Study on Landscape Patches Inﬂuencing Hillslope Erosion Processes and Flow Hydrodynamics in the Loess Plateau of Western Shanxi Province, China

: Although vegetation restoration plays an important role in the management of surface runo ﬀ and soil erosion, the large-scale restoration of vegetation can increase water consumption and reduce surface water resources, thus a ﬀ ecting the health of river ecosystems. Therefore, vegetation restoration should aim to achieve a vegetation landscape pattern that optimizes protection of soil resources while limiting water consumption. This study established ﬁeld runo ﬀ plots with di ﬀ erent landscape patch types, including bare land, S-road patches, strip patches, grid patches, and random patches, as well as di ﬀ erent quantities patches of 5, 10, 15, and 20. An artiﬁcial rainfall experiment was conducted to determine the e ﬀ ect of di ﬀ erent vegetation patches in reducing runo ﬀ and sediment, and the relationship between the types and number of vegetation patches and hydrodynamic parameters. The results showed that the runo ﬀ yields of the four vegetation patch types decreased by 16.1–48.7% compared with that of bare land, whereas sediment yields decreased by 42.1–86.5%. In addition, the resistance coe ﬃ cients of the poorly connected patch patterns, including strip patches, grid patches, and random patches, ranged between 0.2–1.17 times higher than that of the well-connected S-road patch pattern, and the stream power decreased by 33.3–50.7%. Under a set vegetation coverage rate, an increase in the number of vegetation patches resulted in a signiﬁcant reduction in runo ﬀ velocity, runo ﬀ yield, and sediment yield, increases in surface roughness and ﬂow resistance, and reductions in runo ﬀ shear force and stream power. Besides, the sensitivity of soil to erosion decreased with an increasing number of the patch in the vegetation landscape, whereas the sensitivities of patch combinations with poor connectivity were lower than those with good connectivity. The results of this study highlight the importance of vegetation patch type and quantity for control of soil erosion.


Introduction
Soil erosion has become an ecological and environmental challenge of global concern [1]. The Loess Plateau is known to be one of the most highly erosive regions globally and acts as a major source of sediment to the Yellow River [2]. Serious soil erosion results in not only land degradation and ecosystem damage, but also in bank erosion downstream, which has a huge negative impact on production [3]. The Chinese government has implemented a series of soil and water conservation measures since the 1950s in an attempt to control serious soil erosion occurring on the Loess Plateau. These measures have resulted in a decrease in the annual sediment transport volume of the Yellow River from~1. 34 Gt in 1951-1979to~0.73 Gt in 1980-1999. Many studies over the world have demonstrated that vegetation cover play an important role in the prevention of soil and water losses [5,6]. Consequently, the relationship between vegetation and soil erosion by runoff has become a popular topic within the study of the ecological environment of the Loess Plateau region [3,[7][8][9][10][11][12].
Trees have been planted on a large scale in the Loess Plateau region by the Chinese government since 1999 through the "Grain for Green" project, which has increased vegetation coverage and reduced soil erosion [13][14][15]. The vegetation carrying capacity of the arid and semi-arid Loess Plateau region is limited due to limited rainfall, and the planting of too much vegetation may result in soil desiccation and vegetation degradation [16]. Under limited water resources, reasonable vegetation allocation can improve soil structure, increase soil erosion resistance, and thus reduce soil and water loss [7,17], whereas unreasonable vegetation distribution in arid and semi-arid areas world aggravate soil erosion [18,19]. The slope surface is the basic unit of soil erosion [20], the optimization of the distribution of limited vegetation on the hillslope surface is the key to realizing conservation of water and soil in the Loess Plateau.
Past studies on the optimal allocation of vegetation have mainly focused on the impacts of coverage, type, structure and spatial distribution of vegetation on slope runoff, sediment and hydrodynamic mechanisms [21][22][23][24][25][26], and these studies have usually used a simple vegetation configuration, mainly including hedgerows, grass strips and grass carpet [25,27]. Although Feng et al. analyzed the relationship between spatial patterns of different vegetation types and soil erosion, the distribution of vegetation investigated in that study was uniform [27]. The factors controlling vegetation restoration in the arid and semi-arid regions include topography, inclination, slope direction and soil moisture, among which soil moisture is the key factor controlling vegetation restoration [28]. Limited availability in water resources increases the patchiness of the vegetation distribution [29]. Vegetation patches are generally accepted to be the basis for the study of landscape patterns and soil erosion processes, and are the basic structural units affecting sediment production and sediment transport at different scales. The patches of vegetation in the landscape plays an important role in regulating the hydrological cycle and the ecological balance, and the majority of recent studies on vegetation patch have focused on the impact of the sizes and locations of a single patch or a single type of patch on soil erosion [30][31][32][33]. However, there have been relatively few studies on the impact of patterns of vegetation patchiness in the landscape on hillslope erosion. The selection of an appropriate combination of vegetation landscape patches under particular vegetation coverage is necessary for a comprehensive comparison of the effectiveness of these combinations in reducing runoff and sediment and improving hydraulic characteristics. The current study aimed to evaluate the effects of patch combination type and quantity within the vegetation landscape on surface runoff and soil loss on the slopes of the Loess Plateau. The specific objectives of the current study were to: (1) under a given vegetation coverage rate and using bare land as the control, compare the effects of the types and quantities of patches in different vegetation landscapes on surface runoff and soil loss; (2) compare the effects of the types and quantities of patches in different vegetation landscapes on hydrodynamic parameters; and (3) quantify the relationship between surface runoff and soil erosion in runoff plots for an improved understanding of the impact of vegetation landscape patches on soil erosion. The results of the present study can provide a reference for the optimal allocation of slope vegetation and ecological restoration in arid and semi-arid areas.

