The efficiency of depth-integrating samplers in sampling the suspended sand load in gravel bed rivers

Journal of

Hydrology ELSEVIER

Journal of Hydrology 201 (1997) 138-160

The efficiency of depth-integrating samplers in sampling the suspended sand load in gravel bed rivers D. Murray Hicks*, Maurice J. Duncan National Institute of Water and Atmospheric Research Ltd, P.O. Box 8602, Christchurch, New Zealand

Received 9 October 1996; revised 25 February 1997; accepted 27 February 1997

Abstract

The depth-integrating sampler approach for measuring the velocity-weighted mean concentration of suspended sand in rivers was compared with the point-sampler approach whereby vertical profiles of velocity and sediment concentration are measured then integrated. The aim was to determine, for sand suspension in gravel bed rivers, the uncertainty induced when the depth-integrating sampler traverses the near-bed zone of high sand concentration too quickly to average-out the dominant fluctuations in sand concentration associated with turbulence. Depth-integrated and point samples, velocity profiles, and turbulence measurements were collected from three gravel bed rivers at various flood stages. For two rivers, the sand and silt-clay fractions of the suspended load were determined, while at the third river four separate sand size fractions and the silt-clay fraction were analysed. The results showed that the agreement at-a-vertical between the two approaches improved exponentially as a function of the shear velocity to fall speed ratio, u,/w, ranging from up to ---70% for u,/w < 4 down to about ---5% for u,/w > 30. The exponential trend is consistent with diffusion models for suspended sediment vertical distributions which predict that the mixing increases as a function of the Rouse number w/(Bru,). Thus when the u,/w ratio is close to 1 the suspended sand load is concentrated near the bed and a depth-integrating sampler will only sample it for a small fraction of its total traverse time; conversely, with a large u,/w the sand will be mixed over the flow depth and it will be sampled for the same time by a depth-integrating sampler as by a point sampler. The agreement between the two approaches appeared to saturate at about ± 5 % at high values of u,/w in response to temporal variations in sediment concentration and flow velocity longer than the sampling time of either sampler, i.e. of the order of 1 min or more. © 1997 Elsevier Science B.V. Keywords: Suspended sand load; Gravel bed rivers; Depth-integrating samplers; Efficiency

* Corresponding author. Fax: +64 3 3485548; e-mail: [email protected] 0022-1694/97/$17.00 © 1997- Elsevier Science B.V. All rights reserved PII S0022- 1694(97)00040-1

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

139

1. Introduction Depth-integrating samplers are used world-wide for measuring the suspended sediment load in rivers. A key feature of their design is that they sample the flow isokinetically-that is, they are plumbed so that the river flow enters the sampler nozzle at the ambient flow velocity (Federal Interagency Sediment Project, 1963; Edwards and Glysson, 1988). Thus by traversing them from the water surface down to the bed and back to the surface at a uniform rate, they perform an unbiased mechanical integration of the product of streamwise velocity and sediment concentration. The concentration of sediment in the sample so collected is equal to the ratio of the sediment load over the vertical to the water discharge per unit width and is called the velocity-weighted mean concentration. Multiplying this concentration by the mean velocity in the vertical (determined by current meter) provides the sediment load. The depth-integrating approach is therefore much more rapid than the point-sampling approach whereby the water and velocity are sampled at six to eight points in the vertical so that concentration and velocity profiles can be drawn and integrated. One possible problem with the depth-integrating approach, though, is that it may poorly sample the suspended sand load. Unlike the fine clay and silt fractions of the suspended load, which have fall speeds less than the upward speeds of the stream turbulence and are consequently well mixed through the flow, the fall speed of the sand is of similar order to the turbulent fluctuations and the sand concentration is highest nearest the stream bed (fall speeds range from 0.5 cm s -1 for very fine sand up to 15 cm s -1 for coarse sand--Vanoni, 1977; although rarely measured in rivers, root-mean-square fluctuations in the vertical velocity component are expected to typically range between 1.5 and 12 cm s -l, based on the McQuivey, 1973, data on streamwise turbulence in rivers and canals and assuming that the ratio of vertical/streamwise root-mean-square velocity lies in the 0.5-0.8 range reported by Naden, 1987). Thus the sand load will only be sampled adequately providing the traverse time of the sampler through the high sand transport zone near the bed is as large or larger than the characteristic time scale of the fluctuations in suspended sand concentration, which, for the purposes of this paper, we assume follow the fluid turbulence. The maximum traverse time permitted before a depth-integrating sample bottle becomes over-filled is (Hicks and Fenwick, 1993) Tmax= 4 V / umd27r

( 1)

where V is the sample volume (typically 350 or 700 ml for pint and quart bottles, respectively), Um is the mean streamwise velocity in the vertical, and d is the sampler nozzle diameter (3.2-6.4 mm). The traverse time through the sand layer is therefore

Ts = (Zs/Z)Tmax

(2)

where Zs is the height of the high sand concentration layer above the bed and Z is the flow depth. Typically from our New Zealand experience, when in spate or flood gravel bed rivers have mean velocities of 2 - 4 m s -1 and depths from 1.5 to 10 m. Thus if the sand load is concentrated in the lower half-quarter of the flow then Ts may be as small as 1-2 s for a 4.8-mm nozzle and 350-ml sample volume (such as used in a D-49 or P-61 sampler). Sand

140

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

concentration fluctuations at this or longer periods will therefore be poorly sampled. This matters little if the sand fraction is only a small component of the total suspended load and/ or where there is little interest in the sand load. However, typically in gravel bed rivers the sand fraction is a significant part of the total load and is required to a reasonable accuracy--such as to determine the design capacity of a sand-trap in a flow-diversion system or to predict the yield of sand to the coast. This paper presents data from measurements of suspended sediment and velocity in several flooding gravel bed rivers that permit a check on the accuracy of the depthintegration method for determining the suspended sand load.

