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

doi:10.1007/s11442-015-1245-0

Abstract

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 (T_d) and slope of slope (SOS), were chosen as indicators. There exists a good exponential function relationship between SSCA and gully density, terrain driving force (T_d) 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

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

Figures/Tables 11

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Site	Area name	1: 10,000 DEM
Site	Area name	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

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

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 (T_d)	P_i: Frequency of each slope class a_ij: 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)	f_x: The variation rate of slope along x axis f_y: The variation rate of slope along y axis	Unitless	Reflecting the complexity of the surface

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