Chenier-Plain evolution because it omits ridges created by other means. Thus, the geologic evolution of the Chenier Plain is more complicated than channel avulsions of the Mississippi River, and it involved not only chenier ridges (i.e., transgressive), but also ridges that are genetically tied to regression (beach ridges) and lateral accretion (recurved spits).A six-stage geomorphic process-response model was developed to describe Chenier-Plain evolution primarily as a function of: (i) the balance between sediment supply and energy dissipation associated with Mississippi River channel avulsions, (ii) local sediment reworking and lateral transport, (iii) tidal-entrance dynamics, and (iv) possibly higher-than-present stands of Holocene sea level. Consequently, the geneses of three different ridge types (transgressive, regressive, and laterally accreted) typically occur contemporaneously along the same shoreline at different locations.

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O’Callaghan J F, Mark D M, 1984. The extraction of drainage networks from digital elevation data. Computer Vision,Graphics and Image Processing, 28(3): 323-344.The extraction of drainage networks from digital elevation data is important for quantitative studies in geomorphology and hydrology. A method is presented for extracting drainage networks from gridded elevation data. The method handles artificial pits introduced by data collection systems and extracts only the major drainage paths. Its performance appears to be consistent with the visual interpretation of drainage patterns from elevation contours.

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Rowbotham D N, Dudycha D, 1998. GIS modelling of slope stability in Phewa Tal watershed, Nepal. Geomorphology, 26(1-3): 151-170.Hazards are an inherent but dangerous and costly element of mountainous environments. Conventional maps of mountain hazards provide useful inventories of hazardous sites but provide little insight into the operation of the hazards. Furthermore, this approach tends to rely heavily on subjective interpretation of the landscape, which means that the results can not be replicated or transferred to other areas. Thus, alternative approaches employing the quantitative capabilities of geographic information systems (GIS) to model and predict slope stability are receiving increasing attention. This paper reports on the use of a diverse GIS database, compiled primarily from existing maps and aerial photographs, to construct a regional model of slope stability in Phewa Tal watershed, Nepal. An integral part of the research was to explore an alternative approach to the commonly used grid cell approach by employing geomorphometrically significant terrain units. The terrain units employed were created by generating line networks representing local maxima and minima extracted from elevation and curvature surfaces. One of the chief benefits of applying GIS technology in this research was the ability to georeference all of the attribute data to these terrain units. In doing so, it allowed the database to be exported into an external statistical package, where the terrain units could be statistically explored as the basic analytical unit. The application of a variety of statistical techniques resulted in logistic regression being selected as the most useful. Logistic regression successfully predicted terrain units as being either stable or unstable at a rate of approximately 90% concordance with a conventionally produced map of slope stability. The statistical probabilities of terrain unit stability were imported back into the GIS to produce a map of predicted slope stability that compared well with the conventional map of slope stability. The findings of this research suggest that the use of geomorphometrically significant terrain units extracted from a digital elevation model (DEM) are an efficient alternative to approaches using regular grid cells. In particular, the terrain units facilitated the use of logistic regression, and significantly decreased the amount of computing costs. Finally, this research also suggests that important information can be gathered from existing information sources, such as maps, aerial photographs, and written documents, thereby limiting the need for costly and time consuming field work at the reconnaissance level. Based on this latter finding, other information sources, such as satellite imagery, should be examined.