2. Methods 2.1. Data collection

Measurements were made from bridges at selected verticals in three large moderately steep gravel-bed rivers on the Canterbury Plains of South Island, New Zealand, under flood conditions (Table 1). The verticals were well away from bridge piers. The data collection generally consisted of point or profiled measurements of streamwise water velocity, point-integrated water samples, and depth-integrated water samples. From five to nine approximately equi-spaced points were sampled in each vertical. At the Waiau River, point velocity measurements were made with an Ott propeller-type current meter at six equi-spaced points, with the mean velocity at each point being recorded over at least 40 s. At the Rakaia and Rangitata Rivers, streamwise velocity profiles were measured with a POEM Pressure Operated Electronic current Meter (Smart, 1991), which was traversed between the water surface and bed over a period of some 40 s. The POEM records the average streamwise velocity within each decile of the flow depth. Also at the Rangitata and Rakaia Rivers, the streamwise turbulence was recorded over 100300 s at 28-56 Hz at selected depths in each vertical using a POTATO Pressure Operated Turbulence Appraisal TOol (Smart, 1994). The POTATO, mounted above a Columbus weight, was suspended by a load-bearing coaxial cable and logged to a notebook computer. Table 1 Conditions at the sampling sites River

Waiau at Leslie Hills Br. Rakaia at SHI Br. Rangitata at Arundel Br.

Mean flow (m 3 s -I)

Mean annual flood (m 3 s I)

Bed material ds0 (mm)

Valley slope

Date of sampling

94

1185

35

0.0050

22-Nov-93

203

2506

24

0.0041

96

959

85

0.0073

Flow on day (m 3 s -I)

Suspended sediment concentration on day (mg 1 t)

Verticals (and repeats)

123

146

5 ( x 1)

10-Jan-94

2844

5627

2 ( x 5)

14-Dec-95 15-Dec-95

887 443

4472 1509

1 ( x 1) 2 ( x 1)

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

141

The water samples were collected using a P-61 suspended sediment sampler with a 4.8-mm-diameter nozzle and 900-ml (quart) sample bottle. Samples were collected at specific points in the vertical by leaving the solenoid-activated valve open for between 12 and 36 s (this time was varied from vertical to vertical, depending on the flow velocity, to ensure that the sample bottle was not over-filled, which would have resulted in a biased sample). The lowest point sample was collected with the base of the sampler just touching the bed, with the intake nozzle 110 mm above the bed. The depth-integrated samples involved a uniform-rate return-traverse between the surface and riverbed with the P-61 valve open all the time. With these, the traverse-rate was regulated according to the depth and mean velocity in the vertical so as to obtain an optimal volume of sample (about 700 ml) while ensuring that the velocity-field disturbance around the nozzle was minimized (Edwards and Glysson, 1988). The use of the same P-61 sampler to collect both the point and depth-integrated samples removed any concern that our comparisons might be biased by using samplers with different characteristics. Generally, for each run data were collected in the sequence: velocity profile, first depthintegrated sample, point-sample profile, second depth-integrating sample, then further depth-integrated samples for bulking and particle-size analysis. At the Waiau River, single runs were done at five verticals. At the Rakaia River, five repeat sampling runs were conducted over a period of 40-50 min at two verticals. At the Rangitata River, one run was done at one vertical near the peak of a large flood; this was repeated the following day, along with one run at another vertical. Each sample from the Waiau and Rakaia Rivers was analysed for both silt-clay and sand concentration. The sand was separated out by washing the finer fractions through a 62-#m sieve. Both the fine and coarse fractions were then captured on Whatman GF/C filters. In similar fashion, the samples from the Rangitata River were split into five fractions: >500 #m, 250-500 gm, 125-250/~m, 63-125/xm, and <63/xm. Full particle-size analyses (Fig. 1) were conducted on bulked depth-integrated samples from each river using a Rapid Sediment Analyser.

2.2. Analysis The measured velocity profiles were smoothed by eye and extrapolated on a logarithmic trend to the bed. These profiles were then digitized over 10-12 equal depth increments between 0.11 m above the bed and the surface. For the purpose of this study, the sediment load in the 'unmeasured' zone within 0.11 m of the bed, which was not traversed by the depth-integrating sampler, was ignored. A spreadsheet was used to determine the velocityweighted mean concentration in the vertical (cv) from these digitized profiles, according to the equation

\z=O.ll

u z.Az

where u: and cz are the point velocity and point concentration in the vertical, z is distance above the bed, and Z is the flow depth. These calculated velocity weighted mean

142

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160 100

60

/,

40

/~

Rakaia

/ 0

Wa,au

/

20

........

0.0001

/

0.001

....

Rangitala

..........................

0.01 0.1 Grainsize(ram)

Fig. 1. Particle size gradings of depth-integrated samples from the three studied rivers.

concentrations, for both sand and silt-clay fractions, were then compared with those measured directly with the depth-integrated samples. Shear velocity at each vertical was estimated by plotting the smoothed velocity profiles on semi-log graphs and fitting a straight line to the near-bed region. After Middleton and Southard (1977), shear velocity, u,, was determined as (U2 -- U l)

(4)

u , = r ( 1 n z z - l n zl) where u 2 and Ul are the velocities at elevations z2 and z~ and k is von Karman's 'constant', assumed equal to 0.4. We note that Eq. (3), and indeed the depth-integrating sampling approach, assumes that the streamwise velocity of the suspended sediment matches the fluid velocity. Aziz (1996) showed that the 'slip velocity' between the fluid and the sediment is significant for sand size grains, and so use of the fluid velocity profile can overestimate the suspended load appreciably. For the purposes of this study, however, the same over-estimation should arise from both the depth-integrating and point-sampling approach.

