In A. McLachlan and T. Erasmus, (eds~), Sandy Beaches as Eco 63 sy~tems, D.W. Junk Publishers, ' The Hague, p. 63-85, 1983.
BEACH CHANGES ON COASTS lHTH DIFFERENT WAVE CLHIATES
D. G. AUBREY (Department of Geology and Geophysics, Woods Hole Oceanographic Institution)
severe wave climate) and the lowest / vari abi 1i ty along protected coasts (1 east severe wave climate). All open coast ,r-· locations studied had a seasonal variability SYNOPSIS "'".,. __..-, Seasonal and longer-term oeach which accounted for at least50%of th~ beach variability is quantified for seven U.S. variability. Protected coastal locations beaches exposed to widely varying wave had less pronounced seasonal signatures. climates. One U.S. west coast location These seasonal and aseasonal beach responses (southern California) and six U.S. east mirror corresponding seasonality (or lack coast locations (from North Carolina to thereof) in wave and storm climates. The Massachusetts) form the basis of this study re-emphasizes the need for careful study. Wave exposure varies from complete measurement or estimation of coastal wave exposure to open ocean waves, to partly climate to enable predictive modelling of sheltered locations, and finally to nearly shorelin-e behaviour, and discusses different complete sheltering where locally-generated analysis techniques for analyzing changes in waves dominate. Beach response was beach profiles through time. documented with beach profiles distributeq INTRODUCTION along each of the seven coastal locations, Quantification of spatial and temporal spanning a minimum of 'five years of observa scales of beach change is vital to a wide tion. Frequency of measurement was at least variety of scientific and engineering once per month, with periods of more intense investigations of nearshore environments. weekly sampling lasti~g for up to two years Vertical elevation changes of 2.5 metres, (southern California location). Wave climate mean shoreline transgressions on the order was either measured directly or estimated of 50 metres, and volume changes on the 3 from hindcast and/or compilations of ship order of 102 m /m of beach length can observations. Consequently, wave informa occur on time scales of hours, drastically tion varies in detail from joint statistics altering the physical and biological of wave height, frequency, and direction, to characteristics of beaches (Fig. 1). compilations of local storm history (and Intertidal benthic communities must be able hence inferred wave behaviour). Magnitude to respond quickly and efficiently to these of annual beach variability ranged from 3.3 m3 profile readjustments, since habitat, oxygen per metre of beach to 0.2 m3 per metre of levels, nutrient retention, and other beach, with the greatest variability in environmental factors can be significantly regions exposed to open ocean waves (most
; 64
storms in February, 1980, caused marked RANGE 2 erosion along the beaches in Santa Barbara, exposing underlying beach material which had , 28 80
2 24 80 not been disturbed in the preceding decade ..._ (Fig. 1). During the later stages of the .,"'"' ~ storm, an oil-impregnated horizon which had , .... "' ~ r------~------.~~/~---10 ~ been deposited during February, 1969 was .. § .... _, Gj exposed, and eroded from the beachface. In t this instance, the residence time of the oil
~-- -2 was of the order of 10 years, in contrast to
90 60 30 0 the residence time of months for oil in OFFSHORE .DISTANCE (m) beach sands emanating from local, natural oil seeps in the Santa Barbara Channel. Presence of a persistent hydrocarbon horizon 1) Beach erosion resulting from a series of limits the vertical mobility of biota, and storms battering Santa Barbara, affects the transport of nutrients and California, in February, 1980, causing oxygen through normally permeable beach vertical cuts in the beach of up to 2.5 sands. metres, and hori zonta 1 . beach retreat of The importance of beach variability in up to 60 metres. engineering studies is well-known. Seasonal and aseasonal beach changes can affect the altered in a short time (Steele, Munro and lifetime of coastal structures, and the Giese, 1970; Parr, Diener, and Lacy, 1978). design of beach protection devices. Proper The degree of seasonality in these changes set-back requirements for near-shoreline similarly may affect the viability of development is dependent on long-term trends nearshore benthic communities, since the in coastal change as well as natural seasonal timing of beach changes interacts with the fluctuations in beach level.- Finally, developmental stage of the benthic quantification of beach variability and its community. The seasonality and magnitude of statistical relationship to driving forces beach changes also pl,ay a direct role in can serve as useful input to nearshore retention of hydrocarbons in beach sands sediment transport models, particularly as a with subsequent impact on biota, a test of variation in beach response as a consideration in many beaches exposed to function of different sediment types (grain naturally-occurri,ng or man-induced size, sorting). Empirical guidance for hydrocarbons, in the shallow near.shore. modellers can also be provided through well Rapid beach-changes of large magnitude will constructed statistical studies of driving help rid the beaches of oil naturally; force/beach response, when constructed using
longer-liyed_b~ach_hydrocarbons may _limit insight gleaned from dynamical considera- · · benthic diversi;ty or density. An example of tions (e.g., Aubrey et al., 1980). this longer time, scale for hydrocarbon The basic problem addressed here ii the residence was observed along beaches in quantification of seasonal ,and aseasonal Santa Barbara, California, by the author patterns of beach change along coasts with (unpublished data). A series of major 65
different wave climates, and for beaches Analysis procedures for most of these with different sediment characteristics. studies have varied considerably, with Rigorous statistical technique~ for little uniformity in treatment of the data. quantifying these changes must be developed Consequently we are left with many to allow for meaningful comparison of beach observations of beach change, of highly response at different sites, providing a variable quality, and no capability for " statistical basis for defining differences readily comparing changes at one location in beach behaviour. The ultimate goal is to with changes at another location. The develop a capability for predicting beach resulting lack of comparison leaves us with changes on many spatial and time scales, but a disturbing inability to synthesize these this goal is to be achieved only with data into a meaningful set of observations, careful statistical methods combined with which might provide valuable insight into dynamical (both analytical and numerical l causes and patterns of beach variability. modelling. Work reported in this paper represents Observation of changes in beach planform an attempt to take data from different have been made for the past century, and coasts of the United States,. exposed to relations between these beach changes and widely different wave climates, with the driving forces postulated. For instance, different sediment types, and synthesize it Davies (1964) related beach characteristics in a rigorous fashion to allow quantitative to global patterns of waves (swell coasts, intercomparison of magnitude of seasonal and storm coasts, and protected coasts), using aseasonal beach changes at these different not direct measurement but compilations of locations. The work represents a plea for winds and wave behaviour observed from ships some uniformity in analyzing beach data to and shore. Davies (1964} pointed out that provide results useful to a variety of the major drawback in obtaining statistical disciplines studying this active nearshore relationships between beach behaviour and environment. driving forces is lack of knowledge of the STUDY SITES driving forces, specifically wave activity •. Seven locations were selected for this.· This is still true at the present, although study (Fig. 2), six along the U.S. east progress has been made in the last couple of coast (Fig. 3) and one on the U.S. west decades in measuring nearshore wave coast (Fig. 4). The beaches span a spectrum characteristics (e.g., Pawka et al., 1976; of grain sizes, and range from open ocean Seymour and Sessions, 1976; Thompson, 1977; beaches, to those partly sheltered by Seymour, 1979). offshore shoals and islands, to completely Beach profile monitoring programmes sheltered beaches. A brief description of generally have had the following character each study site follows. istics: limited duration of sampling;, Torrey Pines, California: This southern inadequate sample frequency; inadequate California site (Fig. 4) is a long sandy. spatial coverage, particularly for beaches beach, extending for more than 40 km with no with much longshore variability; inadequate. man-made structures to impede longshore.sand· spatial density of sampling; and poor transport. The beach profile locations are documentation of the driving forces. backed by 100m high sea cliffs, composed of. 66
LOCATIONS OF STUDY AREAS
: NEVADA ' ' ' ' ' ' ' .... CALIFORNIA ' ·.··. '
··:: :::: ..
