Characteristics of sediment profiles in reservoirs

Journal of Hydrology, 87 (1986) 33-44

33

Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

[4] CHARACTERISTICS

OF SEDIMENT

P R O F I L E S IN R E S E R V O I R S

E.L. MATYAS and L. ROTHENBURG Department of Civil Engineering, University of Waterloo, Waterloo, Ont. N2L 3G1 (Canada)

(Received December 3, 1985; accepted for publication April 17, 1986)

ABSTRACT Matyas, E.L. and Rothenburg, L., 1986. Characteristics of sediment profiles in reservoirs. J. Hydrol., 87: 33-44. Published data for sediment profiles in the Harry Strunk, Guernsey, Elephant Butte and Lake Mead reservoirs (U.S.A.) are analyzed. It is shown that the profiles can be described by the equation y = ax b, where x andy are horizontal and vertical distances, respectively, from the "pivot point". This equation can be used to determine the slope of the profile at any specified point and to determine the location of the transition point between the foreset and bottomset beds. Correlations are given which permit an estimate of the longitudinal and vertical extent, and the shape, of the topset, foreset and bottomset components of the sediments. This information can be used to predict the complete sediment profile in a reservoir provided that the horizontal distance of the pivot point from the dam is known or estimated.

INTRODUCTION N u m e r o u s dams a n d t h e i r a s s o c i a t e d r e s e r v o i r s h a v e been c o n s t r u c t e d to c o n t r o l floods a n d to provide w a t e r supplies for m u n i c i p a l , i n d u s t r i a l a n d r e c r e a t i o n a l purposes. Sediments t r a n s p o r t e d by r i v e r c h a n n e l s flowing into these r e s e r v o i r s are deposited a n d t h e c o n t i n u i n g r e d u c t i o n of s t o r a g e v o l u m e due to t h e g r a d u a l a c c u m u l a t i o n of sediments h a s a significant d e t r i m e n t a l effect on the usefulness a n d life of the reservoir. This h a s p r o m p t e d m a n y l a b o r a t o r y a n d field i n v e s t i g a t i o n s to s t u d y t h e problems a s s o c i a t e d w i t h reservoir sedimentation. F i g u r e 1 is a s c h e m a t i c r e p r e s e n t a t i o n of a dam, the reservoir, t h e profile of the o r i g i n a l thalweg, a n d the d e p o s i t i o n of sediments. The r e s u l t i n g f o r m a t i o n is a classical Gilbert-type delta c o n s i s t i n g of topset, foreset a n d b o t t o m s e t beds. The s h a p e a n d d e v e l o p m e n t of the delta are influenced by m a n y p h y s i c a l a n d e n v i r o n m e n t a l f a c t o r s w h i c h h a v e been s u m m a r i z e d a n d described by C o l e m a n (1981). The s e d i m e n t a t i o n of a r e s e r v o i r is also complex a n d depends u p o n m a n y i n t e r r e l a t e d factors. E x c e l l e n t reviews of the processes of s e d i m e n t a t i o n h a v e

0022-1694/86/$03.50

© 1986 Elsevier Science Publishers B.V.

34 15 E ¢,D Z FCO

;,

I0 5

I

^

I

I

I

oTOPOPERATION POOL

I "~.~~:2.~'8"°"

I

Ay

,.

/

:i:

mRESET

o /~

5

O",G,N

LT,

PIVOT

\

LWEG

,

.

.--

.

(..)

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>

20

25

15

I

I

l

J

I0

5

o

5

HORIZONTAL

DISTANCE

Io

( m x I0 3)

Fig. 1. Geometry and profile of a prograding delta. been presented by Brown (1950), Gottschalk (1964), and Simons, Li and Assoc. (1982). Wiebe and Drennan (1973) provided a detailed explanation concerning the principal modes of deposition and their relation to sediment supply, reservoir capacity and operating procedures. Several deterministic methods have been developed to predict the amount of sediment carried into a reservoir as a function of watershed characteristics (Ackermann and Corinth, 1962; Paulet, 1971; Gupta, 1974). In most reservoirs the inflow, water levels, sediment concentration and climatic conditions change with time, and therefore, the long-term storage sediment is stochastic. Accordingly, both deterministic and probabilistic methods have been developed to predict the storage of sediments in reservoirs (Moran, 1954; Soares et al., 1982). Kikkawa (1980) summarized the results of analytical and experimental methods which have been used to predict sediment rates and also presented data on sediment profiles for debris dams in mountainous regions. Pemberton (1980) presented the results of field surveys on a number of large reservoirs and used the results to predict sediment distribution. Such predictions often incorporate empirical methods developed by Cristofano (1953), Borland and Miller (1960), and Heinemann (1961). Matyas (1984) described a methodology to characterize the profiles of an artificial tailings delta, as well as selected modern prograding ocean and lake deltas. The methodology is used in this paper to characterize sediment profiles given by Pemberton (1980). On the assumption that the position of the "pivot point" or "delta lip" can be predicted by existing methods, a numerical model is proposed to permit the prediction of the extent and shape of the topset, foreset, and bottomset beds which form the component parts of a complete sediment profile in a reservoir.

