Sediment transport capacity and its response to hydraulic parameters in experimental rill flow on steep slope

Transcription

1 doi:1.2489/jswc Sedimet trasport capacity ad its respose to hydraulic parameters i experimetal rill flow o steep slope Z. Wag, X. Yag, J. Liu, ad Y. Yua Abstract: Sedimet trasport capacity must be cosidered whe developig physical models of soil erosio. The effects of related hydraulic parameters (e.g., flow discharge, slope gradiet, ad flow velocity), ad of force predictors (e.g., shear stress, stream power, ad uit stream power) o sedimet trasport capacity i rill erosio are still poorly kow o the farmlad of the Loess Plateau i Chia where rill erosio is commo. We coducted a series of experimets to simulate ad evaluate the sedimet trasport capacity of rill flow i a oerodible rill flume. The test sedimet was the loessial soil of the farmlad of the Loess Plateau. Five flow discharges ragig from.22 to m 2 s 1 (.237 to.721 ft 2 sec 1 ) ad five slope gradiets ragig from 15.8% to 38.4% were tested. Sedimet trasport capacity icreased with both flow discharge ad slope gradiet, as expected, but was more sesitive to flow discharge tha to slope gradiet, ulike other similar studies. Mea flow velocity, related to the flow discharge, was strogly correlated with sedimet trasport capacity (r 2 =.93). Stream power was the best predictor of sedimet trasport capacity; shear stress ad uit stream power, with critical values of.55 W m 2 ad.2 m s 1 (.4 mi hr 1 ) respectively, were poor predictors. A empirical equatio of sedimet trasport capacity of the loessial soil for rill flow was developed. Our results preset a differet view, compared to previous studies, of the relatioship of sedimet trasport capacity with discharge ad slopes, especially with lower discharges, steep slopes, ad loessial soil. Further study should be coducted to evaluate the performace of farmlad soil at various slopes ad discharges. Key words: hydraulic parameters loessial soil rill flow sedimet trasport capacity water erosio The trasport of sedimets by ruoff ca potetially alter river courses ad avigability through siltatio; it ca also cotamiate ecosystems with the chemicals carried by the sedimets themselves (Lal 1998). To combat ad predict soil erosio ad its related problems, several physically based models of soil erosio have bee developed, icludig the Limburg soil erosio model (De Roo et al. 1996), the Europea soil erosio model (Morga et al. 1998), ad the water erosio predictio project (WEPP) (Flaaga et al. 21). The efficiecies of the models, however, ca be limited by a rage of problems that iclude isufficiet evaluatio, overparameterizatio, or the use of parameters that are iappropriate for local coditios, resultig i poor performace (Merritt et al. 23). A prior- ity for describig soil erosio is to develop a processig-based erosio model that ca calculate the rate of sedimet detachmet ad the trasport capacity. Foster ad Meyer (1972) documeted that the rate of sedimet detachmet could be estimated separately from trasport capacity ad sedimet load. Nearig et al. (1989) suggested that sedimet trasport capacity could be distiguished from soil-detachmet capacity without ay depositio. Models of sedimet trasport capacity thus assumed that the maximum equilibrium sedimet could be trasported uder certai coditios of discharge. May studies have validated ad calibrated these earlier formulatios or have developed empirical formulatios based o limited laboratory or field ivestigatio of discharges, slopes (gradiet ad legth), grai diameters, ad some hydraulic parameters (Beasley ad Huggis 1982; Govers ad Rauws 1986; Fiker et al. 1989; Govers 199, 1992; Ferro 1998; Zhag et al. 29, 21a, 21b; Gokme ad Vijay 212; Ali et al. 212a, 212b, 213). Beasley ad Huggis (1982) reported that sedimet trasport capacity could be calculated by the equatios: = 146 Sq.5 (q.46), (1) = 146 Sq 2 (q >.46), (2) where is the