Experimental Designs
The present study used a side-spray portable simulated rainfall system developed by the Institute of Soil and Water Conservation, Ministry of Water Resources, Chinese Academy of Sciences [37][38][39]. The system consists of a water supply bag, a water supply pump, a water supply line with a bore diameter of 48 mm, a control valve, a pressure gauge, two tripods with a height of 7 m, and two nozzles ( Figure 3). Rainfall intensity of the system can be adjusted within a range of 30 mm h −1 to 120 mm h −1 and a uniformity of >85% by changing the water pressure and nozzle size in the pipeline using the control valve [38]. Since the effective rainfall coverage area of the system is 5 m × 4 m, the simulated rainfall was concurrently applied to the two adjacent plots. Rainfall intensity was determined before each rainfall experiment to regulate the uniformity and spatial distribution of rainfall [39]. A statistical analysis of several rainfall data for the study area identified two general categories of rainfall: (1) heavy rainfall intensity with short duration; and (2) weak rainfall intensity with long duration. Statistical analysis of rainfall in the first category over the most recent 3 years identified average rainfall intensity to be 7.37 mm in 5 min. Therefore, the average rainfall intensity of the artificial rainfall device was set to 7.5 mm over 5 min, or an artificial rainfall intensity of 90 mm h −1 .

Experimental Treatments and Measurement
Simulated rainfall experiments were conducted from July to August 2018. Soil water contents of all runoff plots were controlled to be equal by measurement of the soil water content of each plot before the experiment using time domain reflectometry (TDR) and adjusting soil water content if required ( Table 2). The slope of each plot was covered with a plastic sheet and left to stand for 24 h before the experiment. The duration of each simulated rainfall event in the experiment was ~65 min, The present study selected a hillside with the same site conditions to avoid the influence of different site conditions (Figure 1). The terrain of the experimental plot was relatively flat, with an average slope gradient of~15 • . The experimental plot had similar vegetation and soil types. Table 1 shows the soil properties to a depth of 0-10 cm in experimental grassland. The runoff plot was made of polyvinyl chloride (PVC) with dimensions of 5.0 m (length) × 0.5 m (width) × 0.3 m (height). A PVC board was inserted into the ground to a depth of 15 cm so that the top of the board was 15 cm higher than ground level. A V-shaped groove was set at the lower end of the runoff plot into which a PVC pipe with a diameter of 10 cm at the outlet was installed and connected to a bucket for collection of runoff and sediment. Previous studies have shown that, under the condition of limited water resources, the effective coverage of vegetation on the Loess Plateau ranges from 29.26% to 50.94% [36]. Therefore, considering the vegetation coverage of the study area, the present study selected a vegetation coverage of 50%. Two types of runoff plots were designed in the present study ( path, and random patches, under a common coverage of 50%; and (2) a uniform distribution of patches under a common coverage of 50%, but with varying numbers of patches (5, 10, 15, and 20). In the first combination, the number of patches of horizontal bars and field grids were 5 and 10, respectively, which was used in the patch pattern of 5 and 10 in the second combination, and each patch combination had two runoff plot replicates. The redundant vegetation in the runoff plot was eradicated during September 2017 according to the runoff plot design scheme, and the bare surface was leveled off. Table 2 shows information for each runoff plot. rainfall. The time required to produce initial runoff during a simulated rainfall event was recorded, and, after this point, samples of runoff and sediment were collected every 2 min for the first 10 min, and every 5 min thereafter, until a total of 15 runoff samples were collected. The total runoff of each plot was measured after each experiment. After 24 h of sediment precipitation, the clear liquid super stratum was separated from the sediment, and sediment was transferred to a large aluminum box and dried in an oven at 105 °C for 24 h. The dye tracer method [23] was applied to 1-m sections of the upper, middle and lower slopes of the runoff plots to measure surface velocity by recording the time taken for KMnO4 solution to pass through the measured section. Flow velocity was measured every 10 min during the entire experiment, and the average flow velocity at three different slope positions was taken to be the runoff velocity at that period.