35 A E b.Z

I0

i

5

(o)

2

LLI

~. 0.5 O3 •

i--

o = 2 7 8 x 10-4

0.2

b = 1061

0.I

I

I''"1

(b ~

Z

I b-0

I

'

'

f''"l

BOTTOMSETPROFtLE--.~ O:

3,02 = I0-t

~

-

5

o_

Z

/

"- FORESET PROFILE a = 8.72 x I0 -4

0.5

b = 1.222

~ 0.2 F--

..~ 0.1

J

,

,

I

5

,L,,I

I

,

,

I,J,H

20 50 I00 200 HORIZONTAL DISTANCE FROM PIVOT POINT (m xlO 2) 2

I0

Fig. 2. Guernsey reservoir (1947): (a) log x vs. log y for topset profile; (b) log x vs. log y for foreset and bottomset profiles.

DELTA FORMATION

A classical Gilbert-type prograding delta consists of topset, foreset and bottomset beds. Under certain physical and environmental conditions, the topset beds may have both subaerial and subaqueous segments and the shape of the profiles is influenced by the geometry of the reservoir. When the reservoir is significantly wider than the river channel, the sediments will tend to be deposited in a true delta shape and the flanks will be slightly steeper than the profile along the axis (Matyas, 1984). In many reservoirs, there are large annual fluctuations in the water levels and this will also have a significant effect on the distribution of sediments. At low reservoir stage and during extreme flood flows, sediments are likely to be reworked and redeposited closer to the dam.

36 SEDIMENT PROFILES On most sedimentation profiles the "pivot point" or "delta lip" can readily be identified due to a sudden change of slope. Accordingly, this point has been found to provide a convenient location for the origin of horizontal and vertical reference axes as shown in Fig. 1. Before sedimentation commences, the origin is at O1 and this point is used as a reference point for the thalweg profile. Figure 1 illustrates the original thalweg profile (1927) and the delta profile (1947) for the Guernsey reservoir. Profile data plotted on a log-log scale (Fig. 2) are typically linear and the data points can be analyzed by linear regression. Figure 2b shows two distinct straight-line segments and the point of intersection defines the transition from the foreset bed to the bottomset bed. The profile of the original thalweg or any of the delta beds can be expressed by the relationship: y

=

(1)

ax b

where x and y are horizontal and vertical distances from the reference axes, and a and b are coefficients obtained from the linear regression analyses. The coefficient a represents the ordinate at x = 1, and the coefficient b defines the slope of the straight-line relationship. The magnitude of the coefficients depends on the location of the reference axes as well as the units of length. In this paper, all distances are in metres. The co-ordinates of the point of intersection of two straight-line segments can be determined graphically (Fig. 2b), or by evaluating eqn. (1) for each segment and equating. The slope S = d y / d x of the profile at any point is given by differentiating eqn. (1) to give: S

=

(2)

a b x b-1

In order to compare profiles from different sites, it is convenient to use normalized distances X and Y; thus eqn. (1) becomes: Y

=

(3)

AX B

Distances can be normalized with respect to some selected reference length e.g. Pemberton (1980) normalized horizontal distances with respect to D, the total horizontal distance from the dam to the extreme upper end of the reservoir. Vertical distances were normalized with respect to H, the total depth from the base of the dam to the top operating pool level. Thus, Pemberton's data can be expressed by: X

=

x/D

and

Y

=

y/H

(4)

Data plotted in terms of X and Y also yield straight-line relationships with A = 1.0 and B = b. Thus eqn. (3) becomes: y

=

with

HD-bx

b

H D - b = a.