3. Results and discussion 3.1. Waiau River

The measurements at the Waiau River involved single 'runs' at five equi-spaced verticals (Table 1, Fig. 2(a)) made during a period of essentially steady water level on the recession of a 'fresh'. The velocity and concentration profiles obtained from the point samples are plotted in Fig. 2(b)-(d), while details of the sampling times and the directly depth-integrated and computed Cv results are listed in Table 2. Fig. 2(c) shows that the silt-clay concentrations were essentially uniform with depth and across the flow, averaging 90 mg 1-l with a standard deviation of 4 mg 1-l over all 30 samples. In contrast with the well-mixed fine fractions, Fig. 2(d) shows the sand concentration increasing with depth and varying considerably between verticals. The average sand concentration over all point samples was 56 mg 1-~ (38% of the total suspended load). Both the highest sand concentrations overall and the greatest concentration gradients

143

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160 Surface

b

=

0

0.2 1

O3 O3

0.4

0.6

a

I

0

5

Sampling verticals 2 3

0.8

5

Bed

J

1

0

1

0.5

1.5

2

2.5

Velocity (m.s-1)

3

~.

a

i

1

Surface

4

c 4

8 Distance from

12

16

20

Silt-Clay

0.2 a

Loll Bank (m)

0

O3

0.4 0.6

fie

e 300

Bed

[]

A

~'_ 2 5 0

0.8

-T. C, S

Depth-integrated

E 200

T

i

1 0

0 ~ Point-sampled

L

50

J

i

100 150 200 250 300

Concentration (mg.I 1 )

T

g Surface

150 c 0

o

C/oy-sil~)

100

S

d =_

(~

50

oO3

0

0.2

l

Sand

0.4

>

0.6

0 0

4

8

12

Distance from Loft B a n k

16

20

n0.8

(m)

Bed

1

50

100 150 200 250 300

Concentration (mg.1-1 )

Fig. 2. Results from the Waiau River. (a) Location of sampling verticals. (b) Velocity profiles (numbers label verticals). (c) Concentration profiles for the silt-clay fraction. (d) Concentration profiles for the sand fraction. (e) Velocity-weighted mean concentrations determined from depth-integrated samples and computed from the pointsampled data.

occurred at Verticals 2 and 3, not at the thalweg. The greatest rate of increase in sand concentration with depth occurred in the lower 0.25 of the depth (within about 0.6-1.1 m of the bed, depending on the vertical). Relating the thickness of this high sand concentration zone to the depth-integrating sampler traverse rate at each vertical shows that this zone was traversed in some 3 - 5 s (Table 2). Comparing the two depth-integrated and computed cv results (Table 2 and Fig. 2(e)) shows very good agreement for the silt-clay component of the load at all five verticals (depth-integrated cvs within 2% of the computed cvs), reasonably good agreement for the sand load at Verticals 1, 4, and 5 (depth-integrated CvS within 22% of the computed values), but relatively poorer agreement at Verticals 2 and 3, where the sand load was

4.26

4.65 1.0

0.9 24

24

20 5.5

4.6

5.0

3.6

2.8

42

296

77

40

53

87

82

40

56

0.078

1.28

1.0

14 20

32

74

17

61

129

114

49

1.3

89

86

87

90

89

94

DI#1 (mg 1 i)

DI#2 (mg 1 1)

DI#1 (mg l -i)

Computed (mg l -t )

Silt clay cv

Sand c,

70

0.043

1.31

3.96

0.6

0.6

Time in sand zone (s)

95

0.047

1.67

3.33

3.01

Sampling duration (s)

% Error on computed c

0.073

1.66

Span of high sand conc. zone (m)

Average

0.065

1.95

Depth (m)

19

Shear velocity (m s i)

Mean velocity (m s i)

22

Vertical

90

89

86

89

93

95

Computed (mg 1 I)

2.0

89

90

78

92

86

97

DI#2 (mg I -i)

Results from Waiau River measurements, c~ designates the velocity-weighted mean concentration of suspended sediment in the vertical

Table 2

147

185 25

139

176

386

108

175

166 129

135

134

108

Computed (rag 1-I)

DI#1 (mg 1~l)

Total c~

11

163

107

139

221

200

146

DI#2 (rag I -t)

ox

i

oe

~

bo

~

~:

.~

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

145

highest. At Vertical 3 in particular, the two depth-integrated sand concentrations, with the high-load zone sampled for only 5 s, were 1.5 and 3.5 times larger than the computed Cv that was based on sampling the high-load zone for 20 s. The Verticals 2 and 3 data suggest that sand concentration fluctuations at periods between a few and less than 20 s were occurring there and were not well sampled by the depth-integrating sampler. While the high concentration (296 mg 1-l) of the first depth-integrated sample at Vertical 3 might possibly be due to the sampler nozzle intersecting a sand wave as the sampler momentarily touched the bed, this is unlikely given that the Waiau River bed material is substantially gravel-sized. Our favoured explanation for this value is a burst of high near-bed sand concentration associated with turbulence. To some extent the poor sampling of the sand load by individual depth-integrated samples will be evened out when the concentrations from all verticals are combined (on a simple average or flow-weighted basis) to derive the cross-section mean concentration. For the Waiau section (where each vertical is reasonably representative of equal proportions of the total flow) the average of the concentrations at the 5 verticals (Table 2) suggests an uncertainty in the cross-section mean concentrations due to the depthintegrating technique of 1% in the silt-clay load, 3 2 - 7 0 % in the sand load, and 11-25% for the total suspended load. These figures reduce to 20-32% for the sand load and 9 - 1 1 % for the total load if the possibly anomalous first depth-integrated sample at Vertical 3 is ignored, and further reduce to 6% for the sand load and 1% for the total load when the before-and-after depth-integrated concentrations are averaged. 3.2. Rakaia River