sedimet trasport capacity, S is the slope gradiet (m m 1 ), ad q is the uit discharge per uit width of slope (m 2 s 1 ). These two equatios were subsequetly used i the Areal Nopoit Source Watershed Eviromet Respose Simulatio (ANSWERS) model. Discharge was the oly limitig factor cosidered for sedimet trasport eve though other models emphasized the eed to cosider slope gradiet ad/or mea flow velocity. However, Julie ad Simos (1985) foud that the relatioship of sedimet trasport capacity could be expressed as a power fuctio of slope ad discharge, with the expoet derived from the actual coditio of its use. Based o a series of laboratory experimets with a hydraulic flume, Govers (199) developed a geeral equatio that described the relatioship betwee sedimet trasport capacity ad both discharge ad slope: = Aq B S C, (3) Zhali Wag is a professor i State Key Laboratory of Soil Erosio ad Drylad Farmig o the Loess Plateau with the Istitute of Soil ad Water Coservatio at Northwest A&F Uiversity i Yaglig, Chia; ad the Istitute of Soil ad Water Coservatio at the Chiese Academy of Scieces ad Miistry of Water Resources i Yaglig, Chia. Xiaomei Yag is a PhD studet i the State Key Laboratory of Soil Erosio ad Drylad Farmig o the Loess Plateau with the Istitute of Soil ad Water Coservatio at the Chiese Academy of Scieces ad Miistry of Water Resources i Yaglig, Shaaxi, Chia; ad the Soil Physics ad Lad Maagemet at Wagige Uiversity i Wagige, Netherlads. Ju e Liu is a PhD studet i School of Resources ad Eviromet at Northwest A&F Uiversity i Yaglig, Shaaxi, Chia. Yi Yua is a master studet i School of Resources ad Eviromet at Northwest A&F Uiversity i Yaglig, Shaaxi, Chia. 36 JAN/FEB 215 VOL. 7, NO. 1

2 where A, B, ad C are coefficiets associated with grai size ad with lamiar ad turbulet-flow regimes. The relatioship betwee sedimet trasport capacity ad discharge ad/or slope has bee studied, but the domiat cotributio to capacity by either discharge or slope ca vary. Govers (199) ad Everaert (1991) reported that the effects of slope o trasport capacity was greater tha that of discharge, while Zhag et al. (29) cocluded that discharge cotributed more tha did slope gradiet. Several studies have bee coducted with hydraulic flumes with either oerodible or erodible beds. The surface roughess of oerodible beds is substatially differet from that of erodible beds (Hu ad Abrahams 26). Usig oerodible beds ad sad of variable coarseess, Ali et al. (212a) developed a empirical equatio with expoets ad showed that sedimet trasport capacity was more sesitive to slope tha to discharge, where the derived expoets were 2.89 ad 1.46, respectively. These differet results could all be explaied by uit discharge, slope gradiet, ad test material (diameter ad texture), which i various combiatios ca lead to a large variety of experimetal coditios. Trasport capacity has close relatioships with several hydraulic parameters other tha discharge, slope, ad grai diameter. Flow velocity, the oly parameter detected directly (Zhag et al. 21a), is iflueced by discharge, slope, ad the surface roughess of the flow bed, which are all related to the rate of sedimet detachmet ad trasport capacity. Zhag et al. (29) reported that the relatioship betwee mea flow velocity ad sedimet trasport capacity could be described by a liear fuctio, while may other studies have show that mea flow velocity was idepedet of sedimet trasport capacity (Nearig et al. 1999; Gimeez ad Govers 21). Aother importat hydraulic parameter, shear stress, was calculated by the formula of Yali (1963): τ = ρghs, (4) where τ is the shear stress (Pa), ρ is the water mass desity (kg m 3 ), g is the gravity costat (m s 2 ), ad h is the depth of flow (m). This equatio was used i WEPP to estimate sedimet trasport capacity (Nearig et al. 1989), but its reliability remais i doubt (Julie ad Simos 1985). Bagold (1966) emphasized eergy expediture, ad expressed as a fuctio of