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Shary P A, Sharayab L S, Mitusov A V, 2002. Fundamental quantitative methods of land surface analysis.Geoderma, 107(1/2): 1-43.Effective quantitative land surface analyses in soil science need scale-free land surface attributes (morphometric variables, MVs) to be introduced for making comparable results obtained at different scales. To investigate the problem in more detail, a conceptual scheme and curvatures studied earlier in Shary (1995) [Math. Geol. 27 (1995) 373] are further developed in this paper, formulae for a complete system of 12 curvatures and some other MVs are given, and modified Evans鈥揧oung algorithm for curvature calculation is described that does not emphasize grid directions. The conceptual scheme is based on that MVs often describe not the land surface itself, but rather the system 鈥渓and surface+vector field鈥, where vector fields of common interest are gravitational field and solar irradiation. Correspondingly, morphometric variables and concepts may (1) refer to this system description (field-specific), or (2) be invariant with respect to any vector field (field-invariant), that is, describing the land surface itself, its geometrical form. From the other side, MVs and concepts may be (1) local, (2) regional, which need extended portions of a restricted part of land surface for their determination at a given point, or (3) global (planetary), when elevations of all the Earth are needed for their determination at a given point. Global MVs do not consist subject of this paper; so, the four classes of MVs are considered here: class A (local field-specific MVs), class B (regional field-specific), class C (local field-invariant), and class D (regional field-invariant). MVs of these classes permit description of geometrical land form, pre-requisits of surface runoff, thermal regime of slopes, and altitude zonality. Class A contains three independent MVs expressed by first derivatives of elevation Z by plan coordinates (slope steepness, slope direction, solar insolation) and seven curvatures expressed by second derivatives of Z ; class C contains five curvatures; class B contains two variables (catchment and dispersal areas); MVs of class D are not introduced yet. Also, some non-system MVs of class A are described, sense of all MVs is described, and interrelationships between MVs are shown. Three curvatures are independent, not two, as this is often implied. It is experimentally shown that average depth of a depression defined in class B may not depend upon scale, while local MVs may not have limit values for large scales. Scale-free morphometric variables are defined here as those that have limit values for large scales. It is experimentally shown that maximal catchment area (class B) is a scale-free variable for thalwegs. These results show that local MVs are scale-specific (except elevation), but scale-free regional MVs might be introduced as a generalization of curvature concept. Two surface runoff accumulation mechanisms are considered in their relation to local and regional field-specific MVs; although the first one is generalized to a regional MV (catchment area), there is no regional MV for the second one description, although it is of great importance in soil science as describing slow profile changes. Geometrical forms were little studied in soil science; arguments are given that they may be useful for studying memory in soils, which is determined by temporal shifts between land surface formation and soil formation processes. The following topics are discussed: the current state of morphometry, an ambiguity in land form definitions, and a possibility to generalize curvature concept for regional scale-free MVs. The consideration is restricted by methods of the general geomorphometry; partial approaches are considered only by selection.

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Shi Hui, Shao Mingan, 2000. Soil and water loss from the Loess Plateau in China.Journal of Arid Environments, 45(1): 9-20.Physical, geological, climatic and land forming factors in north China are described and the effect of human activities on soil and water erosion are discussed. The proposed measures for the control of soil and water loss are: engineering and biological strategies for reducing runoff, changes in land use, improved grassland and forestry management practices, construction of dams, terraces and s...

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Tang Guoan, Li Fayuan, Liu Xuejunet al., 2008. Research on the slope spectrum of the Loess Plateau. Science in China (Series E:Technological Sciences), 51(1): 175-185.A new concept dealing with digital analysis of loess terrain,slope spectrum,is presented and discussed in this paper,by introducing its characteristic,represen-tation and extracting method from DEMs. Using 48 geomorphological units in dif-ferent parts of the loess as test areas and 5 m-resolution DEMs as original test data,the quantitative depiction and spatial distribution of slope spectrum in China's Loess Plateau have been studied on the basis of a series of carefully-designed experiments. In addition,initial experiment indicates a strong relationship between the slope spectrum and the loess landform types,displaying a potential importance of the slope spectrum in geomorphological studies. Based on the slope spectrums derived from the 25 m-resolution DEM data in whole loess terrain in northern part of Shaanxi,13 slope spectrum indices were extracted and integrated into a compre-hensive layer with image integration method. Based on that,a series of unsuper-vised classifications was applied in order to make a landform classification in northern Shaanxi Loess Plateau. Experimental results show that the slope spec-trum analysis is an effective method in revealing the macro landform features. A continuous change of slope spectrum from south to north in northern Shaanxi Loess Plateau shows an obvious spatial distribution of different loess landforms. This also proves the great significance of the slope spectrum method in describing the terrain roughness and landform evolution as well as a further understanding on landform genesis and spatial distribution rule of different landforms in the Loess Plateau.

