AS A aCe Cag Mba. Gee T.M.8
U.S. Army

— Coastal Engineering
Research Center

SEDIMENTATION AT AN
INLET ENTRANCE

RUDEE INLET-VIRGINIA BEACH,VIRGINIA

TECHNICAL MEMORANDUM NO.8
December 1964

DEPARTMENT OF THE ARMY
CORPS OF ENGINEERS

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UIP A A A

IOHM/18IN

SEDIMENTATION AT AN
INLET ENTRANCE

RUDEE INLET-VIRGINIA BEACH, VIRGINIA

by

W. Harrison
W.C. Krumbein
WwW. S. Wilson

TECHNICAL MEMORANDUM NO.8
December 1964

Material contained herein is public property and not subject to copyright. Reprint or re-publication of any
of this material shall give appropriate credit to U.S.Army Coastal Engineering Research Center

LIMITED FREE DISTRIBUTION OF THIS PUBLICATION WITHIN THE UNITED STATES IS MADE BY THE U. S.ARMY
COASTAL ENGINEERING RESEARCH CENTER 5201 LITTLE FALLS ROAD. N. W., WASHINGTON D.C. 20016

FOREWORD

Few data are available on the patterns of sorting and size gradation
of sediments at the mouths of tidal inlets. Also lacking is a rapid,
objective, and statistically rigorous method for defining the limits of
the effects of the ebb flow from an inlet on the normal littoral process
of sorting and size gradation. This study was undertaken with the objective
of formulating a general model of the distribution of sorting and mean size
parameters around the mouth of an inlet, for a rather restricted set of
dynamic conditions. A further objective was the testing of trends in
patterns of sedimentation predicted by the model by means of a rapid method
of formal statistical analysis known as trend-surface analysis.

Diagrams showing steps in the development of the conceptual fluid
process-sediment response model are presented, as well as a series of trend-
surface and residual maps for the observed natural inlet data. An objective
method for delineating the pattern, magnitude, and limits of inlet in-
fluence on the otherwise unaltered beach sediments is also presented.

This report was prepared by Dr. Wyman Harrison, Associate Marine
Scientist of the Virginia Institute of Marine Science, in vursuance of
Contract DA-49-055-CIVENG-63-6 with the U. S. Army Coastal Engineering
Research Center, in collaboration with Dr. William C. Krumbein, Professor
of Geology, Northwestern University, and consultant to the Coastal Engineer-
ing Research Center,andMr.W. Stanley Wilson, graduate student at the
Virginia Institute of Marine Science.

This study was supported by the Coastal Engineering Research Center
(formerly the Beach Erosion Board of the Corps of Engineers), under the
general supervision of J. V. Hall, Jr., G. M. Watts, and N. E. Taney of
the Engineering Development Division. The Computing Center at Northwestern
University extended every cooperation, and the programs used in the
analysis were largely developed with supporting funds from the Geographic
Branch of the Office of Naval Research, under general supervision of Miss
Evelyn Pruitt and R. A. Alexander.

Mr. C. Kiley, Virginia Beach City Engineer, and Mr. A. Gregg aided by
laying groundwork for the field work. The following graduate students of
the Virginia Institute of Marine Science aided in sampling: Messrs. M. P.
Lynch, R, Morales-Alamo, R. B. Stone, C. Kyte, and R. Tuck. Lt. G. M.
Griswold, U. S. Navy Fleet Weather Facility, arranged for aerial photo-
graphic coverage of the study area. Wave data were furnished by the
Research Division of the Coastal Engineering Research Center. The U. S.
Army Transportation Corps, Ft. Story, Virginia, provided amphibious
support for offshore sampling. Weather data were supplied by the U. S.
Weather Station at Ft. Story.

This report is published under authority of Public Law 166, 79th
Congress, approved July 31, 1945, as supplemented by Public Law 172,
88th Congress,approved November 7, 1963.

TABLE OF CONTENTS

ABSTRACT
INTRODUCTION

General Considerations
Problem and Approach

THE MODEL
STUDY AREA
FIELD OBSERVATIONS
LABORATORY MEASUREMENTS

Determination of Sediment Parameters
ORGANIZATION OF DATA
TREND SURFACE ANALYSIS

Linear Surface

Quadratic Surface

Cubic Surface

Sum of Squares Evaluation of Trend-Surface Maps
ANALYSIS OF MEAN PARTICLE SIZE DATA
THE AREA OF INLET INFLUENCE ON MEAN PARTICLE SIZE
ANALYSIS OF SAND SORTING DATA

Trend Surfaces of the Sorting Coefficient
SUMMARY REMARKS
ADDENDUM
REFERENCES
LIST OF FIGURES

FIGURES 1 THROUGH 22

Page

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SEDIMENTATION AT AN INLET ENTRANCE
Rudee Inlet-Virginia Beach, Virginia
by

W. Harrison i
U. S. Coast and Geodetic Survey, Washington, D. C., and
Virginia Institute of Marine Science, Gloucester Point, Virginia

W. C. Krumbein
Northwestern University, Evanston, Illinois

and

W. S. Wilson
The Johns Hopkins University, Baltimore, Marylandl

ABSTRACT

A physical model is presented of the wave, longshore-
current, and ebb~-tidal-current systems as they determine the
distribution of mean particle size and the degree of sorting
at the mouth of a controlled inlet. The model is based upon
theoretical considerations as well as observations on both
scale-model and natural inlets. Forty-one bottom samples
were taken at Rudee Inlet, Virginia Beach, Virginia, under
conditions appropriate for testing the model. Resultant size
and sorting data were subjected to trend-surface analysis in
an effort to verify trends predicted by the model. Corres-
pondence between the model and the natural situation was
found to be good. The pattern, magnitude, and extent of inlet
influence on the otherwise unmodified beach sediments could be
determined by subtracting a trend surface for mean size for
the unmodified beach from its counterpart for the area of the
inlet entrance. The area of inlet-current influence was found
to be rather limited in extent.

lpresent address. Study completed while at the Virginia Institute
of Marine Science.

INTRODUCTION
General Considerations

Despite new and improved methods for measuring waves, currents, and
other shore process elements, it remains relatively difficult to gain
full understanding of the effects of wave and current systems on the
size grading and sorting of beach and nearshore sands under natural field
conditions. Simultaneous observation of water and sediment movement is
complicated by the number of variables that must be measured, and by the
local "noise" that tends to obscure underlying systematic effects. Asa
result, an empirical model is commonly used, in which the patterns of
areal variation in sediment properties are used to infer the nature of
the process elements that are operative, and to evaluate their relative
influence on the sediment properties. The empirical method generally in-
cludes preparation of contour-type maps of the observed sedimentary
attributes. These maps are useful for dynamical interpretations, but
they may fail to bring out secondary effects; or, where these are dis-
cernible, the maps may require highly subjective evaluation to distinguish
between "meaningful" variations and local "noise."" Formal methods of map
analysis (trend-surface analysis) have been applied successfully in
various branches of geology, including the study of beach phenomena. In
this paper the use of trend analysis is illustrated in a beach area in-
volving a tidal inlet.

