Seasonal variation of mid-foreshore sediments at a Delaware beach

Sedimentary Geology, 61 (1989) 37-47

37

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

Seasonal variation of mid-foreshore sediments at a Delaware beach ROGER N. DUBOIS Department of Geography, Universityof Maryland Baltimore Count)', Baltimore, MD 21228 (U.S.A.) Received March 22, 1988; revised version accepted September 6, 1988

Abstract Dubois, R.N., 1989. Seasonal variation of mid-foreshore sediments at a Delaware beach. Sediment. Geol., 61: 37-47. From March 1982 through April 1983 at a Delaware beach, there was a modest, but significant relation between the first three moments of mid-foreshore sediment distributions and surge variability. Based on monthly averages as surge variability increased from summer to winter, that is, as the magnitude and frequency of storm waves increased, the mean grain size increased, sorting improved, and skewness became more positive; the reverse was also noted from winter to summer. The results of stepwise regression analysis showed that mean particle size was highly influenced by the percentage of fine sands between 2.25 and 2.75q~ (Fines) which was relatively high in summer and low in winter. Sorting was most sensitive to the extent of the coarse tail in a sediment sample; as this tail was extended, sorting became poorer. The extent of the coarse tail and the percentage of Fines explained most the variance of skewness. As the coarse end of a sediment sample was extended and as the percentage of Fines increased, skewness became more negative.

Introduction As part of an investigation which focused on documenting the seasonal variation of beach topography and beach volume at a Delaware beach, a study was conducted to note whether the textural properties of mid-foreshore sediments would vary on a seasonal basis as did the wave regime. Extra-tropical storms frequent the midAtlantic coast during the fall, winter, and early spring and cause some degree of beach erosion. In late spring and summer, the magnitude and frequency of these storms decrease, and in turn, swells rebuild the beach. As the wave regime changed, it was expected that textural characteristics of mid-foreshore sediments would likewise change following the path noted by McLaren (1981). He suggested that if a normal sediment population were subjected to erosional processes at a stable energy level, then the amount of sedi0037-0738/89/$03.50

© 1989 Elsevier Science Publishers B.V.

ment eroded would progressively decrease from fine to coarse. Because some of the fine fraction would have been removed, the remaining sediments should be coarser, better sorted, and more positively skewed than the original sediment population. The lags would be positively skewed because after a portion of the fines has been winnowed from a sediment population, the residual sediment population displays a relatively large percentage of coarse grains and a relatively small percentage of fine grains which, in turn, yields a distributional curve with a positive tail (Komar, 1976, p. 344). For this Delaware study, it was expected that foreshore sediments would progressively become coarser, better sorted, and more positively skewed from summer to winter as fines were removed by storm waves and vice versa from winter to summer as fines were redeposited by swells. It was assumed that sediments eroded from a berm would be deposited in the nearshore, and

38

PA

4 f"*",J ' :

MD

LEWE',

N

I,

DELAWARE MARYLAND

75 ° 1S"

Fig. l. Location of the study area.

DE

0

25. MILES

39 in turn, be redeposited on the beach to reform a berm. Thus, from one fully developed berm to another, in this case from one summer to the next, the textural characteristics of mid-foreshore sediments would remain the same.

