Shoreline erosion in a reef-beach system

Shoreline Erosion in a Reef-Beach System

BRUCE P. HAYDEN ROBERT DOLAN Department of Environmental Sciences Clark Hall University of Virginia Charlottesville, Virginia 22903

SCOTT HOFFMAN Department of Environmental Regulation State of Florida Montgomery Building--2562 Executive Center Circle East Tallahassee, Florida 32301

ALAN ROBINSON National Park Service Denver Service Center 755 Parfet St.--Box 25287 Denver, Colorado, 80225

ABSTRACT/Beach erosion on Cinnamon Bay in the U.S. Virgin Islands results from storm waves in the North Atlantic. The net trend of erosion, however, is due to local environmental degradation. Reef die-back, initiated during the period of high sedimentation associated with 18th and 19th century sugar cane cropping, has reduced the rate of generation of new coral sands. Sand losses to deep water during periods of storm waves are not replenished. Engineering measures designed to check erosion at Cinnamon Bay have had little effect in this environment of low wave energies, but sand deficiency. The appropriate environmental focus for managerhent of reef-beach systems is reef health and thus, water quality.

Coral reefs and white sand beaches are among the most attractive coastal resources of the tropics and sub- tropics. While these biological systems may appear to be as stable as the rocky landscapes they fringe, they are not. Coral reefs are highly dynamic biophysical systems that undergo continuous physical, chemical, and biological change. One product of these processes is the white coral sands that are deposited in and on the adjacent bays and beaches. Simultaneously, the living coral polyps rebuild the reef and maintain its structure. The reef-beach system is in equilibrium if the mechanical losses are balanced by the biological production.

The most frequent cause of reef degradation is reduced biological productivity. Maintenance of the reef- forming coral polyps requires: 1) clear water and limited sedimentation, 2) water temperatures between 18~ and 29~ 3) a persistent wave and current-induced circula- tion, and 4) pollution-free waters. Unfortunately, rapid development and construction in tropical and subtropical coasts are leading to reduced water clarity and quality, increased sedimentation of terrestrial materials, and in some cases higher water temperatures.

Degradation of the reef-forming coral system leads directly to a reduction in the supply of fresh coral sands to the adjacent bays and beaches and, in some cases, shoreline erosion. If typical coastal management practices of the mid-latitudes are applied, various engineering KEY WORDS: Shoreline erosion, Reef die-back, Reef-beach system,

Beach erosion

Environmental Management, Vol. 2, No. 3, pp. 209-218

measures may be considered. It is suggested in this paper that these measures may accelerate degradation of the reef-forming organisms rather than solve the erosion problems. The results of a study of a shoreline problem on St. John in the U.S. Virgin Islands are presented.

For several years the Virgin Islanas National Park has been concerned about the beach erosion and preserva- tion of the Danish warehouse on Cinnamon Bay (Fig. 1). Cinnamon Bay is the primary center for visitors in the Park. Major recreational attractions include excellent white sand beaches, clear blue water, and nearshore reefs. Camp sites and small cottages, some of which are located within 100 m of the shoreline, accommodate approximately 500 persons. Other attractions at Cinna- mon Bay include a Danish warehouse of some historic importance and a large Kapok tree, both of which are near the active shoreline.

By 1966 waves had eroded the beach to within one meter of the warehouse and a rock revetment was con- structed to prevent further shoreline recession (Fig. 2). Review by the National Park Service in 1971 resulted in a proposal for the construction of an artificial reef, which would function as an offshore breakwater. Reinforce- ment of the revetment in 1973 and 1975 was necessary as the rock structure had deteriorated seriously in several places.

The Virgin Islands National Parle, in conjunction with the Office of Natural Science, Washington, supported a one-year research program in 1973 to study beach

0364-152X/78/0002-0209 $02.00 �9 1978 Springer-Verlag New York Inc.

2 0 9

210 Bruce P. Hayden, Robert Dolan, Scott Hoffman, Alan Robinson

Figure 1. Location of t.he three coral-reef beach systems on St. John: A = Hawksnest Bay, B = Trunk Bay, and C = Cinnamon Bay.

dynamics on St. J o h n and a modes t moni to r ing p rogram since then. T h e objective o f this p r o g r a m has been to ascertain the possible envi ronmenta l effects of an artificial reef s t ructure and o ther engineer ing measures on the beaches and reefs o f C i n n a m o n Bay and to provide basic informat ion needed by resource managers . Dur ing the e leven-month field investigation ( 1972-1973) and a fol- low-up s tudy (1976), data were systematically collected on

Shoreline Erosion in a Reef-Beach System 211

Figure 2. The rock revetment and seawall on Cinnamon Bay.

wave heights, beach sediments, beach elevation, and offshore sediments at several bays.