Problem and Approach

The problem under study is two-fold, involving (1) the distribution
pattern of sediment size and sorting in the vicinity of the mouth of an
inlet during an “instant" of maximum outflow, and (2) the pattern
magnitude, and extent of inlet influence on the otherwise normal sediment
distribution along the shore during this instant. Our approach to this
problem is likewise two-fold, and involves (1) formulation of a model of
the fluid-velocity distributions and resulting sediment responses associ-
ated with the wave, longshore-current, and ebb tidal-current systems, and
(2) analysis of the predicted trends in sedimentary responses, using
appropriate natural data.

THE MODEL

A fluid process - sedimentary response model of an inlet entrance
can be developed by first constructing the process-response model for an
unmodified beach; i.e., one without an inlet. The general fluid motions
over a gradually shoaling beach within the shoaling-wave, breaking-wave,
and swash—backwash zones are described in various studies (cf. Eagleson,
Glenne, and Dracup, 1963). Dynamic zones and directions of increase in

fluid velocities are sketched diagrammatically in the left half of

Figure 1. A model of the changes (responses) in grain size and sorting
for this dynamic pattern was proposed by Miller and Zeigler (1958), and
it is shown in the right half of Figure 1. The largest grain sizes and
best sorting may be expected in the highest energy zone - that of the
breaking waves - where the greatest turbulence exists. Because the fluid
velocities diminish in directions away from the breaker zone, the mean
particle size decreases and the sorting becomes poorer, as explained below.
(Sorting worsens as more size classes are significantly represented in the
size distribution.) The second step in construction of the inlet model
studies here involves consideration of the velocity distribution of the
"jet" issuing from the inlet channel into the ocean (Figure 2A) and its
effect, in the presence of waves, upon the sediments at the entrance.
French (1960) derives the velocity distribution at the exit for a two-
dimensional channel issuing into relatively deep water. Bates and
Freeman (1952) demonstrate that the theory of a two-dimensional jet issu-
ing from a slot may be applied to sediment-laden inlet water entering the
ocean, and that the theory explains the lunate shape of bars found off
tidal inlets. For the velocity of outflow and channel dimensions of the
inlet studied here, the angle of separation of the still-water boundaries
approximates that shown in Figure 2B.

A more realistic dynamic model requires assessment of the idealized
jet flow (Figure 2B) both in the presence of waves and at a shoaled
entrance. Figure 3A shows the general geometry of the nearshore bottom,
based partly upon the scale model study of inlet development made by
Saville, Caldwell, and Simmons (1957, Test 5) for an inlet system of
similar dimensions to the natural inlet of this study, and partly upon
the model postulated by Bruun and Gerritsen (1960, Figure 53). The zone
of greatest turbulence in this model lies within the zone of breakers
where they are intersected by outflow from the inlet (Figure 3B). The
model predicts that the mean particle size (Mz) will decrease and the
degree of sorting (Sj) will generally become poorer in directions of
decreasing velocity gradient, as shown in Figure 3C. The progressive
decrease in mean size is anticipated because of the well-established
relation between bottom shear stress and transporting power (cf. Bruun
and Lackey, 1962). A study of the sediments of the Beaufort Inlet area,
North Carolina, by Batten (1962) shows this expected distribution of mean
particle size. The fact that sorting will generally become poorer in
directions of decreasing velocity gradient is dependent upon certain
additional factors and assumptions.

The sediment load in the outflowing current of the particular inlet
under study has its origin in essentially one source, that caused by
stirring up of material from the channel under turbulent flow conditions.
This material consists of sand with a grain size distribution extending
over five Wentworth sizes classes, as well as coarse silt and granules,
usually as less than 8 percent of a given sample.

The sorting tendencies for the inlet are modeled in part from
Inman's (1949, p. 63) analysis of sorting of shallow-water sediments under
unidirectional flow. For the particular inlet studied | gorge depth of
6 to 9 feet (180-270 cm)] , the out-flowing current lise ft/sec. (110
cm/sec.) at the surface| in the channel is assumed to produce a stress
on the bottom sufficient to move all bottom material. Toward the seaward
extremity of the inlet entrance, and laterally from its sides (Figure
3A), we postulate a rapid decrease in the threshold velocity, producing
the rapid decrease in mean diameter of the bottom samples. As the out-
flowing current passes into the relatively quiescent water of the
entrance, just shoreward of the breakers in Figure 3B, the average friction
velocity will drop somewhat. We assume that the friction velocity in the
waters of the inlet entrance will tend to fluctuate between the threshold
velocity for fine and coarse sand. If this is so, the bottom samples
will show a tendency to be rather well sorted (Inman, 1949, p. 64).

It can be further assumed that as the outflowing current enters the
breaker zone, the turbulence conditions are such that nearly all but the
largest sized particles (which will have previously dropped out of sus-
pension) will be maintained in suspension. Bottom samples here can be
expected to be better sorted than elsewhere and the mean diameter to be
larger than that of the surrounding samples. Figure 3C shows this
situation schematically. Just seaward of the breakers, a rapid decrease
in friction velocities and turbulence can be expected, and the larger
particles that pass through the breaker zone will come to rest almost
immediately; these larger particles will rest upon or become mixed with
the finer particles of the beach sands of the shoaling-wave zone (Figure
1) of the previous tide. Because progressively finer particles drop
rapidly out of suspension in a seaward direction, sorting beyond the
breakers will abruptly become poorer, and the poorest sorting will occur
at a relatively short distance beyond the breakers. Sorting farther out
into the sea will improve, but will not equal that of the breaker zone
where it is best (Figure 1). Batten's (1962) study of the Beaufort Inlet
sediments indicates the relatively well-sorted nature of the sediments
in his "zone of wave action" seaward of the surf zone. The mean diameter
of the bottom particles will decrease gradually in a seaward direction,
as summarized in Figure 3C.

The ultimate model to be used here provides for the wave fronts
approaching at an angle to the shoreline, rather than parallel to it as
in Figure 2A. The longshore current thus generated adds a final compli-
cating feature to the model. (Figure 4A shows the relations, assuming
moderate to low wave heights and moderate longshore-current velocity.)

To simplify the dynamic model somewhat, we assume that the inlet outflow
is of such velocity that it is deflected only a moderate amount by the
longshore current (Figure 4A). Both currents will then intermix and
become a single current in a direction dictated by simple vector addition.

