Journal of Hydrology 534 (2016) 630–637

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Journal of Hydrology

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Comparison of rill flow velocity over frozen and thawed slopes withelectrolyte tracer method

http://dx.doi.org/10.1016/j.jhydrol.2016.01.0280022-1694/� 2016 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: College of Water Resources and Civil Engineering,China Agricultural University, Beijing 100083, China.

Yunyun Ban a, Tingwu Lei a,b,⇑, Zhiqiang Liu a, Chao Chen a

aCollege of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, Chinab State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Chinese Academy of Science and Ministry ofWater Resources, Yangling, Shaanxi Province 712100, China

a r t i c l e i n f o

Article history:Received 10 October 2015Received in revised form 13 January 2016Accepted 14 January 2016Available online 22 January 2016This manuscript was handled by GeoffSyme, Editor-in-Chief

Keywords:Flow velocityFrozen/thawed soilRill erosionElectrolyte method

s u m m a r y

Freeze–thaw erosion is the primary soil water erosion form in high altitude and/or high latitude regions.The water flow velocity along an eroding rill over frozen and thawed slopes is vital to understanding ofrill erosion hydrodynamics. This study experimentally measured rill flow velocity over frozen and thawedslopes using electrolyte trace method under Pulse Boundary Model. The experiments used three flowrates of 1, 2, and 4 L min�1, three slope gradients of 5�, 10�, and 15�. The temperature of the rill flow waterwas supplied at 0 �C as controlled with ice–water mixture. Seven sensors were used to measure flowvelocity by tracing the solute transport process at 10, 110, 210, 310, 410, 510, and 610 cm distances fromthe electrolyte injection position. The measured velocity became steady at a distance of about 3 m fromthe electrolyte injection location, where the effect of the pulse boundary condition on the analytic solu-tion to the partial differential equation becomes negligible. Results showed that flow velocity increasedwith slope gradient and flow rate on frozen slopes. A significant effect was observed on the steepest slopeor at the highest flow rate over the thawed slope, which changed slightly on the gentle slopes and lowflow rates. Flow velocity was about 25%, 30%, and 40% higher on the frozen soil than on the thawed slopeat 5�, 10�, and 15� slopes and about 30% higher over the frozen slope at all flow rates. This study demon-strates that water over a frozen slope flows much faster than over a thawed slope. This study helps in thestudy and further understanding of the hydrodynamics of soil erosion and sediment transport behaviorsof frozen and thawed slopes.

� 2016 Elsevier B.V. All rights reserved.

1. Introduction

Freeze–thaw erosion is one of the main types of soil erosion inthe world. In high altitude and/or high latitude cold regions,freeze–thaw erosion is the primary soil water erosion form. Thearea of freeze–thaw erosion in China is 1,268,900 km2 or about22% of the national territorial area.

High altitude mountain and latitude areas featured with snowand glacier coverages are widely distributed throughout the worldand have dominant control on the flows and sediment transport ofmost major rivers (Singh et al., 2005). Erosion from frozen–thawedsoils is an important process in much of the northern parts ofAmerica, Europe, and Asia (Johnsson and Lundin, 1991; Hayhoeet al., 1992; Seyfried and Flerchinger, 1994; Vasilyev, 1994). Higherosion rate of seasonal frozen soils due to snow-melting runoffin cold regions, such as the Chinese Tibet Plateau, is also common.

The interaction between melted-water and frozen–thawed soilleads to upper slope soil removal and downstream river sedimen-tation (Emmanuel et al., 2008). Regions partially covered with gla-ciers may generate and deliver sediments at a much higher ratecompared with non-glacier-fed basins (Singh et al., 2003).