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Tang Guoan, Zhao Mudan, Li Tuanwenet al., 2003. Simulation on slope uncertainty extracted from DEMs at different resolution levels: A case study in the Loess Plateau.Journal of Geographical Sciences, 13(4): 387-394.<a name="Abs1"></a>Slope is one of the crucial terrain variables in spatial analysis and land use planning, especially in the Loess Plateau area of China which is suffering from serious soil erosion. DEM based slope extracting method has been widely accepted and applied in practice. However slope accuracy derived from this method usually does not match with its popularity. A quantitative simulation to slope data uncertainty is important not only theoretically but also necessarily to applications. This paper focuses on how resolution and terrain complexity impact on the accuracy of mean slope extracted from DEMs of different resolutions in the Loess Plateau of China. Six typical geomorphologic areas are selected as test areas, representing different terrain types from smooth to rough. Their DEMs are produced from digitizing contours of 1:10,000 scale topographic maps. Field survey results show that 5 m should be the most suitable grid size for representing slope in the Loess Plateau area. Comparative and math-simulation methodology was employed for data processing and analysis. A linear correlativity between mean slope and DEM resolution was found at all test areas, but their regression coefficients related closely with the terrain complexity of the test areas. If taking stream channel density to represent terrain complexity, mean slope error could be regressed against DEM resolution (X) and stream channel density (S) at 8 resolution levels and expressed as (0.0015S<sup>2</sup>+0.031S-0.0325)X-0.0045S<sup>2</sup>-0.155S+0.1625, with a R<sup>2</sup> value of over 0.98. Practical tests also show an effective result of this model in applications. The new development methodology applied in this study should be helpful to similar researches in spatial data uncertainty investigation.

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Tong Chiming, Zhou Chenghu, Cheng Weiminget al., 2014. Morphological characteristics and developmental stages of loess tablelands based on DEM.Progress in Geography, 33(1): 42-49. (in Chinese)DEM-based terrain analysis has been widely used in geomorphology. Currently most researches are qualitative or semi-quantitative, whereas quantitative analyses of large areas based on a variety of parameters are few and far between, and most studies use artificial field measurement with a small scale in the aspect of the relative age of the landscape entity. So, in this article, by using 30 m ASTER-GDEM, GIS and digital terrain analysis method, we extracted morphological parameters of a wide range of the areas of loess tablelands and determined their relative ages. We tried to provide basic knowledge of multi scale representation of the loess tablelands and fine landforms, achieved quantitative descriptions of the similarities and differences among the loess tablelands, and calibrated their developmental stages. First, we extracted positive landforms less than 15&#176; in the Loess Plateau. Then, we acquired the top surface of the loess tableland using two parameters: gradient and waviness. We determined 1106 loess tablelands based on the subtraction between positive landform layer and the top surface layer. We selected 106 loess tablelands as samples to calculate average slope, axial ratio of top surface, gully density, top and bottom area ratio, percentage of negative terrain. The geometric mean of these five parameters was used as an index to estimate the relative age of the loess tableland. The index (abbreviated to <i>I</i>) was categorized into three levels: early development (<i>I</i><1.74), middle development (1.74≤<i>I</i><2.12) and late development (<i>I</i>≥2.12). The results showed that: (1) the morphological parameters of loess tablelands are different from one another in different developmental stages; (2) developmental stages are also inconsistent for the subtypes; (3) transitional type exhibits the characteristics more similar to the type of the previous stage. After calculating <i>I</i> of each subtype, we found that from early to late stages of the loess tablelands, <i>I</i> value increases gradually, which is consistent with other researchers' conclusions on the developmental stages of loess landforms.

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Tucker G E, Catani F, Rinaldo Aet al., 2001. Statistical analysis of drainage density from digital terrain data.Geomorphology, 36(3/4): 187-202.Drainage density (), defined as the total length of channels per unit area, is a fundamental property of natural terrain that reflects local climate, relief, geology, and other factors. Accurate measurement of is important for numerous geomorphic and hydrologic applications, yet it is a surprisingly difficult quantity to measure, particularly over large areas. Here, we develop a consistent and efficient method for generating maps of using digital terrain data. The method relies on (i) measuring hillslope flow path distance at every unchanneled site within a basin, and (ii) analyzing this field as a random space function. As a consequence, we measure not only its mean (which is half the inverse of the traditional definition of drainage density) but also its variance, higher moments, and spatial correlation structure. This yields a theoretically sound tool for estimating spatial variability of drainage density. Averaging length-to-channel over an appropriate spatial scale also makes it possible to derive continuous maps of and its spatial variations. We show that the autocorrelation length scale provides a natural and objective choice for spatial averaging. This mapping technique is applied to a region of highly variable in the northern Apennines, Italy. We show that the method is capable of revealing large-scale patterns of variation in that are correlated with lithology and relief. The method provides a new and more general way to quantitatively define and measure , to test geomorphic models, and to incorporate variations into regional-scale hydrologic models.

