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Slope gradient is one of the critically important factors which drive the erosional response of microtopographic surfaces. This study investigates the effect of slope gradient on the evolution of erosion under accumulative rainfall in laboratory experiments and calculates critical slope values that help evaluate land suitability for farming and similar purposes. Dynamics of accumulative runoff, accumulated sediment and their rates in each erosion stage are studied when the slope gradient varies. The critical slope value for the microtopographic surface was calculated according to the relationship between the sediment yield and slope gradient. The amount of eroded soil downhill in each erosion stage was calculated using DEM data of point cloud. Results show that 1) a steeper slope would increase cumulative runoff; 2) cumulative sediment increases rapidly initially and then stabilizes with the increase of slope; 3) the critical slope value for the whole erosion is determined as 10 °. The findings of the dynamics of interrill erosion and sediment characteristics are useful information for future research of erosion prediction and conservation of soil and water in the Chinese Loess Plateau.

Slopping farming land accounts for nearly two-third of the total land of the Loess Plateau in China, and the average annual erosive modulus is as high as 25,000 t∙km^{−2}∙a^{−1} [

The microtopographic surfaces are created by using farm tillage tools to form undulating terrains which comprise a mixture of soil grains, aggregates and clods, and whose height variance is rather small [

The evolution of erosion is a complicated multi-scale profile changing process. The soil erosion patterns show irregularities when they are observed on different scales. For example, DEMs are nowadays used to produce basic data for the soil erosion study, and fractal and anisotropic properties could be more prominent and distinct with a higher grid resolution used [

The soil used in the experiment was collected from a plough layer (0 - 20 cm) from tilled farmland surfaces in Yangling, Shaanxi province, located at the southern edge of the Loess Plateau (107.56˚ - 108.08˚E, 34.14˚ - 34.20˚N, and an

elevation of 435 - 563 m), a warm temperate semi arid zone affected by the monsoon. Long-term annual rainfall at the study site ranges between 635.1 mm and 663.9 mm, and most occurs in summer. The mean annual temperature is 12.9˚C. The loutu soil (Earth-cumuli-Orthic Anthrosol) is gray brown, loose and granular with silty sand aggregates. The bulk density is 1.30 g·cm^{−3}. The basic physical texture of soil is shown in

Air-dried soil was crushed and passed through a 10 mm sieve, and soil tanks (2.0 m × 1.0 m × 1.0 m) were constructed for the study and each was packed with 10 cm layers of soil to a depth of 100 cm. Each soil layer was raked even before packing the next layer to ensure uniformity of the soil structure, and the bulk density was controlled at 1.30 g·cm^{−3} (a mean outdoor bulk density). After the filling, the soil surface was contour tilled to form rows of furrows (

The laboratory experiment was carried out at the National Soil Erosion and Dryland Farming Laboratory in China. A rainfall simulator was mounted and the downward nozzles placed and adjusted at a height of 18 m, which ensured terminal drop (tap water) velocity. The nozzles could cover an area of 27 m × 18 m and rainfall uniformity was higher than 90% [

Prewetting was conducted on the soil surfaces with a rainfall intensity at 30

Aggregate size/mm | <0.001 | 0.005 - 0.001 | 0.01 - 0.005 | 0.05 - 0.01 | 0.25 - 0.05 | >0.25 | Clay |
---|---|---|---|---|---|---|---|

Weight percentage/% | 36.28 | 12.89 | 6.88 | 41.13 | 2.7 | 0.12 | 56.05 |

mm·h^{−1} applied until surface flow occurred. The duration lasted about 10 minutes with a purpose to consolidate loose soil particles, maintain consistent soil moisture with certain stable water content, and reduce the spatial variability of soil surfaces. Then the surfaces were covered with plastic sheet after the pre-rain to keep the water content of soil, and stood for 24 hours.

The slope gradient of the soil tanks was set at 5˚, 10˚, 15˚ or 20˚, respectively. The rainfall intensity was set at 90 mm·h^{−1}, which represented a strongest 30 minute storm which takes place once every 30 years in Yangling of Shaanxi.

A simulation rainfall experiment was carried out to apply consecutive artificial rainfall in different events and in different erosion stages, i.e. initial phase, splash erosion, sheet erosion and interrill erosion [

A 3-D terrestrial laser scanning system (Leica, the vertical error less than 1 mm) was mounted to scan the surfaces before and after a rainfall event, and cloud data of point elevations for different erosion stages were obtained. The information from each scan was converted into a set of (x, y, z) coordinates which were imported into ESRI ArcGIS software (see: https://www.esri.com) to create the corresponding high resolution (6 mm × 6 mm) digital elevation models (DEMs) [

SPSS 22.0 was run for regressional statistics and Origin 8.0 was used for mapping.