A conceptual model was developed f rom previous literature and f rom our prior field studies in order to assess the significance o f various elements within the system; a series of field experiments were then designed to test the hypotheses inherent in the conceptual model. Of particu- lar concern to this project were the sediment-exchange processes o f the subaerial beach and o f the nearshore zone. Although assessment o f the sediment-exchange processes along the erosion-prone beach at Cinnamon Bay was a pr imary objective, concurrent study o f adjacent, apparently stable, reef-beach systems was funda- mental to the investigation. Consequently, Hawksnest Bay and Trunk Bay were also included in the research program (Fig. 1).

The Reef -Beach System

The general dynamics of a reef-beach system can be described in terms of four elements (Fig. 3).

The Offshore Zone

In the deep water offshore zone, wave motion is oscil- latory and wave interaction with the bottom is minor. The offshore bathymetry in the Virgin Islands is highly complex, a manifestation of complex geology as well as coraline-growth forms. As the waves move onshore f rom

deep water, energy is dissipated on the reefs, inshore bottom, and the subaerial beach deposit. Unlike the reef- beach systems facing the trade winds, maximum excitation of these nor thward facing reef-beach systems occurs during the period of October through April when large waves, generated as extratropical storms move offshore along the mid-Atlantic coast o f Nor th America, reach St. John. High waves of local origin reaching the nor th shore of St. John are also observed dur ing the winter season. Waves reaching the north shore of St. John during the May-October period are in the one-foot range except when tropical storms move through the Caribbean.

The Reef

Reefs play an important role in the overall balance o f the reef-beach system. Beach sediments f rom local fringing and patch reefs are t ransported to the beach by wave action. In addition, the reefs act as an energy buffer. As waves move across the reefs, they shoal or break, dissipat- ing energy that would otherwise reach the subaerial beach.

Since the reef is a living entity, constant growth is an essential characteristic. One o f the most impor tant variables in reef health is water quality. The algal component of the coral polyps is light dependent , so turbid water can be detrimental. Excess suspended sediments and detrital material f rom adjacent terrestrial sources can cause retar- dation in reef growth eventually resulting in deeper


Reef 1 Boy Beach 1 Terraces

b /

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

Ponds f'~,

Figure 3. The reef-beach system. The offshore zone is seaward of the reef and the inshore, landward of the reef.

water over the reef and thus, exposure of the beaches to high wave energies.

The Inshore

Coraline sands removed from the reef are deposited in the inshore zone, or bay bottom. During periods of high energy, the bay bottom is a sediment reservoir for sands moved from the subaerial beach. As the storm waves dissipate, sands from the bay bottom and reef move onshore and are incorporated in the subaerial beach. During low wave conditions sediments are exchanged by currents circulating between the bays and the offshore zone. Sediment loss to the offshore area caused by these currents may be significant.

The Subaerial Beach

The subaerial beach includes sand deposits that are acted upon by the swash of waves that break near the shoreline. Here hydraulic action differs appreciably from that in other parts of the reef-beach system. Sheet-like masses of translatory water move upward and, after reaching a stillstand, return down the beach face with increasing acceleration. The linear to-and-fro swash con- stantly redistributes the beach-face sediment. If the quan- tity of material caused by the uprush is in balance with that moved by the backwash, equilibriuna exists; however, when the reef-beach system is excited by storm waves, swash action moves great quantities of sediment down the beach face and into the nearshore zone.

This exchange process results in a transfer of beach material from one part of the system to another. In the process, some of the material is lost to the deep water zone, some is pushed landward over the beach berm in the form of overwash deposits, and some is mechanically reduced in size in the Surf zone and is transported out of the system. Therefore / balance within the system depends upon a resupply of sediment from the reefs and from the inshore sediment reservoir.

