J. Mt. Sci. (2017) 14(3): 527-538 e-mail: jms@imde.ac.cn http://jms.imde.ac.cn DOI: 10.1007/s11629-016-3934-2

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Abstract: Understanding the relationship between hillslope soil loss with ephemeral gully and rainfall regime is important for soil loss prediction and erosion control. Based on 12-year field observation data, this paper quantified the rainfall regime impacts on soil loss at loessial hillslope with ephemeral gully. According to three rainfall parameters including precipitation (P), rainfall duration (t), and maximum 30-minute rainfall intensity (I30), 115 rainfall events were classified by using K-mean clustering method and Discriminant Analysis. The results showed that 115 rainfall events could be divided into three rainfall regimes. Rainfall Regime 1 (RR1) had large I30 values with low precipitation and short duration, while the three rainfall parameters of Rainfall Regime 3 (RR3) were inversely different compared with those of RR1; for Rainfall Regime 2 (RR2), the precipitation, duration and I30 values were all between those of RR1 and RR3. Compared with RR2 and RR3, RR1 was the dominant rainfall regime for causing soil loss at the loessial hillslope with ephemeral gully, especially for causing extreme soil loss events. PI30 (Product of P and I30) was selected as the key index of rainfall characteristics to fit soil loss equations. Two sets of

linear regression equations between soil loss and PI30 with and without rainfall regime classification were fitted. Compared with the equation without rainfall regime classification, the cross validation results of the equations with rainfall regime classification was satisfactory. These results indicated that rainfall regime classification could not only depict rainfall characteristics precisely, but also improve soil loss equation prediction accuracy at loessial hillslope with ephemeral gully. Keywords: Rainfall regime; Soil loss; Rainfall character indices; Loessial hillslope; Ephemeral gully

Introduction

Rainfall regime not only have complex interactions with soil hydrological responses (Morin et al. 2006), but also play a key role in water erosion process (Li et al. 2000; Nearing 2001; Bürger 2002; De Lima and Singh 2002; Endale et al. 2006; Moody and Martin 2009). Therefore, understanding the relations between soil loss and rainfall regime characteristics is not only important

Received: 10 November 2015 Revised: 29 April 2016 Accepted: 16 November 2016

Effects of rainfall regime and its character indices on soil

loss at loessial hillslope with ephemeral gully

HAN Yong1, 2 http://orcid.org/0000-0003-2369-0019; e-mail: hanyong2006@163.com

ZHENG Fen-li1, 3* http://orcid.org/0000-0002-3203-3427; e-mail: flzh@ms.iswc.ac.cn

XU Xi-meng3 http://orcid.org/0000- 0002-0058-5040; e-mail: xuxm@nwsuaf.edu.cn

* Corresponding author

1 State Key Laboratory of Soil Erosion and Dryland Farming on Loess Plateau, Institute of Soil and Water Conservation, Chinese Academy of Sciences, Yangling 712100, China

2 University of Chinese Academy of Sciences, Beijing 100049, China

3 Institute of Soil and Water Conservation, Northwest A&F University, Yangling 712100, China

Citation: Han Y, Zheng FL, Xu XM (2017) Effects of rainfall regime and its character indices on soil loss at loessial hillslope with ephemeral gully. Journal of Mountain Science 14(3). DOI: 10.1007/s11629-016-3934-2

© Science Press and Institute of Mountain Hazards and Environment, CAS and Springer-Verlag Berlin Heidelberg 2017