Climate change caused by global greenhouse gas emissions isexpected to increase regional and global air temperatures andcause changes in meteorological conditions, which can likely affectsubsurface thermal conditions (Kurylyk et al., 2014). Rapid climatewarming, which results in increased temperature, has been givensignificant attention in recent decades (Bloomfield et al., 2013;Menberg et al., 2013). The glacier area and the proportion of snowcoverage have been declining in recent years (Romshoo et al.,2015). This phenomenon, along with global warming, wouldsubstantially alter the natural stream flow characteristics and ulti-mately increase meltwater erosion in cold areas (Immerzeel et al.,2010; Thorsteinsson et al., 2013). The rise in air and subsurfacetemperatures induces permafrost thawing, which alters the surfaceand subsurface hydrology and soil erosion in high altitude and/or

Y. Ban et al. / Journal of Hydrology 534 (2016) 630–637 631

latitude regions and could accelerate the rate of anthropogenic cli-mate change by releasing carbon stored in the frozen soils into theatmosphere (Kurylyk et al., 2014). Day and night circulations andseasonal air temperature fluctuations cause temperatures in sur-face soil and water to increase, thereby causing permafrost thaw-ing. The snow and/or glacier melt water runs off the frozen soiland/or thawed soil surface in high erosion regions, which couldaffect surface or subsurface hydrology (Kurylyk et al., 2014), suchas flow velocity.

Flow velocity is an important parameter in the study of over-land flow and soil erosion and eroded sediment transportation.The mean flow velocity of shallow overland flow is important insoil erosion modeling because it is related directly to soil detach-ment and the sediment transport capacity of the water flow, whichdetermines the fates of sediments and pollutants (Rahma et al.,2013). Flow velocity is related directly to flow discharge, slope gra-dient, topography, and surface conditions (Lei et al., 2010; Zhanget al., 2003). Water in cold regions may flow over frozen or thawedsoil surfaces. Flow velocity over a frozen soil surface is much higherthan that over a thawed soil slope and causes more severe soil ero-sion. However, limited research has focused on measuring flowvelocity quantitatively. Ferrick and Gatto (2005) had done someresearches to quantify the effect of a freeze–thaw cycle on soil ero-sion, but the flow velocity data were not acquired.

A number of methods have been used for measuring the veloc-ity of shallow water flow. The measurement of water flow velocityoften involves tracer use. Commonly used tracers include dyes(Abrahams et al., 1986; Zhang et al., 2010), salts (electrolytes)(Lei et al., 2005; Planchon et al., 2005), magnetic materials(Ventura et al., 2001), heat pulses (Angermann et al., 2012), naturalwater isotopes (Berman et al., 2009), radioisotopes (Gardner andDunn, 1964), and floating objects (Tauro et al., 2010, 2012a). Trac-ers of different materials are used frequently to determine the sur-face or peak flow velocity and estimate the velocity of water flow.

In the recent decades, scientists have paid great attention in thestudy of soil erosion of frozen–thawed soils in the high altituderegions of India and Pakistan as well as China, high latitude areasof northern Europe and northern America. Their onsite or GIS dataindicated that the snow or ice melting water produced surface run-off of high velocity to delivery considerable amounts of suspendedand/or bedload sediments through routes over ice surface, insideand underneath glaciers.

Singh et al. (1995) used wooden floats to measure flow velocityof Dokriani Glacier in the Garhwal Himalayas based on linear traveltime of the floats when the time duration to travel this distancewas determined with a stopwatch. Their measured data indicatedthat the maximum and minimum flow velocities were 3.75 and1.54 m/s when the highest and lowered daily discharges were7.58 m3/s and 3.29 m3/s respectively. Singh et al. (2005) alsoapplied wooden floats to measure the velocity of melt flow, usingthe time and distance traveled by the floats, at Gangotri Glacierin the Garhwal Himalayas. The float traveling length at the gaugingsite was about 25 m. The channel was divided into four segmentsto measure water flow velocity. The mean flow velocity was deter-mined by multiplying the surface velocity by 0.90. Wooden floatsare too big to be used for velocity measurement in small erodingrills with low flow rate.