Study area and methodology The study was conducted in the Delaware Sea Shore State Park at Key Box Road (Fig. 1). The beach is part of a transgressing baymouth barrier (Kraft, 1971) and is eroding at a rate of 0.6-0.9 m / y r (Kraft et al., 1978). The net littoral drift is northward where sediments eventually are deposited on the bayward side of Cape Henlopen (Fig. 1). The tides are semi-diurnal with a mean range of about 1.2 m. During storms wave breaker height can be 2-3 m while swells generate heights of 1 m or less. From March through June of 1982, foreshore sediment samples were collected once a week at low tide at two sites, 200 m apart. From July 1982 through April 1983, the beach was visited one to three times per month and samples were collected at both sites during each visit. In all 34 samples were retrieved from each of the two sites. Surface sediments from both profiles were collected in the mid-foreshore (Bascom, 1951) from the corners of a one meter grid and combined to form one sample so as to reduce sampling error (Krumbein, 1934). These samples were taken from the matrix of the foreshore sediment population. Although at times clastic and bioclastic materials ranging from pebbles to cobbles were scattered on the foreshore slope, none of these materials was included in a sample. The weight of one aggregated sample was about 200 g. In a laboratory, the sediments were washed and dried, and then split to about 35 g. A split sample was sieved at 1 / 4 q~ interval. The method of moments was used to obtain the descriptive statistics of a sediment sample (Griffiths, 1967). After the moments were calculated for all 34 cases, the t-test was used to determine if there was a significant difference between the mean of each moment for samples collected at site 1 and 2; the results showed no significant difference at the 90% level. Thus, the moment data from both sites were combined, and all descriptive statistics of

moments presented in this paper are based on the average of samples collected from both sites. The surge level was used as a surrogate of general wave conditions (Dubois, 1988). The surge was obtained by subtracting the predicted tidal level from the observed level at high tide for each day. The National Oceanic and Atmospheric Administration provides tide tables that give the predicted tide levels, and the same agency recorded water levels in the Indian River Bay near the Indian River Inlet. For each day the average of surges at the two high tides was used as an index of surge level for that day.

Results and discussion The surge levels are shown in Fig. 2A and are a reasonable surrogate for a wave-climate regime. When compared with weather data gathered at three-hour intervals by the U.S. Coast Guard at the Indian River Inlet, all positive surge spikes, such as the two noted in October 1982, were generated by extra-tropical storms, and all negative surge values were associated with strong offshore winds. During the fall and winter seasons, extra-tropical storms created large surges, but with the passage of a storm, winds changed from the northeast to the west-northwest and generated small or negative surge values. Thus, the effect of storms causes large variations in surge levels. During the spring and summer the magnitude of storms decreased and so did the variation in surge levels (Figs. 2A and 3). Based on the magnitude of spikes, it seems that the severity of storms decreased after February 1982 and remained relatively low during the summer until the last week of September when the severity increased again. No hurricanes or tropical storms struck the coast during the summer and fall of 1982. From spring through summer of 1982, the beach accreted as storm frequency decreased, and with the return of "northeasters" during the fall of 1982, beach volume was reduced (Figs. 2B and 4). At the beginning of the study, the beach shape was concave skyward, and the swash dissipated over the face of the foreshore. By July swells had rebuilt the beach, and its shape was now convex; the foreshore slope was about 9° which caused some

40

e')

~u

T

//

d

u Z J

// \\

/"

\ ©

g',.i

I

I

<:2 -LU :D

Z <: rr (D Z

-1(D

u_

O

Z - rr

or,

q 6 (1~0) ] O U n S

(~'c!~) ]IAIR]OA

(IHd} NVqI~

o

o

Q

rq

6

(IHd) ©NI±~IOS

SS3NM]>tS

L~

41

80

MAXIMUM

70

60/ 50-

2

uJ T (.9 II

/

,

/

/

'

,

,

4030-

\\\\

STANDARD "~ATION

\

20-

;. :)~

~ ~o

.....

,.,~ ~,j /. *

~

THREE MONTH R U N N I N G M E A N OF STANDARD DEVIATION

//

0

/ -10 -

jr-

.~'~.~

\\

MINIMUM

,

//

-20 -

-30 -

Jan T Feb ~Mar I A p r I M a y I j u n e ' J u l y ~ A u g ISept ~ Oct ~Nov I Dec FJan ~ Feb I M a r ~ A p r ~ 1982 1983 TIME

Fig. 3. Monthlydescriptivestatistics of surge levels(after Dubois, 1988).