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for soil erosion mechanism and prediction model research, but also necessary for effective erosion control (Laflen et al. 1991). During the past decades, many researches had focused on the relations between soil loss and rainfall characteristics. Some studies showed that soil loss was influenced by the interaction of rainfall character indices such as precipitation (Wischmeier and Smith 1978), rainfall intensity (Lal 1976) and rainfall duration (Ran et al. 2012). Since rainfall characteristics (such as rainfall amount and intensity, rainfall duration and rainfall patterns) varied within different rainfall regimes, the relations between soil loss and rainfall regime also showed different variation trends (Wei et al. 2007; Fang et al. 2012; Peng and Wang 2012). In the Karst regions of Southwest China, Peng and Wang (2012) classified natural rainfalls into five regimes by using Hierarchical clustering method, and found that the rainfall regime with high precipitation, high intensity caused the severest soil loss on the hillslope without ephemeral gully. In red soil (Ultisols in the USDA Soil Taxonomy) area of south China, Huang et al. (2010) used runoff plot data to analyze the impact of rainfall regime on hillslope runoff and soil loss and proposed that rainfall regime with high rainfall intensity caused severest soil loss at slope scale. On the Loess Plateau of China, Wei et al. (2007) and Fang et al. (2008), based on runoff plot data, classified natural rainfalls into three regimes and presented that rainfall regime with high intensity and short duration caused the greatest proportion of runoff and soil loss at hillslope without ephemeral gully. However, currently, there is little data available for quantifying how rainfall regime affects soil loss at loessial hillslope with ephemeral gully.

Ephemeral gully erosion is the dominant erosion pattern on the hillslope (USDA 1992). Studies in Belgium, France, USA and the Loess Plateau of China indicated soil loss from ephemeral gullies occupied 19% to 80% of the total soil loss (Foster 1986; Spomer and Hjelmfelt 1986; Thomas et al. 1986; Thomas and Welch 1988; Auzet et al. 1990; Vandaele 1993, 1996; Poesen et al. 1996, 1998; Zheng and Gao 2000; Bingner et al. 2016). In recent 40 years, ephemeral gully erosion has been attached importance due to its crucial role in hillslope soil loss. Most of ephemeral gully erosion studies mainly focused on its distribution

characteristics (Foster 1986; Moore et al. 1988), evolution processes (Casali et al. 1999; Gong et al. 2011; Guo et al. 2015), affecting factors (Lentz et al. 1993; Vandaele et al. 1996; Wilson et al. 2008) and erosion susceptibilities (Lucà et al. 2011; Conoscenti et al. 2014; Angileri et al. 2015). Due to the difficulty of obtaining natural rainfall characteristics and soil loss data, there are few literatures showing how erosive rainfall regime affects hillslope soil loss with ephemeral gully by using field observation data.

Rainfall characteristic is one of most important factors in soil erosion prediction model. The Universal Soil Loss Equation (USLE) used rainfall erosivity (R) to express rainfall characteristic and R was calculated by total rainfall energy (E) multiple maximum 30 min rainfall intensity (I30) (Wischmeier and Smith 1978; Foster et al. 1982), which was widely applied and revised in a wide spatial range over the world. But it is worth noting that USLE was only designed to predict average annual soil loss caused by rill and interrill erosion, and could not be used to predict event based soil loss with other erosion patterns such as ephemeral gully and gully erosion (Foster et al. 2003). However, the area with ephemeral gully erosion occupied 75% of total area of whole hillslope in the hilly-gully region (Tang et al. 1983), and soil loss from ephemeral gully erosion area occupied 31% to 64% of total soil loss at hillslope scale on the Loess Plateau (Zheng and Gao 2000). Therefore, USLE would underestimate hillslope soil loss with ephemeral gully, especially on the Loess Plateau of China due to the great contribution of ephemeral gully erosion to total hillslope soil loss (Capra and Scicolone 2002; Jiang et al. 2005). Moreover, although MUSLE (Modified Universal Soil Loss Equation) could estimate event based soil loss by using product of runoff discharge and corresponding peak discharge volume to replace rainfall erosivity in the USLE (Zhang et al. 2009; Arekhi and Rostamizad 2011), rainfall regime was still not considered. To precisely estimate runoff discharge on the Loess Plateau, Wang and Huang (2008) incorporated rainfall intensity factor into SCS-CN (Soil Conservation Service-Curve number) method, and concluded that prediction accuracy of revised SCS-CN method was much higher than that of non-improved one. In addition, although the Ephemeral Gully Erosion

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Model (EGEM), which is developed by the U.S. Department of Agriculture, was used to estimate average annual soil loss from a single ephemeral gully (Woodward 1999), it did not perform well in various regions (Casalí et al. 1999; Nachtergaele et al. 2001; Capra and Scicolone 2002; Valcárcel et al. 2003; Capra et al. 2005). Therefore, it is important to investigate how the characteristics of erosive rainfall regime affects hillslope soil loss with ephemeral gully on the Loess Plateau, and to fit equations which enable to predict soil loss of individual rainfall event at loessial hillslope with ephemeral gully.