Salt or fluorescent dye is also commonly used as the tracer tomeasure flow velocity. For example, Humphrey et al. (1986) usedturbidity pulses to estimate mean velocity of water flowing frombeneath Variegated Glacier, Alaska. Electrical conductivity had alsobeen used successfully by Collins (1979) for distinguishing the sur-face melt water from basal components of discharge from twoalpine glaciers in Switzerland. Stone et al. (1993) described theconstruction, calibration and field usage of two instruments, onemeasured turbidity and the other measured electrical conductivity

of sub-glacial water. They presented data obtained from beneathTrapridge Glacier, Yukon Territory, Canada, to demonstrate thepotential usefulness of these devices.

Other methods which have been adopted for velocity measure-ments of overlandsheetflowor rillwaterflowcouldalsobeapplicableto measure velocity of water flow over frozen and thawed soil slopes.

Shit and Maiti (2012) believed that when any erosion experi-ment involving rills, it was important to characterize the flow interms of its velocity. Their results indicated that most measured rillflow velocities were between 2 and 8 cm s�1.

Muste et al. (2014) conducted experiments to measure shallowwater flow velocity using Large-scale Particle Image Velocimetry(LSPIV), under laboratory conditions. The surface flow was visual-ized by sawdust particles of cypress wood with a mean diameterless than 1 mm. A digital camera of highspeed image recordingwas used to capture the surface flow. LSPIV measurements werecompared with velocities measured by the salt velocity gauge(VSALT). The analysis showed a proportional relationship betweenthe two methods, VSALT = 0.81 VLSPIV, to verify that the LSPIVtechnique was a depth-averaged measure of surface velocitiesand salt tracing. This method needs to use expensive device formeasurement, which is not convenient to be applied for field mea-surement. Most importantly, themethod needs to visually track themovement of cypress wood in the water flow before its velocity isdetermined. This should cause difficulties for the measurement offlow velocity when the water contains great amount of sediments.

Tauro et al. (2012b) conducted a concept experiment to assessthe feasibility of tracing overland flow on an experimental plotusing a novel fluorescent particle tracer. The experiments usedbeads of 75–1180 lm in diameters, to be sensed through a videoacquisition unit. Particle transits were analyzed with image analy-sis techniques. Average flow velocity was computed by the timemeasurements of the particles moving in the overland flow. Themeasured velocities were compared with those obtained usingrhodamine dye. Experiments demonstrated the potential of themethodology or understanding overland flow dynamics. This hasthe same difficulties as the use of LSPIV.

Based on infrared thermography, João de Lima and Abrantes(2014) presented a technique to allow a quantitative measurementof overland flow and rill flow velocities. Laboratory experimentswere conducted to verify new thermal tracer technique by compar-ing with the traditional dye tracer method by injecting combinedtracers of heat and dye into shallow water flow. The resultsdemonstrated that thermal tracers can be used to estimate bothoverland and rill flow velocities, since the measured velocitieswere similar to those by using dye tracers. This method is promis-ing to measure flow velocity in the eroding rills.

Dye tracers have long been used for shallow overland and rillflow velocity measurements. Numerous studies indicated thatthe proportional coefficient varied under different flow regimes(Foster et al., 1992; King and Norton, 1992; Luk and Merz, 1992).Horton et al. (1934). Theoretic analysis suggested that the coeffi-cient should be 0.65 for laminar flow. Emmett (1970) suggested,based on his laboratory experiments, the use of 0.5–0.6 for laminarflow and 0.8 for transient water flow. He also estimated, throughhis field experiment data sets, that the coefficient should be0.45–0.50. But Luk and Merz (1992) estimated a coefficient of0.52 for laminar flow and 0.75 for transient and turbulent flows.King and Norton (1992) found that when water flow became tur-bulent from laminar flow, the coefficient did not change with flowrate but reversely correlated with slope. All these indicate the dif-ficulties in using dye tracers of different colours for flow velocitybecause of the variations in calibration coefficients, which aredependent on flow velocity and regimes. Another difficulty maycome from the vision difficulties. When the flow containssediments of deep colors, such as those originated from black soils

632 Y. Ban et al. / Journal of Hydrology 534 (2016) 630–637

commonly found in the high altitude and/or high latitude regions,visual tracing of the dye movement in the water flow couldbecome very difficult. This can cause high error in measuring flowvelocity, even if it could be done.