Given this dynamic picture, we must now account for the suspended
sediment stirred up by wave action and transported as littoral drift into
the zone of inlet outflow (Figure 4B). A final simplifying assumption
provides that the materials transported by the longshore current are of
consistently large mean particle size and of relatively good sorting.
Areas of the poorest and of the best sorted materials may be expected to
take somewhat irregular shapes, as 4 result of interaction effects at the
juncture of the two currents. Figure 4B shows the expected response
relations, and the idealized shape of the areas of best and poorest sort-
ing in the figure are based on considerations of velocity and turbulence
dropoff.

The field observations and the methods of trend analysis used with
them are described in succeeding sections, leading to a field test of the
several aspects of the final model just described.

STUDY AREA

The Borough of Virginia Beach (Figure 5) of the City of Virginia
Beach, Virginia, is situated on the Atlantic seaboard 22 miles (35 km.)
north of the Virginia-North Carolina line and 3.5 miles (5.6 km.) south
of Cape Henry. Rudee Inlet, a "controlled" inlet, is located at the
southern end of the borough and connects Lakes Wesley and Rudee with the
Atlantic Ocean. At high tide, water flows from the ocean through Rudee
Inlet into the lakes, and flow is reversed at low tide. At the time of
sampling of bottom sediments around the entrance, the inlet channel was
approximately 400 feet (120 m.) long and 150 feet (45 m.) wide. Owing to
a sandbar on the north side of the channel, maximum flow occurred in a
gorge ranging from 30 to 70 feet (9-21 m.) wide and 1 to 9 feet (0.3-2.7 m.)
deep. The inlet lagoon had an area approximating 1/13 square mile
(0.2 sq. km.) and the tidal prism approximated 6.0 x 10© cubic feet
Ge7 eq0> eusem))-

FIELD OBSERVATIONS

Forty-one sand samples from the immediate vicinity of the inlet
(Figure 6) were taken "simultaneously" (within a 15-minute period) from
2 to 3 hours before low water on the morning of 25 March 1963. The number
of sample stations was limited by available personnel and the time-
consuming process of accurately positioning those taking samples. Sand
samples were recovered by moving bags by hand through the upper 2 cm. of
the bottom sediments. Shortly thereafter, 67 samples were taken along
transects A, part of B, and C (Figure 5) at stations 25 feet (7.5 m.)
apart. Sampling along the three transect lines was accomplished with pipe
dredges having maximum penetration of about 2.5 cm. Details of the samp1-
ing procedures are given by Harrison and Morales-Alamo (1964) and Harrison
and Wagner (1964).

During the period of bottom sampling the rate of seaward flow of
surface water in the Rudee Inlet gorge was 3.3 feet per second
(110 cm./sec.). This was determined by timing the movement of filoures-—
cein-dyed water over a 100-foot (30 m.) distance along the middle portion
of the stone jetty on the south side (Figure 6) of the inlet. The central
zone of outflow (Figure 7) from the inlet was also observed using floures-
cein dye. Aithough neither was measured accurately, the velocity was
observed to decrease and the mixing to increase as the outflow left the
inlet and approached the fishing pier to the north (Figures 6 and 7).
The dyed outflow could not be discerned north of the pier, as at that
distance it had been well mixed with the surrounding water.

Just prior to the sampling time, the average velocity of the long-
shore current (inshore of the breaker zone) was determined at a point
approximately 800 feet (240 m.) south of the inlet. This current was
flowing in a northward direction at 0.76 foot per second (23 cm./sec.).

A red dye (rhodamine B) was introduced into the longshore current just
south of Rudee Inlet and was observed to flow northward. When the
current came into the area of the outflow (dyed green) from the inlet, it
was deflected seaward, and the longshore current itself deflected the
inlet outflow. Just before reaching the fishing pier, both streams had
become intermixed.

The average height of breaking waves at sampling time was 0.75 foot
(23 cm.) and the average wave period, as determined from a relay-type
wave gage, was 6.5 seconds. Wave fronts made an angle (opening northward)
of 29° with the shoreline at a point 1,000 feet (300 m.) from shore. Wind
was from the southwest at 12 to 15 m.p.h. (19 to 24 k./hr.). The position
of the breaker line has been plotted on Figures 7-20 from aerial photos
made at sampling time by the U. S. Navy.

LABORATORY MEASUREMENTS
Determination of Sediment Parameters

Each sand sample was analyzed for its:size-distribution curve using
a Woods Hole Rapid Sand Analyzer (Whitney, 1960) with the procedure out-
lined in Zeigler, Whitney, and Hayes (1960). Details of the methods, and
assumptions involved in the analyses, are given by Harrison and Morales-
Alamo (1964). The following descriptive measures of the resultant grain-
size distributions were calculated:

Mean Nominal Diameter, Mz = 1/3 (Pag + P59 + Pgo)

Sorting, So = (Pgo - P20)/P50

where Py is the value of the grain diameter in mm. at a given percentile
of the grain-size distribution. The measure of sorting is one used as

a matter of convenience in terms of the settling tube. The estimate of
mean nominal diameter used employs the same values used in determination
of So and, in addition, is considered relatively "efficient" (McCammon,

1962).

ORGANIZATION OF DATA

The forty-one sampling stations in the vicinity of Rudee Inlet were
numbered serially and plotted on the base map (Figure 7), using a U-V
co-ordinate system (Krumbein, 1959) that was geographically true. The U
co-ordinate starts with U = O at the top of the swash—backwash zone in
the northwest corner of the map and proceeds south along the shore to
U = 553 at the top of the swash in the southeast corner. The V co-ordinate
extends from V = O at the northwest corner to V = 300 in the northeast
corner. Water depth at this last point was 8 feet. Each station was
numbered and the values for Mz and So were listed for each station.
These data comprise an irregularly spaced set of stations; i.e., the
sampling points do not lie on a rectangular grid.

Data for the three transects were treated separately. Stations were
also numbered serially and coded in true geographic (U, V) co-ordinates.
The origin of this system was at the most inshore station of Transect A
(Figure 5), with the U axis extending southward parallel to shore. The
sampling points of this second system lie at the intersection points of
an orthogonal grid.

TREND SURFACE ANALYSIS

A trend surface may be visualized as a smooth contour surface show-
ing the systematic pattern of variation of a mapped variable from one
map edge to another. This contrasts with the small-scale fluctuations
from one point of observation to the next, superimposed on the trend as
a seemingly non-systematic component.

Most techniques of trend analysis are based on least squares
fitting of polynomial surfaces to the data by a multiregression tech-
nique. When (as is usually the case) geological observations are
scattered irregularly over a map area, the method of analysis commonly
includes fitting successively higher order surfaces to the map data,
including usually the linear, quadratic, and cubic terms. These computed
surfaces and their deviations are examined for their geological implica-
tions. The geologist thus "takes his data apart" in various ways,
sharpening the interpretation of the observed map data. The complete
trend, defined by Grant (1957) as the polynomial of the best fit to the
data, may not always be identified by these low-order surfaces. However,
in many maps the linear and quadratic trends are strongest, with those of
cubic and higher degree diminishing relatively in importance.