·.!
N 2) Location map for seven beach study sites distributed along the U.S. east coast t 0 500 1000 (6) and the U.S. west coast (1). ... I .. METERS
0 2000 4000
FEET OEPTH IN FEET
4) Location map for Torrey Pines, California, with profile· line locations.
2.0 m on the average, and 2.5 during spring tides. The site was described in detail by Nordstrom and Inman (1975), Aubrey et al. (1976), and Aubrey et al. (1980). The beach is exposed to a wave field which is partly sheltered by the islands offshore on the continental borderland (Pawka et al., 1976). The nearshore wave 3) Location map for six u.s. east coast field is dominated by long-period swell from study sites, showing beaches in relation all offshore quadrants. to water bodies over which surface Holden Beach, North.Carolina: Holden ·.gravity waves are generated. Beach is a 13 km-long barrier island located west of Point Fear along an east-west well-indurated deposits which add sediment stretch of coastline (Fig. 3). It is to the nearshore zone upon collapse. Mean. bordered on the west by Shallotte Inlet, and beach width varies from 40 m to 100 m, on the east by Lockwoods Folly Inlet. composed of sand with a median grain size of Average beach width is about 250 metres, about 0.20 mm. Tide range is-approximately 67
with the beach generally narrower near the Jones Beach, Long Island, NY: Jones ends of the barrier, broader near the Beach is a 24-km long barrier beach centre. Beach material is a moderately separating the Atlantic from Great South Bay well-sorted medium sand. Frying Pan Shoals, (Fig. 3). It is bounded on the east by Fire the southerly extension of Cape Fear, partly Island Inlet, and on the west by Jones shelters Holden Beach from waves propagating Inlet. Mean beach width is approximately from the east and southeast. These waves 150 m, with considerable variability (225 m often break on Frying Pan Shoals, losing near Jones Inlet jetty, to 35 metres on the much of their energy, reducing the impact of eastern third of the study area). Beach northeasters which are so damaging to the sand is medium to fine grained. Tides are remainder of the barrier beaches along the semidiurnal, with a mean range of 1.3 North Carolina shoreline. This site was metres, and spring range of 1.5 metres. described in detail by Miller (1982). Offshore bathymetry is complicated by ridges Long Beach Island, NJ: This site and swales, which (unlike Long Beach Island, (Fig. 3) is a barrier island along the south NJ) have no subaerial expression. No struc shore of New Jersey, separating the Atlantic tures interrupt the longshore transport of. Ocean to the east frpm ·salt ~arshes to the sand, with the exception of the jetties west. The study area is bounded to the protecting the entrances to Jones and Fire north by' Barnegat Inlet, and to the south by Island Inlets. The beach with its southerly Beach Haven Inlet, both active inlets. The exposure is not sheltered from Atlantic wave island, with its.eait-southeast exposure, conditions. A more detailed description of has a median sa~d diameter of 0.35 mm the study site is available from Morton et (Ramsey and Galvin, 1977), and stretches a l • ( 1982c ) • about 32 kilometres. Tides are semidiurnal Fairfield/Milford Beaches; CT: Both of with a spring/neap range of 1.5/0.9 metres. these study sites are located along the . The beach itself is heavily structured, with northern shore of Long Island Sound, and are 110 groins, 83 of whi.ch have been built or exposed to the locally-generated waves of rebuilt over the period 1962-1975: The the Sound (Fig. 3) •. Beach behaviour along island is narrow (mean width of about Mil ford Beach is dominated by the impact of 400-500 m), with a nearly continuous dune of the Charles Island Bar, a submerged tombolo height·5 to 8 m, MLW. Complex offshore or bar. To the east, a sandy beach (Sil,ver topography (ridges and swales) imparts Beach) extends for about half a kilometre, considerable alongshore variability to the with no structures in the surf zone, but wave field. Peahala Ridge is one ridge backed by a seawall. Beach material ranges which is presently shore-attached. Except from sand through boulders. To the west of for the effect of the ridges and swales, Charles Island Bar, a series of small beaches Long Beach Island has an open exposure to is disrupted by a number of shoreline Atlantic Ocean waves. Miller et al. (1980) · structures, segmenting the beach. The beach describe the study site in more detail. is backed by a seawall here, also. Beach material ranges from medium sands to boulders. Fairfield Beach is located about 16 km west of Milf.ord beaches,, and stretches 68
1.8 km from Shoal Point to the entrance to up to 30 m in height, and to the south by a Ash Creek. Along this length, there are no marsh (the two southern-most lines are on a shoreline structures to interrupt longshore barrier beach). Beach m~terial is composed sand transport. Beach sand here is medium of unconsolidated drift material derived to coarse in texture. from eroding sea cliffs. Grain size ranges Tidal range at both these locations, for from about 1.0 mm in the north, down to 0.25 spring/mean conditions, is 2.4 m/2.1 m. The mm in the south. No structures exist along site is described in greater detail in the shore, so longshore exchange of material Morton et al. (1982b). takes place unimpeded. Although the range Misquamicut Beach, RI: Misquamicut varies a -little along the study area, Beach is a low-lying barrier beach located spring/mean ranges for this semi-diurnal near the western limit of Rhode Island (Fig. tide are 2.5 m/2.0 m. The northern part of 3). The beach, extending approximately 8.5 the study area commonly exhibits a longshore km from Watch Hill Point to Weekapaug Point periodic shoreline feature, called a hooked on the east, is approximately 125 m in bar by Aubrey (1980), with length scales of width, varying from about 100 m to 150 m. hundreds of metres. Migration of these Beach material is composed primarily of shore-attached features can affect beach fine-to-medium sands, interspersed with behaviour. The study area is completely occasional areas of coarser sands and exposed to open ocean waves progagating in gravel. Offshore bathymetry is relatively from the Atlantic. This study area is complicated. Far offshore, a submarine described in more detail by Miller and ridge focuses waves propagating shoreward Aubrey ( 1982). from the Atlantic. Nearer shore, a number Summary: These seven study sites of scales of bottom roughness are displayed represent a range' of beach conditions and which influence, and are in turn influenced driving forces which can be expected to by, nearsho.r:e_w.a_v_e_s_.__Ti des in the area are provide some insight into different modes semi-diurnal, with a spring/mean range and magnitude of beach change. In partic variation of 0.96/0.78 m. Incident waves ular, these seven beaches have different progagate shorewards from the southerly grain sizes; they are ~xposed to varying quadrant from the continental shelf, and are wave climates, ranging from locally . also locally generated within a restricted generated seas to distant1y-generated swell fetch to the western and eastern quadrants. conditions; they have variable degrees of The eastern part of the study area is structural development in the surf zone, bounded by a tidal inlet (structured). ranging from highly developed along Long Other than th~s inlet, no significant Beach Island, NJ, to completely undeveloped shoreline structures inhibit the longshore as in Torrey Pines, CA, and Cape Cod; MA; exchange of sediment. This study site is , and. they are exposed to different tidal described in more detail in Morton et al. regimes, with different tidal ranges ( 1982a). (although all have semi-diurnal tides). Cape Cod, MA: The Cape Cod study area This range of conditions makes a semi (Fig~ 3) repres~nts an eroding glacial quantitative comparison of beach changes a feature; backed in the north by sea cliffs useful exercise, since this has not been done previously. 69
DATA SETS
Profiles of the beachface from the back 12 0/2.5 MEAN RANGE /SPRING RANGE shore out to approximately mean water level HOLDEN BEACH, N.C •••• 22 ~~ )w1s. were made on each of these beaches for LO~~ BEACH ISLAND······32 ~M I 0.88/1.15 variable lengths of time (Fig. 5), and for a JONES BEACH, •••• 18 LONG ISLAND, NY ~#M 113/15
SAMPLING DURATION FAIRFIEL. 0-MILFORO. 7 CONN W~M )2.0/2.3 TORREY PINES, CA MI~~~AMICUT, • ? W M 1 o 78/o.•• HOLDEN BEACH, NC CAPE COD, MASS -13 )2.012S LONG BEACH ISLAND NJ 10 20 30 NUMBER OF TIDAL RANGE lml JONES BEACH, PROFILE STATIONS LONG ISLAND, NY
FAIRFIELD- MILFORD CONN.