Runoff initiation time for soil surfaces with different slope gradients was respectively, 12.25 s (5˚), 8.75 s (10˚), 5.25 s (15˚) and 3.25 s (20˚). And it would decrease for a steeper slope. The runoff initiation for a 20˚ slope surface occurred 2.8 times as earlier as that for a 5˚ slope.

Through the whole rainfall event, the evolution of runoff flow velocity for different slopes presented similar patterns for change (^{−1} when the runoff was yet to generate; when the runoff began to generate, the runoff rate increased quickly until it reached a relatively stable state. At a same rainfall intensity, the runoff velocity would be greater at a steeper slope, and in all cases it would increase rapidly first and then steadied off. An SPSS regression simulation predicted that the relationship between rainfall and cumulative runoff could be best represented by the Equation (1):

S runoff = b 0 + b 1 x + b 2 x 2 + b 3 x 3 (1)

where b_{0}, b_{1}, b_{2}, b_{3} are regression coefficients, S_{runoff} cumulative runoff (×10^{−2} L) and x rainfall (mm).

During the rainfall event, the evolution of sediment mass and sediment yield rate for different slope gradients showed similar patterns (

whole rainfall event, the evolutions of cumulative sediment mass for different surfaces tended to present similar patterns. At the beginning of rainfall, the sediment mass was 0 g; when runoff initiated, splashes were formed and sediment increased quickly until at a stable level. At the same rainfall intensity, cumulative sediment mass would be greater on a steeper surface and it in all cases would increase quickly and steady off later.

When the rainfall began, the sediment rate was 0 g·min^{−1}; when the runoff began to generate, the sediment yield rate grew rapidly and peaked. When splash erosion evolved into sheet erosion, the runoff became a sheet of water flow which to some extent reduced the loss of soil and sealing came into being, which prevented sediment from being produced and so diminished the sediment yield rate. On the whole, at the same rainfall intensity, the sediment yield rate was greater for a steeper slope and for each individual curve, sediment yield rate tended to grow quickly at first, then peaked in sheet erosion, and declined gradually to a stable level (

The SPSS regression simulation predicted that the relationship between rainfall and cumulative sediment yield could be represented by the Equation (2):

S sediment = c 0 + c 1 x + c 2 x 2 + c 3 x 3 (2)

where c_{0}, c_{1}, c_{2}, and c_{3} are regression coefficients, S_{sediment} cumulative sediment yield (×10^{−1} g) and x rainfall (mm).

Sediment contribution rate is defined as the ratio of sediment yield for the contouring tillage (CT) surfaces to that of the linear slope (CK) surface.

Slope/˚ | Erosion process | CT sediment yield/kg | CK sediment yield/kg | Sediment contribution rate |
---|---|---|---|---|

5 | Splash | 0.1520 | 0.8713 | 0.1745 |

Sheet | 0.1559 | 0.9169 | 0.1700 | |

Interrill | 0.4379 | 0.4406 | 0.9939 | |

10 | Splash | 0.6860 | 0.9584 | 0.7158 |

Sheet | 0.5864 | 0.5544 | 1.0577 | |

Interrill | 0.7549 | 0.4445 | 1.6983 | |

15 | Splash | 0.6704 | 0.6997 | 0.9581 |

Sheet | 1.1096 | 0.8773 | 1.2648 | |

Interrill | 0.7233 | 0.4693 | 1.5412 | |

20 | Splash | 0.4775 | 3.3848 | 0.1411 |

Sheet | 1.3944 | 1.3690 | 1.0186 | |

Interrill | 0.5139 | 1.4321 | 0.3588 |

erosion process, the sediment yield from a CT surface was smaller than that of a CK surface, but at a steeper slope, the CT sediment yield began to increase and catch up with CK sediment yield and finally overtook it. So it could be inferred that there was a critical slope value which influenced sediment contribution rate this way: when at a slope gradient smaller than the critical slope value, the CT sediment yield would obviously be smaller than the CK sediment yield; while at a greater slope value, the CT sediment yield would obviously be bigger than the control’s, which meant a bigger contribution rate, even bigger than 1.