The Virginia Beach data were analyzed at the Northwestern University
Computing Center with an IBM 709. The program computes a (U,V) matrix and
a series of vectors for each variable. The matrix is inverted and post-
multiplied by the vectors to obtain a set of polynomial coefficients.
These in turn are used to compute the trend-surface values. Some of the
underlying theory and a description of the program are given by Krumbein
(1959). Whitten (1963) describes the program in detail.

When a trend surface is fitted to map data, a computed value is
obtained for each control point. These are plotted on a base map and
contoured by hand; alternatively, the computer generates a field of com-
puted values and prepares a trend map either directly or through use of an
X-Y plotter. The computed trend value for a given map point commonly does
not agree exactly with the observed value, so that a deviation (which may
be positive or negative) is associated with each map point. Thus, if X is
the observed value of the mapped variable at point (U,V), and if X' is the
computed trend value, then the deviation from the fitted surface is defined
as R = X - X'. These deviations may also be mapped to see what the varia-
tion pattern is after one or more low-order trend surfaces have been ex-
tracted. Deviation maps are commonly contoured by hand; and, because some
freedom in drawing contours is usually present, the deviation maps presented
here were all prepared by linear interpolation between a given point and
surrounding points.

Linear Surface. The linear surface is fitted to irregularly spaced
map data by setting up the relation:

ak = a S Gy oR)

where X is the observed value at point (U,V); A; is a constant that
represents the "height" of the trend surface at (U,V) = (0,0); and Br and
Cr are the coefficients of the linear surface. The deviation, R,, contains
trend components higher than linear, plus some unknown content of non-
systematic, seemingly random fluctuations.

The computed linear trend value, X;', is obtained from the relation
Xy' = Ay + BLU + CLV by multiplying the U-coordinate of a given point by
BL, multiplying its V-coordinate by C;, and adding A; to the sum of the
two products. Rp, as stated, is simply the numerical difference between
the observed and computed values at each point of observation.

Quadratic Surface. The complete quadratic surface includes two
linear and three quadratic terms, and is fitted by setting up the relation:

X = AQ + BQU + CQv + DQu2 + EQUV + Fv? + RQ

Here, X is again the observed value of the mapped variable at a given (U,V)
point, Ag is a constant, and Bg, Cq, --., Fa are the polynomial coefficients

of the quadratic surface. The quadratic is computed as a whole because
the numerical values of the constant and of the coefficients change as
higher surfaces are considered, as shown by the change in subscripts from
IL, UO @.

The remainder RQ now contains trend components higher than quadratic
plus purely random fluctuations. As before, if Xg' is the computed value
of the quadratic surface at a given control point, then Xo) 26 = OKO)"

Cubic Surface. The complete cubic trend contains two linear, three
quadratic, and four cubic terms, as well as a constant A. Inasmuch as
the numerical values of the coefficients again change, the coefficients
on the cubic surface are subscripted as shown:

a eB CUNHCcVale DCUCRA NM ECUVE HaREViCN MAGES) A pHEUCV) on JeuUV =) Ke Viole

The deviations on the cubic surface, R,~, contain trend terms higher than
cubic, as well as some content of random variations. Our analysis did not
extend beyond the cubic surface.

Sum of Squares Evaluation of Trend-Surface Maps. The total sum of
squares of a mapped variable is a measure of the variability of map data.
It is expressed as the sum of the squared differences of the observed
valués from their mean:

zt Tae
SSy = (X = X)
The expression represents the sum of the squared deviations of X from
their mean value, X, at all control points. The sum of squares of the
deviations is computed as:
SSp = R2
since the sum of R over the whole map is zero.

The sum of squares associated with the computed values, X', can be
expressed as:

where X is the mean of the observed X; in trend analysis the computed mean,
X', is the same as the mean of the observed data, X.

The "strength" of a trend surface can be evaluated informally by
noting how much of the total map variability is "accounted for" by the
fitted surface. This is computed as 100(SSx'!/SSx).

Evidently, if the percentage reduction is small, the trend surface
is weak; indeed, if the deviations are truly random components in such
instances, the question could be raised whether there is in fact any trend
present at all. We shall see that this latter assumption is not correct
in the Rudee Inlet study. Computer programs for more formal analysis of
fitted surfaces, including setting confidence intervals around them
(Krumbein, 1963), became available while this final draft was written,
and reliance here is placed upon substantive evaluation of the trend maps
computed in this study.

ANALYSIS OF MEAN PARTICLE SIZE DATA

Figure 8 shows the pattern of mean particle size observed in the
study area. "Observed maps" show the contour pattern of the original "raw
data," and in many instances these maps are very informative, especially
when the contours show relatively strong patterns. When the pattern is
weak, or complicated by numerous irregularities in the contour lines, sub-
stantive evaluation is more difficult, and there may be some doubt whether
a definite trend is present.

iad

In the present map we notice a "ridge" of relatively large values
that coincides with the zone of outflowing current shown on Figure 3. At
a point just seaward of the breaker line (dotted) is a pronounced hump of
high values. The linear trend surface fitted to these data is shown on
Figure 9. The linear surface dips to the northeast at 0.02 mm. per 87
feet (26 m.), indicating a decrease in mean size in the direction of
current flow. This reflects the negative current velocity gradient from
Rudee Inlet seaward, because of the known variation (cf. Bruun and Lackey,
1962) in the diameter of sediment particles with the critical tractive
force, which is in turn velocity dependent. The linear surface for mean
size is in fact quite weak, inasmuch as only 11.3 percent of the total sum
of squares can be attributed to it.

Figure 10 shows the deviations from the linear mean size surface.
These deviations show a pattern trending roughly parallel to outflow from
the inlet, and an area of high values similar to the one noted on the
observed map. This suggests the presence of trend components higher than
linear in the deviations. Hence, it was deemed worth while to examine the
quadratic surface.

The quadratic surface for mean grain size is shown in Figure 11. The
contours parallel to the shore are to be ignored for the moment; the
quadratic surface itself is a simple ellipsoid with maximum values near
the inlet mouth, and a systematic decrease in mean grain size symmetri-
cally away from the higher portion. The quadratic surface accounts for
47.7 percent of the total sum of squares; and because the linear surface
accounted for only 11.3 percent, the contribution of the “pure quadratic"
is 36.4 percent. The deviations on the quadratic surface are shown in

Figure 12. Comparison with the deviations from the linear surface (Figure
10) shows that the area of relatively high positive deviations again
delineates the general area of maximum mean particle size that occurs in
the observed map of Figure 8.

