Rainfall intensity and inflow rate effects on hillslope soil erosion in the Mollisol region of Northeast China

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1 Nat Hazards (2015) 79: DOI /s y ORIGINAL PAPER Rainfall intensity and inflow rate effects on hillslope soil erosion in the Mollisol region of Northeast China Leilei Wen 1,2 Fenli Zheng 1,2 Haiou Shen 1,2 Feng Bian 1,2 Yiliang Jiang 2,3 Received: 9 December 2014 / Accepted: 30 May 2015 / Published online: 13 June 2015 Springer Science+Business Media Dordrecht 2015 Abstract Soil erosion in the Mollisol region of Northeast China is increasingly severe and directly affects national food security and sustainable development. However, few attempts have been made to create a clear distinction between the effects of rainfall and inflow on hillslope soil erosion. A laboratory study was conducted to discuss the roles and contributions of rainfall intensity and inflow rate to hillslope soil erosion and to fit equations based on variations of rainfall intensity and inflow rate (RI? IR) for soil erosion. A soil pan (8 m long, 1.5 m wide and 0.6 m deep and with an adjustable slope gradient of 0 35 ) was subjected to designed rainfall intensities (0, 50 and 100 mm h -1 ) and inflow rates (0, 50 and 100 mm h -1 ). The results showed that the effects of RI? IR treatments on hillslope soil loss were significantly greater than those on runoff. Furthermore, the effect of rainfall intensity on hillslope soil loss was significantly greater than the effect of inflow rate. Under the same total water supply, an increase in rainfall intensity resulted in greater average soil loss rates and stronger fluctuations in soil loss than an increase in the inflow rate. The occurrence of rill erosion significantly increased sediment transport capacity on the hillslope, which resulted in an increase in soil loss. Utilizing rainfall intensity and inflow rate, runoff and soil loss equations were generated and validated, and the performances of the two equations were satisfactory. Furthermore, it was determined that both equations are most applicable to the prediction of hillslope soil erosion under long rolling hillslope conditions. For the Mollisol region of Northeast China, the key factor affecting soil erosion on hillslopes is soil particle dispersion caused by rainfall. Therefore, taking measures to cover the soil, such as corn straw mulching, would & Fenli Zheng flzh@ms.iswc.ac.cn College of Natural Resources and Environment, State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest A & F University, Yangling , Shaanxi, People s Republic of China Institute of Soil and Water Conservation, CAS & MWR, No. 26, Xi nong Road, Yangling , Shaanxi, People s Republic of China Institute of Soil and Water Conservation, Northwest A & F University, Yangling , Shaanxi, People s Republic of China

2 382 Nat Hazards (2015) 79: effectively reduce rainfall erosivity and have significant positive effects on soil erosion prevention and control. Keywords region Rainfall intensity Inflow rate Soil erosion Soil loss equation Mollisol 1 Introduction The Mollisol region is an important commodity grain production base in China. The soil erosion status of this region directly affects water quality in local streams and rivers, national food security and agricultural sustainability (Yu et al. 2003; Liu et al. 2010). Soil erosion belongs to a natural hazard, which has intensified debris flow, flood disaster, desertification, etc. In recent decades, soil erosion and land degradation have become increasingly severe in the Mollisol region, which is one of the most critical regions in China facing potential soil erosion issues (Yang et al. 2003; Liu et al. 2011; Fang et al. 2012). The A-horizon thickness of the soil profile in the region is only cm at present, which is the result of a decrease of cm due to severe soil erosion that has occurred since the Mollisol land was largely cultivated in the 1950s (Zhang et al. 2007). Additionally, the viscous parent material under the Mollisol layer contains very little organic matter, which can hardly foster the plant growth. The Mollisol resource is precious because it is difficult to regenerate (Xu et al. 2010). It takes years to form 1 cm of Mollisol. Therefore, it is very important to control soil erosion, protect soil productivity and increase crop production. Although the cultivation history of the Mollisol region is shorter than that of other regions in China, severe soil erosion is known to be widespread across this region (Wang et al. 2009). Widespread soil erosion has occurred because most croplands are located on long rolling hillslopes in gentle, hilly areas (Cui et al. 2007). These hillslopes are so susceptible to soil erosion that the area affected is quickly expanding (Xu et al. 2010). The long slope length and gentle gradient are two of the most important geomorphic characteristics of the Mollisol region. Most slope gradients are between 1 and 8. Although the