Experimental Designs
The present study used a side-spray portable simulated rainfall system developed by the Institute of Soil and Water Conservation, Ministry of Water Resources, Chinese Academy of Sciences [37][38][39].
The system consists of a water supply bag, a water supply pump, a water supply line with a bore diameter of 48 mm, a control valve, a pressure gauge, two tripods with a height of 7 m, and two nozzles Water 2020, 12, 3201 5 of 16 ( Figure 3). Rainfall intensity of the system can be adjusted within a range of 30 mm h −1 to 120 mm h −1 and a uniformity of >85% by changing the water pressure and nozzle size in the pipeline using the control valve [38]. Since the effective rainfall coverage area of the system is 5 m × 4 m, the simulated rainfall was concurrently applied to the two adjacent plots. Rainfall intensity was determined before each rainfall experiment to regulate the uniformity and spatial distribution of rainfall [39]. A statistical analysis of several rainfall data for the study area identified two general categories of rainfall: (1) heavy rainfall intensity with short duration; and (2) weak rainfall intensity with long duration. Statistical analysis of rainfall in the first category over the most recent 3 years identified average rainfall intensity to be 7.37 mm in 5 min. Therefore, the average rainfall intensity of the artificial rainfall device was set to 7.5 mm over 5 min, or an artificial rainfall intensity of 90 mm h −1 .
Water 2020, 12, x FOR PEER REVIEW 6 of 19 Figure 3. Schematic of the side-spray rainfall simulation system used in the present study.

Data Analysis
An index representing the hydrodynamic characteristics of the slope was selected to accurately describe the mechanical relationship between the landscape patch and the rainfall erosion process.
The mean flow velocity (m s −1 ) is the product of different flow patterns of slope runoff and their correction coefficients.
In Equation (1), is the mean flow velocity (m s −1 ), represents the actual measured flow rate (m s −1 ), and is the correction coefficient, where values of for laminar flow, transition flow, and turbulent flow are 0.67, 0.7, and 0.8, respectively [40].
The sectional water depth was relatively shallow due to the long slope of the runoff plot and the influences of the slippery surface, raindrops, and patches of ground, resulting in large errors in the direct measurements. Therefore, the mean water depth was estimated by the following formula: ( In Equation (2), ℎ is the average surface water depth (mm), is the runoff over flow time (m 3 ), is the cross-section width of the runoff plot (m), and is the sampling time (s). The Reynolds numbers (Re) and Froude numbers (Fr) can reflect the flow state: In Equation (3) and Equation (4), is Reynolds number (dimensionless), means hydraulic radius (m), which is approximately equal to water depth h (m), represents the kinematic viscosity