An electrolyte tracer method was suggested by Lei et al. (2005)for measuring shallow water flow velocity. The method accuratelymeasures shallow water flow velocity by detecting the transportprocess of electrolyte in the flow as it passes a sensor at a knowndistance. This method predicts velocities accurately at relativelylong distances from the tracer/electrolyte injection location, wherethe time to travel to the position is long enough that the inputboundary condition can be treated as a pulse input.

The flow velocity is closely related to hydrodynamics, whichdirectly related to the detachment of soil from channel bed andthe transportation or deposition of detached sediments along theeroding routes. Therefore, the study on flow velocity of frozenand thawed soil is of interest.

This study used the electrolyte tracer (Lei et al.’s, 2005) methodto (1) investigate the method of measuring the velocity of waterflow over frozen and thawed soil surfaces, (2) experimentally mea-sure and compare the velocity of water flow over different soilsunder different hydraulic conditions as determined by flume slopeand flow rate, and (3) analyze the characteristics and influences ofslope gradient and flow rate on flow velocity.

2. Methodology

2.1. Solute transport model

Salt solution is transported in the water flow through convec-tion and dispersion mechanisms. Many factors influence the trans-portation process, such as flow rate, flow velocity, and waterquality. A shallow water flow can reasonably be assumed a steadyflow and approximated as a one-dimensional flow along thestream line. Its transportation is well defined and quantified by apartial differential equation.

When the flow is regarded as steady and uniform, the convec-tional and dispersion processes of salt (chemical) in a steady waterflow are defined by Fick’s law and mass conservational law andgiven by partial differential equation for the 1-D solute transport as

@C@t

þ u@C@x

¼ DH@

@x@C@x

� �ð1Þ

where C is the electrolyte concentration (kg m�3), which is a func-tion of distance x and time t and proportional to the electrical con-ductivity of the solution, x is the coordinate along the slope (m), u isthe flow velocity (m s�1), t is time (s), and DH is the hydrodynamicdispersion coefficient (m2 s�1).

When the upper boundary condition is assumed to be a pulse,the initial and boundary conditions for Eq. (1) are given as

Cðx ¼ 0; tÞ ¼ C0dðtÞ; ð2aÞ

Cðx ¼ 1; tÞ ¼ 0; ð2bÞ

Cðx; t ¼ 0Þ ¼ 0: ð2cÞThe solution to Eq. (1) as a time-dependent function is given by

Lei et al. (2005) as

Cðx; tÞ ¼ C0x

2tffiffiffiffiffiffiffiffiffiffiffiffipDHt

p exp �ðx� utÞ24DHt

!: ð3Þ

The data obtained experimentally were fitted with Eq. (3) basedon the least square method (Lei et al., 2005). This fitting processsimultaneously yields the initial concentration (C0), flow velocity(u), and hydrodynamic dispersion coefficient (DH).

2.2. Experimental materials and methods

The deposited soil materials were collected from watershed-deposited sediments at an altitude of 3682 m a.s.l. The soil wasair-dried and passed through a 2-mm sieve prior to measurementof its compositional fractions. The soil contained 28.0% of sand,64.2% of silt, and 7.8% of clay particles.

Soil flumes were composed 3 m long, 10 cm wide, and 12 cmdeep steel. The length of the flumes made it easier to place theminto the freezer to create frozen soil samples. The prepared soilmaterials were packed into the flume at a depth of 10 cm beforethe flume was filled with water to saturate the soil materials andsimulate the water-deposited sediments. The soil surface elevationnear the flume walls was filled slightly higher than that in the mid-dle surface to avoid the effects of the flume side walls on the waterflow. The soil-filled flumes were then saturated further andallowed to equilibrate for a day (24 h) before each experimentalrun to provide an even initial water content distribution and elim-inate any effects of uneven packing. The soil-filled flumes wereplaced into the freezer, with temperatures adjusted between�30 �C and 0 �C to freeze the soil flumes for more than 24 h at con-trolled temperatures of �25 �C to �15� C.