slope gradients are gentle, soil loss is large. Soil erosion in this region has been proven to be more severe than recognized before (Cui et al. 2007; Liu et al. 2010). Soil erosion studies on the Mollisol region of Northeast China have been carried out for several years. However, only a few studies have analyzed the soil erosion mechanism using runoff plot experiments and model fitting methods (e.g., Zhang et al. 1992; Cui et al. 2007) in the Chinese Mollisol region. Other studies have focused on soil erosion severity descriptions, influence factors and management measures (Yang et al. 2003; Xu et al. 2010; Liu et al. 2011; Fang et al. 2012; Dong et al. 2013). Ellison (1944, 1947a, b, c) divided the erosion process into rainfall erosion, runoff erosion and rainfall transport, and runoff transport. A dual soil pan system was used to investigate the effects of rainfall intensity, slope gradient, surface hydrological conditions and sediment concentration on loessial soil erosion (Huang 1998; Huang et al. 1999; Zheng et al. 2000). The results showed that both rainfall erosion and runoff erosion played significant roles in soil erosion. There are significant effects of soil properties on soil erodibility (Korkanc et al. 2008; Yuri et al. 2011; Li et al. 2015). Wang et al. (2013) summarized soil properties from four main soil regions in China (the Mollisol region, the Cambisol region, the Ultisol region and

3 Nat Hazards (2015) 79: the Entisol region) according to field station data and a literature review. The differences in the soil particle distribution, soil organic matter content, etc., caused different soil erodibility (Cheng et al. 2008). The differences in soil properties probably cause different responses of soil erosion to rainfall intensity and inflow rate. However, few studies of this topic have been conducted in the Mollisol region of Northeast China. Therefore, modeling soil erosion based on rainfall intensity and inflow rate is necessary to evaluate the effects of rainfall and inflow on Mollisol hillslope soil erosion. Walker et al. (1977) noted that the sediment transport rate under rainfall intensity was 5.0 times higher than that under the same equivalent inflow rate. Guy et al. (1987) proposed that rainfall and runoff resulted in 85 and 15 % of sediment transport capacity, respectively. An et al. (2013) noted that soil loss decreased by % on Mollisol hillslopes when nylon netting was placed over the soil pan to eliminate raindrop impact. In addition, Fullen (1998) noted that leys were highly effective in protecting soil from potentially erosive rains. Although rainfall has significant influences on hillslope soil erosion processes, the effect of runoff on soil erosion should not be ignored, as it is still an important factor in the soil erosion process. Several important results regarding rainfall erosion and runoff erosion have been obtained in previous studies. Nevertheless, it is difficult to clearly distinguish between the effects of rainfall and runoff on soil erosion because of the complexity of experimental processes and observational constraints. To promote field studies in the Mollisol region of Northeast China, more experimental laboratory studies are necessary to first understand the processes of soil erosion under controlled conditions. Therefore, a laboratory study was conducted by placing the tested soil pan, supplying inflow equipment and a rainfall simulator system under such experimental conditions. This study analyzed different variations of rainfall intensity and inflow rate (RI? IR) to distinguish and discuss their roles in and contributions to hillslope soil erosion. Furthermore, the results were used to fit equations based on variations of RI? IR for soil erosion. 2 Materials and methods 2.1 Experimental equipment and materials The study was carried out in the rainfall simulation laboratory of the State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Yangling City, China. A sidesprinkler rainfall simulator system (Zheng and Zhao 2004) was used to apply rainfall. This rainfall simulator can be set to any selected rainfall intensity ranging from 20 to 300 mm h -1 by adjusting the nozzle size and water pressure. The fall height of raindrops was set at 16 m above the ground, which allows all the raindrops to reach terminal velocity prior to impact with the soil surface. The simulated rainfall, with drop uniformity [90 %, was similar to natural rainfall in both raindrop size and distribution (Zhou et al. 2000). The experiments were conducted in a slope adjustable soil pan 8 m long, 1.5 m wide and 0.6 m deep, with holes (2 cm aperture) at the bottom to facilitate water discharge. The slope gradient ranged from 0 to 35 with adjustment intervals of 5. The overflow tank used for supplying inflow was attached to the upper end of the soil pan (Fig. 1). A runoff collector was installed at the bottom of the soil pan, which was used for collecting runoff samples during the experimental process.

