Determining the sediment trapping capacity of grass filter strips

Journal of Hydrology 405 (2011) 209–216

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Determining the sediment trapping capacity of grass filter strips Chengzhong Pan a, Lan Ma a,⇑, Zhouping Shangguan b, Aizhong Ding a a

Key Laboratory of Water Sediment Sciences, College of Water Sciences, Beijing Normal University, Beijing 100875, PR China State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Chinese Academy of Sciences, Yangling, Shaanxi 712100, PR China

b

a r t i c l e

i n f o

Article history: Received 4 September 2010 Received in revised form 23 March 2011 Accepted 18 May 2011 Available online 26 May 2011 This manuscript was handled by L. Charlet, Editor-in-Chief, with the assistance of Dr. Jiin-Shuh Jean, Associate Editor Keywords: Grass strips Sediment trapping capacity Model Slope gradient Grass cover

s u m m a r y Sedimentation resulting from soil erosion degrades the surface water environment. This study determines the sediment trapping capacity (STC) of grass filter strips and how slope gradient and vegetation cover affect it. STC is defined as the maximum sediment trapped within vegetative filter strips (VFS) under given conditions. An exponential model was derived to mirror the relationship between instantaneous sediment trapping efficiency and runoff duration, with findings that STC is closely related to the initial efficiency and attenuation coefficients. The model effectively describes the sediment trapping process, and demonstrates that STC decreases with increasing slope and increases with vegetation cover. Grass strips have a small sediment trapping thickness measured in mm or cm, and grass stems and leaves have little influence on STC, which indicates that reasonable forage cutting may have little influence on sediment removal. STC is an intrinsic characteristic of VFS, and it can be recommended to assess the VFS performance in trapping sediment in severe soil erosion areas. A sediment trapping modulus at the watershed scale based on STC, can offer help to effectively evaluate soil and water conservation engineering and transformation of cropland into forest and grassland in China. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Soil erosion is one of the most serious eco-environmental problems worldwide. Sediment often results from soil erosion, and many chemical pollutants and pathogens tend to accumulate in sediment, deteriorating surface water quality (Muñoz-Carpena et al., 1999). Vegetative filter strip (VFS) use is one of the best management practices (BMP) to control erosion and non-point source pollution, and has been widely used in the US and Canada (Dillaha et al., 1989; Robinson et al., 1996). Generally, the removal of sediment from surface runoff by VFS is mainly attributed to filtration, deposition, and infiltration (Dillaha et al., 1989). VFS can increase surface roughness, decrease flow velocity and strengthen soil infiltration, which further decreases sediment transport capacity (Borin et al., 2005; Pan and Shangguan, 2006). However, some reports show that backwaters occurring ahead of any VFS play a more important role in removing sediment (Ligdi and Morgan, 1995; Ghadiri et al., 2001). Hussein et al. (2007a,b) found that over 90% of sediment was deposited on the upslope of grass strips, at slopes ranging from 1% to 5%. The sediment trapping process of VFS has not been clearly understood. Numerous studies have shown that the sediment removal performance of VFS is mainly influenced by slope, strip width,

⇑ Corresponding author. Tel.: +86 10 58802736. E-mail addresses: [email protected], [email protected] (L. Ma). 0022-1694/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2011.05.027

vegetation type, and runoff and sediment characteristics (Jin and Römkens, 2001; Liu et al., 2008; Zhang et al., 2009). Sediment trapping effectiveness generally increases with increasing strip width, but decreases with slope steepness. However, major differences exist among different researches: Daniels and Gilliam (1996) showed that sediment trapping efficiency ranged from 57% to 62% for a VFS of 6 m width at slopes of 2.1% and 4.9%, while Blanco-Canquia et al. (2004) observed that the trapping efficiency reached as high as 93% for a VFS of 4 m width at a slope of 5%. Although Liu et al. (2008) revealed by meta-analysis method that strip width and slope steepness were the two major factors influencing sediment removal, little information is available concerning quantitative analysis on the trapping mechanism. The literature reveals that experiment slopes mainly range from 2% to 16% (Liu et al., 2008); but in China most vegetation is reestablished to conserve soil and water on steeper slopes, and the critical slope for abandonment of farmland in the hilly Loess Plateau has been recommended as 25% (Tang et al., 1998). Therefore, there exists a gap in the sediment trapping process due to different slopes and runoff sediment conditions. Sediment trapping efficiency (STE) refers to the ratio of trapped sediment to inflow sediment, and it is widely used to represent the performance of VFS. However, in severely eroded areas, it is difficult to calculate the efficiency due to the difficulty in predicting soil loss from the upslope. Meanwhile, there is a large difference in soil loss from different rainfall events, and the STE cannot effectively mirror the sediment deposited within a VFS. Thus it is better