(5)

37 TABLE 1 Coefficients a n d dimensions of profiles Point Fig. 3

1 2

3

4 5

6

7

8 9

10

11 12

13

Reservoir

Harry Strunk Harry Strunk Harry Strunk Harry Strunk Harry Strunk Harry Strunk Harry Strunk Guernsey Guernsey Guernsey Guernsey Guernsey Guernsey Guernsey Guernsey Guernsey Guernsey E l e p h a n t Butte E l e p h a n t Butte E l e p h a n t Butte E l e p h a n t Butte E l e p h a n t Butte E l e p h a n t Butte E l e p h a n t Butte Lake M e a d Lake M e a d Lake Mead Lake Mead Lake Mead Lake Mead Lake Mead

Year

1949 1951 1951 1951 1962 1962 1962 1927 1937 1937 1937 1947 1947 1947 1957 1957 1957 1915 1935 1935 1935 1969 1969 1969 1935 1949 1949 1949 1964 1964 1964

Profile

Thalweg Topset Foreset Bottomset Topset Foreset Bottomset Thalweg Topset Foreset Bottomset Topset Foreset Bottomset Topset Foreset Bottomset Thalweg Topset Foreset Bottomset Topset Foreset Bottomset Thalweg Topset Foreset Bottomset Topset Foreset Bottomset

Coefficients

Dimension (m)

a

b

r

x

y

3.61E - 03 8.31E - 05 2.49E - 02 3.68E-01 4.28E - 04 1.04E-02 3.41E - 01 3.50E - 03 6.42E-05 2.41E - 02 1.17 2.78E - 04 8.72E - 04 3.02E-01 1.30E - 04 2.81E-04 (none) 1.24E - 03 1.18E-03 3.13E - 03 3.64E - 02 1.74E - 03 2~38E - 03 1.88E - 01 1.52E - 01 1.32E - 03 6.40E - 01 4.38 6.04E - 05 1.02 2.69

0.891 1.182 0.700 0.402 1.005 0.801 0.403 0.887 1.172 0.731 0.272 1.061 1.122 0.412 1.139 1.153

0.998 0.978 0.994 0.985 0.975 0.995 0.988 0.996 0.994 0.994 0.986 0.997 0.999 0.991 0.989 0.999

22,000 8,800 8,400 4,800 10,780 6,500 4,720 24,000 14,100 4,660 5,230 15,120 5,700 3,180 13,680 10,320

26 3.8 13.9 2.7 4.8 11.7 3.0 29 4.7 11.6 2.6 7.6 10.7 2.1 6.7 11.9

0.965 0.919 0.896 0.652 0.898 0.950 0.487 0.582 0.893 0.464 0.284 1.136 0.418 0.330

0.998 0.993 0.998 0.998 0.996 0.999 0.970 0.998 0.976 0.997 0.995 0.998 0.999 0.996

66,000 28,400 29,000 8,600 46,200 12,500 7,300 195,000 70,200 43,800 81,000 78,000 56,800 60,200

60 14.6 31.2 6.0 26.9 18.6 4.7 177 28.1 91.2 31.4 21.8 99.6 27.2

Profiles given by Pemberton (1980) for various stages of sedimentation in the Harry Strunk, Guernsey, Elephant Butte and Lake Mead reservoirs were analyzed and the results of the computations are summarized in Table 1. These results can be used to draw the thalweg profiles or the complete delta profiles for these particular reservoirs. Figure 1 is a typicaI example which compares the actual profiles with computed profiles and it is seen that the comparisons are good. In fact, for this example, there are no notable differences in the actual and computed profiles for the foreset and bottomset profiles. The good agreement between the actual profiles and the profiles given by eqn. (1) is a reflection of the magnitude of the correlation coefficient which typically exceeded 0.99. Also, it may be noted that some discretion was used in eliminating obvious anomalous points on the surveyed profiles. Accordingly,

38

loll

I

I

~?O2f3 /-BOTTOMSET 0 ~-7 log o : 1758 - 5,085b

5o%

i0°

2.~:~,~ ~FORESET0

i0-~

-

D-Z w 10-2 b_ b_ W 0

i0 -~

10-4

I0

I

0

0.5

ALL POINTS logo = 1.801-4916 b I

1.0 COEFFICIENT (b)

1.5

Fig. 3. Coefficients a and b for topset (v), forset (D) and bottomset (o) profiles. Refer to Table I for key to numbered points.

the method is only intended to model the average profile. Figure 1 and Table 1 also present other information concerning the profiles and reference to this information is made in a subsequent section of the paper. A plot of b vs log a results in a linear relationship (Fig. 3) for each segment of the profile. When b < 1, the profile is concave; b = 1 gives a straight line, and b > 1, results in a profile t h a t is convex. As yet, there is no theorectical or physical explanation to account for these relationships. However, it has been speculated (Matyas, 1984); t h a t the depth of water at, or near, the toe of the profile has a significant influence on the shape of the delta profile and this aspect is considered in a subsequent section of the paper.