Parts of the soil flumes were taken out to unfreeze the soil com-pletely before use in running the experiments on the thawed soil.Parts of the flumes were kept inside the freezer and will be used tosimulate experiments of water flow over frozen soil. The 3-m longtotally thawed and frozen soil flumes were connected end-to-endto form 6-m long flumes on the platform to run the experimentsunder different combinations of flow rates and slope gradients.The platform can be adjusted to desired slopes between 0� and 35�.

The experimental flume system consisted of the following com-ponents: a water distributor to supply a steady water flow at thedesigned rate into the flume, a soil flume, and a flow velocity mea-surement system.

The water distributor was used to supply uniform and steadywater flow into the flume at a controlled and constant flow rateto the soil flume at its upper end. The water flowwas supplied witha cylindrical tank, which was mixed with ice cubes to maintain thesupplied water at about 0 �C.

The flow velocity measurement system consisted of a computer,a data logger, sensors, and a solute injector. A specially designedsoftware was installed in the computer for controlling the mea-surement process and the computation of velocity and data man-agement. The specially designed data logger was used as aninterface unit to interpret computer information to control thepulse signal input unit, the digitalization of the measured continu-ous signal of the sensors, local data logging, and data transfer to thecomputer. The sensors detected the electric conductivity of thewater flow. The solute injector was used to inject the electrolytesolution into the water flow as a velocity measurement tracerwithin the designated duration.

The experimental equipment system was set up as shown inFig. 1.

The solute injector was set up in the water distributor at a dis-tance of 10 cm from the upper end of the flume. Seven electrolytesensors connected to the data logger were inserted into the soil atthe bottom of the flume at distances of 10, 110, 210, 310, 410, 510,and 610 cm from the solute injector to measure the solute trans-port process before flow velocities were calculated at thesepositions.

The experiments involved a combination three flow rates (i.e., 1,2, and 4 L min�1) and three slope gradients (5�, 10�, and 15�) forboth frozen and thawed soils in three replicates. The reason wasthat the experiment could not be conducted when the flow ratewas higher than 4 L min�1 and slope gradient was higher than15� because the soil materials which had been saturated before

Fig. 1. The experimental equipment system.

Y. Ban et al. / Journal of Hydrology 534 (2016) 630–637 633

freezing, would slide down the flume before the experiments weredone.

Regulated icy water flow (0 �C) was introduced into the flume atthe upper end. The system began to work when the computer ini-tiated the start of the experiment. The highly concentrated KCl(about 6 mL) was injected into the water flow for a period of lessthan 500 ms at a location 10 cm away from the upper end of theflume or the location of the first sensor. The injection of salt solu-tion into the water flow was performed by a computer-controlledelectromagnetic valve. The data logger started to register the solutetransport processes from the signals of the sensors at a rate of 10points per second. Electrical conductivity values at seven locationswere logged into the computer by a specially designed data logger,which was controlled by a specially developed software.

3. Results and discussion

3.1. Electrolyte transport processes in the water flow

Fig. 2 shows the experimentally measured data (dotted curves)under different slope gradients and flow rates of frozen andthawed soils. The curves under different conditions were fittedwith the analytical solution function (smooth curves) as given byEq. (3).

Fig. 2 shows that S1 to S7 are normalized concentration datasets, which are the functions of time of sensors at seven positions.S1 represents the first sensor, which is located nearest to the injec-tor, and S7 is the last sensor at the other end of the flume. Fig. 2shows that the analytical solution well follows the peak and therising and falling limbs of the experimentally obtained curves,especially at the positions far from the solute injection position.This indicates that Eq. (3) correctly simulates the major featuresof the solute transport process in water flow on two soils andagrees with the suggestion made by Dong et al. (2015), who indi-cated that the analytic solution can estimate velocity accuratelywhen the distance is long enough for the solute to cover it in morethan 4 s. The third sensor was 2.1 m away from the salt injector.Hence, the time for the solute to cover this distance requires 5–8 s.