Experimental Treatments and Measurement
Simulated rainfall experiments were conducted from July to August 2018. Soil water contents of all runoff plots were controlled to be equal by measurement of the soil water content of each plot before the experiment using time domain reflectometry (TDR) and adjusting soil water content if required ( Table 2). The slope of each plot was covered with a plastic sheet and left to stand for 24 h before the experiment. The duration of each simulated rainfall event in the experiment was~65min, and the water temperature was measured using a mercury thermometer before starting the simulated rainfall. The time required to produce initial runoff during a simulated rainfall event was recorded, and, after this point, samples of runoff and sediment were collected every 2 min for the first 10 min, and every 5min thereafter, until a total of 15 runoff samples were collected. The total runoff of each plot was measured after each experiment. After 24 h of sediment precipitation, the clear liquid super stratum was separated from the sediment, and sediment was transferred to a large aluminum box and dried in an oven at 105 • C for 24 h. The dye tracer method [23] was applied to 1-m sections of the upper, middle and lower slopes of the runoff plots to measure surface velocity by recording the time taken for KMnO 4 solution to pass through the measured section. Flow velocity was measured every 10 min during the entire experiment, and the average flow velocity at three different slope positions was taken to be the runoff velocity at that period.

Data Analysis
An index representing the hydrodynamic characteristics of the slope was selected to accurately describe the mechanical relationship between the landscape patch and the rainfall erosion process.
The mean flow velocity (m s −1 ) is the product of different flow patterns of slope runoff and their correction coefficients In Equation (1), v is the mean flow velocity (m s −1 ), v m represents the actual measured flow rate (m s −1 ), and k is the correction coefficient, where values of k for laminar flow, transition flow, and turbulent flow are 0.67, 0.7, and 0.8, respectively [40].
The sectional water depth was relatively shallow due to the long slope of the runoff plot and the influences of the slippery surface, raindrops, and patches of ground, resulting in large errors in the direct measurements. Therefore, the mean water depth was estimated by the following formula: In Equation (2), h is the average surface water depth (mm), Q is the runoff over t flow time (m 3 ), B is the cross-section width of the runoff plot (m), and t is the sampling time (s).
The Darcy-Weisbach's friction coefficient ( f ) and Manning's roughness coefficient (n) were used to represent the resistance along the slope flow: In Equations (5) and (6), f is the Darcy-Weisbach coefficient, and J is the hydraulic energy slope (m m −1 ), namely the tangent of slope gradient.
Runoff shear force refers to the runoff force that can result in the mobilization of soil particles: In Equation (7), τ is runoff shear force (Pa), ρ is the density of water (kg m −3 ), g is the gravity constant (9.8 m s −2 ), and h is mean water depth (m).
Runoff power (W) characterizes the power consumed by water flow per unit area and reflects the power required for a certain amount of soil erosion: In Equation (8), W is the flow power (W m −2 ). Analysis of variance (ANOVA) in the statistical software package IBM SPSS Statistics 25.0 (International Business Machines Corporation, Armonk, New York, USA) was used in the present study to test for significant differences among runoff rate, sediment transport rate, and hydrodynamic parameters of different patch combinations and numbers. The Shapiro-Wilk statistical method was used to test the normality of all dependent and independent variables, and all variables that did not conform to the normal distribution where transformed using the natural logarithm treatment. Excel 2016 was used to record and process experimental data. Regression analysis and correlation analysis among various indicators were conducted in SPSS 25.0. Origin 2017 (OriginLab, Northampton, MA, USA) was used to map the experimental results.

