Multifactor analysis and simulation of the surface runoff and soil infiltration at different slope gradients

The surface runoff and soil infiltration exert significant influence on soil erosion. The effects of slope gradient/length (SG/SL), individual rainfall amount/intensity (IRA/IRI), vegetation cover (VC) and antecedent soil moisture (ASM) on the runoff depth (RD) and soil infiltration (INF) were evaluated in a series of natural rainfall experiments in the South of China. RD is found to correlate positively with IRA, IRI, and ASM factors and negatively with SG and VC. RD decreased followed by its increase with SG and ASM, it increased with a further decrease with SL, exhibited a linear growth with IRA and IRI, and exponential drop with VC. Meanwhile, INF exhibits a positive correlation with SL, IRA and IRI and VC, and a negative one with SG and ASM. INF was going up and then down with SG, linearly rising with SL, IRA and IRI, increasing by a logit function with VC, and linearly falling with ASM. The VC level above 60% can effectively lower the surface runoff and significantly enhance soil infiltration. Two RD and INF prediction models, accounting for the above six factors, were constructed using the multiple nonlinear regression method. The verification of those models disclosed a high Nash-Sutcliffe coefficient and low root-mean-square error, demonstrating good predictability of both models.


Introduction
The surface rainfall and soil infiltration are the key factors affecting the soil erosion [1,2] by a highly nonlinear dynamic mechanism influenced by many factors. Studies on the runoff yield and soil permeability for individual rainfall events are very important for understanding and controlling erosion processes [3].
The rainfall is the dominant factor controlling the surface runoff and soil infiltration. The higher the rainfall amount, the higher the runoff volume [4]. A greater rainfall intensity does not necessarily lead to higher soil infiltration [5]. When the rainfall intensity is relatively small, its increase can induce the better permeability, but an excessive rain intensity may damage the top soil structure and seal the soil, as well as significantly reduce the infiltration rate [6,7]. The slope gradient and length significantly influence the runoff and infiltration. Fox et al [8] proved indirectly that the runoff volume was growing with the slope gradient under laboratory conditions. However, Govers [9] has revealed the opposite trend under field conditions. With other influence factors kept constant, the runoff volume became larger with the slope length, when the latter was relatively small [10]. However, when the slope length exceeds a threshold value, the runoff volume displays a downward trend [11,12]. Janeau et al [13] found that the steady final infiltration rate increased sharply as a result of a growing slope gradient in a series of laboratory experiments with 1.0 m 2 soil bins. Although there is no consensus on the slope gradient/length effects on the runoff and infiltration, the existence of the slope gradient and length threshold values is widely supported in studies [14][15][16]. The vegetation cover influences the runoff and infiltration changing the rainfall-runoff-infiltration process on the slopes [17,18]. The vegetation cover can significantly reduce the surface runoff by the interception of the rainfall, and increase the soil infiltration by reducing raindrop impacts [1]. The antecedent soil moisture is also considered the important factor controlling the runoff and infiltration [19][20][21]. The more the antecedent soil moisture and less the infiltration capacity, the larger the runoff volume [22]. However, Luk [23] indicated that effect of the antecedent moisture was not only confined to the enhanced runoff capacity in the tested soils, having the cohesive structure.
Since most previous studies discussed the effect of only one or two factors on the slope runoff or soil infiltration, it is topical to elucidate the effect of multiple factors on their patterns. Therefore, the object of this study, making use of the field data, is to (1) investigate the quantitative relationships between the slope runoff, soil infiltration and the influence factors, and (2) construct the prediction model of the slope runoff and soil infiltration in the course of individual rainfall events. The data were obtained in the course of natural rainfall events from 261 runoff plots of five field catchments in the southern China. The localities of these five catchments are depicted in figure 1. Main soil types and vegetation species, as well as several physical soil properties of the soil for these five catchments are shown in table 1. These five catchments (sites A, B, C, D and E) have 10, 12, 12, 13 and 8 runoff plots of different sizes, whose detailed parameters are also given in table 1.

Measurements
The runoff volume for a given period was used to randomly determine the frequency of measurements (ranging from 5 min to 30 min) for the collection of the surface runoff volume with a cylindrical container of a 3000 mL volume. After the collection and clarification of turbid water, the clear water volume was regarded as the runoff volume. The deposited sediment was air-dried and weighted to determine the sediment yield. The rainfall data were measured automatically by an electronic rain gauge.
There was one sample point per 25 m 2 to collect soil samples for determining soil mositure, and moisture levels were measured by the oven drying method. For each plot, the soil sampling points should be uniformly distributed over the slope surface. According to the weather forecast information, soil moisture measurements were carried out before the rainfall and, as soon as possible, after it.
The crown cover and undergrowth were assessed by the photographic method [1]. The specific steps are as follows: firstly, take three to five JPEG format photos with a digital camera to record the data on the current state of the crown cover and undergrowth; secondly, convert the JPEG photos into the ITFF format with a lab color channel using the Photoshop software package; finally, the crown cover and undergrowth are calculated using the Image-J software package. We chose three to five sampling points and repeated measurements 2-3 times per sampling point in each plot. The average value of the crown cover and undergrowth was regarded as the vegetation cover.
For a given individual rainfall event, let IRA, RD, INT represent the rainfall amount, runoff volume and vegetation intercept water, respectively, and assume that the evaporation and water filling of the concave over the slope surface during rainfall are negligible. Based on the water balance equation, the soil infiltration water (INF) can be assessed from the following expression:

INF=IRA-RD-INT
(1) Here the INT calculation refers to our previous study, and detailed information can be found elsewhere [24]. (ns) insignificant.