In this study, rainfall and soil loss data of 115 erosive rainfall events collected from hillslope with ephemeral gully from 2003 to 2014 were used to classify the rainfall regimes and to quantify the impacts of rainfall regime on soil loss at hillslope with ephemeral gully. The objectives of this study are: 1) to investigate the characteristics of rainfall regime and its character indices; 2) to determine responses of soil loss at hillslope with ephemeral gully to different rainfall regimes; and 3) to fit event based soil loss equation for different rainfall regimes and validate prediction accuracy of equations.

1 Materials and Methods

1.1 Study area description

The field observations were conducted at Fuxian Observatory for Soil Erosion and Eco-environment (36°5.4′N, 109°8.9′E) located at Wayaogou watershed, Fuxian County, Shaanxi Province of China (Figure 1). The study area is situated in loess hilly-gully region with elevation ranging from 1187 to 1374 m. Due to long-term cultivation, ephemeral gully on loessial hillslope of this area is completely developed with distribution density of 20 to 40 km km-2 (Zheng 2006) and interval distance of 10 to 25 m (Zhang et al. 1991). Mean annual precipitation is 576.7 mm and approximately 70% of precipitation concentrated in rainy season from June to September. The maximum monthly precipitation is equivalent to 70% of the annual total, and the maximum daily precipitation is 131 mm. The soil type of this area is Typic-Loessi Orthic Primosols (Chinese Soil

Taxonomy, 3rd edition 2001) developed from primitive or secondary loess mother materials, its depth evenly range within 50 to 130 m (Cheng et al. 2012).

1.2 Field runoff plot establishment and data collection

According to field survey of topography features, the runoff plot in this study was established on a representative hillslope with ephemeral gully (Zhu 1956) in 1988 and the observations were applied from 1989. The project area of runoff plot is 995 m2. Mean width of this plot is 13.5 m and the length is 73.7 m. The slope gradient varies from 5° at upslope to 35° at down-slope. The upper boundary of the runoff plot is the hilltop and the bottom boundary is down-slope. Therefore, the plot covered a whole ephemeral gully at the loessial hillslope (Figure 2). The runoff plot is surrounded by concrete block borders (extending 10 cm above the surface and 10 cm below the surface) for isolation. Surface treatment of this runoff plot is bare, fallow, tilled up and down along the slope direction at every early April according to the surface treatment of standard runoff plot described by USLE, and plowed depth is 20 cm. For this reason, although ephemeral gully is filled in partially or completely by tilth in early April, it still recurs in the same location every rain season.

A man-made “V” iron runoff gathering trough and three collecting tanks (the diameter of the three collecting tanks is 95 cm and height is 100 cm) were settled at the outlet of runoff plot to collect runoff and sediment. Nine-slot divisors (the diameter of slots is 9 cm, the height from the tank bottom to slots is 65 cm) were installed on the first and second collecting tank in case they could not hold all of the runoff and sediment in an extreme rainfall event. After each runoff event, water level in each tank was measured to calculate runoff volume, and three to ten runoff samples were collected with 1-liter plastic bottles from each collecting tank according to the water level of the tank. These samples were weighed and left to sit more than 24 hours 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.

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Rainfall events during rainy season were measured by the SJ1 auto-siphon udometer (made in Shanghai Meteorological Instrument Factory Co., Ltd.) which was placed nearby the runoff plot (10 m away from the bottom of the runoff plot). Rainfall character indices (i.e., precipitation, rainfall duration and rainfall intensity) of each rainfall event were then calculated based on the rainfall process curve. A total of 115 erosive rainfall events that generated runoff during 12 years from 2003 to 2014 were included in this study.