MISQUAMICUT, R.I. 6) The number of survey lines (left) and
CAPE COD, approximate tidal range (right) for each MASS.
1960 1965 1970 1975 1980 of the seven survey locations making up . this stuqy. Lines were surveyed over 5) Duration of beach profile sampling at the period shown in Fig. 11. each of the seven study sites. Sampling was on approximately a monthly basis for NUMBER OF PROFILES ANALYZED TORREY PINES, ooo) most of the beaches. CA
HOLDEN BEACH, NC
variable number of survey lines (Fig. 6). LONG BEACH ISLAND,...------2-15--,8 Consequently, the total number of beach JONES BEACH, 1701 profiles analyzed for each site is variable ~G ISLAND, NY (Fig. 7), with a maximum of 2158 profiles
analyzed from 32 1 ines on Long Beach Island, MISQUAMICUT, R I
NJ, to a minimum of 378 profiles analyzed CAPE COO, MASS. from 7 lines at Fairfield/Milford, CT. . 200 600 1000 1400 1800 2200 Duration of sampling ranged from about thirteen years at Long Beach Is 1and ( NJ) , Jones Beach (Long Island, NY), and Misquamicut Beach (RI), to a short length of 7) The number of beach profiles used in the five years at Cape Cod (MA), with other analysis described in this study varied,· sample lengths intermediate to these ranging from a low of 378 at the extremes. Fairfield/Milford beaches, to a high of All profiles examined were wading 2158 profiles on Long Beach Island, NJ. profiles, taken with engineer's level and survey rod, extending from an.onshore activity, and vested interest of.the survey benchmark along a profile line to the water parties. A more complete description of line. The different data sets were obtained survey procedure can be .found in Aubrey with different degrees of accuracy, (1979). All survey notes were carefully reflecting in part climate extremes, wave .J / 70
checked for errors, both in the field and for intercomparison. One thrust of this later in the laboratory, to assure high data paper is a plea to consider the need for standards. The data were checked as part of later synthesis in any analysis scheme, so this study as well, to minimize outlying concepts of beach change can be determined points of dubious validity. Profiles for not just for a single beach, but rather for all sites except Torrey Pines, CA, were many beaches. obtained as part of the Beach Erosion The beach profiles are analyzed here by Programme of the Coastal Engineering empirical eigenfunction analysis (also known Research Center (USA Corps of Engineers). as principal component analysis, empirical The Torrey Pines data set was collected orthogonal·function analysis, eigenanalysis, initially under the aegis of CERC through or factor analysis, a close relative). The Scripps Institution of Oceano·graphy ( D.L. empiricai eigenfunction technique has been. Inman, principal investigator), and later used by other investigators to determine·the funded through the Office of Naval modes of varfabi l ity of periodic beach Research. For all profiles, accurate profile measurements. The method can be benchmarks were established to provide both useful in showing .the spatial location at vertical and horizontal control for which the major amount of, beach variability repeatability of surveys. occurs along the profile line. Temporal METHODOLOGY eigenfunctions also show seasonal or other Analysis of beach profile data sets in periodic trends in the data that may be less the past has taken a number of different obvious from other methods of analysis. forms, ranging from heuristic approaches to Properly used in conjunction with other, much more dynamical approaches. Common more conventional methods of analysis, the measures of net profile change which have empirical eigenfunction technique provides a been used are volume changes on the beach useful tool for understanding beach vari foreshore, migration of Mean Sea Level (MSL) ability. Noble and Daniel (1977) provide a intercept or other vertical datum, or beach general explanation of the techniques. stage models. Each of these techniques Specific applications to the coastal zone provides insight· into the behaviour of and beaches are provided by Winant, Inman, beaches at a particular locality; however, and Nordstrom (1975); Vincent, et al. comparison of beach change at different loca (1976); Resio, et al. (1977); Aubrey (1978, tions is difficult using these methods of 1979); and Bowman (1981). analysis. Synthesis of changes· at beaches The objective of eigenfunction analysis with different characteristics exposed to is to separate the temporal and spatial different driving forces is difficult dependence of the data set so that it can be without some common analysis technique. represented as a linear combination of This paper utilizes a method for quantifying corresponding functions of time and space:
beach change in a manner amenable to n synthesis at a later time. Although the h(x,t) =I: c (t)e (x) (>..nn)l.o (.l) k = l k k k X t author feels this methodology is useful and provides insight into patterns of beach ~. change, others may prefer alternate methods
>· 71 where Empirical eigenfunctions, then! h(x, t) = a profile sample at any point x objectively represent the variation in the and time t, n = the lesser of nx and beach profile configuration in terms of nt (the number of points along each distance from fixed data points, and in profile line and the number of times the terms of temporal changes in the profile profile was measured, respectively), over the period of the study. Comparison of ck(t) = temporal beach eigenfunc- the variability of eigenfunctions from a tions, ek(x) = spatial beach series of profiles taken along the beach may ei_genfunctions (BEF), >.k = show differences due to the presence of eigenvalues associated with each structures or change in shoreline orienta eigenfunction pair (ck,ek). tion. This representation helps identify processes Since the empirical eigenfunctions form responsible for profile changes, assists in an orthogonal se-t, they are similar in some evaluation of.their relative importance, and respects to the more familiar Fourier aids the identification of specific events. analysis. in Fourier analysis, a sinusoidal The following properties of empirical variatio~in the data set is assumed, and eigenfunction make it a desirable tool for one best fits the data to a s.eri es of sines analysis of beach profile data (Aubrey, and cosines. This method assumes beforehan4 1978): some given form for the orthogonal functions; (1) Empirical eigenfunctions provide in empirical eigenfunction analysis, the the most efficient.method of compressing data themselves determine the form of the data; i.e., the most dense orthogonal functions which are used in the representation of a data set in the analysis. sense that the first n terms in the Applied to systematic measurements of expansion represent more of the data beach elevation, the eigenfunction variability than the first n terms of representation is a concise means of any other orthogonal expansion. representing beach profile variability. The (2) Since both the spatial and temporal eigenfunction modes can be used to distin eigenfunctions are orthogonal sets, each guish between variability on different time corresponding set (>.k,ek(x), ck(t) l scales. Though a large number of eigen may be regarded as representing a mode values are determined, Aubrey (1Q78) fou~d of variability which is uncorrelated that more than 99.75 per cent of the mean with any other mode. square value of his data set could be (3) The eigenfunction representation is accounted for by the_ three eigenfunctions convenient when using the method of associated with the three largest eigen minimum mean square error estimation. values. The second through fourth eigen The eigenfunctions provide a useful ~ values accounted for approximately 90 per priori method for reducing the number of cent of the variability in 4-year data sets variables in this estimation theory, and of beach profiles in southern California. also provide a means of removing the This conc.ise representation of beach profile noise (or less predictable part of the variability. is desirable when trying to datal from the data set. compare different locations, especially for data sets spanning long periods of time. 72