The Design

Most of the St. John sand beaches a re within embay- ments that are irregular in shape and bounded by rock headlands. Fringing reefs at the base of the headlands and patch reefs directly offshore are the sediment sources for these beaches. Field experiments were con- ducted at 3 bays on the northwest coast of St. John (Fig. 1). A summary of the characteristics of the 3 bays and their subdivisions is presented in Table 1.

The conceptual relationships between components of the reef-beach system provide a greatly simplified explanation of a highly complex biophysical system. Testing and measurement, even of this general model, are diffi- cult. Although any one component of the reef-beach system could be investigated, the role of waves in the material-exchange processes of the subaerial beach has been demonstrated to be important (Dolan 1966, Wad- dell 1973).

The energy delivered to the reef-beach system was estimated from measurements of breaking waves. Thirty to forty waves at a minimum of two beaches were measured daily. A graduated staff was used to measure the


Table 1 Characteristics of the Reef-Beach system studied

Trunk Bay Cinnamon Bay

Hawksnest West East West East

Beach length (meters) 183 Beach width (meters) 12 Mean wave height (meters) 0.3 Period (seconds) 5.0 Maximum wave height (meters) 1.8 Period (seconds) 7.8 Minimum wave height (meters) <0.1 Period (seconds) 2.3 Mean grain size 1.8 Standard deviation 0.14 Grains with mean diameter less than 125 microns (%) 1.25 Mean beach elevation (meters) 0.56 Maximum beach elevation (meters) 0.89 Minimum beach elevation (meters) 0.38

290 84 366 335 15 9 5 26 0.4 0.2 0.4 0.5 5.8 3.8 5.8 6.4 3.0 1.8 2.7 3.0

13 8 12 13 <0.1 <0.1 <0.1 <0.1

2.3 2.2 2.3 2.4 2.2 2.11 2.5 2.2 0.59 0.41 -'0.68 0.76 4.34 5.54 18.71 13.37 0.27 1.00 0.43 0.59 1.07 1.34 0.93 1.37 0.22 0.64 0.05 0.59

distance from the trough to the crest as the waves peaked before breaking. Waves higher than 1,5 m, which occurred only 8 times during the study period, were estimated from the shore. Wave period was measured by using a stop watch to record the period of time it took 30 waves to pass fixed points on each bay.

Beach responses to various energy conditions were measured during the semi-diurnal tidal cycles and under storm conditions. Sediment characteristics and beach elevation changes within 12-hour tidal cycles were measured weekly. Elevation-control stakes on the beach were measured at each of the 20 sampling points within a 15 ft • 75 ft grid area covering the tidal zone of the beach face. The height from the top to sand level was measured at low tide and at the following low tide, 12 hours later, the distances from the stake tops to sand level were again measured. The difference between the measurements was the gross change in the sand level within a tidal cycle. In addition, a small plug of colored sand was inserted into the beach near each stake. At the following low tide, the colored plug of sand was dissected so as to reveal its position relative to the beach section. The top of the red plug represented the low point of the beach (erosion) during the tidal cycle and any material positioned above the plug represented sediment deposited by the falling tide. Beach and sediment characteristics under different storm conditions were measured in a similar manner.

Seasonal variations in sediment characteristics (grain size) along or across the subaerial beach were collected every 3 months from the top 1 cm of the dune, berm, and swash zones along 7-m spaced lines.

The relationship between beach change and the stabil-

ity of the Cinnamon Bay Warehouse was of primary interest t.o the Virgin Islands National Park. Therefore, two subaerial beach profiles, one from each side of the warehouse, were taken weekly at Cinnamon Bay. To provide documentation of the rates of beach retreat at Cinnamon Bay West, a set of profiles at 15 m intervals was surveyed in May 1973, beginning at the warehouse.

In order to monitor the long term changes in 3 beaches, 2 permanent pipes were located near the centers of the east and west beaches of these bays on each of the 3 study beaches: Hawksnest, Trunk, and Cinnamon Bays. In addition, profiles were taken at 15 m intervals west of the old Danish warehouse for a distance of 180 m. Pro- files surveyed in 1976 were compared to the base-line profiles collected in October 1972. Photographs and vis- ual observations were taken to complete the field studies.

Analysis Although the conceptual model of the reef-beach sys-

tem provides a general explanation of the interaction of various elements, statistical analyses of the data sets collected on St. John provide quantitative verification of both the existence and the degree of these interactions. The analyses were designed to answer these questions:

I. Is there any significant variation of beach-material size and of beach elevation along and/or across the beach faces within semi-diurnal tidal cycles?