1.3 Data analysis

In this study, K-mean clustering analysis and Discriminant analysis were used to classify rainfall regime (Hong 2003). Before classification, cluster number and initial center should be designated by trial and error testing under numerous criteria (Perruchet 1983). When the most suitable cluster number was appointed, each data was assigned to ‘‘similar’’ center to form the class. The classification should meet the ANOVA criterion at the 95% confidence level. Pearson correlation analysis was used to select the key rainfall index that has the closest relationship with soil loss from 11 rainfall character indices.

Linear regression analysis was adopted to fit soil loss equation based on individual rainfall event. Before fitting equation, rainfall events without

antecedent rainfall within five days were selected to eliminate the impacts of initial soil moisture (Han et al. 2012). Cross validation was used to evaluate the accuracy of these fitted equations. When validating the equations, the determination coefficient (R2) and the Nash-Sutcliffe simulation efficiency (ENS) (Nash and Sutcliffe 1970) were used to evaluate the prediction accuracy of the fitting equation. The R2 value indicates the strength of relationship between observed values and calculated values. The ENS value indicates how well the observed value versus calculated value fits the 1:1 line. If the values of R2 and ENS are close to 1, the model prediction is considered ‘perfect’. If values of R2 and ENS are close to 0, the model

Figure 1 Location of study area and runoff plot in Wayaogou watershed.

Figure 2 The photo of runoff plot covered the whole ephemeral gully at loessial hillslope in the study.

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prediction is considered ‘poor’. When R2 > 0.6 and ENS > 0.5, the equation prediction is acceptable or satisfactory (Santhi et al. 2001).

2 Results and Discussions

2.1 Rainfall regime classification and characteristics

Based on precipitation (P), duration (t), and maximum 30 min rainfall intensity (I30), 115 erosive rainfall events were classified into three rainfall regimes by using K-mean clustering analysis. To test the distributions of three rainfall regimes, Discriminant analysis was used and the results showed that three rainfall regimes gathered in three concentrated area respectively (Figure 3), meaning that the classification results were quite satisfactory.

The characteristics of three rainfall regimes were quite different (Table 1). Average values of rainfall characteristic indices showed obvious differences. Rainfall Regime 1 (RR1) had large I30 (25.8 mm h-1) with low precipitation (19.3 mm) and short duration (2.2 h); Rainfall Regime 3 (RR3) had small I30 (6.0 mm h-1) with great precipitation (43.1 mm) and long duration (27.7 h); for Rainfall Regime 2 (RR2), precipitation (31.1 mm) was 61.1% larger than that of RR1 and 27.8% smaller than that of RR3, and both of duration (13.5 h) and I30 (12.6 mm h-1) were between those of RR1 and RR3

(Table 1). The classification results of rainfall regime agreed well with other studies conducted in the hilly-gully area of the Loess Plateau (Wei et al. 2007; Fang et al. 2008).

Table 1 also exhibited other characteristics of individual rainfall indices for three rainfall regimes. During 12 observation years from 2003 to 2014, the total frequency of RR1 were 65 times, accounting for 56.5% of the total rainfall events and the precipitation of RR1 occupying 37.2% of the total precipitation; while total frequency of RR2 and RR3 were 50 times, occupying the other 43.5% of the total rainfall events. The precipitation of RR2 and RR3 occupying 62.8% of the total precipitation.

Figure 3 Distribution of the three rainfall regimes by using Discriminant analysis based on K-mean clustering analysis.

Table 1 Characteristics of individual rainfall character indices for three rainfall regimes

Rainfall regime (Frequency /percent)

Rainfall character indices

P (mm)

t (h)

I (mm h-1) PI (mm2 h-1) I10 I15 I30 I60 Im PI10 PI15 PI30 PI60 PIm

RR1 (65/56.5%)

Max 63.0 6.7 123.0 115.4 90.0 59.4 40.6 9900.0 7524.0 5412.0 3564.0 3302.0Min 8.8 0.17 21.2 16.6 13.0 8.8 5.8 39.6 36.3 28.6 19.8 15.7Mean 19.3 2.2 47.4 33.6 25.8 15.0 12.6 1077.8 775.6 581.8 359.9 266.0Total (percent)

1254.3 (37.2%)

RR2 (30/26.1%)