stream power: ω = τv = ρgsq, (5) where ω is the stream power (W m 2 ) ad v is the mea flow velocity (m s 1 ). Yag (1972) later used ocohesive sads to develop a load equatio with uit stream power: P = vs, (6) where P is the uit stream power (m s 1 ). The relatioship ad form of formulatio, however, varied betwee parameters ad sedimet trasport capacity, some of which were eve cotradictory (Yali 1963; Bagold 1966; Yag 1972; Foster 1984; Moore ad Burch 1986; Govers ad Rauws 1986; Govers 199; Nearig 1997; Zhag et al. 29, 21b; Ali et al. 212a, 213). Adaptig suitable hydraulic parameters is thus essetial either to calculate sedimet trasport capacity or to evaluate the respose relatioships amog them. As the most active type of erosio o disturbed uplads, rill erosio is quite differet i its characteristics ad i its coditios of hydraulic eviromets compared to typical chaels of streams ad rivers (Nearig 1989). Rills have small ad ephemerally cocetrated flow paths ad have bee cosidered to be the mai source ad meas of sedimet trasport from hillslopes (Gilley et al. 199; Nearig et al. 1997). As determied by log-term moitorig i field plots, rill erosio is cosidered the mai type of soil erosio i the farmlad o the Loess Plateau (Zhu 1982; Cai 1998). Lei et al. (21) developed a reasoable method of uderstadig sedimet trasport ad its relatioships with rill legth, discharge, ad slope: = S q. (7) Usig the maximum sedimet load, which is equivalet to sedimet trasport capacity, Zhag et al. (29) reported a dual power fuctio of sedimet trasport capacity: = 19,831 S q (8) This fuctio was developed accordig to 64 combiatios of experimets uder steep slopes, larger discharges, ad riverbed sedimets. The grais of loessial soil, though, are obviously differet from uiform sad, which is a drawback for usig equatio 8 to predict sedimet trasport of rill erosio i the farmlad of the Loess Plateau where the itegrated iteractio of meteorology, topography, lad use, ad athropogeic activities affect the erosio processes seriously. Moreover, several fuctios caot adequately predict trasport capacities, particularly at low flow rates (Ali et al. 213). Accordig to field studies, flow discharge from erosio-producig rais varies from. 7 m 2 s 1 to.1 m 2 s 1 (.8 ft 2 sec 1 to.11 ft 2 sec 1 ). Furthermore, the threshold of slopes o farmlad was 46.6% accordig to the Grai for Gree Project. Based o field observatio o efficiecy of combatig soil loss ad lad degradatio, this threshold should be 36.4% demostrated by Tag et al. (1998). We thus focused o steep slopes, which are typical o the Loess Plateau, i combiatio with relatively low discharge rates ad with loessial soil as the test sedimet. The objectives were (1) to determie how the sedimet trasport capacity of rill flow chaged uder differet coditios of steep slopes ad lower discharges ad (2) to determie the respose of sedimet trasport capacity to various hydraulic parameters. Most importatly, sedimet trasport capacity was empirically derived with the ative loessial soil rather tha a artificial test material such as sad grais of uiform diameter. Materials ad Methods Experimetal Facilities. The experimets were coducted i a hydraulic flume at the State Key Laboratory of Soil Erosio ad Drylad Farmig o the Loess Plateau i Yaglig, Chia. Loessial soil was collected from the upper 2 cm (7.9 i) of a cultivated field at the Asai Experimetal Statio i Shaaxi Provice for use as the test material. Soil samples were air dried, crushed to pass through a 2 mm (.79 i) sieve, ad mixed thoroughly. The particle-size distributio of the soil was 8% fie clay (<.1 mm [.39 i]), 5.7% coarse clay (.1 to.2 mm [.39 to.4 i]), ad 86.3% silt (.2 to.5 mm [.4 to.2 i]). Lei et al. (21) had demostrated that sedimet trasport capacity would ot icrease beyod certai values of rill legth ad slope, so we desiged a hydraulic steel flume 4 m (13.1 ft) i legth ad.1 m (.33 i) i width with double-sided PVC JAN/FEB 215 VOL. 7, NO. 1 37