Samples were collected from the Rakaia River on the recession of a large flood, when the normally braided channel was bank-to-bank and over 1 km wide. Measurements were focused at two verticals, both within the same main channel. Five repeat sampling runs were made at each vertical. At vertical 454 m, one velocity profile was measured in the middle of the five sampling runs and was assumed to be constant through-out the 48 rain sampling period. At vertical 530 m, velocity profiles were measured at 12:10 h and 15:30 h. The velocity profile at 13:45 h, the mid-time of the 41-min sampling period, was estimated as the average of the 12:10 h and 15:30 h profiles, and this was assumed constant over the sampling period. The stage fell by approximately 100 mm during the 4 0 - 5 0 min of sampling at each of the two verticals. Profiles of velocity, suspended sediment concentration during each of the five repeat runs, and the coefficient of variation of the concentration over the five runs are plotted in Fig. 3. As expected, the silt-clay concentrations were uniform with depth while the sand concentration increased exponentially towards the bed. Compared with the less energetic conditions measured in the Waiau River, however, the sand mixing in the Rakaia River was more uniform, and a zone of high sand concentration near the bed was less obvious. The sand concentration coefficient of variation was larger at the bed and near the surface, with greater variation observed at the shallower, faster flow at vertical 494 m. At 494 m the silt-clay coefficient of variation showed a slight trend to increase towards the bed, while at 530 m there was no trend. There was a slight trend for decreasing sand and siltclay concentration with time at 494 m, but not at 530 m (Fig. 4(a)). A significant drop in

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

146 a

Rakaia @ 4 9 4 m

2

2 Sand

• Sand o Silt-clay

Si#-clay 1.6

0

s

1.2

1.2

1.2

0.8

~ 0.8

0.8

0.4

0.4

•

0

O. Bed 2

, 2.5

3

3.5

4

0

i 4

2000

4000

i 8

= = 12 16 20

s~/~ (%)

Concentration (rag.l-l)

Rakala @ 5 3 0 m

3.5

3.5

Sand

Surface

g

oo

o

0

Velocity (m.s "I )

b

C~

Silt-clay

o Silt+clay

2.5

~

2.5

2

g

2

~

g

2.5 I o cl 2 •

1.5 LU

[]

1

Bed

0

1

,'n

0.5

0.5 1.5 2 2.5 Velocity (re.s-1)

cl

0.5 F i

0

2000

4000 Concentration (mg.1-1)

0L 0

,9~ , 4 8 12 16 20 s:/C (%)

Fig. 3. Results from the Rakaia River, (a) for vertical 494 m, (b) for vertical 530 m. Plots on left show velocity profile, centre plots show concentration profiles for sand and silt-clay fractions, and plots on right show the profiles of the coefficient-of-variation of concentration.

silt-clay concentration at all depths occurred at 12:25 h, suggesting that this fraction experienced concentration variations over the order of at least 40 rain. The velocity-weighted mean concentrations obtained directly from depth-integrated samples and computed using Eq. (3) are compared in Table 3 and Fig. 4(b). At 494 m, the two approaches agree very well (to within -+4%, when comparing each depthintegrated sample with the average of the two straddling point-sampling runs) for both the silt-clay and sand fractions, apart from the depth-integrated sand concentration sampled at 12:05 h, which was 32% less than the computed value. Including this sample, the average depth-integrated concentration agreed with the average computed value to 4% for the sand fraction, 1% for the silt-clay fraction, and 1% for the total suspended load. Excluding the 12:05 h sand sample, the average depth-integrated and computed sand concentrations agreed to within 1%. When this outlier point and the temporal trend at 494 m is removed, the coefficients of variation for the measured and computed depth-integrated sand concentration were both 3%. At 530 m, for individual runs the two approaches agreed to between +2% and +10% for sand and between - 6 % and +10% for silt-clay. The average values over all five runs agreed to 5% for sand, 0.3% for silt-clay, and 2% for the total

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160 Rakala @ 494 m

a

~

Rakala @ 530 m

5000

~A 5 0 0 0

4000

~

4000

3000

~

3000

"~ 2000

2000

8

1000 11:40

Sand

Sand

~1000

12:00 12:20 Hour

12:40

13:20

13140 14':00 Hour

Elevation (m>I - e - 1.38 I 1.04 I 0.69 I - c - 0.34 0.11

Elevation (m)I

1.32 - o - 0.71 0.11

Rakala @ 494 m

Rakala @ 530 m

5000

5000 Silt-clay 6= E

4000

4000

3000 c o

147

.~

2000

•

SiR-clay

3000 2000

Sand

1000

0 11:30 11:50 12:10 12:30

o O

Sand

1000 13:00

Hour

13:20 13:40

14:00

Hour DI sand

-o- Computedsand I DIsilt-clay q2- Computedsilt-clay

Fig. 4. Results from Rakaia River. (a) Variation in concentration with time at given elevations above the bed at the two verticals. (b) Velocity-weighted mean concentrations determined by depth-integrated samples compared with those computed from the point data.

load. The coefficients of variation of the measured and computed depth-integrated sand concentrations were 2% and 1%, respectively. These results suggest that under the high velocity, high load conditions at the Rakaia, with the exception of one sample, the depth-integrated sampling method performed as well as the point sampling method at estimating the velocity-weighted mean concentration at a vertical for both the sand and silt-clay fractions of the suspended load. In such conditions, the depth-integrating method is acceptable, providing individual depth-integrated samples are inspected and anomalous-looking samples are repeated or rejected. Also, we might conclude that either method would establish the suspended load averaged over five verticals to within -+5% for the sand fraction and to within -+ 1% for the silt-clay fraction. Fig. 5 plots a time series and the spectral density of the streamwise velocity sampled at 56 Hz for 100 s 0.3 m above the bed at vertical 494 m. The largest spectral peak (indicating the greatest turbulence energy) occurs at 50-60 s, with a secondary peak at 7 - 8 s. The

530

1310

0.69

14

14 16 14

1352

1406

16

1404

14

1345

16

1350

15

16

1335

1337

13

1327

1343

16

1325

3.9

3.9

3.9

3.9

4.2

3.6

1916

1887

1856

1978

1962

1916

-4

16

% E~or on averages

3.17

1731

1664

1814

1240

1932

2067

1840

1843

1791

1806

1830

6

115

1818

1661

1824

1776

1851

1978

4

2

2

10

8

5

4

-5

1

-32

1

4

3389

3323

3514

3663

3575

3909

+1

-3

3

107

4032

3958

3933

3937

4136

4051

4179

+ 3

DI (mg I i)

% Error on DI from straddling pts

DI (mg 1-I)

Computed (mg I i)

Silt c~

Sand c~

-32- + 4

0.18

3.0

3.0

3.3

3.0

3.0

3.3

Time in sand zone (s)

Range o f % e ~ o r

C. of var. (%)

2.1

12

1233

13 12

1215 1220 12

12

1210

12

12

1205

1229

12

1158

1225

12

1150

13 12

0.35

Sampling duration (s)

1142

1136

Span of high sand conc. zone (m)

285

1.73

Hour

1741

0.22

Depth (m)

Std dev.