Max 131.0 19.7 68.0 56.2 37.2 20.8 10.2 10178.7 9982.2 3930.0 2126.5 1320.1Min 12.6 8.5 6.6 4.6 3.0 2.4 1.2 41.6 41.5 38.8 30.5 11.7Mean 31.1 13.5 24.6 19.2 12.6 10.2 3.0 1321.2 1081.2 736.8 585.3 382.7Total (percent)

1258.6 (37.3%)

RR3 (20/17.4%)

Max 123.0 39.1 24.2 18.2 13.0 9.6 5.4 3463.4 3080.4 3034.4 2619.9 691.0Min 18.0 22.0 4.8 4.2 3.6 3.0 1.2 109.0 94.5 80.5 64.9 19.8Mean 43.1 27.7 13.2 9.2 6.0 2.6 0.6 531.9 493.1 466.8 356.1 115.3Total (percent)

862.8 (25.5%)

Notes: Percent in the rows of Rainfall Regime and P was the percentage of frequency and precipitation for three rainfall regimes account for total rainfall events and total precipitation, respectively.

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Mean precipitation and mean duration of individual rainfall event increased in the order of RR1, RR2, and RR3.

As one of the most important character indices, maximum rainfall intensity in certain duration could fairly preferable describe the rainfall energy in individual rainfall event (Lal 1976). Among three rainfall regimes, maximum rainfall intensity in certain duration (I10, I15, I30, and I60) and mean rainfall intensity (Im) in RR1 were the greatest, and then followed by RR2, and RR3. Mean I30 in RR1 and RR2 was 4.3 and 2.0 times greater than those in RR3, respectively; mean I60 in RR1 and RR2 was 5.8 and 3.9 times higher than that in RR3, respectively; and mean I30 and I60 in RR1 was 2.0 and 1.5 times larger than those in RR2, respectively. Furthermore, PIm showed the same trend as I30 and I60, but the products of precipitation and maximum rainfall intensity in certain duration (PI10, PI15, PI30 and PI60) among three rainfall regimes showed different trends. The products in RR2 were the highest, followed by RR1 and RR3. Mean PI30 in RR2 was 1.3 and 1.6 times greater than that in RR1 and RR3, respectively; mean PI60 in RR2 was 1.6 times higher than that in RR1 and RR3, respectively. Since precipitation and maximum rainfall intensity in certain duration of RR2 were both higher, its products of precipitation and maximum rainfall intensity in certain duration were the highest among three rainfall regimes.

2.2 Soil loss at hillslope with ephemeral gully for three rainfall regimes

Figure 4 showed annual rainfall frequency, precipitation, and soil loss for three rainfall regimes during 12-years observation. The frequency of RR1 occupied the largest proportion in most cases, ranged from 20.0% to 90.0% with a mean of 56.8%, and standard deviation was 17.4%; while frequencies of RR2 and RR3 were obviously lower than that of RR1, ranged from 0.0% to

50.0% (Figure 4(a)). But the annual precipitation did not act well with their frequency. Annual precipitation of RR1 occupied 41.3% of annual precipitation, ranged from 6.0% to 90.1%; while annual precipitation of RR2 and RR3 accounted for 35.4% and 23.3%, respectively (Figure 4(b)). Compared with frequency and precipitation, soil loss differences among three rainfall regimes were more obvious. Soil loss caused by RR1 accounted for 69.8% of the total soil loss; while soil loss induced by RR2 and RR3 only occupied 20.8% and 9.4%, respectively (Figure 4(c)).

Figure 4 Distribution of frequency, precipitation and soil loss for three rainfall regimes.

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Except that soil loss caused by RR2 in 2013 was over 8000 t km-2 yr-1, soil loss caused by RR2 and RR3 were both lower than 5000 t km-2 yr-1; while soil loss caused by RR1 exceeded 5000 t km-2 yr-1 in seven of 12 observation years; consequently, soil loss in these seven years exceeded 10,000 t km-2 yr-1, ranging from 12,000 to 26,000 t km-2 yr-1 (Figure 4(c)). Soil loss caused by RR1 in other five years was lower than 5000 t km-2 yr-1, which is crucial reason that annual soil loss in these five years was lower than 10,000 t km-2 yr-1, ranging from 1900 to 98oo t km-2 yr-1. It could be concluded that RR1 played a decisive role in soil loss and was the dominant rainfall regime for causing soil loss in study area.