reflection of swash energy from the shore. From March through August 1982 the beach accreted above the zero-meter contour line (National Geodetic Vertical Datum of 1929) by 60 m3/m of shore, and the zero-meter contour line prograded by 16 m. From August through March 1983 storm waves reduced beach volume by 83 m3/m of beach, and the zero-meter contour line retrograded by 32 m. A full discussion of the changes in beach topography and beach volume is forthcoming (Dubois, 1988). The descriptive statistics of all 34 cases are presented in Table 1. On the average the sands were medium size, well sorted, and nearly symmetrically distributed. Because kurtosis by itself can not be linked with any attributes of geomorphic processes (McLaren, 1981), no discussion of the fourth moment is given in this paper. The sands were primarily composed of quartz and feldspars with minute amounts of heavy minerals in the fine end of a distribution. The descriptive statistics of these sediments were similar to those described by Nordstrom (1977) for sediments along the New Jersey coast.

The first three moments were plotted against time (Fig. 2C-E). As the wave regime changed from storm to swell during the spring of 1982, mean particle size decreased from March through June as expected; however, during July and August, particle size increased and continued to increase slightly into the winter and spring of 1983 (Fig. 2C). Sorting and skewness did show modest seasonal cyclic patterns (Fig. 2D, E). Sediments sampled in summer were more poorly sorted and more negatively skewed compared to sediments collected in other seasons. If the sorting value of 0.50(/) was arbitrarily focused on, then from March through June 1982 and from the last week of October through April 1983, sorting values were less than 0.50~ 85% and 90% of the time respectively; whereas, from July through the third week of October, sorting values were greater than 0.50(/) 85% of the time. Skewness was negative 85% of the time from the middle of June through the middle of October; whereas from March 1982 through the first week of June and from November through April 1983, skewness was positive 75% and 85% of the time respectively.

42

A ~2

E

v

Z

o uJ _J LU

MAR MAR MAY JUNE AUG

18, 29 30, 28, 27,

10

1982 1982 1982 1982 1982

96 278 421 49.3 59 9

1399 1.547 2.037 2.173 1783

0 282 0.391 0 405 0 473 0583

0 714 0531 0069 -0 297 -0 194

I

I

I

I

I

L

20

30

40

50

60

70

80

90

DISTANCE (m)

> DATE VOL(m3/m) AUG D;TE 1982 vO

EL] 0

OCT NOV FEB

2, 1982 30, 1982 27 1983

10

288 10.1 129

X~ 1496 1.476 1 459

S¢

Sk

0 447 -0 051 0.306 0428 0431 0536

L

J

I

L

I

I

I

I

20

30

40

50

60

70

80

90

DISTANCE (m) Fig. 4. General pattern of beach accretion from March to August of 1982 (A) and erosion from August of 1982 to February of 1983 (B). The zero elevation is adjusted to the National Geodetic Vertical Datum of 1929. The vertical exaggeration is 10 times. Vol is the volumetric change of beach sediment relative to the first study day. 3 March 1982; .~,~ is the mean particle size. S,~ is sorting, and Sk is skewness.

Each of the three moments was statistically correlated and regressed with surge level which reflected the general wave regime from season to season. Instead of using the magnitude of surge TABLE 1 Descriptive statistics of sediment size ~ Mean Mean (~) Sorting ( ,~ ) Skewness Ctail (,~) Ftail (q~) Fines (%) Coars (%)

S.D. b

Min.

Max.

1.62 0.41

0.23 0.09

1.19 0.28

2.17 0.67

0.09 -0.01 3.43 19.31 6.58

0.29 0.46 0.39 16.30 6.53

- 0.38 -0.87 2.25 3.83 0.22

0.71 0.62 4.00 59.67 28.94

" There are 34 cases. h S.D.: standard deviation.

level as an independent variable, it was decided that the response of the moments might best be explained by the degree of variability (Dubois, 1988). Thus, for each month (total of 14), the mean of the three moments was calculated and correlated with the standard deviation of the monthly mean surge level (Fig. 3). Note that the maximum number of sediment samples collected in a month from each two sites was five while the minimum number was one. When each monthly mean moment was correlated with the monthly surge standard deviation, no significant relations existed. However, when each moment was correlated with the two-month running mean of the standard deviation, the results improved and continued to do so following a third model run which employed a three-month running mean of the

43

0.80

2.10

0.60

A

g w N

1.90

C

03

r2=0.543 Prob.=0,003

r2=0393 Prob.=0.016

0.40

Z

0.20

v

1.70

o

03

Z

0.20

I,U -040

150

50 1.30

g z ~ nO

D

40

0.70

r2=0.522 Prob,=0.004

B

0.60

~

3o

03

"

u,I Z ~..