3.4

494

Shear velocity (m s -I)

Average

Mean velocity (m s -I)

Ve~ical

Results from Rakaia River measurements

Table 3

3483

3604

3530

3591

3556

5

219

3995

3959

3657

3988

4142

4227

Computed (mg 1 i)

~ 3

-1

3

0

10

0

3

3

2

-3

-I

% Error on DI from straddling pts

5305

5210

5370

5641

5537

5825

-1

-9 - + 2

5

305

5774

5689

5597

5751

5376

5983

6246

DI (mg l -t)

Total c~

5323

5447

5321

5397

5386

5

290

5813

5620

5481

5764

5993

6205

Computed (mg 1 i)

0

-3

0

5

3

8

1

1

2

-9

-2

1

% Error on D1 from straddling pts

~'~

I

t~

~.~

.~

,~

.~

% Error on averages

Range of % error

C. of var. (%) +2

+10 +5

--6-+10 +0.3

6

210

3562

DI ( m g l i)

% Error on Dl from straddling pts

DI ( m g l i)

Computed ( m g l I)

Silt cv

Sand c,

I

Time in sand zone (s)

2

Sampling duration (s)

23

Span of high sand conc. zone (m)

1822

Hour

45

Depth (m)

1919

Shear velocity (m s -~)

Std dev.

Mean velocity (m s i)

Average

Vertical

Table 3 continued

1

49

3553

Computed ( m g l i)

% Error on DI from straddling pts

-3-+8 +2

4

230

5481

DI ( m g l ~)

Total c~

1

53

5375

Computed ( m g l i)

% Error on D1 from straddling pts

T~

I

o~

ixa

,,~

-~ t~

~,~

"'

.L.,

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

150

former peak, being at a period approximately half the record length, should be regarded with caution although the time series (Fig. 5(a)) clearly shows variations of this order. If we assume that the sand concentration responds to and has similar spectral characteristics to the streamwise turbulence, we might infer that near-bed suspended sand concentration fluctuations of the order of a few seconds to 10 s i t h a t might be sampled poorly by a depth-integrating sampler (3-4 s sampling in the near-bed region--Table 3) but better by a point-sampler (12-16 s sampling time--Table 3)--were less important than longer term fluctuations that would equally affect both types of samplers. It should be appreciated, however, that the relationship between the suspended sand

a

4[

" L

T ~ !

"

"

T I i

......' tr",! o

0

"

"

~

"

'

UT', l" i'!l")2

60

120

180

Time (s)

b

' ' '"t

L

I0000000

1000000

f

100000

10000

1000

i I

IWt' L~I' .... /

i

0.1

10

i

i

iii

100

Period (s)

Fig. 5. Turbulence at vertical 494 m in the Rakaia River. (a) Time series plot of streamwise velocity 0.3 m above bed. (b) Spectral density plot of this time series.

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

151

concentration spectra and streamwise velocity spectra in gravel bed rivers is uncertain. A prime factor is the nature of the flow structures responsible for entraining most of the suspended sediment. Hardisty (1993) and Kirkbride (1993) suggest that in gravel bed rivers whereas the coarser bedload tends to be initiated by bed-directed sweep events, which have a strong signature in the streamwise flow, the finer fractions of the bed material are entrained by bursting or eddy shedding from bed topography. The latter structures have a higher frequency signature in the vertical velocity component which can have a different spectral shape to the streamwise velocity. Lapointe (1996) demonstrated from a sand bed channel that the suspended sand concentration spectra matched that of the vertical velocity spectra and both had peak frequencies higher than did the streamwise velocity spectra. It remains unclear whether the lower frequency streamwise velocity fluctuations induced concentration fluctuations during our measurements in the Rakaia River, either directly or more likely by modulating the amplitude of the higher frequency bursting (as suggested, for example, by Falco, 1977).

3.3. Rangitata River Samples were collected from two verticals on the Rangitata River during a 10-year flood. Vertical 303 m was measured first near the flood peak on 14 December 1995, then again the following day during the recession. Between the two measurements, much of the flow through the channel at 303 m shifted to another channel on the braided river bed, leaving a much lower velocity and depth at 303 m. Vertical 187 m, in a main braid, was measured once on 15 December. Profiles of velocity and concentration for five size fractions are plotted in Fig. 6. At 303 m on 14 December (Fig. 6(a)), as expected, an exponential decrease in concentration above the bed is shown (note that this shows as a linear trend due to the logarithmic concentration axis) for all sand fractions, with the coarser fractions decreasing more rapidly. The >500-#m fraction decreased in concentration by 70% between the bed and the surface; however, the 63-250-/zm fraction, which comprised 86% of the sand load, decreased in concentration by only 30%. Thus the bulk of the sand load was reasonably well mixed over the 1.5 m depth. Surprisingly, the next day at the same vertical (Fig. 6(b)), with apparently less energetic conditions (Table 4), the sand concentration profiles showed no trend for a reduction in sand concentration above the bed. Rather, they fluctuated, with the fluctuations in-phase for each size fraction. This pattern is believed to be due to temporal variations in the sand load masking the vertical mixing effect. With approximately 4 min between consecutive point samples, an interval something like 8-16 min is suggested for these fluctuations. A similar pattern appears on the concentration profiles from vertical 187 m on the same day (Fig. 6(c)), although there the concentration reduction in the vertical is not completely masked by the signature of the temporal fluctuations. Streamwise turbulence data collected over 5-min bursts at the point sampling depths during each run were too short to verify that this 8-16-min period correlated with velocity fluctuations; however, they did indicate significant velocity fluctuations at periods longer than the inertial range (i.e. greater than a few seconds). Example turbulence time series and spectral densities are plotted in Fig. 7. At 303 m on 14 December, the greatest turbulent energy was at 10 s, with a second peak at 20 s and smaller peaks in the 2 - 4 s