The deviations from the quadratic surface for mean size contain
100.0 - 47.7 = 52.3 percent of the total map variability. Inasmuch as the
deviation map still carries geologically identifiable patterns, it was
decided to fit the cubic surface to the mean size data. The cubic surface
map is shown in Figure 13, and the deviations from it are shown in Figure
14.

The cubic surface is noteworthy in that it shows a bulge of coarse
mean sizes associated with the inlet mouth, but this bulge is somewhat
skewed to the northeast, and in a broad way it is aligned with the path of
the outward-flowing current shown in Figure 6. The deviations on the cubic
surface show clearly that the alignment of the major trend of larger
diameter grains is centered on the zone of inlet outflow. The trend of the
zero-deviation contour in the region of inlet outflow suggests a weak
effect of the outflow current on mean size all the way to the pier in the
northeast corner of the map. This was suggested in a previous study of the
same data (Harrison and Morales-Alamo, 1964) that employed conventional con-
touring techniques. The inference from Figure 14 is that a weak effect of
the inlet current on grain size in the vicinity of the pier may indeed
have existed. That is, the trend surface technique constitutes a sensitive
and objective method for examining the influence of the inlet on grain size
both over the full inlet area and over the smaller zone of the dominant
current.

Patches of the deviation map of Figure 14 that are outlined by
negative contours (-0.05) reveal weak secondary trends toward finer sizes
roughly parallel to the "ridge" of coarse sizes. At least two hypotheses
can be advanced for this pattern: (1) the tendency of the finest particles
to lie on the flanks of the "ridge" is merely a reflection of the magnitude
of the discrepancy between coarse grains (associated with outflow from the
inlet), and the finer grains already present in the inlet prior to initia-
tion of the outflow; or, (2) the tendency toward finer sizes on the flanks
of the ridge reflects an actual realm of sedimentation dynamics in which
successively finer grained particles are progressively deposited over
areas of continuously decreasing current velocity.

Examination of Figure 14 suggests that the latter hypothesis is
probably the more satisfactory one. The weak trend of slightly coarse-
grained materials associated with the breaker zone at the pier is not
present on the north side of the "ridge" of higher values. This suggests
deposition of finer particles on coarse ones that would ordinarily be
present in the breaker zone. If the observed ridge pattern is due to the

addition of larger sizes in the area of the inlet mouth, then the weak
trend of slightly larger sizes associated with the breaker zone would have
been expected to continue from the vicinity of the pier to an intersection
with the "peak" of highest values near the breaker zone, i.e., at the +0.1
contour.

As to the limit ofinfluence of the inlet mouth on nearshore bottom
changes in mean particle size, we returned to the quadratic trend surface
for an experiment in finding this limit to a first approximation. Use of
the quadratic surface rather than the cubic was in part dictated by our
approach, which is described in the next section. As a closing remark on
the cubic surface and its deviation map, we may conclude the sum of squares
discussion with the following summary:

Percent Percent Sum
Sum of Squares of Squares of
Attributable to Deviations From

Surface Surface the Surface
Linear ikl 3} 88.7
Total Quadratic 47.7 52.3
Total Cubic 59.6 40.4

Thus, there still remains 40.4 percent of the total map variability
in mean grain size in the deviations from the cubic. Moreover, the con-
tribution of the "pure" cubic alone is only 11.9 percent, as against the
36.4 percent attributable to the "pure" quadratic. The linear contribu-
tion, as was stated, is 11.3 percent, implying that the total quadratic
component is perhaps the most important one in the complete trend. In our
study of the limit of inlet influence then, we take the cubic and higher
order trend components as being merged with the local, non-systematic
fluctuations that may be present, and return to the total quadratic
surface of Figure 11 for further discussion.

THE AREA OF INLET INFLUENCE ON MEAN PARTICLE SIZE

Figure 11 contains two sets of contour lines of mean particle size.
The heavy lines parallel to the shore represent a portion of the quadratic
surface fitted to the sample data obtained from the three transects of
Figure 5, which were mentioned earlier in passing. This surface for the
whole beach area accounts for only 6.6 percent of the total sum of squares
of mean particle size from all samples from the three transects.

Inasmuch as the map based on the three transects does not include the
sampling points in the immediate vicinity of the inlet (except for the pier
samples on the left of Figure 6), this map represents the large-scale

systematic effects present along the whole stretch of beach. The local
quadratic map in Figure 11, on the other hand, contains the regional
effect as well as the influence of the inlet. As a result, we may sub-
tract one map from the other to obtain a map of the area of influence of
the inlet itself. This (Figure 15) shows that the inlet affects an area
that extends as a bulge seaward from the inlet mouth, diminishing to zero
in the vicinity of the pier as well as oceanward to the southeast. This
bulge is somewhat asymmetrical, reflecting its distortion and displacement
by the northward-flowing shore current. The maximum departure of particle
size equals 0.12 mm.

The implications of Figure 15 are that Rudee Inlet exerts an appreciable
effect on the nearshore bottom sediment in a very limited area, in contrast
to the length of the beach segment between Transects 1 and 3 in Figure 5.
That is, the distance between the limiting zero contours in Figure 11 is of
the order of 0.1 mile (0.16 km.), as against a length of more than 1.5 miles
(2.4 km.) between the end transects. This, in turn, is a short segment of
the essentially straight coastline extending south of Cape Henry for a
number of miles. It may be anticipated from these relative scales that
the influence of an inlet similar to the one studied here could very easily
be missed in subsurface exploration of ancient sediments for oil or gas,
say, or even in the study of present day beach patterns involving a closed
inlet, where its effect would be that of a small deviation on a large-scale
trend surface map.

ANALYSIS OF SAND SORTING DATA

The preceding discussion is based wholly on the patterns of areal
variation in mean grain size. It is appropriate to ask whether the areal
pattern of sediment sorting sheds any additional light on the area of
influence of the inlet, or on the dynamic processes that take place in its
vicinity.

Figure 16 shows the observed map of the sorting coefficient, So, in
the study area. Its pattern is distinctly different from that of mean
particle size in Figure 8, although there is a tendency for low values
(that is, good sorting) to lie approximately in the area of largest mean
grain size. For example, the contour line 0.5 on the sorting map lies
peripherally to the contour of maximum mean grain size (0.50 mm.). A
dominant area of high values (poor sorting) lies beyond the breaker zone on
the seaward side of the inlet current. In general,sorting becomes poorer
to the east, whereas the mean particle size tends to increase northward.