2. Is there any significant seasonal variation in beach configuration as measured by beach elevation and beach-material size?

3. Is there significant variation of subaerial-beach

214 Bruce P. Hayden, Robert Dolan, Scott Hoffman Alan Robinson

grain size and elevation between Trunk Bay, Cin- namon Bay, and Hawksnest Bay?

4. Is there a significant correlation between wave energy and grain size or wave energy and beach elevation?

Variation within a tidal cycle was tested using a 2-way (across and along the beach elevation data) classification analysis-of-variance (ANOV) model. Significant seasonal variation in grain size and beach elevation within each o f the 5 beaches was tested using a one-way classification ANOV model. In addition, correlation coefficients for relationships between wave height and sand grain size were calculated.

Results of Statistical Analyses The statistical analyses of along and across the beach

variation in beach elevations and grain sizes within tides, seasons, bays, and between bays are presented in Table 2. The most striking results are the differences within and between bays. T h e east and west portions o f Cinnamon Bay differed significantly in both grain size and beach elevation. In general, the west beach is characterized by finer sediments and when beach elevations rise on the west beach they tend to fall on the east beach and vice versa. Statistical differences were also noted in grain size

Table 2 Statistical results

Beach Characteristic Variation Correlation Within Within Between with Wave

Bay Tide Seasonal Bays Bays Height

Cinnamon NS NS S West NS S NS S S

Cinnamon NS NS NS East NS S S S S S

Trunk NS NS NS West NS S NS NS S

Trunk NS NS S East NS S S NS NS S

NS S NS S Hawksnest NS S S NS S

S = Significant NS = Not Significant Grain< ) Beach

size i![i{iii!iii:: i~):: i ~r~ ...... elevation L

Along ] beach Across

beach

between bays. This difference results f rom the finer sands at west Cinnamon Bay beach in comparison to the other Hawksnest and Trunk Bay beaches. While o ther statistically significant differences were noted, their relationship to the erosion problem at Cinnamon Bay west is obscure.

Storm Wave Events Swell f rom extratropical storms in the mid-Atlantic

and large waves of local origin excited the reef-beach systems on the northwest coast o f St. John and set in motion sediment-exchange processes. These processes were manifested as significant changes in beach elevations at all bays studied. During the 1972/73 period of field studies, 10 major high wave events were recorded in Hawksnest, Trunk, and Cinnamon Bays. Five of these wave events resulted f rom major storms in the western North Atlantic at the latitude o f Cape Hatteras, North Carolina. The remaining 5 wave events resulted from storms within several hund red miles.

These 2 types of wave events were not distinguishable in terms o f wave height in the 3 bays studied. Rather, the wave period and wave direction differentiate these 2 types of wave events. Waves generated by storms in the western North Atlantic arrive in the Virgin Islands f rom the northwest and nor th directions with a period o f about 10 seconds. In contrast, the "local" storm waves arrive from the west to northwest directions with a per iod of 6 or 7 seconds.

The currents generated by these 2 types o f systems determine the direction of movement of coral sands within and between the bays.

Sediment Transport Events A sediment- transport event is defined here as a signifi-

cant rise in beach elevation resulting f rom deposition on the beach, or a significant fall in beach elevation resulting

Table 3 Type of beach-sediment transport event

N, Atlantic Local Storm Storm

Beach Waves Waves

Hawksnest Rise Rise Trunk East Rise Rise Trunk West Fall Fall Cinnamon East Fall Rise Cinnamon West Rise Fall


from offshore movement of beach sand. During the 1972/73 studies 10 sediment-transport events were recorded. Each event occurred at a time of high waves. The behavior of Hawksnest, Trunk, and Cinnamon Bay beaches is summarized in Table 3.

Both Hawksnest and Trunk Bay East beaches behaved in similar manner, that is, beach elevations increased during both types of storm-wave events. In contrast, Trunk Bay West beach experienced a beach-elevation decrease during both storm-wave event types. Thus, during the storm-wave events, sediments are transported from Trunk Bay West to Trunk Bay East beach. The behavior of Cinnamon Bay is more complex. During wave events of the North Atlantic type, Cinnamon Bay East beach loses sand and the west beach acquires sand. However, during a local storm-wave event this process is reversed. In short, during the North Atlantic storm-wave event, sand moves from east to west in Cinnamon Bay and, during a local storm, sand is transported from west to east in Cinnamon Bay.