In the empirical eigenfunction same period, and eigenanalysis results technique, eigenvalues, Ak' provide intercompared. The magnitude of beach information on weights of the eigenfunc variability (normalized as described below) tions. Each eigenvalue gives the mean was withinl0%for the uniformly sampled and square value of the data (the variance if non-uniformly sampled cases, even when large the mean has been removed) accounted for by seasonal sampling discrepancies were the eigenfunctions. This provides a artificially induced. Seasonal beach convenient means for ranking eigenfunctions signals likewise were apparent in both and assessing the importance of each. This cases, with a clear seasonal signature also provides a convenient means of removing dominating for the non-uniform sampling as noise from the data, if it is assumed that a well. This numerical exercise illustrates function accounting for only a small part of the attraction of using eigenanalysis for the mean square value of the data is not an beach profile data, even for non-uniform important variable in the data. Eigenfunc sampling. Certain degrees of non-uniformity tions whose·eigenvalues are below a certain in sampling are not going to conform to this value can be neglected in estimation rule; clearly each season must be represented problems. These screening techniques are in the sampling, and sample intervals must discussed in detail by Preisendorfer et al. not exceed one or two months, on the average, ( 1981). if seasonal information is derived. If the Since some of the data considered in beach is undersampled, aliasing can.be a this study is non-uniformly sampled in both major problem. space and time, consideration must be given Eigenanalysis determines vectors such to the utility of this somewhat complex that the maximum variance of observed analysis technique for this data. The variables is described (as opposed to factor primary information derived from the analysis, which optimizes·the intercorrela profiles in this study is magnitude of beach tions of all variables, yielding a variability, and seasonality of that correlation-weighted analysis instead of a variability. This information will not be variance-weighted analysis; ·see for example as readily interpretable for a non-uniformly Joreskog et al., 1976). Since we are sampled profile sequence as for a uniformly interested in describing beach variability, sampled beach. However, if the frequency of eigenanalysis is an obvious Choice. As sampling is high compared· to the time scales defined in th~ equation 1, ~e ~ave examined, and the beach is observed for a represented the data by a complete set of long period of time~ then the statistics orthonormal functions (Ak,ck,ek). derived from eigenfunction analysis will The mean square value of the data is given approach those derived from uniform as: n sampling. In order to illustrate this MSV = k ~ l > ,. 73 / eigenfunctions are referred to as 'mean provides a more consistint basii for eigenfunctions,' since they retain comparison, even· though it invbl~Qs ~o~e·· information about the mean state of the definition or assessment of the' active beach. For each profile line, the beach. For our work, this definition has arithmetic time mean can be calculated, and been based on the degree of va~iabilitY of subtracted from the data prior to analysis, the beach at any point a 1ong it. After yielding a new data set h'{x,t), as follows: eigenfunctions have been· deri ~ed "for a· given beach, the first few are suimned·a·s in {1) h' (x,t) = h(x,t)- h(x) (3) {to account for a 1 ar'ge fraction o'f the where h represents the mean {in time) value beach variability), and the weighting for of the elevation at a point x. The eigen all points along the beach profile vectors of covariance matrices formed from ~ompared. The segment definin~ the active h'{x,t) are termed 'de-meaned' eigen beach is selected as that portion of the vectors. In this case, the sum of the profile which excludes those·poi~ts · eigenvalues represents the variance of the accounting for less than some fraction of data set, instead of the mean square value: the total variability along.the profile: In m applying this correction, we have taken care l: >< (4) k=l k not to include back shore area·s with dunes or seacliffs, since this sectibn 6f the beach This variance estimate provides information responds to different forcing than the on the variability in the data per spatial· foreshore. This was necessary, in sampling point and per time sample.· This particular, along the Cape 'Cod {MA) profiles. type of normalization is not always amenable RESULTS to comparison of one beach with another Four aspects of beaches and incident beach which has been sampled differently {in driving forces were·examined in this study. space and/or thro~gh time). Because of the For each location, a wave climate was normalization, and desire to compare results formulated from existing data; these wave· regardless of sampling strategy, a correction climates vary from quantitative at Torrey has been introduced into the analysis. The Pines {CAl to highly qualitative at active beach correction·is a factor Fairfield/Milford {CT) beaches. The · 2 multiplying the variance, a to adjust magnitude of beach variability for each ~ite' the results so they reflect only variance was quantified~ The degree of seasonality along the active part of the beach. If a of beach variability was examined. Finally, long segment of a beach profile comprises as an example of the utility of the method,· inactive parts of the backshore, the variance the effects of grain si~e on teach as defined in equation {4) would be artifici-· variability were quantified for the Cape Cod ally low. The empirical correction for {MAl site. active beach width minimizes this problem: WAVE CLIMATE. 2 - 2 Documentation of the driving forces is' 01 - 01 . w (5 )' an essential, but difficult, aspect of· where W = total length of profile/total formulating modelS of beach variability, and length of active beach. The new variance 74 in verifying or testing. these models. In CAPE COD, MA. situ measurements of wave behaviour is the 60 best way to document wave climate at this X time, although numerical models-of wave ~50 > growth, propagation, and shoaling show much a: "'UJ 1J SPECTRUM METHOD promise for the. future. Even then, local i:i 40 0 SMB METHOD ~ " SSMO measurements can provide information on the a: beach for a period of about five years HOLDEN BEACH , N C (Pawka et al., 1976; Aubrey, 1979). Four-times daily measurements of directional wave characteristics have documented the wave climate to a high degree. This information was used in previous studies to \~t~E. ·: : JFMAMJJASONO·.\tJ relate beach changes to driving forces (e.g., Aubrey et al., 1980). WAVE HEIGHT ==::J The wave measurements show the southern WAVE PERIOD ,,,.,,,,,,,,,,,,,,.,, California region to be swell-dominated t. I CT t----1 throughout the year. Locally-generated, higher frequency waves are more common in 160 10 the winter than summer, as local storms pass 140 e through. The major difference between 2 120 8 - !;: !!! summer and winter conditions is in the wave (!) 