BED SLOPES

Original thalweg The slopes of the thalweg profiles were evaluated from eqn. 2 and the results are plotted in Fig. 4. For comparison purposes, the horizontal distances were normalized and the origin of the reference axes was taken at O1 (Fig. 1). Figure 4 demonstrates t h a t the log-log plot results in straight-line relationships and provides a rapid method for obtaining the slope at any point and for comparing

39

0.005,

I-

PLAKE MEAD (00012)

a

},, O.O0F 2"-"C"' J "~...."~' (PE )M .B ~R /T .O1 N 98,0

DAM ]--~J

o.ooi~ 00005r

i

O.OI

,

, i , , , ,i

0.02.

0.05

i

O.I

,

, l ~ J ,'i.i

0.2

0.5

1.0

X : x/D

Fig. 4. Slopes of original thalwegs for four reservoirs.

different profiles. The values given in brackets represent average slopes given by Pemberton (1980).

Delta profiles Figure 5 represents the computed slopes for thalweg and delta profiles for the Guernsey reservoir (refer to Fig. 1). Again, these plots provide easy comparisons. For the example given in Fig. 5b, Pemberton computed that the slope of the topset profile was about 30~/oof the stream slope. As shown, the computed ratio varies from about 0.35 to 0.40 depending on the selected location.

m

0.0

I

~

l.O5J_(b) 0.

I

l

/,-TOPSETSLOPET /HALWES GLOPE -I

(~21I--

--~O.3"-GII'V'E;BY PEMBERTON119801

IO0000

I

IO000

I

I

I000

;00

I IO

I

0.01 (c)

o')

o, U3

0.001

-/#ORIGINAT LHALWEG BOTTOMSET>

0.0001

I I0

HORIZONTAL

f I00 DISTANCE

I I000

I0000

FROM P I V O T P O I N T ( m )

Fig. 5. Guernsey reservoir (1947): (a) slope of original thalweg and topset profile; (b) ratio of slopes; (c) slope of foreset and bottomset profiles.

40 PIVOT POINT

Analyses of other deltas by Matyas (1984) indicated that the depth of water or near, the t o e of the delta was a key factor in the development of the delta profile. In the case of the reservoir deltas, however, the pool levels are not normally constant and therefore, it was postulated that the depth of water below the pivot point would be more meaningful. This depth is given by Yb + Yf in Fig. 1 and the horizontal distance of the pivot point from the dam is given by xb + xf. Figure 6a, which is based on data in Table 1, suggests that there is a linear relationship between the values of xb + xf and Yb + Yf on a log-log plot. Initially, xb + xf = D and Yb + Yf = H, and this point can be plotted on the upper line in Fig. 6a to represent the initial pivot point in a particular reservoir. The pivot point will move towards the dam with time as the thickness of the accumulated sediments increases and therefore other points closer to the origin represent subsequent positions of the pivot point. As indicated in Fig. 1, the thickness Ys of the accumulated sediments must be added to Yb + Yf to obtain the position of the pivot point with respect to the base of the dam. Although Fig. 6a may be used to infer the path of the pivot point, additional information is required to determine the location of the pivot point with respect to time. In practice, the position of the pivot point could be determined by taking periodic soundings only in the area of the reservoir where the pivot point is likely to occur. Predictions could then by made by extrapolation of time-location plots. This information could also be combined with other studies which have been made to predict the accumulation c: sediments in reservoirs. As reported by Pemberton (1980) and others, howev~ r, predictions are difficult due to many contributing factors such as (1) par,icle size of the inflowing sediments; (2) operation of the reservoir; (3) shape ~f the reservoir; and (4) the (a) i

200

r

I

I /

(b)

- Yb+ Yf = 4.08 x 10-31=b + x f )0"e76

I00

5C

A E >.,

50 A

~_o 20

2C

x

I0

E

I0 O,Z"

I°'98'J

BOTTOMSET x b : 1.40 x I0 3 yb1"144

/p7 -~b:2.7~,10"4{~b+~f 5

l

tO

l

20

I

50

l

|

I00 200

Xb * Xf (m x I0 3)

I

J

I

I

2

5

I0

20

50

Yb (rnl

Fig. 6. Horizontal and vertical dimensions of pivot point and bottomset profiles.

