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Journal of Arid Land  2021, Vol. 13 Issue (10): 995-1014    DOI: 10.1007/s40333-021-0085-2
Research article     
Two-dimensional hydrodynamic robust numerical model of soil erosion based on slopes and river basins
KANG Yongde1, HUANG Miansong2,*(), HOU Jingming1,*(), TONG Yu1, PAN Zhanpeng1
1State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China, School of Water Resources and Hydroelectric Engineering, Xi'an University of Technology, Xi'an 710048, China
2Beijing Capital Eco-Environment Protection Group Co. Ltd., Beijing 100028, China
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Erosion is an important issue in soil science and is related to many environmental problems, such as soil erosion and sediment transport. Establishing a simulation model suitable for soil erosion prediction is of great significance not only to accurately predict the process of soil separation by runoff, but also improve the physical model of soil erosion. In this study, we develop a graphic processing unit (GPU)-based numerical model that combines two-dimensional (2D) hydrodynamic and Green-Ampt (G-A) infiltration modelling to simulate soil erosion. A Godunov-type scheme on a uniform and structured square grid is then generated to solve the relevant shallow water equations (SWEs). The highlight of this study is the use of GPU-based acceleration technology to enable numerical models to simulate slope and watershed erosion in an efficient and high-resolution manner. The results show that the hydrodynamic model performs well in simulating soil erosion process. Soil erosion is studied by conducting calculation verification at the slope and basin scales. The first case involves simulating soil erosion process of a slope surface under indoor artificial rainfall conditions from 0 to 1000 s, and there is a good agreement between the simulated values and the measured values for the runoff velocity. The second case is a river basin experiment (Coquet River Basin) that involves watershed erosion. Simulations of the erosion depth change and erosion cumulative amount of the basin during a period of 1-40 h show an elevation difference of erosion at 0.5-3.0 m, especially during the period of 20-30 h. Nine cross sections in the basin are selected for simulation and the results reveal that the depth of erosion change value ranges from -0.86 to -2.79 m and the depth of deposition change value varies from 0.38 to 1.02 m. The findings indicate that the developed GPU-based hydrogeomorphological model can reproduce soil erosion processes. These results are valuable for rainfall runoff and soil erosion predictions on rilled hillslopes and river basins.

Key wordssoil erosion      two-dimensional modelling      rainfall runoff      Green-Ampt model      gully erosion     
Received: 29 April 2021      Published: 10 October 2021
Corresponding Authors: HUANG Miansong, HOU Jingming     E-mail:;
Cite this article:

KANG Yongde, HUANG Miansong, HOU Jingming, TONG Yu, PAN Zhanpeng. Two-dimensional hydrodynamic robust numerical model of soil erosion based on slopes and river basins. Journal of Arid Land, 2021, 13(10): 995-1014.

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Fig. 1 Relationships between flow velocity and time (a), between flow discharge and time (b), and between cumulative erosion amount and time (c)
Parameter RMSE R2 MRE
Flow velocity 0.152 96.5 1.395
Flow discharge 0.059 94.1 1.208
Cumulative erosion 0.037 90.2 1.433
Table 1 Performance evaluation indices of the model developed in this study
Soil type Particle percentage (%)
>1.000 mm 0.250-1.000 mm 0.050-0.250 mm 0.010-0.050 mm 0.005-0.010 mm 0.001-0.005 mm <0.001 mm
Loess 0.00 1.30 32.80 46.70 2.90 5.80 10.50
Natural sand 0.00 62.18 24.60 11.95 1.27 0.00 0.00
Table 2 Particle components of the experimental soil
Fig. 2 Accumulation of slope erosion at different times. (a), 0 and 10 s; (b), 20 and 50 s; (c), 100 and 200 s; (d), 500 and 1000 s.
Fig. 3 Relationship between sediment yield (Y) and rill erosion width (X) at different times
Fig. 4 Variations of rill erosion velocity and rill erosion width with the passage of time
Time (s) Erosion rill velocity (cm/s) Erosion rill width (mm)
1.36 75.20 1.74
30.90 68.10 1.79
58.10 61.50 4.31
93.00 53.40 10.30
108.00 43.50 15.90
145.00 38.60 18.40
187.00 36.90 20.30
236.00 34.70 21.20
284.00 32.90 23.10
339.00 28.30 26.00
395.00 23.90 34.50
470.00 17.80 40.70
521.00 15.30 43.60
584.00 12.70 45.90
660.00 10.20 49.30
742.00 9.02 53.90
795.00 9.04 60.30
858.00 8.20 65.00
921.00 6.99 68.40
966.00 6.89 72.20
1000.00 7.02 76.90
Table 3 Erosion rill velocity and width at different times
Fig. 5 Correlation between the simulated and measured rill erosion values
Fig. 6 Numerical simulation of watershed erosion process of the Coquet River Basin at different times. (a), 1 h; (b), 5 h; (c), 10 h; (d), 15 h; (e), 20 h; (f), 30 h; (g), 40 h.
Fig. 7 Watershed erosion energy exchange. "+" and "-" indicate positive and negative work done, respectively. Positive work corresponds to erosion and negative work to deposition.
Fig. 8 Comparisons of elevations for the measured old riverbed and simulated new eroded riverbed at nine cross sections of the Coquet River Basin (a-i)
Fig. 9 Erosion and deposition depths of riverbed at nine cross sections in the Coquet River Basin. The positive and negative values are expressed as deposition depth and erosion depth, respectively.
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