Abstract

To have accurate runoff velocity, there is need to improve dye tracer method for estimating surface runoff velocity. This can enhance the calculations of relevant hydrologic parameters that will lead to a better understanding of hydrological processes and soil erosion. In this study, an integrated dye tracer and image processing method (IPV) and dye tracer method (AOV), respectively, were used to estimate runoff velocity under three slope gradients (5°, 10°, and 15°) and three slope positions (up-slope, mid-slope, and down-slope). The results showed more variation in runoff velocity under IPV than AOV. Both IPV and AOV were positively correlated with slope gradient. IPV values were close to AOV ones for slope gradients ≤5°, but were significantly different for slope gradients ≥10°. The mean AOV value was 10.6% higher than that of IPV. Regression analysis showed that compared with AOV, IPV overestimated and underestimated runoff under low and high runoff velocity conditions, respectively. The use of image processing in IPV was advantageous because of its ease of use with fewer artificial errors and its suitability for lateral diffusion of runoff. Irrespectively, additional studies are needed to verify and/or improve further the use of this method in runoff velocity analysis.

INTRODUCTION

Surface runoff velocity is a key hydrologic parameter in slope hydrological processes and soil erosion. First, it directly affects sediment yield by controlling the partitioning of rainfall into runoff and infiltration (Zhang et al. 2003, 2016; Chen et al. 2008; Lei et al. 2010; Meral 2016). An accurate estimation of surface runoff velocity is needed for a reliable determination of runoff coefficient and sediment yield (Del Giudice et al. 2014; Zhang et al. 2014). Second, surface runoff velocity is used to derive hydrologic parameters such as Reynolds number and Manning coefficient used to determine slope flow regimes, slope hydrologic processes, and erosion–sediment relationships (Philip 1954; Bissonnais & Singer 1992; Fohrer et al. 1999; Furumai et al. 2005; Ares et al. 2016; Sun et al. 2016). Finally, surface runoff velocity dominates runoff kinetic energy. The accurate estimation of runoff velocity can benefit the calculation of runoff kinetic energy, which can be used to predict sediment carrying capacity and sediment yield (Wilson 1973; Williams & Berndt 1977; Abrahams et al. 1986; Li et al. 1996; Nadal-Romero et al. 2013; Rahma et al. 2013; Shi et al. 2013, 2014; Yan et al. 2013). Hence, the estimation of runoff velocity is critical in soil science and hydrology.

Different technologies and methods have been developed in the past decades to estimate runoff velocity, among which tracer methods are the most popular. Tracers vary from dye (Abrahams et al. 1986; Zhang et al. 2010) to electrolyte pulse (Planchon et al. 2005; Lei et al. 2010), large and light weight particles (Singh et al. 1995, 2005; Tauro et al. 2012a, 2012b; Muste et al. 2014), thermal (de Lima & Abrantes 2014; de Lima et al. 2015), magnetic (Ventura et al. 2001) and heat (Angermann et al. 2012) pulses, liquid water isotope (Berman et al. 2009), and radioisotope (Gardner & Dunn 1964). Of all these, dye tracer is the earliest used tracer, and it is still widely used in laboratory experiments due to its ease of operation and stability. Electrolyte tracers measure changes in runoff solute concentration that is inverted for runoff velocity. This method is based on mathematical solutions to solute transport in shallow runoff conditions (Lei et al. 2010). Moreover, it is easily affected by sediment charge, resulting in poor correlation between runoff velocity and dispersion coefficient. Using a large and light weight particle tracer like sawdust (diameter < 1 mm) to estimate runoff velocity is another option. Sawdust needs image velocimetry that is composed of a high-speed digital camera to record its movement (Muste et al. 2014). On the one hand, sawdust could also affect the surface runoff flow regime and, on the other hand, sediment load can change sawdust movement. Both of them can reduce the reliability of runoff velocity estimation by this method. An ingenious alternative method is the use of fluorescent particle tracer to estimate overland flow velocity (Tauro et al. 2012a, 2012b). Although this method reduces the effects of sediment concentration on runoff velocity measurement, it requires complex devices for fluorography. Thermal tracer technique uses infrared thermography to visualize very shallow flows and allows quantitative measurement of overland and rill flow velocities by injecting a heated dye (Schuetz et al. 2012; de Lima & Abrantes 2014). While injecting high temperature water into runoff is difficult to operate in most rainfall experiments, other tracers like liquid water isotope and radioisotope are expensive and complicated, equipment-dependent and therefore hard to apply in laboratory and field experiments.