41

volume of sediment deposited in the reservoir. These aspects are not covered in this paper.

PREDICTION OF DELTA PROFILE

On the assumption that the position of the pivot point is known, the next step is to predict the shape of the profile. As shown in Fig, 6, there is a good correlation between Xb + Xf with the horizontal and vertical lengths of the bottomset profiles, and from these correlations, the values of x and y for the foreset profiles can be readily determined. Figure 7 indicates an acceptable correlation between the horizontal and vertical dimensions of the topset profile. Thus, if the horizontal distance of the pivot point from the dam is known, Figs. 6 and 7 can be used to estimate the horizontal and vertical extent of each segment of the complete sediment profile. Then, the actual profile can be computed from eqn. (1) by substituting appropriate values of the coefficients a and b. Given values of x and y for a particular segment, there is a unique combination of a and b which will satisfy eqn. (1). This combination is obtained by substituting the equations given in Fig. 3 into eqn. (1) and iterating. Values of b are plotted in Fig. 8 as a function of the profile heights. The various dimensions and parameters can be combined to sketch a complete profile. This profile, and subsequent profiles, can be combined with other techniques to estimate the progress of sedimentation. For example, volume calculations can be facilitated by analytical or graphical methods since the equations for the profile are known.

Numerical example This example is used to illustrate the application of the information given in 50

(b)

1.5

20 E

A .D

I0

I.-

•//•

Yt (TOPSET)

1.0

Yf(FORESET)

Z

5

~ 0 TOPSET 2 I

I

5

I0

I

~'~"~Yt

0

Yt = 9.32 x I0 -4 xf 0"924

I

20 50 x? (m x 103 )

I

I00

0

Fig. 7. Horizontal and vertical dimensions of topset Fig. 8. Coefficient b as a function of profile heights.

* yb (BOTTOMSET) [

I

20 40 60 VERTICAL. HEIGHT (m)

profiles.

80

42

1 A E

T

l ' - - [ - - T - -

101 C ~.":

b~o 2C em

" , yz - . .

I!!

ESET

-3

'

.~-..-:. , ....

.

}-

5c 6C ~D

I0

0

I0

20

30

HORIZONTAL DISTANCE (m x I0 3)

F i g . 9. P r e d i c t e d

thalweg

and sediment

profiles.

this p a p e r to p r e d i c t the shape and e x t e n t of the c o m p o n e n t parts of a deltaic sediment profile. L e t D = 50,000m and H = 53.3m. F o r the original thalweg, the corresponding v a l u e s of a a n d b are 4.06E - 03 and 0.875, respectively. E q u a t i o n (1) is e v a l u a t e d for 0 < x < 50,000 m and the profile is plotted as s h o w n in Fig. 9. After s e d i m e n t a t i o n has been in progress for several years, assume t h a t the pivot p o i n t is l o c a t e d 30,000 m from the dam as s h o w n in Fig. 9. F r o m Fig. 6a, Yb = 6.8m, Yb + Yf = 34.1m and t h e r e f o r e , yf = 27.3m. F r o m Fig. 6b, Xb = 12,600m, and therefore, xf = 17,400m. Now xt = D (Xb + Xf) = 20,000m and from Fig. 7, Yt ---- 8 . 8 m ; therefore, t h e t h i c k n e s s of the a c c u m u l a t e d sediments is y, = 10.4 m. T h e predicted limits for e a c h segment of the profile are plotted as solid points in Fig. 9. O b t a i n b = 1.062, 0.965 and 0.371 from Fig. 8 for the topset, foreset and b o t t o m s e t profiles, respectively. F r o m Fig. 3 o b t a i n the c o r r e s p o n d i n g v a l u e s of a = 2 . 3 7 E - 0 4 , 2 . 2 1 E - 0 3 and 7 . 4 6 E - 0 1 . E v a l u a t e eqn. (1) for v a l u e s of x = 0 to the p r e d i c t e d m a x i m u m values. P l o t t h e complete profile, as s h o w n in Fig. 9.