The imperfect dotted curves may have been caused by theuneven flow of electrolyte transported in irregular rills with ran-dom soil erosion and sediment deposition. The measured data setsshow that the peaks of the curves decreased with distance from thesource point under the same experimental conditions. The break-through time moments of the concentration curves decreased withthe increase in slope gradient.

3.2. Flow velocity over frozen and thawed soil slopes

Flow velocities at seven measurement locations under differenthydraulic conditions over frozen and thawed slopes are presentedin Fig. 3. The red and black symbols represent water flow velocitiesover frozen and thawed slopes, respectively.

Flow velocities were distributed along the distance in similarpatterns (Fig. 3 and Table 1). In addition to the first sensor, the flowvelocities of the second and third sensors were relatively lower,and the rest of the four sensors produced similar and consistentflow velocity values. Most values of the variance in Table 1 rangedfrom 0 cm s�1 to 3.00 cm s�1, indicating that the computed/mea-sured flow velocities were constant at the positions beyond 3 m,where the assumption of pulse boundary condition did not havea significant effect on the measured flow velocities. These resultsagreed with the results reported by Lei et al. (2013) and Shi et al.(2012). Both studies concluded that the analytic solution underthe pulse boundary condition cannot produce accurate measuredvelocities when the measurement location was close to the soluteinjector. The error caused by the analytic solution under pulseboundary condition assumption can be neglected at locationswhere the solute transportation time from the injection locationto the measurement points were sufficiently long.

The flow velocity over frozen soil is shown in Fig. 3. The redsymbols under the same flow rate increased significantly withthe increase in slope gradient. A considerable effect was generallyobserved when the flow was on the steeper slope (Fig. 3) becauseof the increases in gravitational force component. Flow velocityalso increased significantly with increases in flow rate. Flow veloc-ity considerably increased under high flow rate of 4 L min�1 whenthe slope increased from the gentle slope of 5� to the steep slope of15�. The average velocities were about 22.3, 27.0, and 40.6 cm s�1.However, flow velocity increased gradually with the increase inflow rate under different slopes. The results showed that the higherthe slope gradient and flow rate, the higher the flow velocity wasover frozen soil.

The flow velocities of frozen and thawed soils at different slopepositions under different slope gradients and flow rates are pre-sented in Tables 1a and 1b, respectively.

The flow velocities behaved differently over the thawed soilsurface, as shown in Fig. 3. The black symbols indicate a compar-ison of flow velocities over thawed and frozen soil slopes. The slopegradients had significant effects on flow velocity. Minimal differ-ences in flow velocity were observed for thawed soil under lowflow rates of 1 or 2 L min�1 between gentle and moderate slopes(i.e., 5� and 10�, respectively) (Fig. 3a and b). The same flow veloc-ities under flow rates of 1 and 2 L min�1 were about 12 and

0

0.05

0.1

0.15

0 20 40 60

Nor

mal

ized

con

cent

ratio

n

Time/s

slope=5°q=4 L min-1

Frozen soil

S6 S7

S1

S2

S3

S5S4

0

0.05

0.1

0.15

0 20 40 60

Nor

mal

ized

con

cent

ratio

n

Time/s

slope=5°q=4 L min-1

Thawed soilS1

S2S3

S4S5 S6

S7

0

0.05

0.1

0.15

0 20 40 60

Nor

mal

ized

con

cent

ratio

n

Time/s

slope=10°q=4 L min-1

Frozen soilS1

S2S3

S4 S5

S7

S6

0

0.05

0.1

0.15

0 20 40 60

Nor

mal

ized

con

cent

ratio

n

Time/s

slope=10°q=4 L min-1

Thawed soilS1

S2

S3S4

S5 S6

S7

0

0.05

0.1

0.15

0 20 40 60

Nor

mal

ized

con

cent

ratio

n

Time/s

S1S2

S3

S4S5

S6S7

slope=15°q=4 L min-1

Frozen soil

0

0.05

0.1

0.15

0 20 40 60

Nor

mal

ized

con

cent

ratio

n

Time/s

slope=15°q=4 L min-1

Thawed soil

S3

S4S5

S6S7

S1S2

Fig. 2. The measured solute transport processes with fitted curves.