3 Figure 1 Experimetal setup. 4 m Noerodible bed Head tak Flow meter Tap water Storage tak Hopper Gate valve Chamber Elevator device Sedimet.1 m walls. The sedimet trasport capacity with these dimesios of rill chael was the same as that reported by Lei et al. (21). Because bed roughess affects flow hydraulics (Gimeez ad Govers 21), the test soil was glued o the surfaces of the flume walls ad bed to simulate the soil surface reported by Lei et al. (21). Two special desigs were added to esure that the ecessary sedimet trasport capacity was attaied. A.8 m 3 (2.6 i 3 ) hopper was istalled vertical over the flume.2 m (.66 i) from the upper ed. A woode board exteded from the outlet of the hopper to allow the rollig test soil addig to flow, thereby avoidig the effects of hydrophobicity ad trapped air. Also, a chamber 2 cm (7.9 i) i legth, 1 cm (3.9 i) i width, ad 1 cm (3.9 i) i depth was iserted at the upper ed of the flume. The upper part of the chamber was at the same level as the rill bed. Tap water was used for the experimets, which first etered the storage tak ad was pumped to the head tak. The rate of flow ito the head tak was cotrolled ad measured with a calibrated flow meter at the ilet pipe. The slope of the flume was adjustable by a elevatig device from % to 6%. The details of the equipmet are show i figure 1..2 m Chamber.1 m Measuremets. Prior to the experimets, a ucapped.4 cm (.16 i) thick Plexiglass box 19.2 cm (7.6 i) i legth, 9.2 cm (3.6 i) i width, ad 9.6 cm (3.9 i) i depth with several.5 cm (.2 i) diameter holes i the bottom was filled with test soil. The box was set i shallow water for 24 hours to saturate the soil before beig istalled i the chamber. Air-dried soil samples were added to the hopper, ad the slope ad discharge were adjusted to the desired values. Prelimiary experimets were coducted without ay test soil to determie the coditios which were ecessary for obtaiig steady flow discharges i differet slope gradiets (Zhag et al. 29). The feed rates of the test soil for each combiatio of flow discharge ad slope gradiet were determied ad the maitaied throughout the tests. Flow depth is difficult to detect durig erosio due to the coditios of the flow ad the bed surface. I this study, flow depth was thus determied by a electric probe with.1 mm (.39 i) resolutio alog the flow sectio at 2, 32, ad 62 cm (.8, 12.6, ad 24.4 i) above the upper ed of the chamber, providig istataeous detectio at each site i triplicate. Nie depths were measured for each combiatio of flow discharge ad slope gradiet. The average depth was calculated to be the mea flow Gear box Hopper depth for that combiatio of flow rate ad slope gradiet (table 1). Flow velocity was measured usig a dye-tracig techique (Lei et al. 1998) ad the the detected velocity could be validated based o the flow regime to elimiate the effect of dye-tracer dispersio i flow (Luk ad Merz 1992). I order to esure rill flow ca reach up to trasport capacity maximum sedimet cocetratio (table 2) two sedimet sources were added (Zhag et al. 29). Oe was from the hopper ad the other is from the box which ca be iserted i chamber carefully. The edges of the box ad flume bed were sealed with petroleum jelly to prevet leaks. The box was protected by a thi iro sheet before the feed rate of the sedimet ad the flow discharge stabilized. As described by Zhag et al. (29), depositio may occur at the poit where the test soil eters the rill flow. The depositio was thus slightly stirred with a iro rod uder the hopper durig the experimets. Six samples were cotiuously collected for each combiatio of flow rate ad slope gradiet, ad the samplig time was recorded. A series of 25 combiatios of discharge (.22,.33,.44,.56, ad m 2 s 1 [.237,.355,.473,.6, ad.721 ft 2 sec 1 ]) ad flume-bed slope (15.8%, 21.3%, 26.8%, 32.5%, ad 38.4%) 38 JAN/FEB 215 VOL. 7, NO. 1