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Vanacker V, Vanderschaeghe M, Govers Get al., 2003. Linking hydrological, infinite slope stability and land-use change models through GIS for assessing the impact of deforestation on slope stability in high Andean watersheds.Geomorphology, 52(3/4): 299-315.In the Ecuadorian Andes, episodic slope movements comprising shallow rotational and translational slides and rapid flows of debris and soil material are common. Consequently, not only considerable financial costs are experienced, but also major ecological and environmental problems arise in a larger geographical area. Sediment production by slope movement on hillslopes directly affects sediment transport and deposition in downstream rivers and dams and morphological changes in the stream channels. In developing countries world-wide, slope movement hazards are growing: increasing population pressure and economic development force more people to move to potentially hazardous areas, which are less suitable for agriculture and rangelands.This paper describes the methods used to determine the controlling factors of slope failure and to build upon the results of the statistical analysis a process-based slope stability model, which includes a dynamic soil wetness index using a simple subsurface flow model. The model provides a time-varying estimate of slope movement susceptibility, by linking land-use data with spatially varying hydrologic (soil conductivity, evapotranspiration, soil wetness) and soil strength properties. The slope stability model was applied to a high Andean watershed (Gordeleg Catchment, 250 ha, southern Ecuadorian Andes) and was validated by calculating the association coefficients between the slope movement susceptibility map of 2000 and the spatial pattern of active slope movements, as measured in the field with GPS. The proposed methodology allows assessment of the effects of past and future land-use change on slope stability. A realistic deforestation scenario was presented: past land-use change includes a gradual fragmentation and clear cut of the secondary forests, as observed over the last four decades (1963鈥2000), future land-use change is simulated based on a binary logistic deforestation model, whereby it was assumed that future land-use change would continue at the same rate and style as over the last 37 years (1963鈥2000).

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Wang Chun, 2005. The uncertainty of slope spectrum derived from DEM in the Loess Plateau of northern Shaanxi province [D]. Northwest University, 86-94. (in Chinese)

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Xiong Liyang, Tang Guoan, Li Fayuanet al., 2014a. Modeling the evolution of loess-covered landforms in the Loess Plateau of China using a DEM of underground bedrock surface.Geomorphology, 209: 18-26.The evolution of loess-covered landforms is largely controlled by the pre-Quaternary underlying bedrock terrain, which is one of the most important factors in understanding the formation mechanism of the landforms. This study used multiple data sources to detect 1729 outcropping points of underlying terrain, in order to construct a digital elevation model (DEM) of the paleotopography of an area of the Loess Plateau subject to severe soil erosion. Four terrain characteristics, including terrain texture, slope gradient, the hypsometric curve, and slope aspect, were used to quantify topographic differences and reveal the loess-deposition process during the Quaternary. A loess thickness map was then created to show the spatial distribution of loess deposits in the test area. Finally, the geomorphological inheritance characteristics of the loess-covered landforms were evaluated in different landform divisions. The results showed the significant inheritance of modern topography from the underlying topography with a similar general relief trends. The average thickness of loess deposits was computed to be 104.6 m, with the thickest part located in the Xifeng loess tableland area. In addition, the slope aspects of the North and Northwest seem to have favored Quaternary loess deposition, which supported the hypothesis of an eolian origin for loess in China. The modern surface has lower topographic relief compared to the underlying terrain due to loess deposition.

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Xiong Liyang, Tang Guoan, Yuan Baoyinet al., 2014b. Geomorphological inheritance for loess landform evolution in a severe soil erosion region of Loess Plateau of China based on digital elevation models.Science China Earth Sciences, 57(8): 1944-1952.The influence of pre-quaternary underlying terrain on the formation of loess landforms, i.e., the geomorphological inheritance issue, is a focus in studies of loess landforms. On the basis of multi-source information, we used GIS spatial analysis methods to construct a simulated digital elevation model of a pre-quaternary paleotopographic surface in a severe soil erosion area of the Loess Plateau. To reveal the spatial relationship between underlying paleotopography and modern terrain, an XY scatter diagram, hypsometric curve, gradient and concavity of terrain profiles are used in the experiments. The experiments show that the altitude, gradient and concavity results have significant linear positive correlation between both terrains, which shows a relatively strong landform inheritance relationship, particularly in the intact and complete loess deposit areas. Despite the current surface appearing somewhat changed from the original shape of the underlying terrain under different erosion forces, we reveal that the modern terrain generally smoothes the topographic relief of underlying terrain in the loess deposition process. Our results deepen understanding of the characteristics of geomorphological inheritance in the formation and evolution of loess landforms.

