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Frontiers of Earth Science

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Front. Earth Sci.    2016, Vol. 10 Issue (2) : 328-339    https://doi.org/10.1007/s11707-015-0519-2
RESEARCH ARTICLE
Slope spectrum variation in a simulated loess watershed
Fayuan LI1,2,*(),Guoan TANG1,2,Chun WANG3,Lingzhou CUI4,Rui ZHU5
1. State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China
2. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China
3. Land Information Engineering Department, Chuzhou University, Chuzhou 239000, China
4. College of Life and Environment Science, Wenzhou University, Wenzhou 325035, China
5. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China
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Abstract

A simulated loess watershed, where the loess material and relief properly represent the true loess surface, is adopted to investigate the variation in slope spectrum with loess watershed evolution. The evolution of the simulated loess watershed was driven by the exogenetic force of artificial rainfall. For a period of three months, twenty artificial rainfall events with different intensities and durations were carried out. In the process, nine DEM data sets, each with 10 mm grid resolution, were established by the method of close-range photogrammetry. The slope spectra were then extracted from these DEMs. Subsequent series of carefully designed quantitative analyses indicated a strong relationship between the slope spectrum and the evolution of the simulated loess watershed.

Quantitative indices of the slope spectrum varied regularly following the evolution of the simulated loess watershed. Mean slope, slope spectrum information entropy (H), terrain driving force (Td), Mean patch area (AREA_MN), Contagion Index (CONTAG), and Patch Cohesion Index (COHESION) kept increasing following the evolution of the simulated watershed, while skewness (S), Perimeter-Area Fractal Dimension (PAFRAC), and Interspersion and Juxtaposition Index (IJI) represented an opposite trend. All the indices changed actively in the early and active development periods, but slowly in the stable development periods. These experimental results indicate that the time series of slope spectra was able to effectively depict the slope distribution of the simulated loess watershed, thus presenting a potential method for modeling loess landforms.
Keywords slope spectrum      evolution      simulated watershed      loess landform     
Corresponding Author(s): Fayuan LI   
Just Accepted Date: 08 June 2015   Online First Date: 30 July 2015    Issue Date: 05 April 2016
 Cite this article:   
Fayuan LI,Guoan TANG,Chun WANG, et al. Slope spectrum variation in a simulated loess watershed[J]. Front. Earth Sci., 2016, 10(2): 328-339.
 URL:  
https://academic.hep.com.cn/fesci/EN/10.1007/s11707-015-0519-2
https://academic.hep.com.cn/fesci/EN/Y2016/V10/I2/328
Length of watershed/m Max width /m Projective area/m2 Perimeter /m Elevation difference /m Longitudinal gradient of watershed/% Mean slope/(°) Channel level Branch ratio
9.1 5.8 31.49 23.3 2.57 28.24 15 2 4
Tab.1  Geometric character indices of the simulated loess surface
Fig.1  3D terrain visualization of the initial simulated loess surface.
Number of rainfall (sequence of photogrammetry) Date of rainfall (date of photogrammetry) Designed rainfall intensity /(mm·h-1) Measured rainfall intensity/(mm·h-1) Duration of rainfall/min Amount of rainfall/mm
(1st stage) (7-29) Mean: 0.00 Mean: 0.00 Sum: 0.00 Sum: 0.000
1 7-30 30.00 32.4 90.50 48.915
2 8-1 30.00 31.2 89.50 46.540
3 8-3 30.00 29.4 89.50 63.939
4 8-5 60.00 70.8 47.52 65.050
5 8-8 60.00 72.6 45.86 73.580
(2nd stage) (8-13) Mean: 42.00 Mean: 47.4 Sum: 362.88 Sum: 298.024
6 8-14 120.00 144.6 30.53 53.750
7 8-17 60.00 71.4 46.17 51.528
(3rd stage) (8-19) Mean: 90.00 Mean: 108 Sum: 76.80 Sum: 105.278
8 8-20 30.00 34.2 90.18 36.167
9 8-22 30.00 35.4 61.95 55.704
(4th stage) (8-27) Mean: 30.00 Mean: 34.8 Sum: 152.13 Sum: 91.871
10 8-28 60.00 72 47.92 65.360
11 8-31 120.00 129 31.17 65.360
(5th stage) (9-1) Mean: 90 Mean: 106.8 Sum: 79.09 Sum: 130.720
12 9-3 30.00 31.2 62.94 31.896
13 9-5 30.00 34.8 61.53 35.960
14 9-7 30.00 33.6 60.83 34.290
(6th stage) (9-11) Mean: 90 Mean: 33 Sum: 185.30 Sum: 102.146
15 9-11 60.00 67.2 46.82 52.438
16 9-14 60.00 64.8 45.83 49.896
17 9-17 60.00 58.8 47.02 45.256
18 9-20 60.00 62.4 45.37 47.180
(7th stage) (9-21) Mean: 60.00 Mean: 62.4 Sum: 185.04 Sum: 194.770
19 9-24 120.00 127.2 30.37 64.384
20 9-27 120.00 118.8 34.35 67.736