The traditional dye tracer method used to determine surface runoff velocity is done by adding dye to runoff and measuring the time the dyed runoff takes to move over a given distance on a slope. The accuracy of the estimated runoff velocity depends on the selection of calibration coefficient in the velocity calculation, which is closely related to the flow regime (Horton et al. 1934; Emmett 1970; Foster et al. 1984; King & Norton 1992; Luk & Merz 1992). Furthermore, it often induces artificial error when determining the time the dyed runoff flows over a given distance (Luk & Merz 1992; Abrahams & Atkinson 1993). It is also time- and labor-consuming. Currently, high-resolution digital cameras are increasingly used to capture changes on slope surfaces for soil and water processes. Digital cameras only record change in velocity at any time period, but also clearly identify dyed runoff front. Therefore, the use of integrated dye tracer and image processing to estimate slope runoff velocity could reduce artificial error and increase the accuracy of estimation of surface runoff velocity. However, the accuracy and reliability of this method need to be improved by conducting further laboratory experiments.

In this study, rainfall simulation was used to generate runoff on various slope gradients and the runoff periodically dyed to measure runoff velocity by dye tracer method. A digital camera was next used to record the progress of the dyed runoff flow on the slopes. Then we used image processing software to extract images from the recorded video by the camera and to detect the distance that the dyed runoff moved over a given time to calculate runoff velocity. The aim of the study was to: (1) demonstrate the process of runoff velocity estimation using the integrated dye tracer and image processing method; (2) compare the measured velocity under the method with that under only the dye tracer method; and (3) explain the differences between the two methods.

MATERIALS AND METHODS

Materials

The runoff simulation experiment was carried out in a rainfall simulation hall belonging to the State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau. A metal box (3 m long, 1 m wide, and 0.35 m deep) filled with soil was used for the slope runoff simulation. Soil sieved through a 5 mm mesh and air-dried was loaded in the metal box to the depth of 0.3 m and the soil maintained at a bulk density of 1,300 kg·m−3. The soil was collected from a local field surface soil (0‒0.2 m) with a particle composition of 33.6% clay, 39.7% silt, and 26.7% sand, respectively. A digital camera (Sony DSC x-1) was set at a height of 3 m above the ground and 3 m away from the front wall of the metal box (Figure 1(a)). There were three slope gradients (5°, 10°, and 15°) in the rainfall simulation experiment. The general specifications of the digital camera are shown in Table 1. The rainfall intensity was 60 mm·h−1 and each rainfall event lasted for 60 min with a uniform coefficient of 0.9. The dye was potassium permanganate solution with a purple color. The reason for using potassium permanganate solution was that it can dye runoff immediately after application and can last for a long time. Also, the color of potassium permanganate was different from that of the soil and was easily detectable during image processing.

Figure 1

A schematic for the experiment (a) and the determination of runoff velocity under the integrated dye tracer and image processing method (b).

Figure 1

A schematic for the experiment (a) and the determination of runoff velocity under the integrated dye tracer and image processing method (b).