4 384 Nat Hazards (2015) 79: Simulated rainfall Sprayer Supply line valve Constant head tank Supply Over flow pipe Runoff collector Soil pan Slope adjusting device Over flow tank Fig. 1 A schematic representation of the experimental setup The soil used in this study was a Mollisol (USDA Taxonomy) with 3.3 % sand ([50 lm), 76.4 % silt (50 2 lm), 20.3 % clay content (\2 lm) and 23.8 g kg -1 soil organic matter. The pipette method and the potassium dichromate oxidation-external heating method (Liu 1996) were used to analyze soil texture and soil organic matter, respectively. The tested soil was collected at a 0 20 cm depth from the plow layer in a maize field in Liujia Town ( N, E), Yushu City, Jilin Province, in the center of the Mollisol region in Northeast China. The soil erosion conditions of the Mollisol region are different from those of other regions. The most of the landscape is the long slope length with gentle gradient, while long slope length can produce more confluence rates and gentle gradient also causes severe soil erosion (Cui et al. 2007; Liu et al. 2011). 2.2 Experimental procedures and design The tested soil was air-dried. The soil was not passed through a sieve to keep its natural state. But impurities such as organic matter and gravels needed to be removed from the soil. Before packing the soil pan, the soil water content of the tested soil was determined. This was used to calculate how much soil was needed to pack the soil pan and obtain target bulk densities for different soil layers. First, a 10-cm-thick layer of sand was packed at the bottom of the soil pan, which allowed free drainage of excess water. Then, the layers over the sand layer were divided into a sticky loess layer (simulating the plow pan) with a depth of 20 cm and a Mollisol layer (simulating the tilth layer) with a depth of 20 cm. The bulk densities for the sticky loess layer and the Mollisol layer were 1.35 and 1.20 g cm -3, respectively. Additional details about the packing process can be found in An et al. (2012). Slope gradients are mainly between 1 8, and sometimes they exceed 10 in the Mollisol region of Northeast China. Therefore, 10 was determined as the experimental slope gradient representing the gradient of severe soil erosion region. Moderate intensity of soil erosion is generally caused by momentary rainfall intensities C42.6 mm h -1, and in some cases, the momentary rainfall intensity has reached mm h -1 in the typical Mollisol region of Northeast China (Zhang et al. 1992). Thus, the 50 and 100 mm h -1 were designed as the representative rainfall intensities and inflow rates. After preparing the soil pan, a pre-rain with 30 mm h -1 rainfall intensity was applied to the experimental soil pan until surface flow occurred. The duration of this pre-rain was *40 min. One day after the pre-rain, calibrations of rainfall intensity and inflow rate were conducted to reach the experimental requirements prior to running experiments. Then, the

5 Nat Hazards (2015) 79: Table 1 Descriptions of variations of rainfall intensity and inflow rate Total water supply (mm h -1 ) Rainfall intensity (RI) (mm h -1 ) Inflow rate (IR) (mm h -1 ) Variation of RI and IR RI-100? IR RI-50? IR RI-0? IR RI-100? IR RI-50? IR RI-100? IR-100 soil pan was adjusted to a 10 gradient and subjected to the designed rainfall intensities (0, 50 or 100 mm h -1 ) and inflow rates (0, 50 or 100 mm h -1 ). Six experimental variations of rainfall intensity (RI) and inflow rate (IR) were tested (Table 1). Each variation was conducted three times. All experimental treatments had the same run time of 100 min. 2.3 Experimental measurements For each treatment, runoff samples were collected in 15-L buckets as runoff occurred. The samples were measured in 3- or 5-min intervals for the duration of the run (100 min). These samples were weighed and left to sit to allow suspended sediments to settle out. The clear supernatant was decanted, and the remaining sediment was oven-dried at 105 C and weighed to calculate sediment yield. For the treatment of rill occurrence, rill width and depth measurements were performed along each rill channel at intervals of 5 or 10 cm after the experiment (Shen et al. 2015). These measurements were used to calculate the rill volume, which in turn, to compute the soil loss caused by rill erosion. The soil loss was determined by multiplying the rill volume by the soil bulk density (Bewket and Sterk 2003). 