4 Table 1 Flow depth for differet slope gradiets ad flow discharges. Flow discharge Flow depth i differet slope gradiet (mm) (1 3 m 2 s 1 ) 15.8% 21.3% 26.8% 32.5% 38.4% Table 2 Sedimet cocetratio of treatmets. Flow discharge Sedimet cocetratio i differet slope gradiet (g L 1 ) (1 3 m 2 s 1 ) 15.8% 21.3% 26.8% 32.5% 38.4% were tested ad each combiatio was repeated oce. All samples from each experimet were allowed to settle for 24 hours. The superatats were discarded, ad the wet sedimets were ove dried at 15 C (221 F) for 12 hours. Statistical Aalysis. All data were aalyzed by SPSS 16. t-test for comparig the variatios amog the differet experimetal combiatios ad regressio aalysis for developig equatios of sedimet trasport capacity. The results were also compared to the trasport capacities calculated by equatio 1 ad 8 for the experimetal coditios accordig to equatio form ad similar experimetal coditios. Shear stress, stream power, ad uit stream power were calculated by the correspodece equatios metioed above. I additio, the statistic parameters relative error (RE, %), mea relative error (MRE, %), mea absolute relative error (MARE, %), Nash-Sutcliffe efficiecy (NSE), ad coefficiet of determiatio (r 2 ) were used to evaluate the performace of our model based o empirical data ad the performaces of equatios 1 ad 8. The statistical parameters were give by (O i P i ) RE = 1% O, i (9) 1 (O i P i ) MRE = 1% N, (1) i = 1 O i 1 (O i P i ) MARE = 1%, (11) N r 2 = i = 1 O i [ 2 (O i O)(P i P), ad (O i O) 2 (P i P) 2 i = 1 i i = 1 [ (12) NSE = 1 (O i P i ) 2, (13) (O i O) 2 where O i is a observatio value, O is the mea observatio value, P i is the predicted value, P is the mea predicted value, ad is the umber of samples. Results ad Discussio Effect of Flow Discharge ad Slope Gradiet o Sedimet Trasport Capacity. Sedimet trasport capacity icreased with icreases i both flow discharge ad slope gradiet (figure 2). For the same level of discharge, the icrease i trasport capacity was largest whe the slope gradiet icreased from 26.8% to 32.5%. Zhag et al. (29) also oted obvious chages i trasport capacity whe the slope gradiet icreased from 26.8% to 36.4%, which was similar to the chage i our study. Furthermore, the variatios i our study teded to become early parallel to the axis of flow discharge whe the slope reached 32.5%, which suggests that sedimet trasport capacity may ot icrease sigificatly above this slope. Similarly, Lei et al. (21) reported that a slope gradiet of 36.4% could be cosidered a critical slope for the detachmet of loessial soil. Upo further aalysis, we foud that power (r 2 >.92, p <.1) ad expoetial (r 2 >.98, p <.1) fuctios could describe the relatioships betwee trasport capacity ad flow discharge ad slope gradiet, respectively. To determie these relatioships betwee trasport capacity ad flow discharge ad slope gradiet, we used multivariate, oliear regressio aalysis to develop the equatio = S.98 q 1.2 (r 2 =.97, NSE =.99, p <.1). (14) Sedimet trasport capacity calculated by the model developed i this study was similar to the observed values (figure 3). As idicated by the values of the expoets, trasport capacity was more sesitive to chages i flow discharge tha to chages i slope gradiet for the oerodible beds used i this study. The expoets for discharge ad slope gradiet were 26.22% ad 2.25% lower, respectively, tha those obtaied by equatio 8. The expoets for slope gradiet (.98) ad flow discharge (1.2) were also lower tha the average rages for slope gradiet of 1.2 to 1.9 ad for flow discharge of 1.4 to 2.4 reported by Julie et al. (1985), based o the statistical aalysis of data from a series of experimets o trasport capacity ad the average expoets of 1.4 for both slope gradiet ad flow discharge reported by Prosser ad Rustomji (2). I terms of costat coefficiets (67.68), it was also lower tha those obtaied from equatios 1 ad 8. These differeces i expoets ad coefficiets suggested that the relatioships with flow discharge ad