Table 1

General specifications of the digital camera used in the study

Item Unit Specification 
Optical resolution Pixel 1,920 × 1,080 
CMOS size Inch 1/3 
Focal length cm ∼25 cm – ∞ 
Field of view ° 120 
Recording speed Frame per second 30 
Item Unit Specification 
Optical resolution Pixel 1,920 × 1,080 
CMOS size Inch 1/3 
Focal length cm ∼25 cm – ∞ 
Field of view ° 120 
Recording speed Frame per second 30 

Methods

After the runoff had been generated for 5 min, the dye was added every 5 min into the runoff at three slope positions: up-slope (0‒1 m), mid-slope (1‒2 m), and down-slope (2‒3 m) along the top–bottom direction. Two methods (dye tracer, and integrated dye tracer and image processing) were used to estimate surface runoff velocity under the three slope gradients. Runoff velocity determined by the dye tracer method was denoted as AOV and the one determined by the integrated dye tracer and image processing method denoted as IPV.

Dye tracer method

During the simulated rainfall, a 0.5 m long ruler was placed horizontally on the soil surface. When the generated runoff velocity on the slope was steady, the dye was added to the runoff and a stopwatch used to record the time (T) that the dyed runoff flowed over the length (L) of the ruler. AOV was then calculated as:  
formula
(1)
where k is the calibration coefficient of runoff velocity; T is the time that the dyed runoff flowed over the length of the ruler (s); and L is the ruler length (m).

Numerous studies suggest that the coefficient k varies with flow regime. Based on theoretical analysis, Horton et al. (1934) recommended a calibration coefficient of 0.65 for laminar flow. Emmett (1970) suggested different coefficient ranges, which vary from 0.5–0.6 for laminar flow, to 0.8 for transient flow under laboratory conditions, and to 0.45–0.50 under field conditions. Other studies have set the coefficient at 0.52 for laminar flow and 0.75 for transient and turbulent flows (Luk & Merz 1992). The calibration coefficient k was set at 0.65 in this study – a trade-off value for slope length and flow regime (Li et al. 1996; Dunkerley 2001; Zhang et al. 2010).

Integrated dye tracer and image processing method

The IPV procedure was as follows: image acquisition → image rectification and background calibration → runoff velocity measurement. First, we used the digital camera to record the whole runoff simulation process. Then, slope surface images containing information on dyed runoff flow on the slope were extracted from the runoff simulation video at an interval of 2 s using ImageJ software (version: 1.43, developed by National Institute of Health). Second, the projection transformation of the extracted images was taken (generating orthoimages of the slope surface) and background calibration (making the dyed runoff easily distinguishable from soil and non-dyed runoff for runoff front detection) using Photoshop software (version: 15.0) for the next image processing. After that, every four frame sequential images were montaged as one image for IPV calculation in Image-Pro Plus software (version: 5.0).

In this study, three distances through which the dyed runoff flowed on the slope (denoted as L1, L2, and L3) were detected by image processing (Figure 1(b)). Then, the runoff velocity was calculated as follows:  
formula
(2)
where L1, L2, and L3 are the distances through which runoff flows during the three periods (m); V1, V2, and V3 are the velocities for runoff flow over the distances L1, L2, and L3, respectively (m·s−1); and T is the time interval at which the images were extracted from the video (s).
The equation for the calculation of IPV is expressed as:  
formula
(3)
where IPV is runoff velocity determined by the integrated dye tracer and image processing method (m·s−1).

RESULTS

Runoff velocity change during rainfall

The changes in AOV and IPV during rainfall on the three slope gradients are shown in Figure 2. Generally, the trends in both AOV and IPV increased from the start to the end of the rainfall event. Also, both AOV and IPV had the same trend, in that runoff velocity increased with increasing slope gradient. In other words, the values for AOV and IPV were higher under 15° than under 10° slope gradient, which in turn was higher than under 5° slope gradient (the lowest). This result indicated that IPV (determined by the integrated dye tracer and image processing method) captured the relationship connecting runoff velocity, rainfall duration, and slope gradient. However, there were differences in the degree of fluctuation of runoff velocity between AOV and IPV during a rainfall event, with a higher degree of fluctuation in IPV than AOV-generated runoff velocity.

Figure 2

Changes in AOV and IPV-generated runoff velocity during a rainfall event on three different slope gradients.