Effects of Different Types of Vegetation Patches on Runoff and Sediment Processes and Their Hydrodynamic Characteristics
Under the same rainfall condition, the flow yield time required for runoff to develop among the different combinations of vegetation patches was 0.76-2.48 min. The times required for runoff under S-road patches, strip patches, grid patches, and random patches were 0.13 min, 1.13 min, 0.96 min, and 1.72 min slower than that of bare land, respectively. ANOVA indicated that the grid patches required more time for initiation of runoff compared to that of other patch types ( Table 3). The runoff curves of different vegetation patches were similar under the simulated rainfall conditions (Figure 4a). The runoff curve could be divided into three obvious stages: (1) a rapid increase in the runoff rate with increasing rainfall duration during the early stage (0-15 min); (2) a gradual increase in runoff rate (15-45 min); and (3) gradually stabilization (45-60 min). However, the stable yield runoff rate varied widely among different vegetation patch combinations, with those of S-road patches, strip patches, grid patches, and random patches reduced by 16.12%, 49.55%, 51.35%, and 48.56% compared to that of bare land, respectively (p < 0.05). However, there was little difference in the stable yield runoff rate between grid patches and strip patches ( Table 3). The total runoff and average runoff yield rate showed similar changes.
The sediment transport response to patch combinations of different vegetation differed to that of runoff, with sediment transport showing a greater fluctuation compared to that of runoff (Figure 4b).
The sediment yields of bare land and S-road patches increased rapidly in the first 15 min of runoff and gradually decreased with increasing rainfall duration, finally tending to stabilize. However, the sediment yields of grid patches, strip patches, and random patches gradually increased with increasing rainfall duration, finally tending to stabilize, with the stabilization occurring earlier than that under bare land and S-road patches (Figure 4b). The stable sediment yield rates of S-road patches, strip patches, grid patches, and random patches were lower than that of bare land by 42.14%, 68.19%, 71.24%, and 86.54%, respectively (p < 0.05) ( Table 3). There was no significant difference in average sediment yield between grid patches and strip patches. However, the sediment yield of strip patches was smaller than that of grid patches during the early stages of sediment production, whereas the opposite was true during the later stage (Figure 4b). This result can be attributed to strips of vegetation located at the bottom of the runoff plot increasing resistance to flow resistance, thereby promoting water infiltration into the soil and trapping sediment, thereby reducing sediment yield during the initial stage of rainfall. However, sediment yield of strip patches began to increase with progressing rainfall duration due to the limited retention capacity of horizontal strips.
Connectivity paths, and consequently also flow velocity, varied among the different types of landscape patch combinations ( Table 4). The average flow rates of S-road patches, strip patches, grid patches and random patches were lower than that of bare land by 12.72%, 28.98%, 29.33%, and 46.64%, respectively (p < 0.05). However, there was no significant different in average velocity between strip patches and grid patches ( Table 4). The Reynolds number, flow shear stress, and stream power showed similar trends to that of the average flow rate. However, there were no major changes in flow depth among strips, grids, and random patches with poor connectivity paths, with flow depth ranging from 0.84 mm to 0.89 mm. However, these three patch combinations showed stronger flow resistance, with the Darcy-Weisbach resistance coefficient of random patches 59.83% higher than that of bare soil (p < 0.05). Patch combination had little influence on Manning's roughness, with onlyminor differences between S-road patches, strip patches, and grid patches (p < 0.05). However, there were large differences in the Manning's roughness coefficient of up to 0.153 between random patches and other patch combinations.
progressing rainfall duration due to the limited retention capacity of horizontal strips.
Connectivity paths, and consequently also flow velocity, varied among the different types of landscape patch combinations ( Table 4). The average flow rates of S-road patches, strip patches, grid patches and random patches were lower than that of bare land by 12.72%, 28.98%, 29.33%, and 46.64%, respectively (p < 0.05). However, there was no significant different in average velocity between strip patches and grid patches ( Table 4). The Reynolds number, flow shear stress, and stream power showed similar trends to that of the average flow rate. However, there were no major changes in flow depth among strips, grids, and random patches with poor connectivity paths, with flow depth ranging from 0.84 mm to 0.89 mm. However, these three patch combinations showed stronger flow resistance, with the Darcy-Weisbach resistance coefficient of random patches 59.83% higher than that of bare soil (p < 0.05). Patch combination had little influence on Manning's roughness, with only minor differences between S-road patches, strip patches, and grid patches (p < 0.05). However, there were large differences in the Manning's roughness coefficient of up to 0.153 between random patches and other patch combinations.

Effects of the Number of Vegetation Patches on Runoff and Sediment Processes and Their Hydrodynamic Characteristics
The time required to start generating flow increased with increasing number of patches. However, there was no significant difference in time required for generating runoff between patch numbers of 5 and 10, and the time required for flow generation with the number of 10 was the smallest (1.72 min). Figure 5a shows the changes in runoff rates among different patch numbers. The different patch numbers obtained similar runoff curves under simulated rainfall conditions ( Figure  5a). In the early stage of runoff (0-15 min), it increased rapidly as time went on, then entered the fluctuation stage (15-45 min), and finally became gradually stable (4-60 min). However, average