634 Y. Ban et al. / Journal of Hydrology 534 (2016) 630–637

14 cm s�1 on slopes of 5� and 10�, respectively, as shown inTable 1b. However, flow velocities were significantly higher atthe high flow rate of 4 L min�1 under slope gradients of 5�, 10�,and 15�. The flow velocity of 4 L min�1 increased from 18.2 cm s�1

at 5� to 22.5 cm s�1 at 10�. Flow velocities under the steepest slopeof 15� were 17.6 cm s�1 at flow rate of 1 L min�1 and 22.5 cm s�1

and 25.4 cm s�1 at flow rates of 2 and 4 L min�1, respectively.The flow velocity of 4 L min�1 did not increase when the slopesincreased from 10� to 15�. Higher erosion from the steep slope of15� and high flow rate of 4 L min�1 resulted in high erosion of rillbed and produced headcuts along the rill. Rill morphology withheadcuts caused localized ‘‘waterfalls”, which were responsiblefor the non-increasing rill flow velocity. This phenomenon ofsteep slope and high flow rate, which lowered velocity, wasdemonstrated visually by the headcuts shown in Fig. 4.

Areas 1 and 2 in Fig. 5a and b show that the vertical distributionof data points, which indicates that flow velocity over thawed soilremained unchanged and was affected by headcuts at the steepslope and high flow rate. However, the frozen soil slopes producedno headcuts even at high flow rates and slope gradients. Hence,flow velocity over frozen soil slopes continued to increase withthe increase in slope gradients and flow rates.

Less energy was found at low slope and flow rate to produceheadcuts. However, the energy of the slope continued and resultedin an increase in flow velocity with slope gradient and flow rate.

3.3. Comparison of velocities over frozen and thawed soil slope

Flow velocity was significantly affected by soil surface confor-mation, slope gradient, flow rate, and all their interactions. Flow

0

10

20

30

40

50

0 200 400 600

Flow

vel

ocity

/ cm

/s

Distance / cm

1 L min-1 1 L min-1

2 L min-1 2 L min-1

4 L min-1 4 L min-1

(a) 5°

0

10

20

30

40

50

0 200 400 600

Flow

vel

ocity

/ cm

/s

Distance / cm(b) 10°

0

10

20

30

40

50

0 200 400 600

Flow

vel

ocity

/ cm

/s

Distance / cm(c) 15°

Fig. 3. Flow velocities over frozen (red symbols) and thawed slopes (black symbols).

Table 1aFlow velocities on frozen soil (cm s�1).

Slope (�) Flow rate(L min�1)

X (cm) Averagevelocity

Variance

310 410 510 610

5 1 12.4 15.2 16.3 15.6 14.9 2.22 17.8 18.3 17.3 16.3 17.4 0.54 22.6 21.8 23.4 21.3 22.2 0.8

10 1 15.4 15.9 15.1 16.4 15.7 0.22 21.5 24.1 22.2 22.6 22.6 0.94 26.1 28.3 28.3 25.4 27.0 1.7

15 1 23.9 24.1 26.8 21.8 24.2 3.22 27.9 29.1 30.9 30.2 29.5 1.34 45.6 40.6 37.2 39.1 40.6 9.7

X is the distance between the electrolyte injector and the sensors, m.

Table 1bFlow velocities on thawed soil (cm s�1).