Figure 2

Changes in AOV and IPV-generated runoff velocity during a rainfall event on three different slope gradients.

The average values of AOV and IPV-generated runoff velocity under three different slope gradients are plotted in Figure 3. When the slope gradient = 5°, the average value of AOV-generated runoff velocity was close to that of IPV and there was no significant difference between the two methods. When the slope gradient increased to 10° and to 15°, there were significant differences between average AOV-generated runoff velocity and IPV (p < 0.05). The average value of AOV-generated runoff velocity was higher than that of IPV under 10° and 15° slope gradients. Compared with that under 15° slope gradient, the average values of IPV-generated runoff velocity decreased by 14% and 26%, respectively, under 10° and 15° slope gradients.

Figure 3

Average values of AOV and IPV-generated runoff velocities under three different slope gradients. The signs above the box denote significance level.

Figure 3

Average values of AOV and IPV-generated runoff velocities under three different slope gradients. The signs above the box denote significance level.

Runoff velocity change with slope position

We also calculated AOV and IPV-generated runoff velocities at the three slope positions – up-slope, mid-slope, and down-slope. Figure 4 shows the changes in AOV and IPV-generated runoff velocities. The average value of AOV-generated runoff velocity showed an increasing trend from the up-slope to down-slope under the three slope gradients. However, the average value of IPV-generated runoff velocity at the three slope gradients was different from that under AOV-generated runoff velocity. When the slope gradient =5°, average IPV had little variation along the slope. But when the slope gradient = 10°, average IPV increased largely from up-slope to mid-slope, and then decreased slightly at down-slope. As the slope gradient = 15°, average IPV increased from up-slope to down-slope, but the range of change under IPV was smaller than that under AOV.

Figure 4

Changes in AOV and IPV-generated runoff velocities at three different slope positions under three different slope gradients.

Figure 4

Changes in AOV and IPV-generated runoff velocities at three different slope positions under three different slope gradients.

Runoff velocity comparison

We compared runoff velocities determined by the AOV and IPV methods. It showed that both AOV and IPV were not well distributed along the 1:1 line (dotted line in Figure 5), suggesting that differences existed in runoff velocity estimation by the two methods. More specifically, when slope gradient = 5°, IPV-generated runoff velocities were higher than that of AOV (for which runoff velocity was at the lowest level). As runoff velocity increased under the different slope gradients, the average for IPV became close to that for AOV, but with larger variation under IPV. When slope gradients = 10° and 15°, IPV was basically distributed below the 1:1 line. This suggested that runoff velocity was underestimated by the integrated dye tracer and image processing method. Under the two slope gradients, the variation in IPV was still larger than that in AOV. A linear fit of IPV and AOV showed that the fitted slope equations for all the three slope gradients were less than 1.

Figure 5

Plot of AOV-generated runoff velocity against IPV-generated runoff velocity on different slope gradients under the same rainfall event.

Figure 5

Plot of AOV-generated runoff velocity against IPV-generated runoff velocity on different slope gradients under the same rainfall event.

DISCUSSION

For a long time, the estimation of runoff velocity has focused mainly on hydrological processes of slopes. Irrespectively, runoff velocity estimation is still a tedious challenge because of its dependence on so many variables, including observer trait, observation position, sediment load, rainfall event, and slope gradient (Dunne et al. 1991; Fox & Bryan 2000; Chaplot & Le Bissonnais 2003; Assouline & Ben-Hur 2006; Fang et al. 2015; Shen et al. 2016). In this study, we integrated dye tracer and image processing and used it for runoff velocity measurement. The results showed that the change trends in runoff velocity determined by the IPV method (the integrated method) were similar to that determined by the AOV method (dye tracer method) under three slope gradients. However, some differences were noted between the IPV and AOV methods. The results suggested that compared with AOV, IPV overestimated runoff velocity under low runoff conditions, but underestimated it under high runoff conditions. This was mainly attributed to three factors: (1) the position of the observer, (2) the pattern of the ruler on the slope, and (3) the observer judgment of dyed runoff front. For the dye tracer method (AOV), the distance the dyed runoff travels is the length of the ruler. The observer position and ruler pattern on the slope can cause an under-shooting of distance compared with the actual ruler length (Xia et al. 2007). For instance, when the observer stands above the vertical extension cord of the ruler bottom endpoint, the angle between the observer's eye and the ruler endpoint is less than 90° (Figure 1(a)). Then, the distance that the dyed runoff travels is shorter than the ruler length, but the observer reads it as the ruler length, and this results in a shorter time than the actual time the dyed runoff travels through the ruler length. Based on the runoff velocity equation (distance/time), time decreases as velocity increases.