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Xu Yong, Yang Bo, Liu Guobinet al., 2009. Topographic differentiation simulation of crop yield and soil and water loss on the Loess Plateau.Journal of Geographical Sciences, 19(3): 331-339.<a name="Abs1"></a>De-farming slope farmland has been an effective measure in recent years for the improvement of the eco-environment and the mitigation of soil and water loss on the Loess Plateau. This paper, taking the Yangou Basin as a case study and using day-by-day meteorological data of Yan&#8217;an station in 2005, simulated and analyzed the quantitative relation between crop yield, soil and water loss and topographic condition with the aid of WIN-YIELD software. Results show that: 1) topographic gradient has important influence on crop yield. The bigger gradient is, the lower the crop yield. Yields of sorghum and corn decrease by 15.44% and 14.32% respectively at 25° in comparison to the case of 0°. In addition, yields of soya, bean and potato decrease slightly by 5.26%, 4.67% and 3.84%, respectively. The influences of topographic height and slope aspect on crop yield are slight. 2) Under the same topographic condition, different crops&#8217; runoff and soil loss show obvious disparity. Topographic gradient has important influence on soil and water loss. In general, the changing trend is that the soil and water loss aggregates with the increase of gradient, and the maximal amount occurs around 20°. The influence of topographic height is slight. Topographic aspect has a certain effect, and the fundamental characteristic is that values are higher at the aspect of south than north. 3) Topographic gradients of 5° and 15° are two important thresholds. The characteristic about soil and water loss with the variation of topographic gradients show that: the slope farmland with gradient less than 5° could remain unchanged, and the slope farmland more than 15° should be de-farmed as early as possible.

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Yamada S, 1999. The role of soil creep and slope failure in the landscape evolution of a head water basin: Field measurements in a zero order basin of northern Japan.Geomorphology, 28(3/4): 329-344.Field measurements of soil creep and slope stability were conducted on a nose, side-slope and hollow in a zero order basin near Sapporo, Hokkaido, northern Japan, and the preferential location of soil creep and slope failure was determined. Soil creep was continuously measured by the strain probe method at three sites from 1994 to 1995, and was compared with soil moisture conditions and ground temperature. In the summer, active soil creep occurred only when rainfall led to large soil moisture changes and a near-saturated condition, which was most likely induced by shrink–swell activity of soil. In the winter, soil creep was caused by seasonal frost, although the mass transport was limited because of the insulation provided by snow cover. These results indicate that the soil moisture change and soil moisture content during a rainfall event in the summer are the major factors controlling soil creep in this basin. Soil moisture conditions were further measured by a tensiometer at 16 sites in the rainy season in 1994. On the nose and side-slope, active soil-moisture changes took place during rainfall-events. The hollow tended to maintain higher soil-moisture conditions than the nose and side-slope, because subsurface flow was concentrated in the hollow. Thus the soil-moisture variation that encourages soil creep rarely occurred in the hollow. From these results, sediment transport rates caused by creep were estimated to be 207.0, 159.5 and 9.0×10 613 m 3 /yr on the nose, side-slope and hollow, respectively, and the resultant mass balances were calculated at 61207.0, +25.1 and +172.9×10 613 m 3 /yr, respectively. These results clearly show infilling in the hollow and denudation on the nose. Slope stability was analyzed by the infinite slope model. The potential of slope failure was evaluated from the relationship between critical water depth H cr and soil thickness D . The analysis revealed that an increase in D causes a marked decrease in H cr on the side-slope, indicating the high potential of slope failure on the slope. In contrast, both on the nose and in the hollow, the decrease in H cr for the same increase in D was lower than that on the side-slope. However, slope failure on the side-slope and soil creep on the nose infill material into the hollow. Thus, the increase in D in the hollow is higher than that on the other slopes; leading to an increase in slope failure potential. These results indicate that soil creep and slope failure act as infilling and evacuating processes of the zero order basin with differing intensities depending on slope form: soil creep removes soil materials from the nose and deposits them in the hollow, whereas slope failure removes materials from the side-slope and deposits them in the hollow. When infilling develops a sufficiently thick soil accumulation in the hollow, slope failure evacuates the hollow.