050

r2=0,61 Prob.=0.002

z"

20

10

0.40

[

0.30

I

I

8

I

I

I

10

SURGE

I

I

12

I

r

14

VARIABILITY

I

[

16

I

I

8

18

I 10

L

I

I

12

SURGE VARIABILITY

(CM)

I

I

14

I 16

I 18

(CM)

F i g . 5. R e s u l t s o f c o r r e l a t i o n a n d r e g r e s s i o n a n a l y s i s b e t w e e n s u r g e v a r i a b i l i t y a n d m e a n p a r t i c l e size ( A ) , s o r t i n g (B), s k e w n e s s ( C ) , a n d Fines ( D ) .

TABLE

2

Pearson correlation coefficients and probabilities

M e a n ep

S o r t q,

M e a n q,

S o r t q,

Skewness

1.000

0.282

- 0.418

0.946

0.000

0.105

0.013

0.000

-

1.000

-0.658

0.000 Skewness

Fines %

Coars %

F t a i l ~/,

-

-

-

-

-

.

F t a i l q,

C t a i l q,

- 0.646

0.513

0.104

0.000

0.001

0.555

0.458

0.315

0.442

0.006

0.069

0.008

0.000

1.0(30

- 0.532

- 0.147

- 0.099

0.731

0.000

0.001

0.405

0.576

0.000

1.000

- 0.409

0.538

- 0.070

0.000

0.016

0.001

0.691

1.000

- 0.340

- 0.535

0.000

0.048

0.001

-

.

Coars %

0.013

-

-

.

Fines %

.

1.000 0.000

C t a i l q,

.

.

.

.

.

.

-0.766

-0.047 0.791 1.000 0.000

44

standard deviation (Fig. 3) as the independent variable. The results of the third model are show~ in Fig. 5 A - C . Although the explained variance for each regression model was below 55%, the model probabilities were highly significant and made intuitive sense. As the surge variability increased from summer to winter (Fig. 3), mean particle size increased (Fig. 5A), sorting improved (Fig. 5B), and the sediment distribution became more positively skewed (Fig. 5C). Similar results were noted when each of the three moments was statistically correlated with beach sediment volume (Table 2). As volume increased from winter to summer and as the shape of the beach changed from concave to convex skyward (Fig. 4), mean particle size decreased, sorting became poorer, and skewness became more negative. These trends were in line with McLaren's (1981) predictions, but the strengths of the correlations were modest. One reason for the lack of strengths may have been a function of the time difference between a sampiing day and an erosional event in winter. Sediments were often collected several days after an

erosional occurrence when a small amount of sediment may have been redeposited on the beach. Similarly in summer, samples may been taken immediately after a slight amount of erosion had occurred; thus, the sediment texture may have reflected the characteristics of an erosional event although the wave regime was more inclined to rebuild the beach. The next section of this paper examines the sediment fractions that were added or winnowed from a sediment population by swells or storm waves, and how these fractions changed a grain size distribution. By comparing the size frequency distributions of sediment samples taken during erosional and depositional beach stages, the sediment fractions being added or winnowed from the beach could be ascertained (Fig. 6) and used to statistically explain the variance of the first three moments. Fig. 6 shows that some fine and coarse sizes were winnowed during erosional events and redeposited on the beach when swells prevailed. The data revealed large fluctuations in the percentage of

40DEPOSITION 35-

30-

25 ~

o

20

EROSION

X~ So Sk July 15. 1982 1 75 0 664 -0 465 August 2 7 1982 1 70 0.647 -0 217

q /\

/ \\

j

/

March 26. 1983 March 8, 1982

/~

Xo Se 1 69 0368 1.47 0301

Sk +0.438 +0.290

\/

,;