In this study, the observer stood at the upper part of the ruler in order to facilitate dyeing of the runoff, resulting in the error conditions explained above and further causing AOV to be larger than IPV. The pattern of the ruler on the slope affected the estimation of runoff velocity. In theory, the ruler is placed vertically to the wall of the soil box in order to make the ruler length equal to the travel distance of the dyed runoff front. When the ruler is not vertical, the length can mistakenly be read as the travel distance of the dyed runoff front under artificial observation, whereas such error does not occur under image processing. In human observation, the distance that the dyed runoff moves is the length of the ruler (L), whereas the distance in image processing (Li) is equal to the cosine of L (Li = L × cos(ɑ)) (Figure 1). This results in higher AOV than IPV. In the integrated method, the obstacles highlighted above are completely avoided. As dyed runoff front is difficult to determine, researchers often resort to the use of human observation, which gives uncertain travel distances (Xia et al. 2007). It is therefore clear that AOV is, to some extent, uncertain and largely dependent on experience. Conversely, the image processing analyzes color changes that can be used to determine runoff front. Theoretically, this method is far more reliable.

Finally, the calibration coefficient (set at 0.65 in this study) is an empirical number in the dye tracer method that is dependent on flow regime. Several studies recommend a smaller calibration coefficient than the one used in this study (Luk & Merz 1992; Abrahams & Atkinson 1993; Berger et al. 2010; Fang et al. 2015). Thus, the calibration coefficient can also be a factor for the higher AOV than IPV; while in the method of integrating the dye tracer and image processing, we do not need this coefficient. Hence, it is an advantage over the traditional dye tracer method. At the same time, this method could be used for calculating or validating the coefficient used in the traditional dye tracer method.

In general, the reasons for the discrepancies between AOV and IPV could be a lot more complex than the explanations given above. However, the integrated method (dye tracer and image processing) used in this study has strong advantages over the traditional dye tracer method. The integration of dye tracer and image processing avoids the obstacles related to observer trait, observation position, and precision runoff front determination. Above all, the integrated method can calculate lateral runoff diffusion, which is not possible with the traditional dye tracer method. Irrespectively, there is the need to build sufficient data on this method in order to more fully understand its range of strength and weakness.

CONCLUSIONS

A method of integrating dye tracer and image processing was developed (IPV) and used to calculate slope runoff velocity, which was then compared with that of the traditional dye tracer method (AOV). The results showed that the integrated method captured well the changes in runoff velocity for the simulated rainfall event. The estimated runoff velocity by the integrated method was positively related to slope gradient. The average velocity under IPV was close to that under AOV for the 5° slope gradient, but was significantly different for the 10° and 15° slope gradients. The mean velocity for the AOV method was 10.6% higher than that of the IPV method. Compared with the dye tracer (AOV) method, the integrated (IPV) method overestimated runoff velocity under low runoff velocity condition and underestimated it under high runoff velocity condition. The image processing technique used in runoff velocity estimation showed uncertainties in runoff velocity estimation under the traditional dye tracer method and in the selection of calibration coefficient based on flow regime. On the other hand, the integrated dye tracer and image processing method still needs further improvement through rigorous experimentation to ensure higher accuracy and wider application.