0 ~100 0 energy, rather than in the period. This in 6 ii: ~ turn affects the wave steepness, an ~eo ~ !l i!"' indicator of beach erosion and accretion, 1- 4 ~ ~60 according to some studies. z j ··~· Holden Beach, NC: Wave climate from ~40 Holden Beach was established from direct 2 measurements made along a fishing pier along :~~~~F~M~~A~~M~J~~-A¥L~S~+O~N~~D~~m~e~.: Holden Beach (Thompson, 1977) and from Littoral Environmental Observations (LEO) consisting of visual observations (Miller, 9) Wave climate at Holden Beach, .North 1982). The continuous-wire staff measure Carolina, derived from CERC·pressure. ments were made from February 1971 through sensor located off a pie.r along Holden February 1975 (with some periods of inactiv Beach (see Fig. 5). Summary is given in· ity), with 1024 second measurements taken terms of monthly averages of wave period every 4 hours (Fig. 9). The data show a and wave height. Source for data is seasona) ity in wave period (averaged over Thompson (1977). J monthly intervals), with a lower period generally from April through August. Wave mean yearly period is about 7.5 seconds. ·LEO height shows less of a seasonal periodicity. observations provide no additional informa As mentioned earlier, the wave field near tion than the wave staff measurements, other shore at Holden Beach is significantly than some indication of direction of wave affected by Frying Pan Shoals to the east, approach. so the nearshore wave climate is not directly Long Beach Island, NJ: Wave information reflecting the offshore wave climate. Mean available for this study site include a yearly significant wave height is about 0.6 m, nearby (35 km to the south) wave staff located on a pier in Atlantic City, SSMU data, and local visual beach observations •' __ I 76 from 1968-1974.. For the forty-one month ' ' period from April 1964 through December STEEL PIER, ATLANTIC CITY, NJ 1967, mean significant wave height is 0.81 m, 1962 19631------j and mean wave period is 8.2 seconds (Fig. 10). 1964f------1 Since the Steel Pier gauge at Atlantic City 19651------'------1 did not have directional capabilit_ies, the 1966!------j 19671------j WAVE HEIGHT ==:::J only directional information available near 19661------~-----j WAVE PERIOD .:J 19691------1 shore are the beach observations, which have .! lu 1------i 1970 coarse directional resolution. 1971 j Jones Beach, Long Island, NY: Wave '--J--'-F-L...M-'--A-'--M-'-J-'--J,...... ,A,-'-:S,-'-:O,-'-:-N,-'-:0:-' i nformati.on for .Jones Beach is _cqmpil ed from a varjety of diverse sources. Hindcast data 2.0 are presented in Panuzio (1968), as are 14.0 results from occasional wave gauging from 1950-1954 off Fire Island Inlet. Results 13.0 1.5 from the wave gauging yield an average height 12.0 of 0.4 m for the period of measurement, which was neither continuous nor representative of 11.0 1- the entire year. A surf observation programme. ~ 1.0 10.0 - from 1954-1957 yielded a probability,distribu "'J: 9.0 c* 0 tion for breaking waves in the area (Short ii: a. Beach LifebOat Station), indicating waves .... 6.0 "' :i 0.5 generally less than 1.25 metres. A CERC wave u "'iii ;;: 7.0 ;o gauge located at Steel Pier, Atlantic City, z "c;; New Jersey, was discussed in the previous 6.0 section; it is the closest CERC gaging 0 5.0 location'to.Jones Beach. Results from that gage may not be representative, because it fs 4.0 1ocated 160 kni to the south of Jones Beach. · L..L..J '-7-F.LM'-:-'-A!-'-:MJ,-1-JL...LJL..J...A!-'-:S!-'-:O!-'-:N':-'-;0~-'-::m~eo'-n....L 3·0 Beach Erosion Programme surf'observations were made along the beach from 1968 to 1974 along Jones Beach. Although poorly sampled 10) Wave climate at Atlantic City, New through the year (JulY th'rough September show Jersey, derived from a CERC wave staff almost·no·observations), they provide an located off Steel Pier, in Atlantic City indic'ation of surf activity. The mean wave (south of Long Beach Island). Summ·ary is period was 6.5 seconds, and mean-significant given in terms of monthly ·averages of wave height was 0.8 m, with some variation in' wave period and wave height. Source for these numbers month-by-month (Fig •. 11). _ cia.ta is Thompson (1977)." Waves genera 1iy appr·oach the beach from the ·; southeast. · · · wave observation's are not available, and Fai rfiel d/Mi lford Beaches·, CT: There is there have been no long-term pressure sensor no quantitative information about the wave field off Fairfield/Milford Beaches~ Visual 77 deployments within the western. part of Long period, were not available for detailed Island Sound. Waves incid~nt on these analys{s; only a summary of results could be beaches are all locally generated, with found. The summary indicates that over the energetic periods limited to about six peri~d of study, wave height was less than seconds or less. Because of a restricted 1.5 m98%of the time (in 8 m water depth). fetch, wave height is similarly limited. Ninety-two per cent of the time significant This area, then, is dominated by locally wave height was less than one metre (Raytheon generated high-frequency wind waves, which Corporation, 1975). Visual observations were are significantly modified by offshore taken from January 1968 through December bathymetry and shoreline irregularities (such 1975, with an average of 22 visual as Charles Island Bar). observations per month. Yearly mean breaker height was approximately 0.5 metres, with a JONES BEACH, LONG ISLAND, NY mean period of 8.6 seconds. Mean wave Olrecllan H•l<~ht ~rlod • lm) {oecl direction was just east of south. CERC measurements were made from 23 January 1964 through 18 April 1975 by pressure gauge. Mean annual significant wave .height (in 19.2 m water depth) was 0. 75 m, with a mean per.i od of about 7 seconds (Fig. 12). 19741--~-- Cape Cod, MA: Wave data for this section of shoreline consist of two hindcast J F M A M A S 0 N D techniques, SSMO visual wave observations, Mean helqht lml 0 72 080 0.90 077 0.83 Meanpoorlod(ol 6.8 6,7 6.4 6.1 8.1 !1.3 and in-situ gaugiM· The.first three of these have already been discussed in a 11) Wave climate for Jones Beach, Long previous section (Fig. 8). LEO data,.taken Island, New York. Source for data are in the format described by Balsi)lie (1975}, Beach Erosion Program Visual Wave were taken near the northern and southern Observations from 1968-1974. Both yearly limits of the study area. These were not mean height and period are given, as well used to compile mean periods and height.s •. as monthly means. Coverage of the. time The gauging data consists of some pressure period is shown in main graph, sensor data obtained off the south end of the illustrating lack of observations during study area by CERC, but the results are n.ot .. the summers. generally available, and so were not used in this study. The final set of observations. Misquamicut Beach, RI: Wave information consist of directional wave estimates made by consists of visual observations taken as part the author from 1980 to present; using a of the BEP programme, pressure. sensor two-axis electromagnetic current sensor with measurements taken at nearby. Charlestown a pressure gauge (Aubrey, 1980). Although Inlet by Raytheon Corporation, and CERC the data. from this study have not been pressure gauge measurements made at Buzzards compile9,in a manner similar to other. .• Bay Tower close to the study site. The locations, mea!l wave periods range from about Raytheon data, collected over a one-year 8 to 14 second:;; with wave,hei.g~ts gen~.raJJy ,,, 78 the da~a. This value was then normalized to .BUZZARDS BAY TOWER, MASSACHUSETTS account for the active beach, and to obtain an annual beach variability. Results for WAVE HEIGHT c:=::J WAVE PERIOD k·"···,•c·l each profile line at each of the seven sites tier were then averaged to obtain a mean variabi lity for each site (Fig. 13). The three open 2.0 ANNUAL BEACH VARIABILITY 13.0 DE-MEANED EIGENFUNCTIONS TORREY PINES, o8sl 12 0 CA 1.5 HOLDEN BEACH, 11.0 NC ~g 10.0: LONG ~EJACH ISLAND,IL------,------2.