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to seek a practicable index to represent sediment removal effectiveness instead of STE. Although many models including GRASSF, VFSMOD, CREAMS and GUSED have been used to evaluate the performance of VFS, more attention should be paid to the principal physical processes affecting sediment transport (Flanagan et al., 1989; Haan et al., 1994; Dillaha and Hayes, 1991; Muñoz-Carpena et al., 1999; Abu-Zreig et al., 2001; Hussein et al., 2007b). Meanwhile, these models were developed and tested under gentle sloping, low runoff and sediment discharge conditions. In the Loess Plateau area in China, steep slopes and severe soil erosion make the above models difficult to be applied. As the transformation of farmland into forest and grassland has been carried out since 1999 in China, it is necessary to develop an effective tool to evaluate the soil and water conservation effect. This study investigates the sediment trapping processes of grass strips in a severe erosion area, analyzes the influence of the steep slope gradient and vegetation cover on sediment removal, and develops a sediment trapping model. The study can be helpful to understand the sediment trapping mechanism of VFS, and provide a useful tool to evaluate the impact of transforming farmland to forest and grassland in China. 2. Model development

Instantaneous sediment trapping efficiency e(t) is defined as the ratio of the sediment trapped by VFS to inflow sediment at runoff duration t (Pan et al., 2010), that is

ð1Þ

rðtÞ ¼ ðS0 ðtÞ  Si ðtÞÞQ ðtÞ

ð2Þ

where Q(t) is the flow rate (m3 s1). Introducing Eq. (1) into Eq. (2), we can get:

rðtÞ ¼ S0 QeðtÞ

ð4Þ

Total sediment R(t) trapped by VFS during runoff duration t can be expressed as:

0

rðsÞds ¼

Z

t

ðS0 ðsÞ  Si ðsÞÞQ ðsÞds ¼ S0 Q

0

Z

t

eðsÞds

ð5Þ

0

where ds is a variable of integration, and s is used to differ from the upper limit t at definite integrals. Sediment trapping efficiency E(t) is defined as the ratio of the trapped sediment R(t) to inflow sediment during runoff duration t, that is

Rt Z S0 Q 0 eðsÞds 1 t RðtÞ EðtÞ ¼ eðsÞds ¼ ¼ S0 ðtÞQ ðtÞt t 0 S0 Qt

dRðtÞ ¼ aðRm  RðtÞÞ dt

ð7Þ

where Rm is sediment trapping capacity; and a is a constant (a > 0), which can be called the attenuation coefficient of sediment retention. As a increases in value, trapped sediment more significantly affects instantaneous intensity r(t). At the beginning of runoff, when no sediment is deposited within VFS, the initial condition of Eq. (7) can be written as:

ð8Þ

An analytical solution to Eq. (7) can be obtained by the method of separating the variables:

RðtÞ ¼ Rm  Ceat

C ¼ Rm Therefore, trapped sediment at runoff duration t can be expressed as follows:

RðtÞ ¼ Rm ð1  eat Þ

dRðtÞ dðRm ð1  eat ÞÞ ¼ ¼ aRm eat dt dt

2.2. Hypothesis and derivation Generally, the instantaneous sediment trapping efficiency of VFS decreases with runoff duration, and it could approach or reach zero

ð10Þ

Incorporating Eq. (4) into Eq. (10), we can obtain:

rðtÞ ¼ QS0 eðtÞ ¼ aRm eat Therefore, e(t) can be expressed as:

eðtÞ ¼

a Rm eat QS0

ð11Þ

As seen from Eq. (11), under the same inflow rate Q and sediment concentration S0 conditions, instantaneous sediment trapping efficiency e(t) decreases with runoff duration t in an exponential manner. When the runoff duration t in Eq. (11) approaches 0, the limit of e(t), which is actually initial sediment trapping efficiency e0, can be written as follows:

e0 ¼ lim eðtÞ ¼ ð6Þ

ð9Þ

Clearly, as runoff duration t approaches infinity, the value of R(t) equals to Rm. Instantaneous sediment trapping intensity r(t) can be derived by differentiating the runoff duration t in Eq. (9):

ð3Þ

If inflow sediment concentration S0(t) and flow rate Q(t) do not change with runoff duration t, Eq. (3) can be simplified as:

t

rðtÞ ¼

rðtÞ ¼

rðtÞ ¼ S0 ðtÞQ ðtÞeðtÞ

Z

The equation can be written as follows:

where C is a constant. C can be obtained using Eq. (8):

S0 ðtÞ  Si ðtÞ Si ðtÞ ¼1 S0 ðtÞ S0 ðtÞ

where S0(t) and Si(t) represent inflow and outflow sediment concentration, respectively (kg m3), and t is runoff duration. Instantaneous sediment trapping intensity r(t) is defined as the difference between inflow and outflow sediment delivery at t runoff moment (Jin and Römkens, 2001), and it can be written as:

RðtÞ ¼

(1) Under given conditions, the maximum sediment deposited within VFS is defined as sediment trapping capacity (STC), which theoretically equals the total trapped sediment when runoff duration t approaches infinity; (2) Instantaneous sediment trapping intensity r(t) is positively proportional to the difference between STC and deposited sediment during runoff time t, that is, r(t) / (Rm  R(t))

RðtÞjt¼0 ¼ 0

2.1. Mathematical expression

eðtÞ ¼

(Jin et al., 2002; Le Bissonnais et al., 2004; Pan et al., 2008, 2010). This indicates that when the instantaneous sediment trapping efficiency equals zero, VFS will no longer remove sediment from runoff. Therefore, there may be a maximum sediment amount trapped by a given VFS, and the hypothesis can be expressed as follows:

t!0

aRm QS0

ð12Þ

Consolidating Eq. (12) into Eq. (11), e(t) can be expressed as follows:

eðtÞ ¼ e0 eat

ð13Þ

where the parameters e0 and a can be obtained from experiments. Meanwhile, sediment trapping capacity (Rm) can also be expressed from Eq. (11) as:

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Rm ¼

e0 QS0 a

ð14Þ

From Eq. (14) we find that sediment trapping capacity Rm is positively proportional to initial sediment trapping efficiency e0, inflow rate Q and sediment concentration S0, while it is inversely proportional to the attenuation coefficient a. Using dimensional analysis, (e0/a) has a dimension of time (s), and can be called the equivalent time of STC, that is, inflow sediment during equivalent time equals the STC.

3. Experiment materials and methods The VFS sediment trapping experiments were carried out under laboratory simulated rainfall conditions, and a perennial black rye grass (Lolium perenne L.) was grown as the VFS. Silt-laden runoff was obtained by mixing a proportion of soil with water in a water tank installed with an electric stirring device. The soil used had a median size of about 10 lm, and the size of more than 75% of the particles ranged from 2 lm to 50 lm. Inflow rate was controlled with a valve. The two experiments with differing slopes and covers were designed to test the derived model and calculate sediment trapping capacity. The experiments with differing slopes were carried out in a removable and slope-adjustable runoff plot of 5 m long and 1 m wide, and the experiment slopes were 3°, 6°, 9°, 12° and 15°, respectively. Grass strips had a row spacing of 25 cm with a density of about 2000 stems m2 and coverage of 50%. The strips included four treatments: intact grass control (C); no litter (NL), that is, dead grass material covering the soil between plants was removed; BNL representing NL with higher sediment load; and no litter or leaves (NLL), which represented being 2–3 cm grass stems above soil surfaces with roots reserved after grass cutting or grazing. The dry weight of the removed litter and stems (leaves) were 72.3 and 118.5 g m2, respectively. Each treatment consisted of five tests at slopes from 3°, 6°, 9°, 12° and 15°, e.g. treatment C included test C3, C6, C9, C12 and C15. This experiments had twenty tests, including C3–C15, NL3–NL15, BNL3–BNL15 and NLL3–NLL15. Both inflow rate and sediment concentration were adjusted at approximately 15 L min1 m1 and 60 kg m3 for treatment C, NL and NLL, and a

higher sediment concentration of 120 kg m3 was used for treatment BNL. All tests had the same runoff duration of 30 min and rainfall intensity of 0.5 mm min1. The experiments with different covers were conducted in runoff plots made of steel sheets with its dimension of 2 m long and 55 cm wide at 15°, a common slope gradient on the Loess Plateau in China. There were five grass coverage levels: 20%, 40%, 60%, 70% and 90%, respectively. The grass density varied from 1090 to 1692 stems m2, and the dry and wet weight of aboveground biomass ranged from 142.3 to 515.9 g m2 and 533.5 to 1733.5 g m2, respectively. There were two treatments (high (H) and low (L)) in the runoff and sediment loads, with inflow rates of about 30 L min1 m1 and 15 L min1 m1 and sediment concentrations of 26.62–38.8 kg m3 and 21.9–24.4 kg m3, respectively. Rainfall intensity and duration were respectively 1.5 mm min1 and 15 min for treatment H, and 1.0 mm min1 and 23 min for treatment L (Table 1). During the experiment process, silt-laden runoff was pumped to a fixed tank above the upslope, and flowed over the grass strips by gravity. Runoff samples were collected in a pail at 2 min intervals. Sediment was deposited, separated from the water, oven-dried for 24 h at 105 °C and weighed to determine outflow sediment load. Sediment concentration was obtained by dividing discharge, which excluded rainfall, by sediment load. Sediment trapping efficiency (STE) was defined as the ratio of the sediment trapped by strips to inflow sediment (Pan et al., 2010). The model parameters were calculated using curve regression, and the differences between each test/treatment were analyzed by the paired t-test method.