slope gradiet were cofirmed, but the formulatios varied with test bed, test material, ad rill width, icludig the combiatio of slope gradiets ad flow discharges. Accordig to the study of Zhag et al. (29), riverbed sedimet was selected as the testig material which particle cohesio was completely differet from soil used i this study. Furthermore, with respect to flow discharges ad slope gradiets, they were all selected based o field observatio (Tag et al. 1998) i this study, ad the results are meat to reflect the realistic situatio rather tha the ideal oe. Therefore, sedimet trasport capacity would be overestimated or uderes- JAN/FEB 215 VOL. 7, NO. 1 39

5 Figure 2 Sedimet trasport capacity for differet (a) flow discharges ad (b) slope gradiets. (a) Sedimet trasport capacity Flow discharge (1 3 m 2 s 1 ) Slope gradiet (%) Figure 3 Predicted (usig equatio 14) vs. observed sedimet trasport capacity ( ). Predicted :1 lie Observed (b) Sedimet trasport capacity Slope gradiet (%) Flow discharge (1 3 m 2 s 1 ) timated i the farmlad of Loess Plateau if the equatios 1 ad 8 are cosidered. Comparative aalyses betwee predicted ad observed sedimet trasport capacities usig equatios 1 ad 8 are preseted (table 3; figure 4a ad 4b). The predicted trasport capacity usig equatio 1 was lower tha the trasport capacity from the experimetal observatios above.11 kg m 1 s 1. Relative error, r 2, ad NSE were approximately 13.2% to 59.3%,.83, ad.1, respectively. These parameters suggested that the equatio of Beasley ad Huggis (1982) uderestimated trasport capacity i our experimet eve though the flow discharge of this study was withi the rage of their aalysis. I cotrast, all the sedimet trasport capacities predicted by equatio 8 were higher tha the observed capacity, idicatig that Zhag s model would overestimate the capacity, especially at lower discharges supported by NSE. Respose of Sedimet Trasport Capacity to the Hydraulic Parameters of Rill Flow. Flow velocity is oe of the mai factors that directly determies sedimet trasport capacity. Velocities that are measured directly, however, should be modified based o the flow regime (Nearig et al. 1997; Lei 4 JAN/FEB 215 VOL. 7, NO. 1

6 Table 3 Assessmet of models based o the coefficiet of relative error (RE), the coefficiet of mea relative error (MRE), the coefficiet of mea absolute relative error (MARE), the coefficiet of determiatio (r 2 ), ad the coefficiet of Nash-Suticliffe model efficiecy (NSE) betwee observed ad predicted trasport capacity usig equatios 1 ad 8. Model RE (%) MRE (%) MARE (%) r 2 NSE = 146 Sq.5 (q.46) 13.2~ =19,831 S q ~ et al. 1998; Zhag et al. 21a). The mea flow velocities used to determie the other hydraulic parameters cosidered i this study were thus obtaied by multiplyig the measured velocities by.7. Govers et al. (199) ad Nearig et al. (1999) reported that velocity could ot icrease much with icrease i flow discharge ad slope gradiet i erodible rills. I cotrast, i our oerodible bed, the mea velocity of rill flow icreased with higher flow discharges ad slope gradiets (figure 5a ad 5b). For slopes steeper tha 21.3%, velocity icreased more rapidly, perhaps because the sie compoet of gravity icreased rapidly ad affected the flow dow the flume. Because flow velocity chaged with flow discharge ad slope gradiet, the sedimet trasport capacity also varied differetly. This study showed that the best equatio to describe the relatioship betwee sedimet Figure 4 Predicted ([a]equatio 1 ad [b] equatio 8) vs. observed sedimet trasport capacity. (a) Predicted trasport capacity ad mea flow velocity was a power fuctio (figure 6a): = 3.3 v 4.52 (r 2 =.93, NSE =.93, p <.1). (15) From figure 6a we ca lear that trasport capacity icreased as velocity icreased. Zhag et al. (29) came to a similar coclusio but foud that a liear fuctio adequately described the relatioship. These authors also reported a critical velocity (.58 m s 1 [1.3 mi hr 