To further quantify the relationship between soil loss and rainfall regime, 10,000 t km-2 yr-1 was selected as a threshold to divide 12-year observation data into two types (Table 2). The frequency, precipitation and soil loss of three rainfall regimes all showed different trend in two types. In Type I, when annual soil loss was over 10,000 t km-2 yr-1, RR1 occupied the largest proportion of precipitation with a mean of 47.5%, followed by RR2 and RR3 with a mean of 32.1% and 20.3%, respectively. Correspondingly, soil loss induced by RR1 occupied 78.7% of the annual soil loss on average and with the scope from 48.2% to 99.7%; while soil loss induced by RR2 and RR3 took up 15.7% and 5.5%, respectively. For Type II, when annual soil loss was lower than 10,000 t km-2 yr-1, RR2 occupied the largest proportion of precipitation with a mean of 44.8%, followed by RR3 and RR1 with a mean of 33.1% and 22.1%, respectively; and soil loss induced by RR1, RR2 and RR3 occupied 36.3%, 40.5% and 23.2% of the annual soil loss, respectively. Therefore, RR1 was not only the dominant rainfall regime causing soil loss at loessial hillslope with ephemeral gully, but

also the rainfall regime led to extremely intensive annual soil loss. In some year, annual soil loss caused by RR1 even exceeded 20,000 t km-2 yr-1.

Since rainfall event with high intensity could increase runoff rate and intensify soil loss (Ran et al. 2012), RR1 caused the severest soil loss among three rainfall regimes. Similar evidences were also obtained by Wang et al. (1998), Huang (2010) and Fang (2012). Therefore, prediction and preventing extreme soil loss caused by RR1 should be paid more attention.

2.3 Soil loss equations fitting based on individual rainfall event

2.3.1 Key rainfall character parameter selection

Pearson correlation analysis was performed to determine the key rainfall character parameter from 11 rainfall character indices. The 11 rainfall character indices include six single character indices and five combined character indices. The six single character indices were P, I10, I15, I30, I60 (maximum 10, 15, 30, 60 min rainfall intensity, respectively), and Im (mean rainfall intensity). The five combined character indices were PI10, PI15, PI30, PI60, and PIm (product of P and I10, I15, I30, I60, and Im, respectively). The coefficients of Pearson correlation are listed in Table 3.

Correlations between soil loss and single character indices (P, I10, I15, I30, and I60) as well as combined character indices (PI10, PI15, PI30, PI60, and PIm) were all significant at the 99% confidence level. Among 11 rainfall character indices, correlation coefficients between soil loss and PI30 were the highest (Table 3). Similar statistical analysis results were also obtained by Wang and Jiao (1996) and Jiang and Zheng (2004). Moreover, since rainfall energy data were not available in

Table 2 Frequency, precipitation and annual soil loss for three rainfall regimes

Types (soil loss (t km-2 yr-1))

Rainfall regime

Frequency Precipitation Annual soil loss Range (times)

Percent(%)

Range(mm)

Mean(mm)

Percent (%)

Range(t km-2 yr-1)

Mean (t km-2 yr-1)

Percent (%)

I (soil loss ≥10000)

RR1 5−9 65.0 89.0−200.3 135.6 47.5 7266.8−23371.2 14330.4 78.7

RR2 0−4 20.0 0.0−239.0 91.5 32.1 0.0−8403.8 2867.5 15.7

RR3 0−4 15.0 0.0−136.0 58.0 20.3 0.0−4802.0 1009.8 5.5

II (soil loss <10000)

RR1 2−5 43.5 21.0−88.2 60.9 22.1 261.0−3991.5 1861.9 36.3

RR2 2−5 34.8 40.0−186.8 123.6 44.8 297.4−4808.2 2074.3 40.5

RR3 0−5 21.7 0.0−234 91.4 33.1 0.0−4222.0 1186.6 23.2

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most filed observation stations, EI30

was replaced by PI30 in many literatures (Renard and Freimund 1994; Xu 2005; Zhang et al. 2005). Accordingly, in this study, PI30 was selected as a key rainfall character parameter to establish soil loss equation for estimating soil loss in individual rainfall event at loessial hillslope with ephemeral gully.