4. Results and analysis 4.1. Experiments with different slopes With the exception of the BNL treatment, there were no intersection points among the calculated curves in the sediment trapping processes (Fig. 1). This indicates that the influence of slope gradient on sediment deposition continued for the entire runoff duration. The exponential equation eðtÞ ¼ e0 eat was used to calculate the relationship between STE and runoff duration, and a

Table 1 Summary of grass strip experiments on sediment trapping with differing covers. Test

L1 LR1 L2 LR2 L3 LR3 L4 LR4 L5 LR5 H1 HR1 H2 HR2 H3 HR3 H4 HR4 H5 HR5

Grass cover

Density* (stems m2)

Aboveground biomass (g m2) Wet weight

Dry weight

0.2 0.2 0.4 0.4 0.6 0.6 0.7 0.7 0.9 0.9 0.2 0.2 0.4 0.4 0.6 0.6 0.7 0.7 0.9 0.9

1090 1090 1114 1114 1563 1563 1556 1556 1692 1692 1090 1090 1114 1114 1563 1563 1556 1556 1692 1692

533.5 533.5 723.1 723.1 976.2 976.2 1065.6 1065.6 1733.5 1733.5 533.5 533.5 723.1 723.1 976.2 976.2 1065.6 1065.6 1733.5 1733.5

142.3 142.3 228.0 228.0 258.0 258.0 348.2 348.2 515.9 515.9 142.3 142.3 228.0 228.0 258.0 258.0 348.2 348.2 515.9 515.9

SC refers to sediment concentration. Grass density was defined as the number of grass stems per unit area.

*

Slope (deg)

Rainfall intensity (mm min1)

Inflow rate (L min1 m1)

Inflow SC (kg m3)

Runoff duration (min)

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

0 1.0 0 1.0 0 1.0 0 1.0 0 1.0 0 1.5 0 1.5 0 1.5 0 1.5 0 1.5

13.0 15.9 14.8 15.5 13.9 14.9 15.7 17.1 13.6 14.6 29.1 31.8 32.6 28.6 32.2 36.1 30.7 31.0 29.9 34.9

23.79 22.37 24.25 23.30 23.32 21.90 24.10 22.77 24.40 24.00 35.89 31.39 29.75 31.61 28.32 26.62 36.20 32.74 38.80 35.50

23 23 23 23 23 23 23 23 23 23 15 15 15 15 15 15 15 15 15 15

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C. Pan et al. / Journal of Hydrology 405 (2011) 209–216

1.0

(C) 0.8 0.6 0.4 0.2 3°

6°

9°

12°

15°

sediment trapping efficiency

Sediment trapping efficiency

1.0

0.0

0.6 0.4 0.2 3°

6°

9°

12°

15°

0.0 0

5 10 15 20 25 30 35 Runoff duration(min)

0

5

10 15 20 25 30 35

Runoff duration(min)

1.0

1.0

(BNL) 0.8 0.6 0.4 0.2 3°

6°

9°

12°

15°

0.0

Sediment trapping efficiency

Sediment trapping efficiency

(NL) 0.8

(NLL) 0.8 0.6 0.4 0.2 3°

6°

9°

12°

15°

0.0 0

5 10 15 20 25 30 35 Runoff duration(min)

0

5 10 15 20 25 30 35 Runoff duration(min)

Fig. 1. Sediment trapping processes of grass strips with differing slopes from 3° to 15° for intact grass control (C), grass without litter (NL and BNL with higher sediment load) and grass without litter or leaves (NLL).

Table 2 Sediment trapping capacity of grass strips with differing slopes. Testa

e0

a

R2

(e0/a)/min

Inflow rate Q/m3 min1

Inflow SC S0/kg m3

STC Rm/kg m2

C3 C6 C9 C12 C15 NL3 NL6 NL9 NL12 NL15 BNL3 BNL6 BNL9 BNL12 BNL15 NLL3 NLL6 NLL9 NLL12 NLL15

0.7385 0.7169 0.6184 0.5900 0.4864 0.7865 0.6832 0.6565 0.5969 0.5411 0.7197 0.6703 0.5403 0.4438 0.5198 0.6875 0.7232 0.6714 0.6659 0.4644

0.0050 0.0117 0.0077 0.0126 0.0108 0.0065 0.0076 0.0081 0.0170 0.0189 0.0171 0.0106 0.0119 0.0106 0.0283 0.0103 0.0102 0.0135 0.0208 0.0172

0.40** 0.82** 0.87** 0.83** 0.29* 0.79** 0.44** 0.82** 0.80** 0.73** 0.77** 0.63** 0.49** 0.29* 0.71** 0.60** 0.67** 0.80** 0.93** 0.85**

147.70 61.27 80.31 46.83 45.04 121.00 89.89 81.05 35.11 28.63 42.09 63.24 45.40 41.87 18.37 66.75 70.90 49.73 32.01 27.00