2.4 Data analysis The average runoff rate and average soil loss rate were the mean of a whole experimental process. The 3-D surface figures of rainfall intensity, inflow rate and average runoff rate/ average soil loss rate for different variations of RI? IR were plotted using SigmaPlot 10.0 software (Systat Sofeware Inc, California, USA). The multiple linear regression analysis was performed to fit the runoff equation by SPSS 19.0 software (SPSS Inc, Chicago, IL, USA). A nonlinear fitting method was applied to fit the soil loss equation by MATLAB software (MathWorks Inc, Massachusetts, USA). To ensure the independence of the data used to establish and validate the equations, two-thirds of the data were randomly selected to establish the equations and the remaining one-third of the data were used to validate them. When validating the equations, the determination coefficient (R 2 ) and the Nash Sutcliffe simulation efficiency (E NS ) (Nash and Sutcliffe 1970) were used to evaluate the prediction accuracy of each equation. The R 2 value indicates the strength of the relationship between observed and simulated values. The E NS value indicates how well the plot of observed versus simulated values fits the 1:1 line. If the R 2 and E NS values are very close to one, the equation prediction is considered perfect. When R 2 [ 0.6 and E NS [ 0.5, the equation prediction is acceptable or satisfactory (Santhi et al. 2001).

6 386 Nat Hazards (2015) 79: The statistical analysis was performed using SPSS 19.0 software. Analysis of variance (ANOVA) was conducted to examine significant differences in runoff, soil loss and sediment concentration. For the results of multiple comparisons, the method of least significant difference (LSD) procedure was used and the values were statistically significant at the 95 % confidence level. 3 Results and discussion 3.1 Runoff and soil loss Table 2 displays runoff, soil loss and sediment concentration for different variations of rainfall intensity and inflow rate (RI? IR). Runoff increased with an increase in total water supply. Increases in rainfall intensity resulted in more runoff than increases in the inflow rate. This might be due to the effects of raindrop impact on soil dispersion. As rainfall intensity increased, raindrop impact increased correspondingly. This led to greater soil compaction and sealing, which decreased soil infiltration and resulted in more rainfall being converted into runoff. The changing trend in soil loss was similar to that of sediment concentration under the same total water supply (Table 2). For a total water supply of 100 mm h -1, the RI-100? IR-0 treatment resulted in the greatest soil loss and sediment concentration. The two values were 6.4 and 5.5 times greater than those from the RI-50? IR-50 treatment, and and times greater than the results from the RI-0? IR-100 treatment. An increase in rainfall intensity in variations of RI? IR under the same total water supply caused an increase in raindrop impact. This induced greater dispersion and splash of hillslope soil particles. It also caused an increase in hillslope runoff, which promoted soil particle transport. There were some differences in the trends between soil loss and sediment concentration for variations of RI? IR under different total water supplies (Table 2). Soil loss significantly increased with increasing total water supply. The reason was that an increase in total water supply produced greater rainfall erosivity and runoff erosivity, which caused soil loss to increase. However, there was no significant