2.3.2 Soil loss equations fitting

The initial soil moisture was an important factor affecting soil loss (Luk 1985; Luk and Hamilton 1986; Bhuyan et al. 2003), and antecedent rainfall greatly influenced initial soil moisture (Wei et al. 2007; James and Roulet 2009; Lal et al. 2015). Han et al. (2012) proposed that if no rainfall occurred within five days on loessial hillslope, the influence of antecedent rainfall on initial soil moisture could be neglected, especially in 0–40 cm depth of soil profile. Therefore, to eliminate the impacts of initial soil moisture, the rainfall events that antecedent rainfall occurred within five days were removed. Finally, 33 rainfall events were removed from 115 totals, and remaining 82 rainfall events were used to fit equation, among which RR1, RR2, and RR3 occurred 45, 22, and 15 times, respectively.

To ensure the independence of the rainfall data used to fit and validate equation, 56 rainfalls were randomly selected from 82 rainfall events to establish soil loss equations, among which RR1, RR2, and RR3 occurred 30, 16, and 10 times, respectively. The remaining 26 rainfall events were used to validate the soil loss equations, among which RR1, RR2, and RR3 occurred 15, 6, and 5 times, respectively.

As illustrated in Figure 5, soil loss at loessial hillslope with ephemeral gully increased with the increase of PI30, but this increasing rate among

three different rainfall regimes (RR1, RR2, and RR3) and without rainfall regime classification (TRE) was quite different. The line for RR1 had greatest gradient, followed by TRE, RR2, and RR3.

The four linear regression equations between soil loss and PI30 were fitted. All equations were significant at the 95% confidence level.

The soil loss equation without rainfall regime classification could be described as:

+ = == 02

3: 0.88 168.02 ( 0.53, 56)TRE I nS RL P (1) The soil loss equations with rainfall regime

classification were showed as follows:

30

230

2

230

2: 0.51 214.6

1: 1.66 123.81 ( 0.94, 30)

0.82,7 ( )

3: 0.23

1

146.32 ( )

6

0.92, 10

RR SL PI

RR SL PI

RR SL PI R n

R n

R n

= − = == == =

= + = +

(2)

where SL was soil loss for individual rainfall; PI30 was the product of P (precipitation) and I30 (maximum 30 min rainfall intensity).

For three fitting equations with rainfall regime classification, the R2 of Eq. (2) were all over 0.8; while for the fitting equations without rainfall regime classification, the R2 of Eq. (1) was 0.53. This result indicated that the prediction accuracy of Eq. (2) was satisfactory and the prediction results were acceptable.

Figure 5 The relationship between soil loss and PI30 with (RR1, RR2 and RR3) and without (TRE) rainfall regime classification.

Table 3 Pearson correlation between soil loss and rainfall character indices for three rainfall regimes

Rainfall regime P I10 I15 I30 I60 Im PI10 PI15 PI30 PI60 PIm

RR1 (n=65) 0.77** 0.80** 0.85** 0.87** 0.86** 0.53* 0.87** 0.89** 0.90** 0.88** 0.83**

RR2 (n=30) 0.83** 0.78** 0.85** 0.92** 0.91** 0.58* 0.85** 0.81** 0.94** 0.87** 0.80**

RR3 (n=20) 0.77** 0.86** 0.81** 0.91** 0.86** 0.58* 0.88** 0.86** 0.89** 0.83** 0.74**

Note: ** Correlation is significant at the 99% confidence level (2-tailed); * Correlation is significant at the 95% confidence level (2-tailed).

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2.3.3 Validation of soil loss equations

Values calculated by Eq. (1) and Eq. (2) were all plotted in Figure 6 by cross validation. The values calculated by Eq. (2) distributed along the 1:1 line, indicating that those values were relatively close to corresponding observed values. However, values calculated by Eq. (1) were far away from 1:1 line. Moreover, R2 values of Eq. (2) were all over 0.93 and ENS values were all over 0.66, indicating that prediction accuracy of Eq. (2) with rainfall regime classification was satisfactory. However, although R2 values of Eq. (1) were all over 0.93, ENS values were relatively low, indicating that prediction accuracy of Eq. (1) without rainfall regime classification was poor, especially for RR3.