D. Murray Hicks, M.J. Duncan/Journal of Hydrology 201 (1997) 138-160

152

a

Rangitata @ 303 m on 14/12/95

Surface

g

1.6

1.6

1.2

1.2 v c-

c

125-250 .am

._o 0.8

0.8

o >

t

> (D

@ ttl

- . o . - 63-125 p m <63 .am

uJ 0.4

0.4

Bed

0 0

h

i

i

1

2

3

0

J

i

i

10

100

1000

10000

Concentration (mg.l-1)

Velocity (m.s-1)

b

>500 u m 250-500 ~ m

Rangitata @ 303 m on 15/12/95 0.8

0.8

0.6

0.6

Surface

E

Zl

0.4

tO

LI

0.2

w 0.2

tO

>500 klm

0.4

--zk- 125-250 p m --¢-- 63-125 ~ m

t~

13

g w

.-.o-- 250-500 ~ m

<63 kzm

Ll A

Bed

0 0

10

0.2 0.4 0.6 0.8

c

100

1000

10000

Concentration (mg.1-1)

Velocity (m.s-1)

Rangitata @ 187 m on 15/12/95 1.6

Surface 1.6

1,2

1.2 tO

>500 pm

E

E

250-500 lam

t--

0.8

.9 0.8

--dk--- 125-250 .am

>

w

Bed

-¢--

_¢ LU 0.4

0.4

0 0

i

L

L

i

1

2

3

4

Velocity (m .s-t )

0 5

63-t25 pm <63/am

i

i

i

10 100 1000 Concentration(mg.l-1)

10000

Fig. 6. Results from the Rangitata River, (a) for vertical 303 m on 14 December, (b) for vertical 303 m on 15 December, and (c) for vertical 187 m on 15 December. Plots on left show velocity profile. Plots on right show concentration profiles for individual size fractions.

Mean velocity (m s -I)

2.96

0.72

3.75

Vertical

303 on 14/12/96

303 on 15/12/96

187 on 15/12/96

Depth (m)

1.51

0.71

1.58

Shear velocity (m s -I)

0.40

0.10

0.43

Results from the Rangitata River

Table 4

1.58

0.71

1.51

Span of high sand conc. zone (m)

10

36

14

Sampling duration (s)

10

36

14

Time in sand zone (s)

413

389

203

255

1116

1172

423

215

1163

-2.5

-8.1

-5.4

18.8

--4

0.8

1131

1133

1064

1284

3094

3098

D1 (mg I i)

% Error on DI

DI (rag I i)

Computed (mg 1 i)

Silt c~

Sand c,

I 145

1230

3184

Computed (mg 1 i)

1.2

-1.1

- 13.5

4.4

-2.8

2.7

% Error on DI

1544

1522

1267

1539

4210

4269

DI (mg 1 i)

Total c,

1569

1444

4347

Computed (mg I i)

1.6

3

12.3

6.5

-3.2

-1.8

% Error on DI

m

I

",-,i

.~

_~

.~

D. Murray Hicks, M.J. Duncan/Journal of Hydrology 201 (1997) 138-160

154

a Rangitata at 303 m on 14/12/95

1

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, .ll,, Ll~ll ..ll J

1000000 J~lI10000 O0000~ ........JIw ........ [d ~ J]li'd'J '"i' ~

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60

120 180 Time(s)

" 240

r'F

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" 300

........

I o.1

, ........

' 1

i ........

' lO

........

i ,, 1oo

-

,~o

Period(s)

b Rangitata at 303 m on 15/12/95 1.5 ~

~

,

~ , ,

.....

1000000

10o00o

~ 1oooo :~ 0.5 . . . .

! 0

60

1000

I

120 180 Time(s)

240

300

100 0.01

0.1

1 10 Period(s)

100

1000

c Rangitata at 187 m on 15/12/95 5

.

.

.

,f ....

.

.

.

.

.

.

,,,, . , , L , . , ,

.

w'"'i

J,,

10000000 :

. . . . 1. . . .

100000 0

60

120 180 Time(S)

240

300

10000 0.01

' ''""

...............

0.1

,.... 1 10 Period(s)

100

1000

Fig. 7. Time series and spectral density plots of streamwise turbulence in the Rangitata River (a) 1.1 m above bed at vertical 303 m on 14 December; (b) 0.4 m above bed at vertical 303 m on 15 December; (c) 0.6 m above bed at vertical 187 m on 15 December.

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

155

range. The following day at 303 m the 2 - 4 s and 10 s peaks re-occurred but the bulk of the turbulence energy occurred at periods above 30 s. At 187 m on 15 December, the peak energy was at 11 s, a secondary peak occurred at 45 s, and intermittency of minutes duration is also indicated. Possibly, the signals of order minutes duration on 15 December relate to an unsteadiness in the distribution of flow among braids; the absence of this long period turbulence on 14 December may be because the channel was bankfull then. Alternatively, the multi-minute variations may be associated with the passage of bedload sheets (Dinehart, 1992, described multi-minute fluctuations in velocity associated with mobile gravel sheets in the Toutle River). As with the Rakaia River measurements, we remain uncertain as to the mechanisms by which longer period velocity fluctuations might influence suspended sediment concentration. Comparison of the depth-integrated and computed velocity-weighted mean concentrations (Table 4) shows that the two approaches agreed best under the more energetic flow conditions. At 303 m on 14 December, the average concentrations of the two 'straddling' depth-integrated samples agreed with the computed concentrations to within 2% for the combined sand fractions and 3% for the silt-clay fraction. The agreement was slightly less for the runs on 15 December (7% error for sand and 5% error for silt-clay at 303 m; 5% error for sand and 1% error for silt-clay at 187 m). For the individual sandsize fractions (Table 5) the disagreement generally grew progressively larger for coarser fractions. This is consistent with the poorer mixing of the coarser fractions and the limited traverse time of the depth-integrating sampler. The predominance of the well-mixed finer sand fractions in the load ensured that the overall error for the sand load was small. The error in the total suspended load was less than 3% for each run. The conclusion from the Rangitata measurements is that because the finer sand fractions dominated the suspended sand load and were well mixed, there was little difference in the sand loads determined by the depth-integrating and point-sampling approaches. The main source of error between the two approaches appeared to relate to temporal fluctuations in the sand load occurring at periods longer than the sampling duration of either sampler. These will tend to be averaged-out during the collection of a series of point samples, but will introduce a random error to depth-integrated samples. However, since these fluctuations and the resultant errors were proportionately larger with larger sand sizes, their effect on the measurements of total sand load remained small.