Slope (�) Flow rate(L min�1)

X (cm) Averagevelocity

Variance

310 410 510 610

5 1 10.1 12.8 13.2 13.2 12.3 1.72 12.5 12.2 12.0 12.5 12.3 0.14 17.9 18.2 17.5 19.2 18.2 0.4

10 1 11.9 13.9 14.0 13.3 13.3 0.72 12.3 14.9 14.0 14.6 14.0 1.04 20.3 24.0 21.8 23.9 22.5 2.4

15 1 16.2 17.6 17.8 18.8 17.6 0.92 22.4 23.7 22.3 21.5 22.5 0.64 24.2 24.6 26.1 26.5 25.4 0.9

X is the distance between the electrolyte injector and the sensors, m.

Headcut

Fig. 4. Headcuts of thawed slope responsible for lowered flow velocity of rill flow.

Y. Ban et al. / Journal of Hydrology 534 (2016) 630–637 635

velocity was always higher over the frozen soil than over thethawed soil under a given slope position (Fig. 5 and Table 1). Themain reasons were the difference in frictional force and erosionalbehaviors of the two slope surfaces. Frozen soil tended to resultin a decrease in frictional force or resistance to water flow. Theheadcuts caused by erosion of the thawed slope resulted in areduction in flow velocity. The influences of these two factors onflow velocity of frozen soil were much higher than that of thawed

Area 1 A

(a) flow velocity of different slopes (b) flow veloocity of different flow rates

Area 2

Fig. 5. Comparison of the flow velocities on frozen and thawed soil slopes.

636 Y. Ban et al. / Journal of Hydrology 534 (2016) 630–637

soil slope, especially on the highest slope gradient and flow rate, asshown in Fig. 5.

A significant difference was observed in the flow velocity underdifferent slopes (Fig. 5a). The flow velocities of frozen soil under allflow rates were about 24%, 29%, and 39% higher than those ofthawed soil with the coefficients of determination (R2) of 0.83–0.93. Frozen soil required less energy to overcome frictional forceand headcuts compared with thawed soil, and more water flowenergy was necessary to maintain higher flow velocity. The flowvelocity over frozen soil was much higher than that over thawedsoil slope when the slope increased. The percentages were about25%, 30%, and nearly 40% on the slope of 15�. Therefore, the steeperthe slope, the higher the increase in flow velocity in the slopes.

No significant difference was observed in the proportional coef-ficient of the flow velocity under different flow rates, as shown inFig. 5b. The flow velocities frozen soil were approximately 29%,33%, and 34% higher than those on thawed soil slopes. The flowrates used in the experiments had a slight influence on the rela-tionship of flow velocity between frozen and thawed soils. Hence,the balance between gravity and frictional force was affected byflow rates. Flow rates had a minimal contribution to the variationsin flow velocity between frozen and thawed soils. Flow velocityover frozen soil was about 30% higher than that over thawed soilregardless of the amount of flow rate.

4. Conclusion

A series of laboratory experiments were conducted using threeflow rates at 1, 2, and 4 L min�1 under three slope gradients of 5�,10�, and 15� at seven measurement locations from the solute injec-tion position. The experiments were conducted to measure theprocesses of salt transport processes in the water flow and com-pute the velocity of water flow over frozen and thawed soil slopes.The flow velocities increased with slope gradients and flow rates,but the extent of increase was notably different. For frozen soilslopes, the higher the slope gradient and flow rate, the higher theflow velocities. The flow velocity over thawed soil slopes wasreduced for the high slope of 15� and flow rate of 4 L min�1 andeffects of the headcuts created by erosion. The frozen soil layerreduced frictional force with no headcuts and resulted in higherflow velocity over the frozen soil slope than that over the thawedsoil slope. The percentages were 29%, 34%, and 39%. Much higherflow velocities occurred over frozen soil slopes than those overthawed soil slopes over a steep slope, and were about 30% higher

on average under different flow rates. The study is important inunderstanding the hydrodynamics of soil erosion and sedimenttransportation of frozen and thawed soil slopes.

Acknowledgements

This work was financially supported by the ‘‘National NaturalScience Foundation of China” – ‘‘China” under Project No.41230746 and ‘‘Agricultural water transformation based onmulti-process driving mechanism for improving water use effi-ciency” (No. 51321001).

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