These transport patterns are illustrated in Figs. 4A and 4B. The distribution of sand masses in the shallow water adjacent at the headland between Trunk and Cin- namon Bays suggests that here there is a net export of coral sands to deeper water. This constitutes a loss from the reef-beach system. The Sand transport illustrated in Figs. 4A and 4B is substantiated by sediment characteristics in Trunk and Cinnamon Bays. Mean grain size, the standard deviation of grain size, and the percentage of fine sands (Table 4) indicate that sands become finer toward the point between the 2 bays.

Cinnamon West Beach Survey Field In 1972 and again in 1976 the area of the rock revet-

ment and the beach immediately to the west were sur-

Figure 4. Sand transport directions within and between bays during a storm in the North Atlantic (A), and during a local storm (B).


Table 4 Sand grain size within Trunk and Cinnamon Bays

Trunk Cinnamon

West East West East

% of sand grains less than 0.125 mm 4.3% 5.5% 18.7% 13.4%

Mean grain size 0.23 mm 0.22 mm 0.18 mm 0.21 mm Standard deviation

of grain size (q5 units) 0.59 0.41 0.68 0.76

veyed at 15 m intervals along the beach. While the subaqueous beach has remained unchanged since the 1972 survey, the beach head has eroded landward significantly. The movement of the beach scarp landward varied f rom about 0.3 m per year at the west end of the revetment to 1.2 m per year.

The retreat o f the erosional scarp since 1972 is illustrated in Fig. 5. The scarp has a crescentic form (point A), with a wave length of about 90 m. At point B there has been a 6" m landward movement o f the erosional scarp since 1972; 90 m fur ther to the east at the Cinnamon Bay Amphi theater portions of the rock revetment were lost and the revetment had to be reinforced in 1975.

A shorter crescentic periodicity of 15 m wave length was also observed to the west o f the revetment. The profile survey lines fell at the horns o f the 15 m cusps. These cusps were evident on the beach head and along the scarp line. At the scarp line the ampli tude o f the cusps was measured at 1.8 m, that is, scarp erosion was 2 m greater at the center o f the cusp than at the horns (Fig. 6).

Figure 5. Erosion of Cinnamon Bay West scarp between 1972 and 1976.

A 1976 SCARP

r

Figure 6. Crescentic erosional forms on Cinnamon Bay West.

It is especially significant that these crescentic features are present. We have learned that along the United States Atlantic coast these shoreline rhythms are indicative of instability of the beach-sand prism, and one would expect that, as the erosion proceeds toward a new beach equilibrium form, the ampli tude of these rhythms will decrease. At the present time we must conclude that the system remains highly unstable and severe erosion will continue. Thus, the vulnerability o f the warehouse increases yearly.

A contoured elevation chart o f the Cinnamon Bay beach in the vicinity of the warehouse was p repa red (Fig. 7). The 90 m wave length o f the beach topography is clearly evident. During periods of high water and high waves, water depths at the center o f this shoreline feature are deep, thus permitt ing waves to break close to the land. It is evident that there is a deep t rough immediately west o f the cement seawall and that high waves would refract around the seawall and continue to cut away at the land. A continuation of this back-cutting will lead to fur ther undermin ing of the seawall and the rock revetment. Wholesale decay o f the structure is forecast. At such time the warehouse is in immediate danger.

Discussion Perhaps the most significant documentat ion o f our

study was the excitation of north-shore beaches o f St. John by waves generated by extratropical storms moving offshore along the mid-atlantic coast well to the north o f the Virgin Islands, as well as by storm waves o f local origin. This responsiveness to extratropical storms distin- guishes these areas f rom general tropical reef-beach systems and unites them, f rom a dynamic perspective, with


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the temperate-latitude beaches of the mid-atlantic coast. Much of the knowledge gained over past decades about beach processes and shoreline variability becomes, to some degree, applicable to the reef-beach systems of the north shore of St. John if they are classed with the temperate-latitude beaches. This does not imply, however, that management of these systems should be similar to that of the sand beaches and barrier islands to the north. The existence of the reefs alone clearly sets these sites apart.