Effects of the Number of Vegetation Patches on Runoff and Sediment Processes and Their Hydrodynamic Characteristics
The time required to start generating flow increased with increasing number of patches. However, there was no significant difference in time required for generating runoff between patch numbers of 5 and 10, and the time required for flow generation with the number of 10 was the smallest (1.72 min). Figure 5a shows the changes in runoff rates among different patch numbers. The different patch numbers obtained similar runoff curves under simulated rainfall conditions (Figure 5a). In the early stage of runoff (0-15 min), it increased rapidly as time went on, then entered the fluctuation stage (15-45 min), and finally became gradually stable (4-60 min). However, average runoff rate decreased with increasing patch number, with significant differences in average runoff rate among the different patch numbers ( Table 5). The average yields 10, 15, and 20 vegetation patches decreased by 5.10%, 10.48%, and 16.94%, compared to that of 5 vegetation patches, respectively. The present study observed no significant difference between the combined total runoff yield rate and stable runoff yield rate under similar patch numbers.
Sediment yields showed similar variation to the runoff process among the different number of patches (Figure 5b). Although sediment yield increased rapidly in the first 10 min after runoff yield, there were significant differences in average sediment yield among different patch number combinations after 15 min (Figure 5b and Table 5). The sediment yields of 10, 15, and 20 vegetation patches decreased by 9.59%, 21.10% and 29.26% compared that of 5 vegetation patches, respectively (p < 0.05). A similar pattern was observed for total sediment yields of different vegetation patch number combinations. However, there was no significant differences in sediment yield between patch numbers 5 and 10 and between patch numbers 15 and 20. flow depth ranging from 0.84 mm to 0.89 mm. There were increases in surface roughness and runoff resistance with increasing number of patches in the vegetation landscape, with the Manning's roughness coefficient increasing from 0.114 to 0.130 and the Darcy-Weisbach resistance coefficient increasing from 10.62 to 13.99 under 10 and 20 vegetation patches, respectively. Under the same rainfall conditions, an increase in the number of vegetation patches in the vegetation landscape resulted in a decrease in flow shear stress and stream power, with flow shear stress decreasing from 2.37 to 2.27 from 5 to 20 vegetation patches, whereas stream power decreased significantly by 17.71%.   Figure 6). The relationship between runoff rate and single patch area could be described using a power function (y = 0.4502x 0.1274 , R 2 = 0.9247, p < 0.01). Sediment yield showed the same relationship, and regression analysis showed a significant power function relationship between sediment yield and patch area (y = 12.018x 0.2459 , R 2 = 0.9481, p < 0.01).
Water 2020, 12, x FOR PEER REVIEW 10 of 19 Figure 6. Between the rate of runoff (a), sediment transport (b), and patch area within an experiment. Table 7 and Figure 7 show the relationships between slope runoff and soil erosion under different patch types and quantity. All the relationships conformed to the power function = , (p < 0.01). The coefficient of the function can be expressed as soil loss per unit runoff and can be used as a parameter to reflect the sensitivity of soil erosion [22]. A comparison of sediment yield of different vegetation patch types showed that the order of the different patch types according to the value of coefficient a was: bare land > S-road patches > strip patches > grid patches > random patches, with a maximum of 147.437 and minimum of 33.396. In addition, coefficient a decreased with increasing patch number, with a maximum and minimum of 95.9 and 52.3, respectively.      Note: The data in the table represent averages ± standard error (SE). The same lower-case letter indicates no significant difference at p < 0.05 between the different numbers of vegetation patches.

The Relationship Between Runoff and Soil Loss Under Different Patch Types and Quantity
Water 2020, 12, 3201 11 of 16 Table 7 and Figure 7 show the relationships between slope runoff and soil erosion under different patch types and quantity. All the relationships conformed to the power function y = ax b , (p < 0.01). The coefficient a of the function can be expressed as soil loss per unit runoff and can be used as a parameter to reflect the sensitivity of soil erosion [22]. A comparison of sediment yield of different vegetation patch types showed that the order of the different patch types according to the value of coefficient a was: bare land > S-road patches > strip patches > grid patches > random patches, with a maximum of 147.437 andminimum of 33.396. In addition, coefficient a decreased with increasing patch number, with a maximum andminimum of 95.9 and 52.3, respectively. Note: x, surface runoff (mm); y, soil loss (t km −2 ).