A more interesting phenomenon was showed in Figure 6, there was a critical threshold for different prediction results. When PI30 values of individual rainfall event were lower than 400 mm mm h-1, soil loss values calculated by Eq. (1) were close to the observed values, but they were higher than values calculated by Eq. (2), which indicated that the Eq. (1) could overestimate soil loss. While when the PI30 values were higher than 400 mm mm h-1, soil loss values for RR1 calculated by Eq. (1) were lower than observed values, and Eq. (1) could underestimate soil loss. For RR2 and RR3, soil loss values calculated by Eq. (1) were obviously higher than observed values. Consequently, Eq. (1) could overestimate the soil loss. The critical threshold of PI30 value for preciously estimate soil loss in RR1 was approximately equal to 400 t km-2.Therefore, the prediction results estimated by the Eq. (1) without rainfall regime classification were mainly determined by the values of PI30, while the prediction results by the Eq. (2) with rainfall regime classification could well estimate soil loss and eliminates the influences of rainfall character indices such as PI30 at loessial hillslope with ephemeral gully.

Mean relative errors predicted by Eq. (2) with rainfall regime classification were −11.6%, −7.9% and −20.5%, respectively, while mean relative errors predicted by Eq. (1) without rainfall regime classification was 56.4%, indicating that Eq. (1) would obviously overestimate soil loss due to high mean relative error and Eq. (2) had acceptable accuracy. The reason was that Eq. (1) did not reflect the effects of different PI30. Jia (2011)

applied the erosion model with ephemeral gully developed by Jiang et.al (2005) to Zhifanggou watershed (near to the study area) and concluded that the predicted accuracy was poor because mean relative error was 57.8%. Eq. (2) was also

Figure 6 Cross validation of equations for with and without rainfall regime classification for the three rainfall regimes. Csl and Osl represent calculated and observed values of soil loss, respectively. The black spots in (a), (b) and (c) represent soil loss calculated by Eq. (2) for RR1, RR2 and RR3. The black circles in (a), (b) and (c) represent soil loss calculated by Eq. (1).

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performed to the Zhifanggou watershed by using the same set of data, and the results showed that prediction accuracy was 87.7%, indicating that Eq. (2) was suitable for predicting hillslope soil loess with ephemeral gully. Hence, rainfall regime classification was important for accurately predicting soil loss at hillslope with ephemeral gully in loess hilly-gully area.

3 Conclusions

In this study, the 115 individual erosive rainfall events were classified into three rainfall regimes by using K-means clustering based on P, t, and I30. Statistical features of the 11 rainfall character indices varied greatly into three different rainfall regimes. Generally, soil loss caused by RR1 was the greatest, followed by RR2 and RR3. As the dominant rainfall regime, RR1 had large I30 with low precipitation and short duration. RR3 had low

I30 with great precipitation and long duration. The precipitation, duration and I30 values of RR2 were all between those of RR1 and RR3. Among the 11 rainfall character indices, PI30 had the closest relation with soil loss and was selected as key rainfall character parameter to fit soil loss equation based on individual rainfall event. Two sets of linear regression equations between soil loss and PI30 with and without rainfall regime classification were fitted. Validation results showed that prediction accuracy of the soil loss equations with rainfall regime classification was much higher than equation without rainfall regime classification, especially for extremely intensive soil loss event. It indicated that rainfall regime classification should be considered in establishing the event based soil loss equations at loessial hillslope with ephemeral gully. The results in this study have implications for depicting natural rainfall characteristics and improving soil loss equation prediction accuracy in loess hilly-gully region.

Acknowledgement

This study was supported by the National Natural Science Foundation of China (Grant No. 41271299) and by the Opening Fund of MWR

Laboratory of Soil and Water Loss Process and Control in the Loess Plateau of China (Grant NO.2017001).

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