0.0137 0.0147 0.0142 0.0141 0.0095 0.0150 0.0164 0.0158 0.0162 0.0152 0.0160 0.0153 0.0171 0.0174 0.0159 0.0187 0.0164 0.0182 0.0172 0.0184

64.7 54.3 53.1 63.0 82.1 67.8 74.8 58.0 61.1 52.4 116.9 108.3 121.3 110.4 110.2 70.4 59.9 61.7 64.0 56.9

26.18 9.80 12.16 8.34 7.04 24.54 22.10 14.86 6.94 4.56 15.70 20.98 18.88 16.12 6.42 17.56 13.92 11.20 7.04 5.66

SC and STC refer to sediment concentration and sediment trapping capacity, respectively. e0 and a were calculated using Eq. (13) (eðtÞ ¼ e0 eat ), and e0, a and (e0/a) represent initial efficiency, attenuation coefficient of sediment trapping and equivalent time, respectively. STC was calculated using Eq. (14) (Rm ¼ ea0 QS0 ). * Significant at the P = 0.05 level between the determined results and the values calculated using Eq. (13). ** Significant at the P = 0.01 level between the determined results and the values calculated using Eq. (13). a Intact grass control (C), grass without litter (NL and BNL with higher sediment load) and grass without litter or leaves (NLL) represent experimental treatments, and 3, 6, 9, 12 and 15 are slope gradients, e.g. C3 refers to the test for intact grass control (C) at 3° slope.

significance at the P = 0.01 level was found for most tests except for at C15 and BNL12, which had a significance at the P = 0.05 level (Table 2), indicating that eðtÞ ¼ e0 eat can well describe the sediment trapping processes of VFS with different slopes.

Initial sediment trapping efficiencies e0 and attenuation coefficients a using Eq. (13) ranged from 0.5 to 0.8 and 0.005 to 0.0208, respectively (Table 2). Generally, as the slope steepness increased, e0 and a respectively had decreasing and increasing

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C. Pan et al. / Journal of Hydrology 405 (2011) 209–216

4.2. Experiments with different covers

Sediment trapping efficiency

In treatment H with a high inflow sediment load, the strips with 20% grass cover had a low sediment trapping effectiveness, and during the later phase of runoff no sediment was removed (Fig. 2). This result also validated the above hypothesis that VFS has a maximum sediment trapping capacity.

0.8 L1

L2

L3

L4

L5

0.6

0.4

0.2

0 0

5

10

15

20

25

Tests H1 and HR1 had negative instantaneous sediment trapping efficiencies during the later phase of the experiments due to the relatively low grass cover, and they have not been analyzed. Under the same experiment conditions, the grass strips with 90% cover had significantly greater STE than those with the other covers, and there were relatively small differences between the covers of 20–70% (Fig. 2). This may be because the grass strips with 90% cover were distributed in rows with a high density, and the others were distributed in clusters. Except for test H5, the fitted curves had extremely significant correlations (P < 0.01) between STE and runoff duration using Eq. (13) (Table 3), which further bolstered the validity of the derived sediment trapping model. The calculated e0 exhibited a tendency to increase with the increase in grass cover. Rainfall had no significant influence on the e0 values under the same runoff and sediment conditions. Treatments L and LR had greater e0 values than treatments H and HR, which indicates that inflow rate and sediment concentration had a negative correlation to initial trapping efficiency. Attenuation coefficient a negatively related to grass cover, which indicates that greater cover can help VFS have a lasting effectiveness in trapping sediment. Equivalent time (e0/a) increased with increasing grass cover, and the (e0/a) values (except for the 90% cover) were less than 10 min. The small (e0/a) may be due mainly to the small strip width of 2 m, the steep slope of 15° and high inflow rate. The sediment trapping capacity of 20–90% grass covers ranged from 0.7 to 12.9 kg m2, and the capacities increased with increasing cover (Table 3). Treatments LR and HR had greater STCs than treatments L and H, respectively. This showed that rainfall had a positive influence on STC, and rainfall would increase surface roughness and decrease sediment transport capacity of overland

Sediment trapping efficiency

tendencies. This indicates that the bad performance of VFS on sediment removal at steeper slopes was attributed to not only the small initial sediment trapping efficiency, but also to the quickly decreasing effectiveness with runoff duration. The equivalent time (e0/a) decreased with the increasing slopes. The (e0/a) values during the NL and NLL treatments at 3° were 4.7 and 2.5 times greater respectively than those at 15°. For the C treatment, at slopes of 3° and 15°, the grass strips could each trap all sediments from inflow runoff at about 150 min and 45 min (Table 2). Sediment trapping capacity at 3–15° slopes ranged from 4.5 to 26.2 kg m2, and STC decreased with increasing slopes for the same treatment (Table 2). Under the same runoff and sediment conditions, there were small differences between the three treatments (C, NL and NLL). This may be due to the small influence of the grass litter, stems and leaves in the backwater ahead of the strips (Ghadiri et al., 2001; Hussein et al., 2007a,b; Pan et al., 2010). The BNL treatment had a higher sediment concentration (about 120 kg m3) than the others (about 60 kg m3). Under the same inflow rate, there were no significant differences in STC between the NL and BNL treatments from 3° to 15° using the paired t-test method. This result indicates that sediment concentration may have little influence on trapping capacity, but have an effect on the sediment trapping process (Table 2 and Fig. 2).