I I

/\

//

March 26, 1 9 8 3 " ~ - J I / // f,

/

/l/4.,,.~March 8, 1982

//

15-

10-

0

375L0.50'-025' O0'0.25~050ro75~1.00~125r150'l 75'200 ~225~250~2.75~300'325r3~0'3~5' Phi 1~)

Fig. 6. The frequency distribution of four sediment samples. Two (March) were taken after storm wave episodes while the other two (July and August) were taken following periods of swells. X÷ is the mean particle size, S~ is sorting, and S k is skewness.

45

fine sands between 2.25 and 2.75~. Thus, for each sample, the total percent of sediment weight found in the 2.25, 2.50, and 2.75q~ sieves was recorded and used to represent concentration of fines (Fines) in a sediment sample. In the coarse area of sediment distributions (Fig. 6), the amount of materials concentrated in the 0.50, 0.75, and 1.00~ sieves fluctuated with erosional and depositional events. The concentration of coarse grains (Coars) was taken as the total percent of sediment weight found in the 0.50, 0.75, and 1.00q~ sieves. In addition, the phi values were recorded of the coarsest sieve (Ctail) where sediments first accumulated and of the finest sieve (Ftail) where the last sediment fraction accumulated. The descriptive statistics of these four variables (Fines, Coars, Ctail and Ftail) are shown in Table 1. The mean monthly values were calculated for each of the four variables and were statistically correlated with surge variability, the three-month running mean of the surge standard deviation. Only Fines was significantly related with surge variability; for the other three variables, values of the F-test exceeded the 0.10 level. As surge variability decreased from winter to summer, Fines increased in the midforeshore zone (Fig. 5D). Using stepwise regression, each of the first three moments was set as a dependent variable and regressed with the independent variables of Fines, Coars, Ctail and Ftail. The significance level was set at 0.10 for inclusion and exclusion of independent variables in the regression models (Koch and Link, 1970; Engstrom, 1974). The independent variables were not strongly related to one another (Table 2). In the first model, 97% of the mean particle size variance was explained by Fines, Coars, and Ctail," Ftail was not accepted in the regression model (Table 3). As the concentration of Coars increased and Ctail was extended, mean particle size increased, whereas an increase in the concentration of Fines caused mean grain size to decrease. Fines was the most important variable which explained the variance of mean particle size (Table 3, partial r2), and being modestly related with surge variability (Fig. 5D), it suggested that as the beach built from winter to summer (Fig. 4A), fines were added to foreshore sediment population, making the material finer in texture and at

TABLE 3 Stepwise regression analysis D e p e n d e n t variable: M e a n R 2 = 0.974 Probability = 0.0000 S t a n d a r d error of estimate = 0.0395 Intercept = 1.521 Regression

Proba-

Partial

coefficient

bility

r 2

Fines %

0.0112

0.0000

0.9318

Coars %

- 0.0193

0.0000

0.6614

0.0512

0.0381

0.1356

Variable

Ctail ,#

Variable not in equation Variable

Probability

Ftail ~

0.5801

Partial r 2 0.0107

times bimodal in distribution (Fig. 6). From summer to winter, fines were winnowed, and the foreshore sediment texture became coarser and unimodal (Figs. 4B and 6). During the rebuilding phase, a small percentage of coarse and very coarse sands was also added to the foreshore; and at times on the landward side of a developing berm, large concentrations of pebbles and cobbles (clastics and bioclastics) were deposited by the overtopping swash. These coarse materials were then removed from the beach by storm waves. Sonu (1972) observed similar sediment responses during beach recovery and after beach erosion on the Outer Banks, North Carolina. In the second model, sorting was most influenced by Ctail, followed by Fines, Ftail, and Coars, in that order (Table 4, partial r2). As either tail was extended or as the concentration of Fines or Coars increased, sorting became poorer. Except for Fines, no other independent variable, by virtue of its lack of association with surge variability, varied with the seasons. But the total impact of the independent variables caused sorting to modestly change with the seasons; sorting was relatively poor in summer when reflective beach stages prevailed, and better in winter when dissipative beach stages existed. Bryant (1982) reported similar findings for foreshores in Australia.