difference in sediment concentration for variations of RI? IR where total water supplies were 100 and 150 mm h -1. When water Table 2 Runoff, soil loss and sediment concentration for different variations of rainfall intensity and inflow rate Total water supply (mm h -1 ) Variation of rainfall intensity (RI) and inflow rate (IR) Runoff (mm) Soil loss (kg m -2 ) Sediment concentration (g L -1 ) 100 RI-100? IR d a 0.57c 4.67b RI-50? IR de 0.09d 0.84c RI-0? IR e 0.00e 0.03d 150 RI-100? IR b 0.96b 4.57b RI-50? IR c 0.12d 0.72c 200 RI-100? IR a 4.30a 14.91a a Values followed by identical letters are not significantly different at P \ 0.05 according to the LSD test

7 Nat Hazards (2015) 79: supply was increased from 100 to 150 mm h -1, soil loss increased, but the rate of increasing water supply was greater than that of increasing soil loss. On the other hand, sediment concentration under a total water supply of 150 mm h -1 was similar to that at 100 mm h -1, while sediment concentration based on a total water supply of 200 mm h -1 was significantly higher than concentrations at 100 and 150 mm h -1. This result occurred because the rate of increasing soil loss was significantly greater than that of increasing water supply from 150 to 200 mm h -1. Overall, the effects of rainfall intensity on runoff and hillslope soil loss were significantly greater than those of inflow rate given the same total water supply. That is, under the same total water supply, an increase in rainfall intensity would result in greater runoff and soil loss than an increase in the inflow rate. In treatments of RI? IR with different total water supplies, soil loss was a better indicator of soil erosion rates than sediment concentration. Runoff rates for variations of RI? IR under the total water supplies of 100 and 150 mm h -1 are plotted over time in Fig. 2, which was used to analyze the effects of variations of RI? IR on hillslope runoff processes. Under the same total water supply, an increase in rainfall intensity accelerated the initial runoff time, caused greater average runoff rates and resulted in stronger fluctuations in runoff than increases in the inflow rate. As mentioned above, this was due to the effects of increases in raindrop impact on soil compaction and runoff on the hillslope. Under the condition of only rainfall, the effects of raindrop impact dispersion and turbulence on runoff were stronger. Fluctuations in runoff rates were also greater, with the 100 mm h -1 rainfall intensity without an inflow rate (RI-100? IR-0) treatment producing the strongest fluctuations. In contrast, under the 100 Runoff rate (mm h 1 ) Runoff rate (mm h 1 ) RI IR mm h 1 RI-50 + IR-50 RI-0 + IR RI IR mm h 1 20 RI-50 + IR Run time (min) Fig. 2 Runoff rates versus run time for treatments of rainfall intensity and inflow rate under total water supplies of 100 and 150 mm h -1

8 388 Nat Hazards (2015) 79: condition of only inflow, water flowed through the soil surface in the form of sheet flow. Without rainfall scouring, changes in runoff rates depended solely on fluctuations in sheet flow (Parlange et al. 1981; Kirkby 1990; Baird et al. 1992; Tayfur and Kavvas 1994) and blockage by large soil particles. Thus, fluctuations in runoff rates were smaller under the condition of only inflow than under the condition of only rainfall. For instance, the 100 mm h -1 inflow rate without rainfall intensity (RI-0? IR-100) treatment exhibited the smallest fluctuations. Soil loss rates versus run time for variations of RI? IR under the total water supplies of 100 and 150 mm h -1 are plotted in Fig. 3, which was used to analyze the effects of variations of RI? IR on hillslope soil erosion processes. Under the same total water supply, an increase in rainfall intensity resulted in greater average soil loss rates and stronger fluctuations than changes in the inflow rate. Soil loss rates sharply increased at the beginning of the test and then decreased before finally stabilizing over time. Loose soil