The Relationship Between Runoff and Soil Loss under Different Patch Types and Quantity
Water 2020, 12, x FOR PEER REVIEW 10 of 19 Figure 6. Between the rate of runoff (a), sediment transport (b), and patch area within an experiment. Table 7 and Figure 7 show the relationships between slope runoff and soil erosion under different patch types and quantity. All the relationships conformed to the power function = , (p < 0.01). The coefficient of the function can be expressed as soil loss per unit runoff and can be used as a parameter to reflect the sensitivity of soil erosion [22]. A comparison of sediment yield of different vegetation patch types showed that the order of the different patch types according to the value of coefficient a was: bare land > S-road patches > strip patches > grid patches > random patches, with a maximum of 147.437 and minimum of 33.396. In addition, coefficient a decreased with increasing patch number, with a maximum and minimum of 95.9 and 52.3, respectively.

Discussion
Vegetation patches play an important role in the prevention and control of soil erosion and have important effects on surface runoff, sediment transport, and hydrodynamic parameters [41][42][43]. This study monitored runoff and erosion resulting from simulated rainfall under the same vegetation coverage rates, but with combinations of different vegetation patches. The results showed that different vegetation patches types and numbers resulted in significantly reduced runoff and sediment production compared to those of bare land. The results of the present study are consistent with those of [27,31,44], who demonstrate that vegetation patches significantly reduce soil erosion, improve soil structure, increase soil porosity, and improve the resistance of soil to erosion. Previous studies have shown that surface mulch can increase the resistance of soil to water erosion [42,45,46] being contrary for bare soils [47,48]. The present study showed that vegetation patches of different types and numbers can reduce runoff velocity and flow sediment concentration (Table 3), improve flow resistance, and reduce runoff shear force and flow power by increasing surface roughness and runoff path extent (Table 5). An increase in the Darcy-Weisbach resistance coefficient and a decrease in flow shear stress indicated that more energy was used to overcome water flow resistance, resulting in less energy being available for soil erosion and sediment transport.
Previous studies have demonstrated a relatively clear relationship between vegetation coverage and soil erosion, and there has also been extensive study of the effect of vegetation on water flow resistance [43,49]. However, the majority of studies have focused on vegetation with a uniform distribution, including grass strips, grass carpet, and hedgerows, and relatively few studies have considered the relationship between landscape patches and hydrodynamics [50,51]. The lower rainfall and generally higher proportion of erosive rainfall in the arid and semi-arid Loess Plateau region have resulted in serious soil erosion [22,27], insufficient water resources, and fragmented distribution of vegetation patches [32,33]. The fragmentation of vegetation patches results in an increase in surface roughness and changes to the connectivity path, which in turn affect the path and strength of surface runoff and sediment transport on the Loess Plateau [45].
A strong interaction between vegetation patches and hydrologic process exist [43], and many studies have demonstrated that banded patches play an important role in soil and water conservation. For example, artificial grass zones placed at different locations can delay the generation of runoff compared with that of bare fields, thereby reducing the runoff coefficient by 4-20% and soil loss by >77% [27]. Slopes with mountain roads produce 2-3 times more runoff and 6-200 times more sediment than slopes with natural vegetation [52]. The present study showed that, under the same vegetation coverage rate, connecting paths differed among patches of different vegetation types, resulting in significant changes in the runoff process and sediment transport. The yield time of runoff and sediment transport was short for roads with good connectivity, resulting in the generation of more runoff. In contrast, the yield times were extended and yield was limited for patch combinations with poor connectivity, such as strip patches, grid patches, and random patches. This result can be mainly attributed to patch combinations with poor connectivity resulting in increased runoff paths and increased soil infiltration, thus reducing surface runoff [53]. In addition, the decreases in surface runoff, velocity, runoff shear force, and sediment transport capacity [50,53] resulted in great reductions in the sediment yields of vegetation patches with poor connectivity. Although different patch combinations showed the same results, the influence of patch number on runoff and sediment was lower than that of patch type [54]. This result can be mainly attributed to the fact that, although different numbers of vegetation patch combinations did not extend the runoff path, they did result in runoff passing through the vegetation patches many times, which increased flow resistance, reduced flow velocity, and shortened the distance of runoff through the bare land, thereby preventing the formation of large runoff [25,43].
The present study showed that the power function coefficient a between surface runoff and soil loss in different combinations of vegetation patches and vegetation coverage can be interpreted as the amount of soil loss per unit of runoff, and can be used as a parameter within the assessment of soil erosion. The value of the coefficient a is positively correlated with the susceptibility of soil to erosion [22]. The present study showed that the values of coefficient a for vegetation landscapes with poor connectivity were far less than that those of well-connected patch combinations due to the extension of runoff paths, reduction in flow rate, improvement in soil infiltration rate, and reduction in runoff, thereby reducing the susceptibility of soil to erosion. The coefficient a decreased with the increasing patch number (Table 7). This results can be mainly attributed to the increase in vegetation patch numbers, shortening of the bare land runoff path and increasing surface roughness, thus resulting in a decrease in surface runoff velocity and an increase in soil infiltration [40,45]. In addition, the main vegetation species examined in the present study was Potentilla chinensis, which is characterized by fusiform root tubers and a developed root system, thereby greatly improving the resistance of surface soil to water erosion [55,56].
The results of the present study showed that strip patches, grid patches, random patches, and high-density patch combinations can be used as the methods of identifying appropriate vegetation types and extent within the construction of vegetation for control of soil erosion on the Loess Plateau. The optimal allocation of vegetation patches on slopes not only reduces soil and water loss but also changes the runoff and sediment transport process. The mode used to connect vegetation patches results in changes to the flow resistance and runoff connecting paths, as well as affects the water-sediment transport process and hydrodynamic parameters [19].
The scientific and rational optimization of vegetation can be an effective means of controlling soil erosion on the Loess Plateau and can promote sustainable development of the Yellow River Basin. However, the majority of past studies on the optimal allocation of vegetation have focused on the impact of changes in land use and vegetation cover on hydrological processes, while ignoring the comprehensive impact of vegetation landscape patches on runoff flow resistance and hydrological connectivity [52,57]. The low rainfall and high evaporation of the arid and semi-arid Loess Plateau region results in patch distributions of vegetation [29]. The optimization of the allocation of vegetation patches is important under limited water resources. The present study explained the mechanism of sediment yield on a slope by examining changes in sediment yield and hydrodynamic parameters of vegetation patches of different types and quantities, following which the optimal slope vegetation distribution pattern was determined to provide a reference for the optimal allocation of artificial vegetation in the Loess Plateau vegetation restoration process. The results of the present study are of great significance for establishing the quantitative relationship between patterns of landscape vegetation patches and hydrodynamic parameters, which can be applied to hydrological process models. It is generally accepted that many factors affect slope soil erosion, particularly rainfall intensity, slope, and vegetation coverage [26,30,58,59]. However, the present study did not consider the effects of other vegetation coverage, rainfall intensity, and slope conditions on soil erosion, which was not conducive to the calibration of hydrological model parameters. Future studies should therefore conduct comprehensive studies to determine the effects of vegetation patches on runoff and sediment transport under different conditions.