Two coupled variables of the reef-beach system are central to the management question. The first is the form of the reef shadowing the beach. Along the northwest shore, the reef form is characterized by distinct shallow- water fringing reefs of scattered coral heads. There is also a system of extensive patch reefs rising to within 2-6 m of the snrface. Along much of the southward- and the eastward-facing shores, the water depth increases more rapidly offshore and much of the shallow-water coral growth consists o[ scattered colonies on hard rock. Few significant offshore patch reefs are found.

Figure 7. Beach topography along Cinnamon Bay West. Contour interval is 9.33 m.

The second variable is the areas's wave cfimate. The north-shore bays containing patch and fringing reefs are in areas characterized by occurrences of waves generatd by extratropica] storms to the north and local storms; whereas, scattered colonies along the southern and east- ern shores are in areas largely under the domination of waves generated by the trade wind systems. Those areas without reefs are shadowed by adjacent islands from extratropical storm and/or trade-wind waves; that is, they are only exposed to small, locally generated waves.

The beaches fronted by scattered coral formations and under the influence of trade winds undergo adjustment on a continual basis because of the consistency of the wave environment. In contrast, the beaches fronted by patch and fringing reefs and responsive to extratropical storm waves respond and adjust at periodic intervals. Beach-sediment changes in these systems are, therefore,


episodic in contrast to the evolutionary changes of those areas dominated by trade-wind waves.

The north-shore bays of St. John exhibit similar responses to the episodic, high-energy conditions that occur approxim~itely 10 times each year. During these meteorological events, morphol0gic M changes within the system cause large volumes of sediment to be exchanged between the inshore zone and the subaerial beach and losses to deep water. Grains of sediment with a mean diameter of less than 123 microns (fine sands, silts, and clays) are most easily placed in suspension by the stresses associated with breaking waves. The average percentage of beach material less than 125 microns is given in Table 3 for all samples taken at Trunk and Cinnamon Bays.

Under natural conditions, the reefs on the north shore of St. John barely tolerate present volumes of fine sediment; this is evident from the present marginal health of the reefs. If an alteration of the exchange processes were to occur, more of the fine fraction could be winnowed out of the subaerial beach and moved across the inshore zone onto the reefs or into the offshore zone. This would result in major changes in the beach configuration as well as significant damage to the reefs.

Alterations to the system, such as the rock revetment in front of the warehouse on Cinnamon Bay, can cause even more dramatic changes. The revetment causes wave reflection rather than energy dissipation and thereby increases scour at the base of the wall. Sediment plumes observed directly offshore from the warehouse are significantly larger than plumes found in other areas. The Cinnamon Bay beach was completely subaqueous during high-energy conditions and the sediment losses were significant. When our 1973 profiles were compared with the National Park Service surveys made in 1971, the results showed that the beach along Cinnamon Bay West had retreated approximately 2 m within the past 3 years except directly in front of the warehouse where the rock revetment retarded beach erosion. This rate of change has continued to 1976 with changes of 6 m immediately to the west of the rock revetment.

The prevailing erosional trend at Cinnamon Bay West, coupled with the results of this investigation, suggest that the volume of fine sands removed from the beach during storms exceeds the volume returned during fair weather. The surplus material must either remain in the inshore zone or be transported beyond the reef to the offshore zone where it is effectively lost from the reef-beach system.

In our opinion, further engineering could cause even greater amounts of sediment to move from the inshore

zone and/or the subaerial beach to the reefs or past the reefs to deeper, offshore waters. In either case, dramatic changes in the subaerial beaches will occur with possible, complete destruction of the already marginal reefs along the north shore and a reduction in coral sand resupply. Because of the evidence pointing towards these probable results, it is our specific recommendation that no struc- tures be used for beach management purposes on north- shore beaches within the Virgin Islands National Park. In general, we recommend that shoreline engineering measures in interacting reef-beach systems be avoided.

Literature Cited

Dolan, R., and J. Ferm. 1966. Swash processes and beach characteristics. Professional Geographer 17 (4): 210-213.

Waddell, Evans. 1973. Dynamics of swash and its implication to beach responses. Coastal Studies Institute Technical Report No. 39. Louisiana State University. Baton Rouge, Louisiana. 139 pp.

Shoreline erosion in a reef-beach system

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