1 ]) beyod which sedimet could be trasported. The grais of the test sedimet (with a media diameter of 28 µm [.1 i]) used i Zhag s experimet seemed to be suspeded ad/or deposited i the rill flow below the critical velocity. However, our study had o critical velocity, probably due to the test material, loessial soil, rather tha to the uiform sedimet, test bed, flow discharge, or slope gradiets. (b) Predicted Furthermore, Nearig et al. (1989) reported that shear stress was also a good parameter for calculatig sedimet trasport capacity. I our study, the measured sedimet trasport capacity could be expressed by a power fuctio better tha by other estimated fuctios associated with shear stress (figure 6b): =.2 τ 1.65 (r 2 =.54, NSE =.6, p <.1). (16) With the above fuctio, shear stress performed poorly o sedimet trasport capacity i our study ad i that by Ali et al. (212a). The form of relatioship betwee shear stress ad sedimet capacity, however, was similar to that by Nearig et al. (1989) ( = τ 3/2 ; WEPP model), Zhag et al. (29) ( =.54 τ ), ad Ali et al. (212a) ( =.85 τ 2.6 ). The expoet was about 1% higher tha that of WEPP ad 17% ad 2% lower tha that by Zhag et al. (29) ad Ali et al. (212a), respectively. The variatio i these results is likely due to experimetal coditios ad test materials, lower slope gradiets i the WEPP model, differet grai size i the erodible bed of Ali et al. (212a; 212b), ad uiform sad i a oerodible bed with steep slopes ad higher discharges Observed Observed 1:1 lie JAN/FEB 215 VOL. 7, NO. 1 41

7 Figure 5 Respose of mea flow velocity to differet discharge ad slope. (a).7 (b).7 Mea flow velocity (m s 1 ) Mea flow velocity (m s 1 ) Flow discharge (1 3 m 2 s 1 ) Slope gradiet (%) Slope gradiet (%) Flow discharge (1 3 m 2 s 1 ) by Zhag et al. (29). The predictio of sedimet trasport capacity uder both high ad low flow discharges ad differet test beds thus plays a vital role i the accuracy of the models of soil erosio (Ali et al. 213). Stream power or uit stream power has bee cosidered a sesitive hydraulic parameter for developig models of empirical trasport capacity (Yag 1972; Bagold 1966; Moore ad Burch 1986). Stream power ad uit stream power had sigificat liear relatioships with sedimet trasport capacity eve though the coefficiets of determiatio were.79 ad.59, respectively (figure 6c ad 6d). The liear fuctios for stream power ad uit stream power suggested critical values for stream power (.55 W m 2 ) ad uit stream power (.2 m s 1 [.4 mi hr 1 ]), which are supported by similar studies (Yag 1972; Moore ad Burch 1986; Govers ; Zhag et al. 29). Several statistical parameters were also used to evaluate the performace of the equatio developed by hydraulic parameters (table 4). Sedimet trasport capacity was calculated by these regressio equatios ad was compared with observatio. Sedimet trasport capacity was evaluated well by flow velocity, i agreemet with Ali et al. (212a). However, flow velocity was ot a good predictor for estimatig sedimet trasport, due to the itrisic drawback of direct detectio. Stream power was the best hydraulic parameter for predictig sedimet trasport capacity, i agreemet with Zhag et al. (29). I terms of other parameters, further research is required to validate the equatio related to trasport capacity Summary ad Coclusios This study ivestigated the sedimet trasport capacity of flows withi artificial rill chaels at various discharge rates ad slope gradiets usig a loessial soil as the sedimet source material. Sedimet trasport capacity otably icreased with icreases i both the flow discharge ad the slope gradiet. Flow discharge had a greater effect o trasport capacity tha did slope gradiet. A power fuctio relatig sedimet trasport capacity to discharge ad slope was well fitted by the data. By compariso, predictig sedimet trasport capacity resulted i a poor fit, ad the predicted values were lower tha the observed values calculated by