__,561 > :1: 5 i&j 1.0 9.0 Q 2 4 6 "':1: ~g~~ 1s~~~~~NY -~L------·_.1 0: "'> "'0. 8.0 FAIRFIELD-MILFoRo, Do 193 ; CONN. . > z .. 7.0 "~ 0.5 z 6.0 CAPE COO, 3.28 ;;;"' MASS 50 0 0.5 1.0 15 2.0 2.5 3.0 VARIANCE I YEAR (m2) O.O L-JL-L-FL-L-ML-L-A....U.M..I...":J"'--'J"'-7A-'--:"S-'--:"0"-':-N '--.':'-0'--'-':-"-•·a 13) Beach variability at each of the seven 12) Wave climate at Buzzards Bay Tower, study sites, where the variability is Massachusetts, derived from a CERC normalized as in equation 5. pressure sensor located in 63 m water depth in the middle of Buzzards Bay. ocean beaches showed the greatest variability Summary is given in terms of monthly (Cape Cod, MA, Long Beach Island, NJ, and averages of wave period and wave '·height. Jones Beach, NY), with an average annual Source for data is Thompson (1977). variability ·of 2.76 m2• The two most closely'located beaches, Long Beach Island of the order of 1 m. The statistics for and Jones Beach, which are separated by only waves at this location are currently being 100 km, have variances of 2.56 and 2.46 m2, generated. This study area has the most respectively, within 4% of each other, as one energetic.wave climate of the seven sites might expect, given similar grain sizes and ex ami ned. similar wave climates. Torrey Pines (CA) and BEACH VARIABILITY Misquamicut Beach (RI) have lowe~ variances Using the profiles from each of the study by a factor of four, and represent partially areas, eigenfunctions were.calculated after sheltered coastal reaches.' Smallest variance removing the mean profile from each profile is at Fairfield/Milford Beaches, which are (yielding de-meaned eigenfunctions). The sum completely sheltered from open ocean wave of the eigerivalues for each profile· 1 ne was conditions, and expose~ only tb locally determined. to repres'ent the variabil ty in generated seas. 79 Analysis of beach variance can provide ebb delta influence on wave refraction, sand insight into beach processes on a more local bypassing across inlets {a periodic event scale as well. Two examples are given here. for some types of bypassing), dredging and Holden Beach {NC) is a continuous barrier dredge spoil disposal. Beach variability island, bounded to the west by Shallotte along the remainder of the barrier island is Inlet, and to the east by Lockwoods Folly fairly constant, reflecting roughly uniform Inlet. Along this beach are distributed 21 distribution of driving forces alongshore. profile lines, with line one to the east, The second example is from Cape Cod and line 21 to the west. Beach variability {MA), which has an alongshore gradient in shows a strong longshore trend {Fig. 14), median grain size, decreasing in size from north to south {Fig. 15). Beach variability HOLDEN BEACH, NC also has a north-south gradient, with greater variance in the north than in the south, mirroring the grain size trend. Wave refractionperformed along Cape Cod show no systematic longshore variation in energy or 2.0 w energy flux {Isaji et al., 1976), suggesting u z that a variable driving force is not ~" 1.5 responsible for this trend in beach :I: ~ 1.0 w variability. Tidal range shows a very CD 0.5 slight longshore gradient, but incomplete WEST data does not allow us to rigorously assess 21 20 19 IS 17 16 15 14 13 12 II 10 9 8 7 6 5 4 3 2 I its control over beach variability. The STATION NUMBER influence of grain size on beach-variability 14) Beach variability as defined by equation has been suggested before; this example 5, a_long the barrier island of Holden shows the importance of including this Beach. Variability is much higher near parameter in modelling studies. the active inlets of both ends of the SEASONAL BEACH VARIABILITY barrier, reflecting inlet processes A certain portion of the annual beach {including sand bypassing, dredging/ variability can be attributed to a seasonal spoil disposal, and wave/current cycle in beach change. This seasonality has interactions). long been recognized for u.s. west coast beaches {e.g., Shepard, 1950), but has been with the greatest variance along profile a matter of debate along the U.S. east lines 1-3 and 18-21, which are all within coast, although investigators have shown 2.5 km of the two bounding inlets. This some seasonality to exist {e.g., Everts and greater beach variability is not related to Czerniak, 1977; Goldsmith, Farrell, and grain size, or to longshore wave variability Goldsmith, 1974; Dewall, 1977 and 1979; and {according to wave refraction analysis Everts et al., 1980). Eigenfunctions will discussed in Miller, 1982), except that show seasonal trends if they are energetic · scattering behaviour associated with the ebb enough, so eigenanalysis has also used to tide deltas of the inlets. The variability document seasonality of beach r~sponse is probably due to inlet processes, including {Aubrey, 1979). Computer simulations of the ,80 ,. . ;_ ... beaches where there is an almost total CAPE COD, MA absence of seasonal signature. Weak . VAR' J seasonality can be due to a number of QL factors, some of which are related to tne· n• • _1_1 physical regime, some of which are due to inadequate sampling.· Structures, ·such as 02 groins and jetties, can affect the response of a beach to seasonality in wave climate. QL This is likely a contributing factor in the Long Beach'Island (NJ) case. Offshore 04 TEMPORAL EIGENFUNCTIONS SOUTH RANGE 0:w 0005 :::E- :::> z z_!2_ 0 i= ~06 (/) QL Q .40 , ~ .. ..;t 30 09 ~ .20 !L ·2 0 lQ_ 30 "· I I I I 1 I! I I I I I I I I I I I I I I I I I I I I I I I I! I I I I I I I 1 I I! 1 I I I I I!, I I I I I I I ,I 1.0 0.5 J A 0 0 F A J A 0 .D F A J A 0 0 F A J A 0 0 f A J A 0 0 F A J A 0 0 1972 • 1973 1974 1975 1976 1977 (m2/YR) cf -UNITS 16) Temporal beach eigenfunctions for Torrey 15) Beach variability along Cape·Cod beaches Pines Beach, Cal-ifornia. Second beach as a funtti'on of .grain size •. Independent eigenfunction shows distinct seasonal studies· show the- wav'e climate is trend, ·and accounts for nearly 80% of the consiste~t along~this l~ngth of beachi variability in the data set. so g~ain size ~ppears ·to be a ·dominant factor·in explainin~ the increasing bathymetry may also limit seasonal response; beach variability to the north. this is a contributing factor to Holden Beach, where Frying Pan Shoals severely sensitivity of -eigenanalysis to noise level modifies the incident wave climate. is described briefly .in Aubrey ( 1978 ).; Seasonality is also absent where the wave Strong-seasonal signals are found in climate is not seasonal or only weakly so; tempo raT ei genfuncti'ons from Torrey Pines this is the case in restricted fetch regions (CAl and Gap·e God (MA) (Figs. 16 and ·17):. such as Fairfield/Milford Beaches. Seasonalfty was found·over·some profile Poor sampling-can-also affect the lines along·the reinainder.of\the,beaches; seasonal beach signature •.The six U.S. east with the ·exception ~f-Fatrfield/Milford coast beaches have a pec~liar characteristic 81 of poor sampling in the summer months, t'he highest beach variability and the most particularly July. This type of under energetic: wave 'climate. Cape Cod has both sampling in the summer can lead to poor the high incident wave energy and highest· definition· of seasonal cycles. beach variability. Long Beach Island and Jones Beach have the next most energetic SPATIAL EIGENFUNCTIONS wave·climate and beach variability, with PROFILE LINE t 4 DATA NOT DEMEANED their beach variabilities within 4% of each 0.6--,--·------,7. I other. This similarity in beach response is 0. 