Analysis and simulation of runoff depth
The scatter diagrams for the average values of RD, INF and six factors were plotted, in order to study the quantitative relationship between RD and INF and influence factors for individual rainfall events as shown in figures 3 and 4. RD came down followed by its growth with SG increase from 5°to 35°. The fitted equation reached the significance level, and the coefficient of determination R 2 was 0.944. Assuming that the first derivative of the fitted equation is equal to zero, the hump (knee point) on the fitted curve was obtained as (20.35°, 1.20 mm). RD was growing followed by a fall with SL increase from 10 to 100 m. However, the fitted equation did not reach the significance level, and the knee point was located at (54.22 m, 17.70 mm). RD increased consistently as a result of an increase in IRA and IRI. Both fitted equations reached the significance level with R 2 being equal to 0.902 and 0.857, respectively. The fitted equation for RD and the vegetation cover (VC) displayed an exponential pattern, acquiring the significance level. RD went down sharply with VC for VC<50%, while a drop of RD was slight for VC>50%. RD decreased with a following rise with ASM. The fitted equation reached the significance level and R 2 was 0.9553. The negative hump (knee point) was observed at (10.01%, 1.25 mm), so RD fell down consistently with ASM for ASM<10.01%, while RD grew persistently for ASM>10.01%.
Based on the fitted relationships between RD and influence factors as shown in figure 3, the following multi-parameter nonlinear model for predicting RD was constructed by the regression analysis considering 70% of the data: (2) Note: Blue curves represent the confidence intervals at different significance levels.  Note: Blue curves represent the confidence intervals at different significance levels.

Discussion
The relationship between the six influence factors and the runoff and infiltration for individual rainfall events is systematically analyzed to get a deeper insight into the slope runoff and soil infiltration behavior. The correlation coefficients for IRA, IRI and RD, INF were over 0.60 (P≤0.01), indicating that the rainfall is a very important factor controlling RD and INF values. This was confirmed by earlier studies of Garcia-Rodeja and Gil-Sotres [25] and Huang et al [26,27]. Although higher infiltration rates are often observed with greater IRI, there appears to be no consensus in the literature on the explanation of this phenomenon [28]. Huang et al [5] found that the soil infiltration rate grew with IRI until a critical threshold was reached, its value ranging from 90 to 150 mm h -1 . VC can change the rainfall-runoff-infiltration mechanism and then affect the soil infiltration and slope runoff [29,30]. The results of this study demonstrate that their coefficients were 0.705 and 0.589 (P≤0.01), respectively. RD fell exponentially and INF grew logistically with VC. INF increased sharply and a reduction in RD was almost invariant when VC>60%. Previous studies by Marston [31] and Zhu et al [32] also proved that VC of 40-60% or more can significantly reduce runoff and increase infiltration. Karnieli and Ben-Asher [21], Ceballos and Schnabel [19] and Fitzjohn et al [20] suggested that ASM can also be an important factor controlling the slope runoff and soil infiltration. Zehe et al [33] indicated that ASM at the forest site can explain 92% of the variability in the runoff coefficients.  (2)

Conclusions
This study, based on the data from a series of natural rainfall events in the South of China, generated certain important information for better understanding of the quantitative relationships between the six factors (SG, SL, IRA, IRI, VC, ASM), runoff depth (RD) and infiltration (INF). An empirical model for RD and INF calculation based on the observation data using the above six factors is proposed. The results obtained are as follows: The correlation coefficients for IRA, IRI, VC and RD were over 0.7 (P≤0.01), while those for IRA, IRI, ASM and INF approached 0.7 (P≤0.01). RD decreased followed by its increase with SG and ASM, it grew with a further fall with SL, linearly growing with IRA and IRI and falling exponentially with VC. Meanwhile, RD was rising consistently with SG for SG<20.35°, and then falling continuously with SG for SG>20.35°. RD increased persistently with SL for SL<54.22 m and decreased consistently for SL>54.22 m. INF became higher and then lower with SG, linearly growing persistently with SL, IRA, and IRI, increased logistically with VC, and linearly lowering continuously with ASM. INF increased continuously with an increase in SG for SG<18.16°and was falling consistently for SG>18.16°. When VC was larger than 60%, RD was small and its reduction with an increase in VC was very slight, while INF was sharply growing. Two multi-parameter nonlinear models for predicting RD and INF were constructed using the regression analysis, and their applicability and feasibility were proved by the validation tests.