Trend Surfaces of the Sorting Coefficient. The linear, quadratic,
and cubic surfaces were fitted to the observed S, data of Figure 16. The
surfaces are very weak in comparison even with the mean size surfaces, as
shown by the following sum of squares summary for S,:

Percent Percent

Sum of Squares Sum of Squares of

Attributable to Deviations from
Surface Surface Surface
Linear Wile 88.8
Quadratic 55 84.5
Cubic 20.9 79.1

Thus, the net contribution of the quadratic component is only 4.3 percent,
and that of the cubic is only 5.4 percent. Nevertheless, we present the
linear and cubic surfaces and their deviations to illustrate some aspects
of the sorting pattern.

Figures 17 and 18 show the linear surface and the deviations from it.
The linear S, trend surface slopes to the east, or roughly perpendicular
to the slope of the linear trend surface for mean grain size. The linear
deviation map for sorting shows that the best sorting can be expected at
the point where the inlet current intersects the breaker zone. This
position coincides with the zone of greatest turbulence, as supported by
field measurements (Harrison and Morales-Alamo, 1964) and theoretical
models of beach dynamics (Miller and Zeigler, 1958), which suggest that
it is in this zone that the best sorting and the largest grain sizes occur.

Figures 19 and 20 show the cubic surface of the sorting coefficient
and the deviations from the surface. The pattern on the cubic trend map
is noticeably different from the cubic mean size map, in that the sorting
surface rises from a low just north of the Rudee Inlet jetty, to high
areas (i.e., poor sorting) seaward to the southeast of the inlet and to
the northeast along the pier.

Analysis of the cubic deviation map for Sg shows the best sorting
to be centered at the intersection of the breaker zone with the combined
flow of the inlet current and the longshore current. This is the zone of
maximum turbulence, as noted previously. The zone of best sorting rapidly
gives way to the zone of worst sorting (contour + 0.4) in a down-current
(decreasing-velocity) direction. The actual center of the poorest sorting
is seen to be just seaward of the central zone of inlet outflow. This is
believed to reflect the rapid decrease of the longshore current component
of the combined flow as it passes through the breaker zone. Hence, the
coarser materials in transport along the shore appear to be deposited over
a region of originally fine-grained sand. Thus the spread of the particle
size distribution is greatest here, as shown by the large values represent—
ing poorest sorting.

SUMMARY REMARKS

A model (Figure 4B) of sedimentation at the mouth of a small, con-
trolled tidal inlet has been developed from anticipated fluid-—velocity
distributions. It deals with the distributions of mean size (Mz) and
degree of sorting (Sj), in response to forces induced by the ebb flow
from the inlet channel and by wave fronts that approach the shoreline
obliquely.

The model predicts that the largest particle sizes and the best
sorting will occur in the region where the longshore and inlet currents
intersect, that sorting will be poorest just seaward of this intersection
(also seaward of the breaker zone), and that mean size will decrease and
sorting improve in directions of decreasing velocity gradient beyond the
breaker zone. Observed patterns of Mz and Sy agree with these predictions.

The model also predicts that particles of relatively small diameter
(originating in the inlet and longshore currents) will be deposited upon
a surface of normally sized and sorted beach sands on either side of the
outflowing current. The prediction is confirmed by analysis of weak
trends for Mz and Sg shown on residual maps for cubic trend surfaces, for
the regions flanking the inlet outflow. (The trends can be understood by
assuming that the Mz and S, patterns of the depositional surface have
been inherited from normal fluid-velocity distributions common to the
shoaling wave zone of the previous high tide.)

It is demonstrated that it is possible to delimit the boundary,
estimate the magnitude, and describe the pattern of inlet influence for
a given sediment property (such as Mz and So) upon an otherwise unmodified
beach by subtracting the trend surface for the area of the inlet entrance
from the corresponding trend surface for the unmodified beach.

The present study illustrates that trend surface analysis furnishes
a method for "taking apart'' raw observations in order to distinguish
between large-scale (systematic) effects and small-scale (presumably non-
systematic) effects in map data. It is noteworthy in this study that the
deviation maps are on the whole more informative than the trend surface
maps, although the low-order surfaces, despite their relative weakness on
a sum of squares basis, do present geologically reasonable patterns in
relation to outflow from Rudee Inlet. The large content of the original
map variability contained in the deviation maps, especially for the
sorting coefficient, implies that a substantial amount of geological in-
formation is contained in the deviations, which definitely cannot be
discarded simply as random noise.

In the long run an essential element in beach studies will be the
dynamic model postulated for the situation. If the particular model can
be expressed quantitatively (as it can in some instances), field

observations, even though encumbered by noise, can be used effectively
to test the applicability of the model. Surface-fitting functions other
than polynomials will very likely come increasingly into use as the
physical processes underlying a given beach model are better understood.
Interest is developing in what have come to be called "secondary trend
components" (Allen and Krumbein, 1962), that probably represent some or
all of the terms in surfaces of relatively high degree.

ADDENDUM

Since this report was written, additional computer time was obtained
for the construction of cubic trend maps for the data from the three pier
transects of Figure 5. By subtracting these cubic trend surfaces from
the Mz and So cubic trend surfaces (Figures 13 and 19) for the inlet
entrance, the maps of Figures 21 and 22 have been obtained. They indicate
the pattern, magnitude, and limit of inlet influence on the Mz and So
patterns of the beach.

REFERENCES

Allen, P. and W. C. Krumbein, Secondary Trend Components in the Top
Ashdown Pebble Bed; A Case History, J. Geol., 70, 507-538, 1962.

Bates, C. C. and J. C. Freeman, Interrelations Between Jet Behavior and
Hydraulic Processes Ooserved at Deltaic River Mouths and Tidal Inlets,
Proc. Third Conf. on Coastal Engr., Cambridge, Mass., 165-175, 1952.

Batten, R. W., The Sediments of the Beaufort Inlet Area, North Carolina,
Southeastern Geol., 3, 191-205, 1962.

Bruun, P. and J. B. Lackey, Engineering Aspects of Sediment Transport,
Reviews in Engr. Geol., 1, 39-103, 1962.

Bruun, P. and F. Gerritsen, Stability of Coastal Inlets, North Holland
Publ. Co., Amsterdam, 1960.

Eagleson, P. S., B. Glenne, and J. A. Dracup, Equilibrium Characteristics
of Sand Beaches, Proc. Am. Soc. Civil Engr., Paper No. 3387, 36-57,
1963.

French, J. L., Tidal Flow in Entrances, Comm. on Tidal Hydraul., U. S. Army,
hehe Bullen Sel OOr

Grant, F., A Problem in the Analysis of Geophysical Data, Geophysics, 22,
309-344, 1957.

Harrison, W. and R. Morales-Alamo, Dynamic Properties of Immersed Sand at
Virginia Beach, Va., U. S. Army, Coastal Engr. Res. Center, Tech.
Memo. No. 9, 1964.

Harrison, W. and K. A. Wagner, Beach Changes at Virginia Beach, Va.,
U. S. Army, Coastal Engr. Res. Center, Misc. Paper 6-64, 1964.