CONCLUSIONS

On the basis of t h e detailed analysis of published d a t a o n t h e profiles of sediments in f o u r large reservoirs, a model is proposed w h i c h permits the p r e d i c t i o n of t h e p r o p o r t i o n s a n d shape of t h e t h a l w e g and t h e topset, foreset and b o t t o m s e t segments of a c o m p l e t e deltaic s e d i m e n t profile. T h e c o m p l e t e profile c a n be described by t h e e q u a t i o n y = a x b w h e r e x and y are distances r e f e r e n c e d to t h e " p i v o t point", and a and b are coefficients w h i c h h a v e been e v a l u a t e d for e a c h s e g m e n t of t h e profile. T h e proposed

43

method assumes that the horizontal distance of the pivot point from the dam is known. When the coefficient b ¢ !, the slope of a profile changes continuously, and this slope can be easily computed.

ACKNOWLEDGMENTS

This study was financially supported, in part, by the Natural Sciences and Engineering Research Council of Canada.

REFERENCES Ackermann, C.W. and Corinth, R.L., 1962. An empirical equation for reservoir sedimentation. Int. Assoc. Sci. Hydrol., 59: 359-366. Borland, W.M. and Miller, C.R., 1960. Distribution of sediment in large reservoirs. Trans. Am. Soc. Civ. Eng., 125 (3019): 166-180. Brown, C.B., 1950. Sedimentation in reservoirs. In: H. Rouse (Editor), Engineering Hydraulics. Wiley, New York, N.Y., pp. 825~34. Coleman, J.W., 1981. Deltas, processes of deposition and models for exploration. Burgess Publishing Company, Minneapolis, Minn. 2nd ed., 124 pp. Cristofano, E.A., 1953. Area increment method for distributing sediment in a reservoir. Area Plann. Office, U.S. Bur. Reclam., New Mexico, Albuquerque, N.M. Gottschalk, L.C., 1964. Reservoir sedimentation. In: V.T. Chow (Editor), Handbook of Applied Hydrology. McGraw-Hill, New York, N.Y., Section 17-1. Gupta, S.K., 1974. A distributed digital model for estimation of flows and sediment load from large ungaged watershed. Ph.D. Thesis, University of Waterloo, Waterloo, Ont., 354 pp. Heinemann, H.G., 1961. Sediment distribution in small floodwater retarding reservoir in the Missouri Basin loess hills. U.S. Agric. Res. Serv., Milwaukee, Wisc., ARS 41-44. Kikkawa, H., 1980. Reservoir sedimentation. In: H.W. Shen and H. Kikkawa (Editors), Application of Stochastic Processes in Sediment Transport. Water Resources Publications, Littleton, Colo., pp. 14-1 14-23. Matyas, E.L., 1984. Profiles of modern prograding deltas. Can. J. Earth Sci., 21: 115~1160. Moran, P.A.P., 1954. A probability theory of dams and storage systems. Aust. J. Appl. Sci., 5: 116-124. Paulet, M., 1971. An interpretation of reservoir sedimentation as a function of watershed characteristics. Ph.D. Thesis, Purdue University, Lafayette, Ind. Pemberton, E.L., 1980. Survey and prediction of sedimentation in reservoirs. In: H.W. Shen and H. Kikkawa (Editors), Application of Stochastic Processes in Sediment Transport. Water Resources Publications, Littleton, Colo., pp. 15-1-15-20. Simons, Li and Associates, 1982. Engineering Analysis of Fluvial Systems. Simons, Li and Assoc., Fort Collins, Colo. Soares, E.F., Unny, T.E. and Lennox, W.C., 1982. Conjunctive use of deterministic and stochastic models for predicting sediment storage in large reservoirs. Parts 1 to 3. J. Hydrol., 59: 49-121. Wiebe, K.L. and Drennan, L., 1973. Sedimentation in reservoirs. In: Fluvial Processes and Sedimentation. Proceedings of Hydrology Symposium, Edmonton, Alta. Inland Water Directorate, Dept. of the Environment, Ottawa, Ont.

NOTATION

List of symbols used a, b D H r S xb

-------

coefficients total horizontal length of reservoir total depth of reservoir coefficient of correlation slope (dy/dx) horizontal length of bottomset profile

xf

-- horizontal

length of foreset profile

xt

-- horizontal

length of topset profile

X Yb

-- normalized horizontal distance -- height of bottomset profile

yf

-- height of foreset profile

(x/D)

Yt

-- height of topset profile

Ys

-- thickness

Y

- - n o r m a l i z e d v e r t i c a l d i s t a n c e (y//-/)

of sediments at dam