Conclusions
Two types of experiments were designed under the same vegetation coverage rate to determine whether vegetation patches can reduce runoff and sediment. The main hypothesis was to identify the effects of the type and number of vegetation patches on the hydrodynamic parameters of runoff and sediment. The results showed that the types and numbers of vegetation patches play a significant role in both runoff and sediment detachment. The combination of different vegetation patches showed a significant reduction in the runoff rates and sediment volumes but an increase in surface roughness and a flow resistance. In addition, we observed a reduction in hydraulic shear force and runoff power. Patch combinations of poorly connected vegetation landscapes registered stronger flow resistance and had a large impact on flow and sediment yield. Under a uniform distribution of vegetation patches, the runoff rate and sediment yield decreased significantly with an increased number of patches. Although the increase in the number of vegetation patches also resulted in a decrease in flow shear stress and stream power to different degrees, the differences between the combinations with similar patch numbers were not significant. The correlation between runoff and soil erosion, considering different patch types and vegetation coverages, conformed to the power function relationship. The coefficient a of the power function represented the sensitivity of soil to be eroded. The sensitivity of soil to erosion decreased with an increasing number of vegetation patch types, while the sensitivities of patch combinations with poor connectivity were lower than those with good connectivity. We concluded that, from this perspective, the optimization of vegetation in the Loess Plateau region requires sufficient consideration to reducing the connectivity of vegetation patches and increasing the density of patches.