particles were relatively abundant at the beginning of the experiment, leading to greater soil loss rates in the early minutes of each test (Parsons and Stone 2006). The RI-100? IR-50 treatment had the greatest maximum soil loss rate at g m -2 h -1. The second greatest loss rate occurred during the RI-100? IR-0 treatment, with g m -2 h -1 lost, next followed the RI-50? IR-50 and RI-50? IR-100 treatments. The RI-0? IR-100 treatment produced the smallest maximum soil loss rate. Within the experimental process, soil erosion intensity gradually decreased and tended to reach equilibrium. Thus, soil loss rates decreased and fluctuated predictably. 3.2 Contributions of rainfall intensity and inflow rate to soil erosion The contributions of rainfall intensity to runoff and soil loss were analyzed by comparing runoff and soil loss results from different variations of RI? IR (Table 3). The impact of Fig. 3 Soil loss rates versus run time for treatments of rainfall intensity and inflow rate under total water supplies of 100 and 150 mm h -1 Soil loss rate (g m 2 h 1 ) mm h 1 RI IR-0 RI-50 + IR-50 RI-0 + IR Soil loss rate (g m 2 h 1 ) mm h 1 RI IR-50 RI-50 + IR Run time (min)

9 Nat Hazards (2015) 79: Table 3 Analysis of contributions of rainfall intensity to runoff and soil loss Variation of rainfall intensity (RI) and inflow rate (IR) Increasing rainfall intensity (mm h -1 ) Contribution to runoff (%) Contribution to soil loss (%) Soil erosion pattern RI-0? IR Sheet erosion RI-50? IR-100 Sheet erosion RI-50? IR Sheet erosion RI-100? IR-50 Sheet erosion RI-50? IR Sheet erosion RI-100? IR-100 Sheet erosion? rill erosion rainfall intensity on soil loss was significantly greater than that on runoff. When sheet erosion was dominant on a hillslope, increasing rainfall intensity by 50 mm h -1 (i.e., rainfall intensity changing from 0 to 50 or 50 to 100 mm h -1 ) caused on average 47.9 % of runoff and 94.3 % of soil loss. Once rill erosion occurred on the hillslope, increasing rainfall intensity by 50 mm h -1 (i.e., rainfall intensity changing from 50 to 100 mm h -1 ) contributed 39.6 % to runoff and 97.2 % to soil loss. The results indicated that contributions of rainfall intensity to hillslope runoff and soil loss, respectively, increased and decreased with soil erosion patterns evolving from sheet erosion to rill erosion. Thus, the contribution of rainfall intensity to runoff in the RI-100? IR-100 treatment was smaller than that in the RI-50? IR-100 treatment. In addition, most studies have shown that the magnitude of soil loss on the hillslope depended on whether gully erosion occurred (e.g., Han et al. 2002; Poesen et al. 2003). The occurrence of rill erosion in this study greatly increased sediment transport capacity on the hillslope, which resulted in an increase in soil loss. Therefore, contributions of rainfall intensity to runoff and soil loss stemmed from the magnitude of rainfall intensity and the evolution of soil erosion patterns. Although the primary effects on runoff and soil loss stemmed from rainfall intensity, contributions of the inflow rate to soil erosion should not be neglected because inflow is also important. When sheet erosion was dominant on the hillslope, increasing the inflow rate by 50 mm h -1 caused on average 40.1 % of runoff and 33.8 % of soil loss (Table 4). Notably, the contribution of inflow rate to soil loss was lower than that to runoff. Once rill erosion occurred and played a leading role on the hillslope, as happened when the inflow rate was increased by 50 mm h -1 from the RI-100? IR-50 treatment to the RI-100? IR-100 treatment, the contribution of inflow rate to soil loss increased to 77.6 %. The combined effects of increasing the inflow rate magnitude and the evolution of soil erosion patterns led to this result. Table 4 Analysis of contributions of the inflow rate to runoff and soil loss Variation of rainfall intensity (RI) and inflow rate (IR) Increasing inflow rate (mm h -1 ) Contribution to runoff (%) Contribution to soil loss (%) Soil erosion pattern RI-100? IR Sheet erosion RI-100? IR-50 Sheet erosion RI-50? IR Sheet erosion RI-50? IR-100 Sheet erosion RI-100? IR Sheet erosion RI-100? IR-100 Sheet erosion? rill erosion