ACKNOWLEDGEMENTS

This work was financially supported by the National Natural Science Foundation of China (41371242, 41530854, and 41571130081) and the Key Research Program of the Chinese Academy of Sciences (KFZD-SW-306). We thank the State Key Laboratory of Dryland Farming and Soil Erosion on the Loess Plateau for providing the requirements for the experiment. Special thanks go to the editors and reviewers for the exciting input during the review phase of the paper.

REFERENCES

REFERENCES
Abrahams
A. D.
&
Atkinson
J. F.
1993
Relation between grain velocity and sediment concentration in overland flow
.
Water Resour. Res.
29
(
9
),
3021
3028
.
Abrahams
A. D.
,
Parsons
A. J.
&
Luk
S. H.
1986
Field measurement of the velocity of overland flow using dye tracing
.
Earth Surf. Processes Landforms
11
(
6
),
653
657
.
Angermann
L.
,
Krause
S.
&
Lewandowski
J.
2012
Application of heat pulse injections for investigating shallow hyporheic flow in a lowland river
.
Water Resour. Res.
48
(
12
),
W00P02
.
Ares
M. G.
,
Bongiorno
F.
,
Holzman
M.
,
Chagas
C.
,
Varni
M.
&
Entraigas
I.
2016
Water erosion and connectivity analysis during a year with high precipitations in a watershed of Argentina
.
Hydrol. Res.
47
(
6
),
1239
1252
.
Berger
C.
,
Schulze
M.
,
Rieke-Zapp
D.
&
Schlunegger
F.
2010
Rill development and soil erosion: a laboratory study of slope and rainfall intensity
.
Earth Surf. Processes Landforms
35
(
12
),
1456
1467
.
Berman
E. S.
,
Gupta
M.
,
Gabrielli
C.
,
Garland
T.
&
McDonnell
J. J.
2009
High-frequency field-deployable isotope analyzer for hydrological applications
.
Water Resour. Res.
45
(
10
),
W10201
.
Bissonnais
Y. L.
&
Singer
M. J.
1992
Crusting, runoff, and erosion response to soil water content and successive rainfalls
.
Soil Sci. Soc. Am. J.
56
(
6
),
1898
1903
.
de Lima
J. L.
&
Abrantes
J. R.
2014
Using a thermal tracer to estimate overland and rill flow velocities
.
Earth Surf. Processes Landforms
39
(
10
),
1293
1300
.
de Lima
R. L.
,
Abrantes
J. R.
,
de Lima
J. L.
&
Lima
M. I. P.
2015
Using thermal tracers to estimate flow velocities of shallow flows: laboratory and field experiments
.
J. Hydrol. Hydromech.
63
(
3
),
255
262
.
Dunne
T.
,
Zhang
W.
&
Aubry
B. F.
1991
Effects of rainfall, vegetation, and microtopography on infiltration and runoff
.
Water Resour. Res.
27
(
9
),
2271
2285
.
Emmett
W. W.
1970
The Hydraulics of Overland Flow on Hillslopes. 2330-7102
,
US Government Printing Office
.
Fohrer
N.
,
Berkenhagen
J.
,
Hecker
J. M.
&
Rudolph
A.
1999
Changing soil and surface conditions during rainfall: single rainstorm/subsequent rainstorms
.
Catena
37
(
3–4
),
355
375
.
Foster
G.
,
Huggins
L.
&
Meyer
L.
1984
A laboratory study of rill hydraulics: I. Velocity relationships
.
Trans. ASAE
27
(
3
),
790
796
.
Furumai
H.
,
Jinadasa
H.
,
Murakami
M.
,
Nakajima
F.
&
Aryal
R.
2005
Model description of storage and infiltration functions of infiltration facilities for urban runoff analysis by a distributed model