4 4. 7 w ~ 0 ' /-----...... y:,/ \ encouraging, since the two sites are exposed ,. \ / ...._ \ 0.2 I I -, 2.4 \ \ to nearly the same wave climate. Torrey 5(L \ / / ~ \ / ' / "'--''. Pines Beach is the next most exposed 0.0 \' / / 8 :{ / N /. / H location; with the next highest wave _,..,../ '~ ...... ~---~/---- -2.4 :1. -0.2 climate, followed closely by Misquamicut "D "'z --I -0.4 ----2 -4.7 -·-·-3 Beach. These two have similar beach -0.6 -7. 1 variabilities, but are a factor of four less 120 130 I 40 15B 163 I 70 180 190 2BB 210 220 than the variability at the more open coast DISTANCE (m) beaches. Holden Beach is sheltered in large TEMPORAL EIGENFUNCTIONS part by Frying Pan Shoals to the east, so PROFILE LINE i 4 OAT A NOT DEMEANED its wave climate is much less than that along the ·open ocean beaches close by. Its 0 0.0 variability is consequently much lower than w "' 0 "' "] ~ ;:' -0.5 that at more energetic beaches. The most 'j (L sheltered of all beaches, with 'the lowest 4 " @ 0]0.0 8 N ~ wave energy, is the Fairfield/Milford area, ~ -0.5 exposed only to locally generated wind ii Dz ... ~ waves~ Its beach variability is an ·order of "' _0.2 ' magnitude lower than that at open coast -0.3 . . beaches, and a factor of four lower than the "l--=1970 1971 1972 1973 1974 1975 1976 YEAR partly sheltered Torrey Pines and Misquamicut Beach areas. 17) Seasonal beach changes along Cape Cod, The relationship between beach Massachusetts, beaches. The second variability and energy has been shown before temporal eigenfunction displays the by Aubrey et al. (1980) for a single bea~h. seasonal response to a seasonal wave It has also been discussed elsewh•re for climate. It' accounts for approximately specific beaches, but not quantitatively 75% of beach variability. compared at different sites. The unfortu nate fact ·remains that the wave climate at DISCUSSION most coastal sites is so. poorly known that The results point out a close relation even an empirical relationship between wave ship between the rigorously defined beach climate ·(suitably represented by wave variability and the poorly defined wave eigenfunctions, for instance) ~nd beach climate. Exposed open ocean beaches have change cannot be made at this time. The 82 wave hindcast models now in existence may Examples of inlet influ~nce include modific give us better data sets in the near future ation of the nearshore wave field because of so we can improve on the qualitative wave refraction around the ebb tide delta statements made in this paper (specifically (due both to bottom topography and wave the WES model should be available in the current interactions--steepening and time span of a year or so, providing us with breaking), longshore sand bypassing episodes data coincident with the profiling efforts). along the ebb tide delta imparting large Seasonal beach changes, which respond to signatures to beach change, and dredging/ seasonal patterns in the driving forces, spoil disposal near the inlet channels. have been documented before in many places. This type of longshore dependence of beach This study shows most beaches have a seasonal variance may be reflected in the biological signature unless prevented by one of several communities inhabiting these different factors. The fetch and/or exposure of.a areas, although these effects may be beach.site may be such that the seasonality difficult to see in light of expected in weather patterns may not be reflected in differences in response to different the wave climate. Examples are Fairfield/ physical and chemical conditions due to Milford Beaches where the restricted fetch inlet proximity. limits the size of waves and hence the Another observation clarified by seasonal differences in wave character eigenanalysis is the coincidence of beach istics. An example of exposure limiting variability on grain size, the example here wave seasonality is Holden Beach (NC), wh~re being Cape Cod beaches. Grain size decrease Frying Pan Shoals limits the size of waves from north to south is mirrored by decreasing reaching the barrier island. Large waves beach variability from north to south, will break one or more times on the shoal, despite no apparent longshore gradients in limiting the energy reaching the shore energy flux incident o'n the beach. Grain during large northeast storms which inflict size responds to source proximity and much of the beach erosion on the more longshore sorting of material; this exposed shoreline bounding the study site to difference in grain size is reflected in the north. markedly different beach slopes alongshore. Eigenfunction analysis has graphically The reason for the higher beach variability shown two beach relationships which might in coarser grained beaches is not apparent not otherwise be.apparent.during routine at this time. Possibilities include the analysis of profile ~ata. At Holden Beach influence of greater pore space in coarser (NC), beach variability is greater near the material, increasing permeability, and inlets bounding the barrier island, than transmitting greater fluid pressure to each near the middle of the island. Magnitude of grain of sand. This would allow the sand to beach variability near the centre.of island respond much more quickly to wave activity probably represents the part of the beach than a less permeable sand. This effect has variability driven by the incident wave· not been quantified. field, while the outer parts of the barrier are more affected by inlet behaviour •. 83 CONCLUSIONS only total variability. ·not cross-shore Eigenanalysis has quantified spatial structure. These profile shape relationships between beach change and factors are discussed in a paper presently driving forces along seven beaches with in preparation. ma'rkedly different wave climates. spanning a Patterns of beach variability along a variety of grain sizes degree of and single beach provide insight into some structural shoreline modification. relationships which need to be explained in Neglecting long-term beach trends. open more dynamical terms. Along a barrier island coast beaches have the greatest variability bounded by two tidal inlets (Holden Beach. on an annual basis. while partially NC). annual beach variability was greater sheltered coasts are lower in variability by within 2.5 km of the inlets than in the about a factor of four. Beaches nearly middle of the barrier. This pattern completely sheltered from open ocean wave reflects the influence of the inlet on beach conditions (restricted to short. local processes. particularly through modification fetches) have the least variability. down by of the incident wave field. sand bypassing an order of magnitude from open ocean episodes. and dredging/spoil disposal beaches. A gradation from open coast to operations. Beach variability along the completely sheltered beaches exist. only a middle of the barrier island was nearly sample of which were analyzed in this constant. suggesting that this segment was study. Sheltering can·result from offshore undisturbed by inlet behaviour. islands (Torrey Pines. CAl. convoluted Along a beach with a sharp longshore shorelines (Misquamicut Beach. RI). or gradient in mean grain size (Cape Cod. MAl. unusual bathymetry (Holden Beach. NC) such the magnitude of beach variability increased as shoals. Although the relationship with increasing grain size. even though the between wave exposure and beach change is wave·climate showed no correlative pattern. qualitative. improvement in predictive This data set suggests the possibility of capability can be expected once improved testing more dynamical models of beach wave hindcasting procedures provide us with change as a function of grain size. realistic nearshore wave climates for the Eigenanalysis has proved to be a useful periods coincident with the beach studies. tool in synthesizing beach profile data from Although the profile data examined in this a number of different locations. exposed to study was of variable quality (in terms of different forcing conditions. and sampled both spatial and temporal uniformity). the with highly variable uniformity. The major inadequacy of the data set was in the technique allows some quantitative knowledge of wave climate. which varied from comparison between beach behaviour at well-known (Torrey Pines. CA) to poorly different locations. which has not been known (Fairfield/Milford Beaches. CT). commonly done in the past. Whether or not · Beach variability found in this study is this particular analysis is adopted as a not easily expressed in terms of a single routine procedure for examining beach morphological model (such as Short and profile data. scientists and ~ngineers must Wright. 