3.4. A general trend A trend apparent from the three sites is that the agreement between the measured and calculated depth-integrated sand concentrations improves as the flow becomes more energetic and the median size of the suspended sand decreases. Fig. 8 shows that this agreement improves as an exponential function of the 'suspension ratio' u./w, where w is the sand fall velocity which was estimated as that of quartz spheres equal in size to the suspended sand (using the Rouse, 1937, plot reproduced in Vanoni, 1977). For the Waiau and Rakaia data, the median size of the total sand load are used, while for the Rangitata, the mid-sizes of each sand fraction are used. This result is expected, given that traditional diffusion models for suspended sediment vertical distributions predict that the mixing increases as a function of the Rouse Number

on 15/12/96

187

on 15/12/96

303

on 14/12/96

303

Vertical

221

226

143

168

597

365

230

163

618

-4.1

-1.9

12

3.3

-3.2

-41

96

87

47

56

353

341

D1 c~ (mgl i)

%e~or on DI c~

DI c, (mgl i)

Computed c~ (mgl-i)

125 250

63-125

Size range (#m)

95

37

379

Computed c~ (mgl-i)

Results from the Rangitata River for separate sand size fractions

Table 5

1.3

-8.2

27

51

-6.9

-10

%e~or on DI c~

63

51

12

20

114

105

DI c~ (mgl -I)

250 500

64

II

132

Computed c~ (mgl -I)

-I.3

-20

10

83

-14

-21

%e~or on DI c~

33

25

1

12

52

67

DI c~ (mgl i)

> 500

33

Computed c~ (mgl-i)

-4.2

-27

-75

200

57

102

%e~or on D! c~

oo I

.<

U,

D. Murray Hicks, M.J. Duncan/Journal of Hydrology 201 (1997) 138-160 100 Rangitata Rakaia Waiau

•

60

-

Equation (5)

'• /

157

Averageabsolute error of series

2O IJJ

o~ -20 f Aj -60 -100

0

20

40

60

80

1O0

O./ W

Fig. 8. Percentage error in the depth-integrated sample concentration compared with the velocity-weighted mean concentration computed from point sampled data, plotted as a function of the shear velocity/fall speed ratio. Open circles show the average of the absolute errors from each set of samples. Dashed lines show the trend of Eq. (5).

w/(BKu,), where B and r are generally assumed to be constants (e.g. Rouse, 1937; Vanoni, 1946; Middleton and Southard, 1977). Thus when the u,/w ratio is low (close to 1), the suspended sand load is concentrated near the bed and a depth-integrating sampler will only sample it for a small fraction of its total traverse time; conversely, with a large u,/w the sand will be mixed over the flow depth and it will be sampled for the same time by a depthintegrating sampler as by a point sampler. With the data on Fig. 8, the overall distribution of errors between the two methods does not differ significantly from a normal distribution (as indicated by the K o l m o g o r o v Smith, Lilliefors, and Shapiro-Wilk tests), thus there appears to be no bias towards either under or over-estimation. Also, the residual scatter at high values of u,/w shows the effect of temporal variations in concentration longer than the sampling time of either sampler, longer than the order of 30 s. A regression fit to the average absolute error of each set of depth-integrated versus point-sampled comparisons is: E = 2 0 e -0"044 u, lw

(5)

where E is the % error and the regression coefficient, r, is 0.84. Given the shear velocity and the median size of the suspended sand load, Eq. (5) may be used to estimate the uncertainty in the suspended sand load at a single vertical due to using the depth-integrated approach over the point-sampling approach. Eq. (5) is, of course, matched to the 4.8-mm nozzle and quart sample bottle that we used with our P-61 sampler. A sampler combination that allowed a longer depth-integrating interval, such as a D-77 sampler with a 3-1 sample container (Edwards and Glysson, 1988), would result in a smaller error, whereas a combination with a shorter interval, such as a P-61 with a pint bottle, would induce a larger error.

A final comment is that the traditional diffusion theory of sediment suspension (e.g. Rouse, 1937; Vanoni, 1946; Middleton and Southard, 1977) and sampling strategies for operating sediment samplers (e.g. Edwards and Glysson, 1988) do not incorporate the

158

D. Murray Hicks, 114.,1.Duncan~Journal of Hydrology 201 (1997) 138-160

modem turbulent bursting model of sediment suspension in open channel flows (e.g. Grass, 1983; Jackson, 1976; Sumer and Deigaard, 1981; Best, 1993; Kirkbride, 1993). Although there is some doubt whether 'outer flow' or 'wall' variables are the most important controls on the average periodicity of the bursting process (Luchik and Tiederman, 1987; Best, 1993), in rough open channel flows this periodicity is typically of the order of a few seconds (e.g. Jackson, 1976; Lapointe, 1996)--which may be all the time available for a transitting sediment sampler. Thus a reassessment of sampler designs and sampling strategies would appear to be timely.

4. Conclusions

1. The depth-integrating sampler approach can induce an error in the velocity-weighted mean concentration of suspended sand compared with the point-sampler approach. This is due to the depth-integrating sampler traversing the zone of high sand concentration in a time interval that is too short to adequately sample the fluctuations in sand concentration induced by turbulence. 2. The agreement between the two approaches improves exponentially as a function of the shear velocity to fall speed ratio, u./w. The exponential trend is consistent with diffusion models for suspended sediment vertical distributions which predict that the mixing increases as a function of u,/w. 3. The agreement between the two approaches appears to saturate at about ___5% at high values of u,/w in response to temporal variations in sediment concentration and flow velocity longer than the sampling time permitted by either sampling approach.