Inman, D. L., Sorting of Sediments in the light of Fluid Mechanics, J. Sed.
Pet., 19, 51-70, 1949.

Krumbein, W. C., Trend Surface Analysis of Contour-Type Maps with Irregular
Control-Point Spacing, J. Geophys. Res., 64, 823-834, 1959.

, Confidence Intervals on Low-Order Polynomial Trend Surfaces,
Jour. Geophys. Res., 68,5869-5878, 1963.

McCammon, R. B., Efficiencies of Percentile Measure for Describing the
Mean Size and Sorting of Sedimentary Particles, J. Geol., 70, 453-455,
1962.

Miller, R. L. and J. M. Zeigler, A Model Relating Dynamics and Sediment
Patterns, J. Geol., 66, 417-441, 1958.

Saville, T., Jr., J. M. Caldwell, and H. B. Simmons, Preliminary Report:
Laboratory Study of the Effect of an Uncontrolled Inlet on the
Adjacent Beaches, U. S. Army, Beach Erosion Board, Tech. Memo. No. 94,
1957.

Whitney, G. G., The Woods Hole Rapid Analyzer, Woods Hole Oceanog. Inst.,
Ref. No. 60-36, 1960.

Whitten, E. H. T., A Surface-Fitting Program Suitable for Testing Geological
Models which Involve Areally Distributed Data, Tech. Report No. 2, ONR
Task No. 389-135, Contract NONR 1228 (26), Geography Branch, Off. of
Naval Res., 1963.

Zeigler, J. M., G. G. Whitney, and C. R. Hayes, Woods Hole Rapid Sediment
Analyzer, J. Sed. Pet., 30, 490-495, 1960.

12.

US}

14.

So

FIGURES

Model of beach processes and responses for a gradually shoaling
sandy beach uninfluenced by tidal currents.

(A) Definition sketch of problem; (B) degree of separation of
boundaries of the jet flow for the inlet to be studied in
nature.

Model of (A) shoals at inlet entrance; (B) dynamic conditions
during inlet outflow and under wave action; and (C) tendencies
of mean size (Mz) and sorting (S,) in response to (B).

Conceptual fluid process (A) sedimentary response; (B) model for
area around inlet entrance under ebb tidal flow in presence

of wave fronts approaching shoreline obliquely.

Area of investigation, Rudee Inlet, and three transects where
samples were taken.

Position of inlet channel and sampling stations at Rudee Inlet on
25 March 1963. Coordinates are Virginia Coordinate Systems,
south zone.

Sampling stations and scheme for U, V coordinate systems.

Observed distribution of mean-grain-size values, expressed as
nominal diameters (mm).

Linear trend surface for mean size (mm).

Deviations from linear trend surface for mean size (mm).

Quadratic trend surface for mean size (arcuate contours) based on
Rudee Inlet samples (large dots) and quadratic trend surface
(straight-line contours) for mean size (mm) based on samples
from the three transects (Figure 5).

Deviations from quadratic trend surface for mean size (mm).

Cubic trend surface for mean size (mm).

Deviations from cubic trend surface for mean grain size (mm).

Deviation of quadratic trend surface for whole beach from quadratic

trend surface for Mz for the inlet area. Contour values are
in mm.

16.

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19),

20.

Bake

D2).

Observed distribution of values of sorting coefficient.
Linear trend surface for sorting coefficient.

Deviations from linear trend surface for sorting coefficient.
Cupic trend surface for sorting coefficient.

Deviations from cubic trend surface for sorting coefficient.

Deviation of cubic trend surface for Mz over the whole beach from
cubic trend surface for Mz in inlet area. Contour values in mm.

Deviation of cubic trend surface for Sg over whole beach from cubic

trend surface for Sg in inlet area. Contour values are in
units of the sorting coefficient.

20

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‘O'M ‘utTequniy TIT

‘mM ‘uoSstiieyH [TI

STITL I daIASISSVIONN 8 “ON WNGNVYOWSW IVOINHOAL

S}eTUI “Pp “SNTTE @2@

(FeTULT aepny) Sutpntout ‘dd zp ‘po6T Jaquedsaq ‘uOSTTM “M pue

S}OTUI TePTL “€ uraqunizy"O°M ‘uostizey’m Aq ("eA ‘YyDeagG eTUTSITA

eTUTSITA -}eTUL eepny) FJONVULNA LAINI NV LV NOILVLNAWICES
“yoeog eTUTSITA “2

sassa00ig ar0ysS *T °O°d‘*HSWM ‘°dO ‘UYSLNHO “SHU “OHONA TIVLSVOO AWuV"S*N

*yuazxo UT PayTWIT TayzeI aq 03 punoF SeM adUeNTFUT
yuazIno-yaTUuT FO eare ynq ‘poo3 aq 0} punoF sem uoT}EeNITS TeIn}zeU
pue Tapow uaamzeaq aduapuodsari0g “Tapow Aq pazyotpard spuesry
Aytiaa 04 ‘stskTeue adezins—puar} 0} pazIafqns atom ‘sea ‘yoeag
BTUTSITA ‘}OaTUT saepny ze uaye}, satdwes woyjzog “JoTUT PaTTOT}UOD
e FO yyNOW ay} ye BuTyIOS Fo aaIZap pue azts atIty1ed uvaw FO
UOTINGTISTP 34} sUTWIJazap Aay, Se SWa}zShS jUAaTINO apt}z—qqa pue
‘yuoazain2-azoysS3uoT ‘aAem ay} FO pajuesazd st Tapow Teotskyd y

“S*m ‘UOSTIM AT
“O°M ‘uTaqunzy III
"mM ‘uostiieyH [I
eTIIL =U

daISISSVIONN 8 “ON WONCNVYOWSW TVOINHOSL
“ENE GE

Sutpntour ‘dd gp ‘po6T Taquadeq ‘UOSTTM “M pue
utaquniy*d'm ‘uostizeH’m Aq ("eA ‘yovog erutgitaA
-}eTUT eepny) AONVUINA LAINI NV LV NOLLVINAWICAS

S}2TUL ‘b
(JeTUL eepny)

S}OTUL TePTL “€
eTUTSITA

‘yovog eTUTSITA “2

Sassad01g ar0Yys "O°a‘*HSWM ‘°dO ‘UHINHD “SHY “OYONA IVLSVOO AWaV'S*N

“yUa}Xe UT PayTWTT Ieayj,er aq 0} punozZ sem adUaNT FUT
juazind-jaTuT Fo eare ynq ‘poos aq 0} punoF SeM uoT}eNATS TeIn}zeU
pue Tapow uaamzeq aduapuodseriz0g ‘Tapow Aq pazotperd spusry
AjJtiea 0} ‘stsATeue sdezFIns—pust} 0} payoefqns azem ‘*ea ‘yovag
eTUTSITA ‘}OTUL sepny ze Uaye} SaTdwes woy}og “zoTUT paTTOT}UOD
eB JO yynow 94} ye BuTzIOS FO aaIZap pue aezts atotz1ed uevow Fo
UOT}NQTIZSTP ay} sUTWIazap AayY Se Swa}zsAs JUSTIN apt}—qqa pue
‘yuarzino-aroys3uot ‘aaem ay} FO payuasaid st Tapow Teotsdyd, y