.
Water Sci. Technol.
52
(
5
),
53
60
.
Gardner
R.
&
Dunn
J.
1964
A single-sample radiotracer technique for determining stream flow rates
.
Int. J. Appl. Radiation Isotopes
15
(
6
),
339
344
.
Horton
R. E.
,
Leach
H.
&
Van Vliet
R.
1934
Laminar sheet-flow
.
Eos, Trans. Am. Geophys. Union
15
(
2
),
393
404
.
King
K.
&
Norton
L.
1992
Methods of Rill Flow Velocity Dynamics. Paper – American Society of Agricultural Engineers
.
AGRIS
,
USA
.
Li
G.
,
Abrahams
A. D.
&
Atkinson
J. F.
1996
Correction factors in the determination of mean velocity of overland flow
.
Earth Surf. Processes Landforms
21
(
6
),
509
515
.
Luk
S.
&
Merz
W.
1992
Use of the salt tracing technique to determine the velocity of overland flow
.
Soil Technology
5
(
4
),
289
301
.
Muste
M.
,
Hauet
A.
,
Fujita
I.
,
Legout
C.
&
Ho
H.-C.
2014
Capabilities of large-scale particle image velocimetry to characterize shallow free-surface flows
.
Adv. Water Resour.
70
,
160
171
.
Planchon
O.
,
Silvera
N.
,
Gimenez
R.
,
Favis-Mortlock
D.
,
Wainwright
J.
,
Bissonnais
Y. L.
&
Govers
G.
2005
An automated salt- tracing gauge for flow-velocity measurement
.
Earth Surf. Processes Landforms
30
(
7
),
833
844
.
Rahma
A. E.
,
Lei
T.
,
Shi
X.
,
Dong
Y.
,
Zhou
S.
&
Zhao
J.
2013
Measuring flow velocity under straw mulch using the improved electrolyte tracer method
.
J. Hydrol.
495
,
121
125
.
Shi
Z.
,
Huang
X.
,
Ai
L.
,
Fang
N.
&
Wu
G.
2014
Quantitative analysis of factors controlling sediment yield in mountainous watersheds
.
Geomorphology
226
,
193
201
.
Singh
P.
,
Ramasastri
K.
,
Singh
U.
,
Gergan
J.
&
Dobhal
D.
1995
Hydrological characteristics of the Dokriani Glacier in the Garhwal Himalayas
.
Hydrol. Sci. J.
40
(
2
),
243
257
.
Tauro
F.
,
Grimaldi
S.
,
Petroselli
A.
&
Porfiri
M.
2012a
Fluorescent particle tracers for surface flow measurements
.
Water Resour. Res.
48
(
6
),
W06528
.
Tauro
F.
,
Grimaldi
S.
,
Petroselli
A.
,
Rulli
M.
&
Porfiri
M.
2012b
Fluorescent particle tracers in surface hydrology: a proof of concept in a semi-natural hillslope
.
Hydrol. Earth Syst. Sci.
16
(
8
),
2973
2983
.
Ventura
E.
,
Nearing
M. A.
&
Norton
L. D.
2001
Developing a magnetic tracer to study soil erosion
.
Catena
43
(
4
),
277
291
.
Williams
J.
&
Berndt
H.
1977
Sediment yield prediction based on watershed hydrology
.
Trans. ASAE
20
(
6
),
1100
1104
.
Xia
W.
,
Liu
C.
,
Lei
T.
,
Hu
Y.
&
Zhao
J.
2007
Analysis of faults in theory for measuring flow velocity on slope with tracer method
.
J. Natural Disasters
16
(
1
),
50
54
(in Chinese with English abstract).
Zhang
G.
,
Liu
B.
,
Liu
G.
,
He
X.
&
Nearing
M.
2003
Detachment of undisturbed soil by shallow flow
.
Soil Sci. Soc. Am. J.
67
(
3
),
713
719
.
Zhang
G.
,
Luo
R.
,
Cao
Y.
,
Shen
R.
&
Zhang
X.
2010
Correction factor to dye-measured flow velocity under varying water and sediment discharges
.
J. Hydrol.
389
(
1
),
205
213
.