Acknowledgements NIWA staff John Fenwick, Graeme Smart, Warren Thompson, Pete Mason, and Graeme Davenport assisted with the data collection, and Faye Richards conducted the laboratory analysis. Dr Vladimir Nikora and Dr Randal Dinehart provided constructive reviews of the manuscript. The work was funded by the Foundation for Research, Science and Technology under contracts CO 1417 and CO 1512.

Appendix A. List of symbols B

Coefficient in Rouse number

Cv

Velocity-weighted mean concentration in vertical

C~

Concentration at height z above stream bed Time-averaged concentration

D. Murray Hicks, M.J. Duncan/Journal of Hydrology 201 (1997) 138-160 d

Diameter of sampler nozzle

E

Percentage deviation of depth-integrated concentration from computed cv

r

Linear regression coefficient

Sc

Standard deviation of time-varying concentration

Tmax

Maximum time before sampler fills

T~

Time to traverse layer of high sand concentration

Um

Mean streamwise velocity in vertical

U:

Streamwise velocity at height z above stream bed

U,

Shear velocity

Ul, U2

Streamwise velocity at specific points in vertical

V

Volume of sample bottle

w

Sediment fall speed

Z

Height above stream bed

Zl, Z2

Specific heights above stream bed

Z

Flow depth

Z~

Thickness of layer of high sand concentration

K

Von Karman coefficient

Az

Height interval in flow

159

References Aziz, N.M., 1996. Error estimate in Einstein's suspended sediment load method. J. Hyd. Eng. 122, 282-285. Best, J.L., 1993. On the interactions between turbulent flow structure, sediment transport and bedform development: some considerations from recent experimental research. In: Clifford, N.J., French, J.R., Hardisty, J. (Eds.), Turbulence Perspectives on Flow and Sediment Transport. John Wiley and Sons, Chichester, pp. 61-92. Dinehart, R.L., 1992. Evolution of coarse gravel bed forms: field measurements at flood stage. Water Resour. Res. 28, 2667-2689. Edwards, T.K., Glysson, G.D., 1988. Field methods for measurement of fluvial sediment. US Geol. Surv. OpenFile Report 86-531, Reston, VA, pp. 118. Falco, R.E., 1977. Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20, S I 2 4 S132. Federal Interagency Sediment Project, 1963. Determination of fluvial sediment discharge. Interagency Report 14, St. Anthony Falls Hydraulics Laboratory, Minneapolis, MN, pp. 151. Grass, A.J., 1983. The influence of boundary layer turbulence on the mechanics of sediment transport. In:

160

D. Murray Hicks, M.J. Duncan~Journal of Hydrology 201 (1997) 138-160

Sumer, B.M., Miiller, A. (Eds.), Proc. Euromech 156: Mechanics of Sediment Transport. A.A. Balkema, Rotterdam, pp. 3-17. Hardisty, J., 1993. Monitoring and modelling sediment transport at turbulent frequencies. In: Clifford, N.J., French, J.R., Hardisty, J. (Eds.), Turbulence Perspectives on Flow and Sediment Transport. John Wiley and Sons, Chichester, pp. 35-60. Hicks, D.M., Fenwick, J.K., 1993. Suspended sediment manual - field, laboratory and office procedures for collecting and processing suspended sediment data. NZ Freshwater Miscellaneous Report No. 91, NIWA Christchurch, June 1993, pp. 84. Jackson, R.G., 1976. Sedimentological and fluid dynamic implications of the turbulent bursting phenomenon in geophysical flows. J. Fluid Mech. 77, 531-560. Kirkbride, A., 1993. Observations of the influence of bed roughness on turbulence structure in depth limited flows over gravel beds. In: Clifford, N.J., French, J.R., Hardisty, J. (Editors), Turbulence Perspectives on Flow and Sediment Transport. John Wiley and Sons, Chichester, pp. 185-196. Lapointe, M.F., 1996. Frequency spectra and intermittency of the turbulent suspension process in a sand bed river. Sedimentology 43, 439-449. Luchik, T.S., Tiederman, W.G., 1987. Time scale and structure of ejections as bursts in turbulent channel flows. J. Fluid Mech. 174, 529-522. McQuivey, R.S., 1973. Summary of turbulence data from rivers, conveyance channels, and laboratory flumes. U.S. Geol. Surv. Prof. Paper 802-B, pp. 66. Middleton, G.V., Southard, J.B., 1977. Mechanics of Sediment Movement. Lecture Notes for Short Course No. 3. Society of Economic Paleontologists and Mineralogists, Bingbamptom. Naden, P., 1987. Modelling gravel-bed topography from sediment transport. Earth Surf. Processes and Landforms 12, 353-367. Rouse, H., 1937. Modem conceptions of the mechanics of turbulence. Am. Soc. Civil Eng. Trans. 102, 436-505. Smart, G.M., 1991. A P.O.E.M. on the Waiho (electronic gauging of rivers). J. Hydrol. (NZ) 30 (1), 37-44. Smart, G.M., 1994. Turbulent velocities in a mountain river. In: Cotroneo, G.V., Rumer, R.R. (Eds.), Hydraulic Engineering '94, Proceedings of ASCE National Conference on Hydraulic Engineering, Buffalo, NY. Am. Soc. Civil Eng., New York, pp. 844-848. Sumer, B.M., Deigaard, R., 1981. Particle motions near the bottom in turbulent flow in an open channel, Part 2. J. Fluid Mech. 109, 311-337. Vanoni, V.A., 1946. Transportation of sediment in suspension. Am. Soc. Civil Eng. Trans. 111, 67-133. Vanoni, V.A. (Ed.), 1977. Sedimentation Engineering. Am. Soc. Civil Eng. Manuals and Reports on Engineering Practice No. 54. New York, pp. 745.