46

TABLE 4 Stepwise regression analysis D e p e n d e n t variable: Sorting 4' R 2 = 0.827 P r o b a b i l i t y = 0.0000 S t a n d a r d error of estimate = 0.0409 Intercept = 0.1093 Variable

Regression

Proba-

Partial

coeficient

bility

r2

Ctail 4,

-0.108

0.0001

0.402

Fines %

0.002

0.0014

0.299

Ftail 4'

0.066

0.0043

0.248

Coars %

0.005

0.0515

0.124

In the last model, Ctail followed by Fines and Ftail explained the most variance of skewness (Table 5, partial r 2 ) ; C o a r s was not included. Mason and Folk (1958) commented that if the fine or coarse end of a normal sediment distribution was extended, then skewness would become more positive or negative respectively; the results of this Delaware study are in agreement (Table 5). It has also been suggested that negative skewness would be caused by the winnowing of fine material from a sediment body (Friedman, 1961, 1967; Martins, 1965; Hails and Hoyt, 1969). Note, however, that Fines was inversely related to skewness (Table 5); a decrease in Fines caused a TABLE 5 Stepwise regression analysis D e p e n d e n t variable: Skewness R 2 = 0.820 P r o b a b i l i t y = 0.0000 S t a n d a r d error of estimate = 0.1308 Intercept = - 0.3779 Variable

Regression

Proba-

coefficient

bility

Partial r2

Ctail 4'

0.447

0.0000

0.731

Fines %

- 0.011

0.0000

0.203

0.0058

0.610 0.226

Ftail 4'

Variable not in equation Variable Coars %

Probability 0.572

Partial r 2 0.019

sediment sample to come more positively skewed, just as K o m a r (1976) and McLaren (1981) had predicted. A similar behavior in the coarse region could not be confirmed; that is, a decrease in Coars should have yielded a more negatively skewed distribution. Unfortunately, there was no significant relation between skewness and Coars. Although the results of this study are in general agreement with McLaren's (1981) predictions, there is a notable difference between both studies. In McLaren's study as energy caused erosion, fines as well as some coarse grains were removed, but there was always coarser sediments left behind which could not be removed by the erosional energies (McLaren, 1981, fig. 1, histograms 2 and 5). Thus, in his case the material left behind can be interpreted as a sediment body to coarse to be transported or a true lag deposit; therefore, his sediment model characterized the distribution of a lag deposit. But what if energies are high enough to remove all material sizes? What conceptual model is used in such a case? Given this condition, it would seem that an important sediment property to focus on might be volume or abundance. If sediment abundance is small along a shoreline, then one would expect the removal of much material during erosional events and the exposure of bedrock. On the other hand if the abundance of sediment is large, then storm waves would remove sediments from the beach until a foreshore profile of equilibrium, concave in shape, would be established when no further erosion would take place. At this point, the texture of the remaining material would reflect the characteristics of a sediment body that was most abundant at the time of equilibrium, and not those of a true lag deposit. For the Delaware study, no lag deposits existed. Note that the summer sediment population (Fig. 6) had grain sizes that ranged from - 0 . 7 5 ~ to 3.75q~. By 26 March 1983 following episodes of erosional wave action, much fine sands were removed from the previous summer sediment population; but the coarse tail of the summer sediment body was also removed. For 26 March 1983, grains coarser than 0.50~ were not recorded (Fig. 6). Clearly if wave energies were vigorous enough to remove grains of - 0 . 7 5 ~ , they could have likewise removed all finer sediment sizes from the

47

beach. Therefore, the textural properties of the March sediments may have reflected the influence of the backwash that swept beach sediments to the nearshore and the characteristics of a sediment body that was most abundant at the time of the erosional events.