0.8

H5

0.4 0.3 0.2 0.1 0 0

4

8

12

Runoff duration(min)

10

LR4

LR5

0.4

0.2

0 0

16

Sediment trapping efficiency

Sediment trapping efficiency

H4

5

LR3

15

20

25

Runoff duration(min)

0.5 H3

LR2

0.6

Runoff duration(min)

H2

LR1

0.5 HR2

HR3

HR4

HR5

0.4 0.3 0.2 0.1 0 0

4

8

12

16

Runoff duration(min)

Fig. 2. Sediment trapping processes of grass strips with differing covers from 20% to 90% (L and H refer to the low and high intensity of runoff sediment, respectively; R refer to simulated rainfall; and 1–5 respectively represents 20%, 40%, 60%, 70% and 90% grass covers, e.g. LR1 refer to the test of 20% cover under low runoff sediment and simulated rainfall conditions).

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C. Pan et al. / Journal of Hydrology 405 (2011) 209–216 Table 3 Sediment trapping capacity of grass strips with differing covers. Testa

e0

L1 L2 L3 L4 L5 LR1 LR2 LR3 LR4 LR5 H2 H3 H4 H5 HR2 HR3 HR4 HR5

R2

a

0.4962 0.3589 0.2555 0.3749 0.601 0.3008 0.3371 0.4121 0.3734 0.5944 0.1873 0.2092 0.3157 0.3802 0.2444 0.2885 0.3735 0.3908

**

0.2272 0.1455 0.0906 0.1331 0.046 0.1031 0.0834 0.0986 0.0584 0.0243 0.1321 0.1026 0.1647 0.0356 0.063 0.1056 0.1013 0.0399

0.89 0.95** 0.86** 0.93** 0.94** 0.91** 0.94** 0.84** 0.86** 0.97** 0.84** 0.90** 0.90** 0.62* 0.72** 0.92** 0.91** 0.78**

(e0/a)/min

Inflow rate Q/m3 min1

Inflow SC S0/kg m3

STC Rm/kg m2

2.18 2.47 2.82 2.82 13.07 2.92 4.04 4.18 6.39 24.46 1.42 2.04 1.92 10.68 3.88 2.73 3.69 9.79

0.0130 0.0148 0.0139 0.0157 0.0136 0.0149 0.0145 0.0139 0.0161 0.0136 0.0326 0.0322 0.0307 0.0299 0.0271 0.0346 0.0295 0.0334

23.79 24.25 23.32 24.10 24.40 22.37 23.30 21.90 22.77 24.00 29.75 28.32 36.20 38.80 31.61 26.62 32.74 35.50

0.70 0.92 0.95 1.10 4.51 1.01 1.42 1.32 2.44 8.32 1.43 1.93 2.21 12.89 3.45 2.62 3.69 12.05

(a)

The e0 calculated using Eq.(13)

SC and STC refer to sediment concentration and sediment trapping capacity, respectively. e0 and a were calculated using Eq. (13) (eðtÞ ¼ e0 eat ), and e0, a and (e0/a) represent initial efficiency, attenuation coefficient of sediment trapping and equivalent time, respectively.   STC was calculated using Eq. (14) Rm ¼ ea0 QS0 . * Significant at the P = 0.05 level between the determined results and the values calculated using Eq. (13). ** Significant at the P = 0.01 level between the determined results and the values calculated using Eq. (13). a L and H refer to the low and high intensity of runoff sediment, respectively; R refer to simulated rainfall; and 1–5 respectively represents 20%, 40%, 60%, 70% and 90% grass covers, e.g. LR1 refer to the test of 20% cover under low runoff sediment and simulated rainfall conditions.

could indicate that runoff and sediment characteristics could have an effect on VFS sediment removal.

1.0 0.9

4.3. Test of the Model and STC

0.8

1: 1 line

0.7 0.6 0.5 0.4 0.4

0.5

0.6

0.7

0.8

0.9

1.0

(b)

The e0 calculated using Eq.(13)

The measured e 0 0.8 L

H

0.6

1: 1 line 0.4

0.2

0.0 0

0.2

0.4

0.6

0.8

The measured e 0 Fig. 3. Comparison between the initial sediment trapping efficiency e0 calculated using Eq. (13) and the measured e0 of grass strips with differing slopes (a) and with differing covers (b) (L and H refer to the low and high intensity of runoff and sediment load, respectively in (b)).