10 390 Nat Hazards (2015) 79: Equation fitting between variations of RI 1 IR and soil erosion Runoff equation The 3-D surface figure of rainfall intensity, inflow rate and average runoff rate for different variations of RI? IR is plotted in Fig. 4. This 3-D surface was approximated to the hyperplane, which was in line with the multiple linear regression relationship [Eq. (1)]. Q ¼ 1:094RI þ 0:873IR 29:803 ðr 2 ¼ 0:98; P\0:05; n ¼ 12Þ ð1þ where Q is the average runoff rate (mm h -1 ); RI is rainfall intensity (mm h -1 ); IR is the inflow rate (mm h -1 ). The above relationship acknowledges that when rainfall and inflow coexisted on the hillslope, the influence coefficient for rainfall intensity on the average runoff rate was higher than that for the inflow rate on average runoff. If the inflow rate remained constant, a double rainfall intensity would result in the average runoff rate increasing times. When rainfall intensity was constant, a double inflow rate would cause the average runoff rate to increase times Soil loss equation By plotting the 3-D surface of rainfall intensity, inflow rate and average soil loss rate for different variations of RI? IR (Fig. 5), it was determined that this 3-D surface was not in conformity with the linear regression relationship. The effect of rainfall intensity on soil erosion is usually represented by Eq. (2): E ¼ ari b where E is the soil loss rate (g m -2 h -1 ); a is a constant; b is an exponent. Walker et al. (1978) investigated the sediments of three different particle sizes and noted that the average b value was Meyer (1981) noted that the b value was ð2þ Fig. 4 Relationships of average runoff rate to rainfall intensity and inflow rate

11 Nat Hazards (2015) 79: Fig. 5 Relationships of average soil loss rate to rainfall intensity and inflow rate *2.00 when the soil clay content was \20 %. Parsons and Stone (2006) identified the b value ranged from 1.81 to 4.21 by studying three types of soil under variable rainfall intensities. The size of the a value varies with the soil. It is generally believed that the a value is related to soil erodibility. Rainfall resulted in runoff (Parsons and Stone 2006). Runoff inversely affected raindrop impact. In fact, the inflow rate represented runoff from upslope, which had significant impacts on downslope detachment, transportation and deposition processes (Zheng et al. 2004). Guy et al. (1987) proposed that rainfall and runoff resulted in 85 and 15 % of sediment transport capacity, respectively. Thus, the soil loss rate for different variations of RI? IR was a summation of soil loss rates caused by rainfall intensity and the inflow rate. The soil loss rate on the hillslope is: E ¼ E RI þ E IR ð3þ where E RI is the soil loss rate caused by rainfall intensity (g m -2 h -1 ) and E IR is the soil loss rate caused by the inflow rate (g m -2 h -1 ). The soil loss rate caused by the inflow rate was also expressed according to Eq. (2). Substituting Eq. (2) in Eq. (3), Eq. (4) becomes: E ¼ a 1 RI b1 þ a 2 IR b2 ð4þ where a 1 and b 1 are the constant and exponent of rainfall intensity and a 2 and b 2 are the constant and exponent of the inflow rate. The values of a 1 and a 2 are related to soil erodibility; a 1 is equal to a 2 in this study because the same soil type (Mollisol) was used. Thus, a replaces a 1 and a 2. The relationship of rainfall intensity, inflow rate and average soil loss rate is nonlinear. Therefore, a nonlinear fitting method was applied to fit the above relationship. Additionally, during the specific implementation process, the trust region method was applied, and the physical meaning of the equations considered. Through the above methods, the equation with the optimal fit, based on an adjusted rainfall intensity factor and inflow rate factor, was obtained.