(8th stage) (9-28) Mean: 120.00 Mean: 123 Sum: 64.72 Sum: 132.120
21 9-30 30.00 31.8 91.27 48.373
22 10-9 30.00 33 90.60 49.83
23 10-11 30.00 36 89.72 53.832
(9th stage) (10-12) Mean: 30.00 Mean: 33.6 Sum: 271.59 Sum: 152.035
Tab.2  Artificial rainfall and close-range photogrammetry parameters
Fig.2  Control points distribution.
Fig.3  Hillshade maps of simulated watershed.
Stage Gully density/(m·m-2) Erosion amount/kg
I 0.5086 1,355.2
II 0.7404 1,355.2
III 0.865 1,461.3
IV 0.964 1,423.4
V 1.1609 1,881.7
VI 1.3551 979.7
VII 1.847 1,597.7
VIII 2.0437 965.4
IX 1.9488 777.8
Tab.3  Gully density and erosion amount of the simulated watershed
Fig.4  Slope spectra of simulated watershed in different stages.
Fig.5  Slope maps of simulated watershed in different stages.
Fig.6  variation of H, S with slope class.
Quantitative index Calculation Remark
Mean patch area (AREA_MN) A R E A _ M N = ∑ j = 1 n a i j n i aij: area (m2) of slope patch ijni: patch numberreflecting the shape complexity of slope patch
Perimeter-Area FractalDimension (PAFRAC) P A F R A C = 2 [ n i × ∑ j = 1 n ( ln ? P i j × ln ? a i j ) ] - [ ( ∑ j = 1 n ln ? P i j ) × ( ∑ j = 1 n ln ? a i j ) ] ( n i × ∑ j = 1 n ln ? P i j 2 ) - ( ∑ j = 1 n ln ? P i j ) 2 pij: perimeter (m) of patch ijni: number of patches in the landscape of patch type (class) icomparing the shape complexity of different slope class patch or whole landscape. PAFRAC approaches 1 for shapes with very simple perimeters such as squares, and approaches 2 for shapes with highly convoluted, plane-filling perimeters
Contagion Index(CONTAG) C O N T A G = [ 1 + ∑ i = 1 m ∑ k = 1 m [ ( P i ) ( g i k ∑ k = 1 m g i k ) ] × ( ln ? ( P i ) ( g i k ∑ k = 1 m g i k ) ) 2 ln ? ( m ) ] × 100 Pi: proportion of the landscape occupied by patch type (class) igik: number of adjacencies (joins) between pixels of patch types (classes) i and k based on the double-count method.M: number of patch types (classes) present in the landscape, including the landscape border if present.Describing aggregation degree or of slope patch, CONTAG approaches 0 when the patch types are maximally disaggregated and interspersed. CONTAG = 100 when all patch types are maximally aggregated
Interspersion and Juxtaposition Index (IJI) L J I = [ 1 + - ∑ k = 1 m [ ( e i k ∑ k = 1 m e i k ) ln ? ( e i k ∑ k = 1 m e i k ) ] ln ? ( m - 1 ) ] × 100 eik: total length (m) of edge in landscape between patch types (classes) i and km: number of patch types (classes)IJI approaches 0 when the corresponding patch type is adjacent to only 1 other patch type and the number of patch types increases. IJI = 100 when the corresponding patch type is equally adjacent to all other patch types
Patch Cohesion Index(COHESION) C O H E S I O N = [ 1 - ∑ j = 1 n p i j ∑ j = 1 n p i j a i j ] × [ 1 - 1 A ] - 1 × 100 pij: perimeter of patch ijaij: area of patch ij in terms of number of cellsA:?total number of cells in the landscapedescribing fragmentation of slope patch or whole landscape0≤COHESION≤100. COHESION at the landscape level is similar to CONTAG
Tab.4  Algorithms for the calculation of slope map-patch indices
Fig.7  scatter map of average sediment transport ratio vs rainfall history.
Stage Transport amount/kg Sediment amount/kg Transport ratio
2nd stage 1,355.2 0 1
3rd stage 1,393.2 68.1 0.953
4th stage 1,302.6 120.8 0.915
5th stage 1,880.6 0.078 0.999
6th stage 912.1 67.6 0.931
7th stage 1,580.8 16.9 0.989
8th stage 946.2 19.2 0.98
9th stage 737.1 40.7 0.948
Tab.5  Sediment transport ratio in different stages (according Cui, 2002)
Stage Mean slope Skewness(S) Slope spectrum information entropy (H) (nat) Terrain driving force (Td)
1 16.52° 1.563 2.138 0.283
2 20.76° 1.411 2.59 0.342
3 22.73° 1.419 2.755 0.369
4 25.30° 1.356 2.888 0.406
5 28.79° 1.339 3.033 0.451
6 29.67° 0.875 3.048 0.468
7 31.97° 0.313 3.121 0.498
8 33.24° -0.079 3.157 0.514
9 32.70° -0.231 3.142 0.511
Tab.6  Quantitative indices of slope spectrum in different stages
Fig.8  Comparison of slope spectrum indices with gully density and erosion amount.
Fig.9  Comparison of slope map-patch indices’ distribution in different stages.
Stage AREA_MN/m2 PAFRAC CONTAG/% IJI/% COHESION/%
1 1.982 1.314 55.217 48.958 99.08
2 0.218 1.512 49.865 62.631 95.992
3 0.184 1.538 45.676 63.638 94.438
4 0.166 1.555 42.402 63.37 93.36
5 0.103 1.569 37.325 67.155 90.728
6 0.121 1.565 37.324 64.355 90.655
7 0.116 1.577 35.598 64.979 89.97
8 0.091 1.579 34.26 65.91 87.47
9 0.109 1.576 34.22 64.749 88.197
Tab.7  Slope map-patch indices in different stages at landscape level
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