In the experiments with differing slopes, the initial sediment trapping efficiencies e0 using Eq. (13) were less than the measured values for different slopes (Fig. 3a). This may be related to the initial sampling times. Under the experiment conditions, the first sample was collected at the beginning of outflow generation when the incomplete overland flow had a relatively small discharge, velocity and sediment carrying capacity, and sediment from runoff tended to be trapped within the grass strips. However, there was a significantly positive correlation (r = 0.69, P < 0.01) between the predicted and measured e0. In the experiments with different covers, the scatters of the calculated and measured e0 were almost symmetrically distributed on 1:1 line, and there was a significant correlation (r = 0.61, P < 0.01) between them (Fig. 3b). This indicates that the exponential model can predict well the initial sediment trapping efficiency. Sediment trapping capacity is the maximum sediment deposited within VFS, and it should equal the deposited sediment at the point when VFS will no longer have trapping effectiveness. Under the experiment conditions, STC could not be achieved due to the positive instantaneous sediment trapping efficiency during the runoff time. In fact, STC was difficult to be determined directly due to the short-duration of runoff observation. Therefore, STE had to be used to verify STC. There was a significantly positive correlation (p < 0.01) between STE and STC calculated by Eq. (14) for both the experiments with different slopes and covers (Fig. 4). This indicates that STC can effectively represent filter strip performance on sediment removal. 5. Discussion 5.1. Sediment trapping model

flow (Abrahams et al., 1992; Pan and Shangguan, 2006). The greater STCs of treatments H and HR compared to treatments L and LR

The sediment trapping model with an exponential function eðtÞ ¼ e0 eat was derived based on the hypothesis that

(a)

Sediment trapping capacity(kg m-2)

C. Pan et al. / Journal of Hydrology 405 (2011) 209–216

In the experiments with differing slopes, there was a significant linear correlation with e0 = 0.8–0.02S (R2 = 0.74, P < 0.001) between the calculated e0 and slope gradient S (Table 2). This indicates that there may be a critical slope at which a given VFS will no longer trap sediments. In the experiments with different covers, the calculated e0 varied from 0.2 to 0.65, and it increased with grass cover C with e0 = 0.08 + 0.43C (R2 = 0.47, P < 0.01) (Table 3). This equation confirms the result of Abu-Zreig et al. (2004) who found that bare soil surfaces also had an effect in retaining sediment. The attenuation coefficient a increased with increasing slope, but decreased with cover (Table 2 and 3). This indicates that the smaller the slope and the greater the vegetation cover, the more slowly sediment trapping effectiveness decreases with runoff duration. There was a significant linear correlation between attenuation coefficient a, slope gradient S, and cover C with a = 0.0008S + 0.0058 (R2 = 0.36, P < 0.01) and a = 0.145C + 0.184 (R2 = 0.42, P < 0.01), respectively.

30 25

Rm = 55.6x - 15.78 R2 = 0.75**, n=20

20 15 10 5 0 0.2

0.4

0.6

0.8

Sediment trapping capacity(kg m-2)

Sediment trapping efficiency

(b)

5.2. Sediment trapping capacity

15

L

H

RmH = 49.96x - 3.06

12

R2 = 0.80**, n=8 9

6

3

RmL = 15.12x - 0.46 R2 = 0.61**, n=10

0 0

0.1

0.2

0.3

0.4

0.5

Sediment trapping efficiency Fig. 4. Comparison between sediment trapping capacity Rm calculated using Eq. (14) and sediment trapping efficiency of grass strips with differing slopes (a) and with differing covers (b) (L and H refer to the low and high intensity of runoff and sediment load, respectively in (b)).

instantaneous sediment trapping intensity was proportionate to the difference between the deposited sediment within VFS and sediment trapping capacity. The model effectively described sediment trapping processes of grass strips with different slopes and covers (Tables 2 and 3). However, Jin and Römkens (2001) preferred the exponential model with three parameters ct eðtÞ ¼ a þ be representing the relationship between instantaneous STE and runoff duration. From their equation, when runoff duration t approaches infinity, the instantaneous STE e(t) keeps constant a, and VFS will retain the inflow sediment continuously, which may not accord with field investigation and experiment observations (Deletic and Fletcher, 2006; Pan et al., 2010). Initial efficiency e0 and attenuation coefficient a are the key parameters of the sediment trapping model (Eq. (14)), and they can be obtained by curve calculation with least squares based on experiments (Tables 2 and 3). In addition, e0 also can be directly determined and it is closely related to the time of sampling. The attenuation coefficient a can be calculated by a two-point method with Eq. (15):