Varied curvilinear regression analyses (linear, log, reciprocal, quadratic, cubic, complex, S, growth and exponential) were conducted to describe the relationship between slope and sediment contribution. The results showed that the relationship could be well represented by a cubic polynomial, and a fitting Equation (3) for prediction was obtained by calculation:

y = 0.001 x 3 − 0.030 x 2 + 0.272 x − 0.186 (3)

According to power rule, if applied twice, function (3) produced second derivative function (4):

y ″ = 0.006 x − 0.060 (4)

If y" = 0, then x = 10 which meant there was a possible critical slope angle 10˚. This calculation was applied to fitting all the erosion processes, and three Perdition functions and critical slopes were produced as shown in

Erosion stage | Prediction equation | Critical slope/˚ |
---|---|---|

Splash erosion | y = − 2.851 + 1.327 x − 0.139 x 2 + 0.004 x 3 | 11.58 |

Sheet erosion | y = 2.481 − 0.468 x + 0.034 x 2 − 0.001 x 3 | 11.33 |

Interrill erosion | y = − 0.460 + 0.331 x − 0.036 x 2 + 0.001 x 3 | 12.00 |

The changes in the area before and after the four stages were shown in ^{2} (

When compared the measured erosion amount with the calculated erosion amount, it showed that the error would decline over the evolution of erosion which occurred at a same slope. During a same erosion stage, the error tended to increase and then diminish when the slope gradient for surfaces increased. The error between the measured value and calculated value ranged from 0.004 to 0.127 and the average error was 0.053, which was relatively small. These results proved that the application of 3-D laser scanning techniques allowed more immediate and precise representation of interrill erosion, reflected a more realistic topography and therefore reduced errors.

Tests were conducted on sloped bare surfaces at four gradients on which contour tillage and cumulative rainfall (90 mm·h^{−1}) were applied, and the evolution of interrill erosion was characterized and analyzed thoroughly.

In the same stages, erosion rate tended to increase first and then decrease when the slope increased. The critical slope values for different stages of splash erosion, sheet erosion and interrill erosion were determined as 11.58˚, 11.33˚ and 12˚, with a general possible critical slope 10˚ during the whole erosion development process, by operation of regression analyses for sediment contribution rate and slope. However, during the interrill stage, the maximum erosion

rate (2.67 kg/min) occurred at a 10˚ slope gradient, which is more approximate to the critical slope 12˚. Therefore, The critical slope value should be further addressed in future research to reduce the gap between the experimental value 10˚ and the calculated value 12˚, which provides important information for evaluation of land suitability. On the other hand, the critical slope value was obtained with experimental slope length only 2 m, therefore, different slope lengths should be taken into account in the future experiment.

During the same erosion stages, 3-D area of the region of interests increased and their surface volume decreased when slope gradient increased. This was because once interrill erosion started to occur on the surface, the erosion would increase multiplefold or even dozen fold [

However, since the tests for this work were carried out under cumulative rainfall, complete interrill erosion processes could not be guaranteed. The scanning of the elevation points on the surfaces could be affected because the intervals between rainfall events could not be controlled precisely for some laboratory and natural factors. Hence, when designing those tests, it is necessary to gain sufficient experience and knowledge by observing the evolution of interrill erosion under a complete rainfall, which could help improve and supplement the current study. Interrill systems on the surfaces are passages for transporting sediments and runoff, so the studies of erosion evolution and hydrologic characteristics are essentially important for water and soil conservation.

Although laboratory rainfall is rather different from natural rainfall, it has many advantages that it is the closest alternative, it can reduce the interval between natural rainfall events, and control the span and timing of an artificial rainfall event.

Contour tillage is a kind of soil conservation tillage methods along the contour line of topography, enhancing water infiltration and storage capacity, regulating runoff and reducing soil erosion, so as to benefit crop growth and increase yield per unit area. The practice of contour farming mainly applies in rocky mountainous regions where slopes are rather steep with fragmented topography or in areas of Loess Plateau where loss of water and soil is severe. This study established that the critical gradient that a slope has for contour plowing under a rainfall of 90 mm·h^{−1} is 10˚.

The relationship between the cumulative runoff, sediment yield and the rainfall of microtopographic soil surfaces under different slope gradients could be described by a univariate cubic equation. This study established that the slope gradient was a sensitive factor for microtopographic modeling of erosion prediction and the findings of the dynamics of interrill erosion and sediment characteristics could be used as a basis for future research of erosion prediction and lay the groundwork for conservation of soil and water in the Chinese Loess Plateau. The examination of the critical slope value is important for individuals and government to make informed decisions on land use and to avoid unnecessary waste of resources. The limitations of this research lie with the calculation methods, because only four slope gradients have been considered, and we don’t know how close this critical slope is to what we expect to be. To have more precise results, we need to try more slope gradients or change our method of calculation. And more experiments and tests are needed to provide more statistical and physical proof to support the existence of such a critical slope in the future.

This work is supported by the National Natural Science Foundation of China (41371273, 41771308).

The authors declare no conflicts of interest regarding the publication of this paper.

Zheng, W., Zhang, H., Jiang, Y., Zhang, X., Tong, Y.W. and Zhang, Q.F. (2019) Effect of Slope Gradient on Erosion Evolution Process at Microtopographic Tillage Soil Surfaces. Journal of Geographic Information System, 11, 481-492. https://doi.org/10.4236/jgis.2019.115029