12 392 Nat Hazards (2015) 79: For the equation based on Eq. (4), the determination coefficient (R 2 ) was \0.6. Further analysis found that the prediction accuracy of this equation was poorer in the RI-100? IR-100 treatment, which resulted in a decrease in the total prediction accuracy of this equation. The reason was that the soil erosion pattern evolved from sheet erosion to rill erosion in this treatment. Once rill erosion occurred in the experiment, soil loss immediately and sharply increased. Thus, the RI-100? IR-100 treatment did not conform to the assumed condition that sheet erosion played an important role on the hillslope. The above factor decreases the prediction effectiveness of the soil loss equation. By removing the data from the RI-100? IR-100 treatment from consideration, a new fitting equation was established as follows: E ¼ 2:75E 04 RI 3:112 þ IR 2:424 R 2 ¼ 0:83; P\0:05; n ¼ 10 ð5þ According to Eq. (5), the exponents for rainfall intensity and inflow rate were and 2.424, respectively. This means the effect of rainfall intensity on soil erosion was higher than that of the inflow rate under the condition that sheet erosion was the primary soil erosion pattern on the hillslope. Furthermore, the effect of inflow rate on soil erosion represented by Eq. (2) was feasible. During erosion on the hillslope, rainfall influenced soil particle dispersion and production, while inflow affected soil particle transport. In the Mollisol region of Northeast China, the key factor affecting soil erosion on hillslopes is soil particle dispersion caused by rainfall. Thus, taking measures to cover the soil, such as corn straw mulching, would effectively reduce raindrop impact and have significant positive effects on soil erosion prevention and control Equation validation The determination coefficient (R 2 ) and Nash Sutcliffe simulation efficiency (E NS ) of Eq. (1) to average runoff rates for Mollisol in Northeast China were 0.97 and 0.95, respectively. The observed and simulated values of average runoff rates were greatly close (Fig. 6). The results from the validation of Eq. (1) indicate that it attained a satisfactory level of accuracy. The R 2 and E NS values of Eq. (5) compared to average soil loss rates in the study region were 0.87 and 0.86, respectively. This also satisfied the prediction accuracy requirements of the equation. The prediction results of Eq. (5) were acceptable Fig. 6 Comparison of observed and simulated values of average runoff rates for different variations of rainfall intensity and inflow rate Simulated value (mm h 1 ) Data points 1:1 line R 2 = E NS = 0.95 n = Observed value (mm h 1 )

13 Nat Hazards (2015) 79: Fig. 7 Comparison of observed and simulated values of average soil loss rates for different variations of rainfall intensity and inflow rate Simulated value (g m 2 h 1 ) Data points 1:1 line 200 R 2 = 0.87 E NS = 0.86 n = Observed value (g m 2 h 1 ) (Fig. 7). Furthermore, the establishment of Eq. (5) did not include the variations of RI? IR during which rill erosion or other gully erosion occurred. Therefore, Eq. (5) is suitable for the prediction of hillslope soil erosion where sheet erosion plays a major role, under the coexisting conditions of rainfall and inflow. Equations (1) and (5) both include factors of rainfall intensity and inflow rate and are based on a Mollisol hillslope and gentle slope gradient. Thus, the equations are most applicable to soil erosion predictions for croplands set on the long rolling hillslopes of the Mollisol region of Northeast China. 4 Conclusions A laboratory study focusing on the effects of rainfall intensity and inflow rate on hillslope soil erosion was conducted to discuss the roles and contributions of rainfall and inflow and to fit equations to RI? IR treatments and related soil erosion. The results showed that the effects of RI? IR treatments on hillslope soil loss were significantly greater than those on runoff. Furthermore, the effect of rainfall intensity on hillslope soil loss was obviously greater than the effect of inflow rate. Rill erosion greatly increased sediment transport capacity on the hillslope, increasing soil loss. Under the above condition, increases in the contributions of rainfall and inflow to runoff and soil loss stemmed not only from increasing the magnitude of rainfall intensity or inflow rate but also from the evolution of soil erosion patterns. The runoff and soil loss equations, based on rainfall intensity and inflow rate, were established and validated. The performances of the two equations were satisfactory. The equations are most applicable to the prediction of soil erosion from croplands on long rolling hillslopes. For the Mollisol region of Northeast China, the key factor in soil erosion on hillslopes is soil particle dispersion caused by rainfall. Therefore, taking measures to cover the soil, such as corn straw mulching, would effectively reduce rainfall erosivity and have significant effects on soil erosion prevention and control. Acknowledgments This study was funded by the National Natural Science Foundation of China (Grant No ) and the National Basic Research Program of China (Grant No. 2007CB407201).

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