a¼

ln e1  ln e2 t2  t1

215

Under a constant runoff and sediment load, STE is an important factor when evaluating sediment removal performance of VFS. However, in severe soil erosion areas, especially in the Loess Plateau in China, there are major differences in erosion sediments flowing over VFS during different rainfall events. Therefore, accurately computing the trapped sediment by multiplying incoming sediment with STE is difficult. STC can be regarded as an intrinsic property of VFS, and it provides the maximum sediment trapping, which may make STC more suitable than STE for assessing VFS performance on sediment removal in severely eroded areas. There appeared to be a contradiction between the two experiments in the relationship between runoff sediment characteristics and STC or STE. Inflow rate and sediment concentration had little influence on STC in the experiments with different slopes, and they had a positive effect on STC in those experiments with different covers (Table 2 and 3). The positive effect may be due to the higher percentage of coarse particles under the higher runoff and sediment load, and generally VFS had a higher trapping effectiveness for coarse sediments than for fine particles (Jin et al., 2002; Han et al., 2005; Pan et al., 2010). In the severe soil erosion areas, extreme storms tend to generate a higher proportion of coarse sediments from runoff which may lead to a greater STC. Therefore, further studies should be conducted to quantify the relationship between STC and runoff sediment characteristics for different soil erosion areas. Under the experiment conditions, STC decreased with an increasing slope, but increased with grass cover (Table 2 and 3). If the deposited sediment was given to a bulk density of 1.0 g cm3, there were deposited thicknesses of 4.5–26.2 mm in the experiments with different slopes, which was greater than those with different covers (0.7–12 mm). The reduced thickness with different covers may be due to the steeper slope of 15° and the scattered distribution of strips with dots or clusters. In general, the sediment deposited within VFS had a thickness measured in mm or cm. In addition, the grass stems and litters had little influence on STC (Table 2). These results indicate that reasonable grazing or mowing grass with a height P 3 cm may have little effect on VFS sediment trapping effectiveness. At the watershed scale, the sediment trapping modulus (MF) of VFS can be defined as trapped sediment mass per unit area in a year, which can be expressed by Eq. (16):

Pn

ð15Þ

where e1 and e2 are instantaneous STE at runoff times t1 and t2, respectively. Eq. (15) can be more appropriate for small sample sizes in the sediment trapping process.

MF ¼

i¼1 Rmi

AT

 AFi

ð16Þ

where Rmi and AFi are STC (kg m2) and area (km2) of VFS for unit i, respectively; A is the total watershed area (km2); and T is time (a).

216

C. Pan et al. / Journal of Hydrology 405 (2011) 209–216

In China, the main objective of transforming cultivated lands into forests or grasslands is to control soil erosion by constructing vegetation. The sediment trapping modulus MF has a negative correlation with the soil erosion modulus. Thus the parameter MF may give an important reference for vegetation rehabilitation and soil and water conservation at the watershed scale. 6. Summary and conclusions Based on the literature and experiments, sediment trapping capacity, that is, the maximum deposited sediment mass for a given VFS was proposed, and it was recommended to assess the VFS performance in trapping sediment in severe soil erosion areas. A sediment trapping model was derived from the hypothesis that instantaneous sediment trapping intensity was positively correlated with the difference between deposited sediment and STC, and the instantaneous STE e(t) decreased exponentially with runoff duration t with a function eðtÞ ¼ e0 eat , where e0 and a were the initial trapping efficiency and attenuation coefficient, respectively. The parameters e0 and a can be acquired by experiments, and they had a close correlation to STC. The experiments showed that the derived model can effectively describe sediment trapping processes of grass strips. The STC calculated by Eq. (14) decreased with an increasing slope gradient, but increased with grass cover. There was a significantly positive correlation both between the determined and calculated e0 and between the determined STE and calculated STC. These results indicate that the derived models are reasonable. While much effort went into the development of the model, it should be compared with other existing models and other independently published data to determine whether the applicability of the model warrants use in other areas in China in the future. Under the experiment conditions, the grass stems, leaves and litter had little influence on STC, and there was a small deposited sediment thickness (<3 cm), which indicates that reasonable grazing and cutting may have little influence on the grass strip sediment trapping effectiveness. STC represents an inherent capacity of VFS to retain sediment from runoff, and has no correlation with runoff duration. The sediment trapping modulus derived from STC at the watershed scale can offer important support for the effective evaluation of soil and water conservation. Acknowledgements This research was supported by the Natural Science Foundation of China Project (40801103), the National Major Project in Water Pollution Control and Management (2009ZX07212-002 and 2009ZX07419-003), the Fundamental Research Funds for the Central Universities, and the PhD Programs Foundation of the Ministry of Education of China (200800271029). The authors would like to express deep gratitude to the reviewers for their valuable suggestions made to improve the manuscript. References Abrahams, A.D., Parsons, A.J., Hirsch, P.J., 1992. Field and laboratory studies of resistance to interrill overland flow on semi-arid hillslopes, Southern Arizona.

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