Summary The results of this study show that a link existed between the wave-climatic regime and the textural characteristics of mid-foreshore sediments at a beach in Delaware from the spring of 1982 to the spring of 1983; and that because the waveclimatic regime fluctuated with the seasons, so did the sediment texture. When wave energy was relatively high in winter as depicted by a large surge variability, foreshore sediments were generally coarser, better sorted, and more positively skewed than sediments found in summer when swells prevailed and surge variability was small. In winter during times of erosional episodes, all sediments sizes ( - 0 . 7 5 to 3.75~) could be removed by the backwash. However, the sediment fraction most affected by winnowing processes was confined to fine sands ranging from 2.25 to 2.75q5; in addition, sediments coarser than 0.50,/, were removed from the shore. In summer, swells retrieved all sand sizes, including a high percentage of fine sands, from the nearshore and redeposited them on the foreshore. In turn, Fines was the most important variable that influenced mean particle size. The dominant variable that explained sorting and skewness was the extent of the coarse tail in a sediment sample; as the tail was extended into coarser sizes, sorting became poorer and skewness became more negative. It was also revealed that as Fines increased skewness became more negative, not positive as some have suggested.

Acknowledgements I wish to thank Patricia Dubois for helping me collect beach data and to thank two anonymous reviewers for their thoughtful comments.

References Bascom, W.N., 1951. The relationship between sand size and beach-face slope. Trans. Am. Geophys. Union, 32: 866-874. Bryant, E., 1982. Behavior of grain size characteristics on reflective and dissipative foreshores, Broken Bay, Australia, J. Sediment. Petrol., 52: 431-450. Dubois, R.N., 1988. Seasonal changes in beach topography and beach volume. Mar. Geol., 81: 79-96. Engstrom, W.E., 1974. Beach foreshore sedimentology and morphology in the Apostle Islands of northern Wisconsin. J. Sediment. Petrol., 44: 190-206. Friedman, G.M., 1961. Distinction between dune, beach, and river sands from their textural characteristics. J. Sediment. Petrol., 31: 514-529. Friedman, G.M., 1967. Dynamic processes and statistical parameters compared for size frequency distribution of beach and river sands. J. Sediment. Petrol., 37: 327-354. Griffiths, J.C., 1967. Scientific Method in Analysis of Sediments. McGraw-Hill, New York, N.Y., 508 pp. Hails, J.R. and Hoyt, H.H., 1969. The significance and limitations of statistical parameters for distinguishing ancient and modern sedimentary environments of the lower Georgia Coastal Plain. J. Sediment. Petrol., 39: 559-580. Kock, G.S., Jr. and Link, R.F., 1970. Statistical Analysis of Geological Data. Wiley, New York, N.Y., 375 pp. Komar, P.D., 1976. Beach Processes and Sedimentation. Prentice-Hall, Englewood Cliffs, N.J., 429 pp. Kraft, J.C., 1971. Sedimentary facies patterns and geologic history of a Holocene marine transgression. Geol. Soc. Am. Bull., 82: 2131-2158. Kraft, J.C., Allen, E.A. and Maurmeyer, E.M., 1978. The geological and paleongeomorphological evolution of a spit system and its associated coastal environments. J. Sediment. Petrol., 48: 211-226. Krumbein, W.C., 1934. The probable error of sampling sediments for mechanical analysis. Am. J. Sci., 27: 204-214. Martins, L.R., 1965. Significance of skewness and kurtosis in environmental interpretation. J. Sediment. Petrol., 35: 768-770. Mason, C.C. and Folk, R.L., 1958. Differentiation of beach, dune, and aeolian flat environments by size analysis, Mustang Island, Texas. J. Sediment. Petrol., 28: 211-226. McLaren, P., 1981. An interpretation of trends in grain size measures. J. Sediment. Petrol., 51: 611-624. Nordstrom, K.F., 1977. The use of grain size statistics to distinguish between high- and moderate-energy beach environments. J. Sediment. Petrol., 47: 1287-1294. Sonu, C.J., 1972. Bimodal composition and cyclic characteristics of beach sediment in continuously changing profiles. J. Sediment. Petrol., 42: 852-857.