equatio 1 ad were higher tha that by Zhag et al. (29), implyig that sedimet trasport capacity requires verificatio eve though several previous models have bee developed. I additio, sedimet trasport capacity was geerally well correlated with the ivestigated hydraulic parameters. Mea flow velocity, which was also related to the discharge, had a strog power relatioship with sedimet trasport capacity (r 2 =.93, NSE =.93). Of the other hydraulic parameters, stream power correlated best with sedimet trasport capacity (r 2 =.79, NSE =.78), while weaker relatioships were obtaied for shear stress (r 2 =.61, NSE =.6) ad uit stream power (r 2 =.59, NSE =.59). Notably, both stream-power parameters were better predictors of trasport capacity tha was shear stress, eve though the former are fuctios of the latter. Furthermore, these parameters had threshold values, which could be termed the critical stream power (.55 W m 2 ) ad the critical uit stream power (.2 m s 1 [.4 mi hr 1 ]) uder the coditios of this study. Sedimet trasport capacity uder these coditios could thus be accurately predicted by the derived empirical relatioship with flow discharge ad slope gradiet or by the relatioship with flow velocity. The differeces betwee the relatioships determied by this study ad those of other studies ca be attributed to the use of a oerodible bed ad loessial soil as the sedimet source ad to rill width ad the rages of flow discharge ad slope gradiet, implyig 42 JAN/FEB 215 VOL. 7, NO. 1

8 Figure 6 Sedimet trasport capacity as a fuctio of (a) mea flow velocity (v), (b) shear stress (τ), (c) stream power (ω), ad (d) uit stream power (P) for all combiatio experimets. (a) (c) Sedimet trasport capacity Sedimet trasport capacity.45 T.4 c = 3.3 ν 4.52 r 2 = Mea flow velocity (m s 1 ).45 T.4 c =.12 (w.55) r 2 = (b) (d) Sedimet trasport capacity Sedimet trasport capacity.45.4 =.2 t 1.65 r 2 = Shear stress (Pa).45.4 = 1.44 (P.2) r 2 = Stream power (W m 2 ) Uit stream power (m s 1 ) Table 4 The coefficiet of relative error (RE), the coefficiet of mea relative error (MRE), the coefficiet of mea absolute relative error (MARE), the coefficiet of Nash-Sutcliffe model efficiecy (NSE), ad the coefficiet of determiatio (r 2 ) o observed vs. predicted sedimet trasport capacity by hydraulic parameters. Hydraulic parameters RE (%) MRE (%) MARE (%) r 2 NSE Mea flow velocity 28.77~ Shear stress 18.6~ Stream power 88.46~ Uit stream power ~ that these relatioships are ofte site-specific. Further experimets will thus be required to evaluate sedimet trasport capacity i other scearios for estimatig total rill erosio over the large scale of the Loess Plateau. Ackowledgemets We wat to thak workers from simulatio rai hall of the State Key Laboratory of Soil Erosio ad Drylad Farmig o the Loess Plateau. We also wat to thak David Warrigto, a guest researcher at the Laboratory of Soil JAN/FEB 215 VOL. 7, NO. 1 43

9 Erosio ad Drylad Farmig o the Loess Plateau, Istitute the America Society of Agriculture Egieers a stoy, semiarid hillslope. Earth Surface Processes ad of Soil ad Water Coservatio, for givig suggestios o 33: Ladforms 24: the iitial mauscript ad two aoymous reviewers for Gimeez, R., ad G. Govers. 21. Iteractio betwee bed Nearig, M.A., G.R. Foster, L.J. Lae, ad S.C. Fiker. their valuable commets. Fudig for this research came roughess ad flow hydraulics i erodig rills. Water A Process-based soil erosio model for USDA- from the Natioal Natural Sciece Foudatio of Chia Resource Research 37: water erosio predictio project. Trasactios of (No & ) ad the Key project of Chiese Gokme, T., ad P.S. Vijay Trasport capacity models the America Society of Agriculture Egieers Academy of Scieces (No. KZZD-EW-4-3). for usteady ad o-equilibrium sedimet trasport 32(5): Refereces i alluvial chaels. Computers ad Electroics i Agriculture 86: Prosser, I.P., ad P. Rustomji. 2. 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