“SM ‘UOSTTM AI
“O'M ‘UTequnzy TIT
“mM ‘uostiieyH [I

aTITL I GHIdISSVIONN 8 “ON WNGNVYOWSW TVOINHOTL
S}eTUL “pb “SNIT?T ¢@2@

(}eTUL eepny) Sutpntout ‘dd gp ‘po6T Taequedeq ‘UOSTTM “M pue
S}2Tul TeptL ‘€ utoquniy’D°M ‘UOSTIIeH"M Aq (‘8A ‘Yyoeag eTUTSITA
erursirA -}21UI eepny) AONVULNA LAINI NV LV NOILVLNAWICHS

‘yoeag eTUTSITA “2
Sasse20rg eToys *T ‘O°d‘*HSVM ‘°SO ‘UHINSO “SHY “OYONA TvLSvoo AWVv’S’n

*yuayxod UT PazyTWIT TayzeI aq 0} punozF sem adUaNT FUT
yuazIno-jaTuT Fo eere nq ‘pood aq 0} punoF sem uoT}eN}TS TeIn}eU
pue Tapow uaamzeq aouapuodsaziogj ‘Tapow Aq pazyItpaid spuss}4
Ajtraa 03 ‘stskTeue adeFIns—pusr} 0} pazyIefqns 21am “seq ‘ydeag
eTuTZITA ‘JaTU asepny ze Uayez, SaTdwes wozyOg “JoOTUT PeTTOT}zUOd
eB JO yyNoW ay} 42 ButT}zIOS FO aaIdap pue azts eTotyied ueaw fo
UOT}NQTIZSTP 94} aUTWIa}ap Aayz se swazshs jUaTIND aptzy-qqa pue
‘quarind-azo0yss3uo, ‘adem ay} FO payuasard st Tepow qTeotsdhyd y

“S°M ‘UOSTTM ATI
“O°M ‘utequnizy TIT
*m ‘uostizeyH IT

STIEL I GaIAISSVIONN 8 °ON WACNVYOWEIW TIVOINHOAL
S}ATUL ‘“b “SNTTE @2@
(aTUI eepny) Sutpntour ‘dd @p ‘po6Tt Tequadeq ‘UOSTTM “M pue
S}eTUI TepTL ‘€ utaquniy’d°M ‘uostizeH’M 4q (‘eA ‘YyDROg erUuTSITA

eTUTSITA -}eTUL eepny) AONVULNA LAINI NV LV NOLLVINAWIGYS
‘yoeog erurTsiItA “2
Sassa00ig sz0US ‘T ‘°O°C‘*HSWM ‘°dO ‘“USLNSO “SHY “OYONA TvLSvOO AWYy"S™N

*yuayxe UT pa}yIWTT Iay}zeI aq 0} puNnoF sem aoUSNT FUT
yuazino-yeTut FO eare 4ynq ‘pood aq 0} punoz sem uoT}eN}TS TeINzeU
pue Tapow uaamzeq aduapuodsartz0g ‘Tapow Aq pazyItperd spus1ty
AJtIAA 03 ‘stsATeue adeFins—pust} 0} pazydefqns stam “sea ‘yoeog
eBTUTSITA ‘zaTUT saepny je udsye} SaTawes wo}},Og *FOETUT PaTTOT}UCD
e FO yynow ayy 3e BurzIos Fo asardaep pue ezts aTItzI1ed ueaw FO
UOT}NQTIZSTP a4} auTWIazap Ady} Se swayshs JUeTIND aptz—-qqa pue
‘yuarzind-aroyssuoT ‘aaem ayy FO payuasaid st Tapow Teotsdyud y

“S*M ‘UOSTTM AT

‘O°M ‘utequniy TIT

"mM ‘uostiieyH [I
aTItL =I daISISSVIONN

8 °“ON WNGNVYOWEW IVOINHOAL

szaqur ° Smee 2
(FeTUL eepny) Sutpntout ‘dd gp ‘po6T Taquesaq ‘UOSTIM “M pue
S}ATUL TePTL uTaquniy"o*mM ‘uosTizeyH’M Aq (‘eA ‘YDReg eTUTSITA
eTUTSITA -}eTUT eepny) FAONVULINA LA INI NV LV NOILVINSWIGaS
‘yoeag eruTSItTA
sassao0ig ar0ys "O°a‘*HSVM ‘°aO ‘UMLNHO “SHY “OHONT IvVLSvOO AWUV'S* Nn

*yua}xe UT pa}yTWTT TayyeI aq 0} punoz sem adUaeNT TUT
yuazino-yaTuT Fo eare ynq ‘pood aq 0} punoz sem uoT}eNATS TeInzeU
pue Tapow uaamzeq a.uapuodsaziogj ‘*Tapow Aq pa}zotpeid spus1r}
AJTIOA 03 ‘stTsATeue adeFIns—pusr} 0} pajyoefqns arom ‘*eA ‘Yydeag
BTUTSITA ‘}OTUT sapny ye uaye}, saTdwes wo,}og “YeTUT PeTTOT}UOD
e FO YyNoW ay} 4e BuT}ZIOS Fo aa1Zap pue oztTs aT2tz1ed ueaw Fo
UOTINGTIISTP 94} aUTWIazap Aayy Se SWazshs yUaTIND ept}y—qqe pue
‘yuazano-azoyssuotT ‘aaem ay} FO pajyuasaid st [Tepow Teotsdkud y

“Sm ‘UOSTTM AT
‘O'M ‘urequnay IIT
"mM ‘uostiieyH [TI
eTITL it daIAISSVIONN 8 “ON WNGNVYOWSW TVOINHOSL
SzeTur ~ “SNTTE @2@
(7eTUL sepny) Sutpntout ‘dd @p ‘po6T Taqueseq ‘UOSTTM *M puke
S}oaTUL TeptL uTaquniy°O°M ‘uostizeH'M Aq (‘eA ‘YydeOg BLUTSITA
eTUTSITA -}eTUT 2epny) AONVUINA LA INI NV LV NOILVINSWICGAS
‘yoeog eruTs1ItA
Sassad0Ig 9104s ‘O°a‘*HSWM ‘°dO ‘UHINSO “SHY “SYONA IVLSVOO AWUV'S" A

pa yeh A

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