1983). because this study addresses consider how best to i ntercompare results from one beach with results from another 84 beach, rather than concentrate on a single 3264-3276. data set. Insight into dynamics of beach Balsillie JH (1975) Sur~ observations and longshore current prediction. U.S. Army change, and guidance to much needed C.E.R.C., Ft. Belvoir, VA, Tech. Memo. 58. modelling of the process, will occur only Bowman D (1981) Efficiency of when we can synthesize existing data, and eigenfunction for discriminant analysis of analyze future data in a manner consistent subaerial nontidal beach profiles. Marine Geology, v. 39, p. 243-258. I> with the need for intercomparison. ACKNOWLEDGEMENTS Davies JLD (1964) A morphogenic approach to world shorelines. Zeitschrift fur Much of the work performed for this geomorphologie, p. 127-142. study was funded through the following Dewall AE, Pritchett PC and Galvin CJ, Jr agencies: U.S. Army Coastal Engineering (1977) Beach changes caused by the Atlantic Research Center in contract to the Scripps coast storm of 17 December 1970. u.s. Army C.E.R.C. Technical Report 77-1, Ft. Belvoir, Institution of Oceanography (D.L. Inman, VA. Principal Investigator), and to Science Dewall AE (1979) Beach changes at Applications, Inc. at Raleigh, NC (Martin C. Westhampton Beach, New York, 1962-1973. Miller, Principal Investigator); and NOAA U.S. Army C.E.R.C. Misc. Report 79-5, Ft. Belvoir, VA. Office of Sea Grant number NASO-AA-D-00077 to the Woods Hole Oceanographic Institution Everts CH and Czerniak MT (1977) Spatial and temporal changes in New Jersey for the Nearshore Sediment Transport Study. beaches. Proceedings of Coastal Sediments Martin c. Miller, J. Karpen, R. Morton, and '77, ASCE Conf., p. 444-459. F. Bohlen contributed to the study of the Everts CH, Dewall AE and Czerniak MT east coast beaches. R. Gorski drafted many (1980) Beach and inlet changes at Ludlum of the figures. Woods Hole Oceanographic Beach, New Jersey. u.s. Army C.E.R.C. Misc. Report 80-3, Ft. Belvoir, VA. Institution Contribution number 5324. REFERENCES Goldsmith V, Farrell SC and Goldsmith YE (1974) Shoreface morphology study, the Aubrey DG (1978) Statistical and south end of Long Beach Island, Little Beach dynamical prediction of sand beaches. Ph.D. Island, and the north end of Brigantine thesis, Scripps Inst. of Oceanography, U.C. Island. Dames and Moore, Inc., Cranford, NJ. San Diego, 194 pp. Helle JR (1958) Surf statistics for the Aubrey DG (1979) Seasonal patterns of coasts of the United States. Beach Erosion onshore/offshore sediment movement, JGR, v. Board Tech. Memo No. 108, U.S. Army Corps of 84, p. 6347-6354. Engr's., 22 pp. plus appendices. Aubrey DG (1980) Our dynamic coast Isaji T, Cornillon P and Spaulding M lines. Oceanus, v. 23, no. 4, p. 4-13. (1976) Nearshore wave climate for the outer Cape Cod shore, Part I: Wave Refraction. Aubrey DG (1981) Field evaluation of Sea Department of Ocean Engineering, U.R.I., Data directional wave gage, (model 635-9). Kingston, RI. Woods Hole Oceanographic Institution Technical Report, WHOI-81-28, Joreskog KC, Klovan JE and Reyment RA 52 pp. (1976) Geological Factor Analysis, Elsevier Scientif1c Publish1ng Company, Amsterdam, Aubrey DG, Inman DL and Nordstrom CE 178 pp. (1976) Beach profiles·at Torrey Pines, California. Proceedings of the 15th Int. Miller MC, Aubrey DG and Karpen J (1980) Conf. on Coastal Engineering, Amer. Soc. Beach changes at Long Beach Island, New Civil Engr., p. 1297-1311. · Jersey, 1962-1973. u.s. Army C.E.R.C. Misc. Report No. 80-9, Ft. Belvoir, VA, 289 pp. Aubrey ·DG; Inman DL and Winant CD (1980) The statistical prediction of beach changes Mi 11 er lv!C ( 1982) Beach changes at Ho 1den in southern California. JGR, v. 85, p. Beach, North Carol ina, 1970-1974. Submitted ~,, 85 to the U.S. Army C.E.R.C., Ft. Belovir, VA. Seymour RJ and Sessions MH (1976) Miller MC and Aubrey DG (1982) Beach Regional ~etwork for coastal engineering changes on eastern Cape Cod, Massachusetts, data, Proc. 15th Coastal Eng. Conf., Amer. from Newcomb Hollow to Nauset Inlet, Soc. Civil Eng., p. 60-71. 1970-1974. Submitted to U.S. ArmY C.E.R.C., Ft. Belvoir, VA, 1 volume. Seymour RJ (1979) Measuring the nearshore wave climate, California Morton RW, Bohlen WF and Aubrey DG experience. Ocean Wave Climate, Marshall D. (1982a) Beach changes at Misquamicut Beach, Earle and Alexander Malahoff, eds., Marine Rhode Island, 1962-1973. Submitted to u.s. Science, v. 8, Plenum Press, NY, p. 317-327. Army C.E.R.C., Ft. Belvoir, VA, 1 volume. Shepard FP (1950) Beach cycles in Morton RW,Bohlen WF and Aubrey OG southern California. U.S. Army Beach (1982b) Beach changes at Milford and Erosion Board Tech. Memo. 20, 26 pp. Fairfield Beaches, Connecticut, 1962-1971. Submitted to U.S. Army C.E.R.C., Ft. .Short AD and Wright LD (1983) Beach Belvoir, VA, 1 volume. systems in high, moderate and low wave environments. This volume. Morton RW Bohlen WF and Aubrey DG (1982c) Beach changes at Jones Beach, Long Steele JH, Munro ALS and Giese GS (1970) Island, NY, 1962-1974. Submitted to U.S. Environmental factors controlling the Army C.E.R.C., Ft. Belvoir, VA, 2 volumes. epipsammic flora on beach and sublittoral sands. J. Marine Biol. Assoc., v. 50, p. Nordstrom CE and Inman DL (1975) Sand 907-918. level changes on Torrey Pines Beach, California, u·.s. ArmY C.E.R.C. Misc. Paper Thompson EF (1977) Wave climate at No. 11-75,,166 pp. selected locations along U.S. coasts. U.S. Army Coastal Engineering Research Center Panuzio FL (1968) The Atlantic coast of Technical Report no. 77-1, Fort Belvoir, VA, Long Island. 11th Conf. of Coastal 364 pp. Engineering, p. 1222-1241. Parr T, Diener D and Lacy S (1978) Effects of beach replenishment on the nearshore sand fauna at Imperial Beach, California, U.S. Army C.E.R.C. Misc. Report No. 78-4, 125 pp. Pawka SS, Inman DL, Lowe RL and Holmes LC (1976) Wave climate at Torrey Pines Beach, California, U.S. Army C.E.R.C. Tech Paper No. 76-5, 372 pp. Preisendorfer RW, Zwiers FW and Barnett TP (1981) Foundations of principal component selection rules. Scripps Institution of Oceanography, SIO Ret. Series 81-4, La Jolla, CA, 192 pp. Ramsey MD and Galvin CJ (1977) Site analysis of sand samples from southern New Jersey beaches. u.s. Army C.E.R.C. Misc. Report 77-3, Ft. Belvoir, VA, 54 pp. Raytheon Corporation (1975) Charlestown hydrographic study, April 1974-1975. Raytheon Corporation, Oceanographic and Environmental Sciences, Portsmouth, Rhode Island. · •, Resio D, Hayden B, Dolan Rand Vincent L (1974) Systematic variations in offshore bathymetry, Univ. of VA Technical Report No. 9, 28 pp. .