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Yang Guifang, Zhang Xujiao, Tian Mingzhonget al., 2011. Alluvial terrace systems in Zhangjiajie of northwest Hunan, China: Implications for climatic change, tectonic uplift and geomorphic evolution.Quaternary International, 233(1): 27-39.This paper reports the latest details from two comprehensive investigations of alluvial terrace sequences in Zhangjiajie, northwest Hunan Province, China. Seven alluvial terrace units along the Maoxi River and four terrace sequences along the Suoxi River record significant regional geomorphic history. Rates of regional Quaternary uplift and climate change are reconstructed using topographic and stratigraphic evidence from terrace and adjacent cave deposits, along with Electron Spin Resonance (ESR) and Thermo-luminescence (TL) dating controls. Between 928ka and 689ka the time-averaged uplift rate (or incision rate) was 0.16m/ka. The rate decreased to 0.05m/ka between 689ka and 347ka, and then increased slightly to 0.11–0.14m/ka after 347ka. The inferred incision rate increased roughly from 0.21–0.32m/ka to 0.51m/ka from the Late Pleistocene to present. The seven alluvial phases (T 7 61T 1 ) and their associated chronology are consistent with climatic variations at regional and/or global scales, suggesting that these terraces represent climate-driven pauses imprinted atop the record of long-term tectonically induced incision by rivers. Insights from these alluvial terrace staircases and cave features indicate that the spectacular sandstone peak forest landscape of the study area has emerged since the middle period of the Middle Pleistocene.

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Zevenbergen L W, Thorne C R, 1987. Quantitative analysis of land surface topography.Earth Surface Processes and Landforms, 12(1): 47-56.Abstract Land surface topography significantly affects the processes of runoff and erosion. A system which determines slope, aspect, and curvature in both the down-slope and across-slope directions is developed for an altitude matrix. Also, the upslope drainage area and maximum drainage distance are determined for every point within the altitude matrix. A FORTRAN 66 program performs the analysis.

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Zhang Liping, Ma Zhizheng, 1998. The research on the relation between gully density and cutting depth in different drainage landform evolution periods.Geographical Research, 17(3): 273-278. (in Chinese)

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Zhou Qiming, Liu Xuejun, 2006a. Digital Terrain Analysis. Beijing: Science Press. (in Chinese)

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Zhou Yi, Tang Guoan, Yang Xinet al., 2010. Positive and negative terrains on northern Shaanxi Loess Plateau.Journal of Geographical Sciences, 20(1): 64-76.<a name="Abs1"></a>The Loess positive and negative terrains (P-N terrains), which are widely distributed on the Loess Plateau, are discussed for the first time by introducing its characteristic, demarcation as well as extraction method from high-resolution Digital Elevation Models. Using 5 m-resolution DEMs as original test data, P-N terrains of 48 geomorphological units in different parts of Shaanxi Loess Plateau are extracted accurately. Then six indicators for depicting the geomorphologic landscape and spatial configuration characteristic of P-N terrains are proposed. The spatial distribution rules of these indicators and the relationship between the P-N terrains and Loess relief are discussed for further understanding of Loess landforms. Finally, with the integration of P-N terrains and traditional terrain indices, a series of un-supervised classification methods are applied to make a proper landform classification in northern Shaanxi. Results show that P-N terrains are an effect clue to reveal energy and substance distribution rules on the Loess Plateau. A continuous change of P-N terrains from south to north in Shaanxi Loess Plateau shows an obvious spatial difference of Loess landforms and the positive terrain area only accounted for 60.5% in this region. The P-N terrains participant landform classification method increases validity of the result, especially in the Loess tableland, Loess tableland-ridge and the Loess low-hill area. This research is significant on the study of Loess landforms with the Digital Terrains Analysis methods.

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Zhou Zhengchao, Shangguan Zhouping, Zhao Duli, 2006b. Modeling vegetation coverage and soil erosion in the Loess Plateau Area of China.Ecological Modelling, 198(1/2): 263-268.Soil erosion is still one of major issues limiting agricultural and forestry productivity in Loess Plateau of China. Vegetation plays an important role in controlling soil erosion, but studies on modeling dynamics of vegetation and soil erosion and interaction between them were hardly reported. We hypothesized that changes of vegetation coverage and soil erosion as affected by climate factors and human activities in the Loess Plateau of China might be simulated using appropriate models. In order to test our hypothesis and to better understanding the interaction between vegetation coverage and soil erosion, we conducted a study at watershed of Zhifanggou, a typical region of Loess Plateau. Soil erosion was negative linearly correlated with vegetation coverage (=0.99***), while vegetation was mainly associated with human activities. Based on climate change, ecological stress factors and human activities, we developed a model to estimate vegetation coverage and soil erosion. Testing the model performance indicated that dynamics of vegetation coverage and soil erosion in the Loess Plateau of China could be precisely simulated. The importance of each factor in the model was also evaluated. The information of this study can be useful for better understanding the relationships between vegetation and soil erosion.

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