Shoreline variability via empirical orthogonal function analysis: Part II relationship to nearshore conditions

Coastal Engineering 54 (2007) 133 – 150 www.elsevier.com/locate/coastaleng

Shoreline variability via empirical orthogonal function analysis: Part II relationship to nearshore conditions Jon K. Miller a,⁎, Robert G. Dean b a

b

Davidson Laboratory, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ 07030, United States Department of Civil and Coastal Engineering, University of Florida, P.O. Box 116590, Gainesville, FL 32611-6590, United States Received 30 January 2006; received in revised form 25 August 2006; accepted 29 August 2006 Available online 2 November 2006

Abstract The method of empirical orthogonal function (EOF) or principal component analysis (PCA) was used to investigate the spatial and temporal variability of shoreline data sets from Duck, North Carolina, the Gold Coast, Australia, and the United States Pacific Northwest. In the present work, an attempt is made to relate the individual modes of shoreline variability identified by the EOF analyses to select parameterizations of the nearshore environment. The parameters considered include the wave energy (E ), the cross-shore and longshore wave energy fluxes (Fx and Fy), the wave steepness (Ho/Lo), the non-dimensional fall velocity parameter (Ω), the profile parameter (P), the surf-similarity parameter (ζ), and a surfzone Froude number (Fr). Correlation analyses were used to evaluate the linear relationship between each of these parameters and the temporal eigenfunctions, ck(t), associated with individual modes of shoreline change. Typically, strong correlations were observed between longshore uniform modes and the monthly means of several of the nearshore parameters. © 2006 Elsevier B.V. All rights reserved. Keywords: Longshore variability; Empirical orthogonal functions; Principal component analysis; Correlation analysis; Duck; Gold Coast; Nearshore

1. Introduction Empirical orthogonal function (EOF) or principal component analysis (PCA) is a powerful data analysis technique that can be used to identify and extract the dominant modes of variability from consistently sampled data sets. The historical development of the EOF method, particularly as it has been applied to coastal studies is discussed in detail in Miller and Dean (2006-this issue), hereafter referred to as MD06. Although equally adept at identifying patterns of longshore variability in a data set, the majority of coastal applications of EOFs have focused on cross-shore or profile variability. Clarke and Eliot (1982) and Clarke et al. (1984) were among the first coastal scientists to utilize EOFs to evaluate longshore variability in their studies on several Australian beaches. MD06 used EOFs in a similar manner to extract the dominant modes of shoreline

⁎ Corresponding author. E-mail address: [email protected] (J.K. Miller). 0378-3839/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2006.08.014

variability from data sets collected at Duck, North Carolina and near the Washington–Oregon border in the United States, and at the Gold Coast in Australia. This paper extends the analysis presented in MD06, by attempting to relate the individual modes of shoreline change identified by the EOF analysis to parameters which are frequently used to characterize the nearshore environment. The results presented in MD06 showed, nearly 95% of the total shoreline variability at each of the sites was contained within the first four eigenmodes (with the exception of two derived data sets). Each of these modes consists of spatial and temporal components which describe characteristic patterns of longshore variability and an associated chronology. Assuming these patterns represent physical modes of shoreline change (which is not implicit to the EOF procedure), the chronology described by the temporal eigenfunctions should be related to the local nearshore conditions. The objective of this analysis is to identify potential linear relationships by calculating the correlation and lagged correlation between time series of several common nearshore parameters and the temporal eigenfunctions. A total of eight parameters were

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considered here: the wave energy (E ), the cross-shore and longshore wave energy fluxes (Fx and Fy), the wave steepness (Ho/Lo), the fall velocity parameter (Ω), the profile parameter (P), the surf-similarity parameter (ζ), and a surfzone Froude number (Fr). The data sets used in this analysis represent three vastly different coastlines where a combination of high-quality shoreline data and detailed wave information (directional in most cases) is readily available. The first site is located at Duck, North Carolina where excellent sets of bathymetric and hydrodynamic data have been collected over the past 20 years by the U.S. Army Corps of Engineers (USACOE). The second site is located in the U.S. Pacific Northwest along the border between the states of Washington and Oregon. Two directional offshore buoys provide excellent wave information, while high-quality shoreline measurements collected as a part of the Southwest Washington Coastal Erosion Study complete the data set. The third site is located along the Gold Coast in eastern Australia, where two buoys provide detailed wave information, and daily shoreline measurements are extracted from an ARGUS (Holman et al., 1993) video monitoring station. Each site represents a different coastal environment, as the hydrodynamic and morphologic conditions vary significantly between the three sites. 2. Background The EOF technique is described in detail in the Appendix to MD06; therefore it is not described here. The interested reader is referred to that work, or any one of the useful texts which describe EOF methodology, such as Davis (1986) or Jackson (1991), for more information. While no physical assumptions are made during the development of EOF theory, the derived eigenfunctions although purely statistical in nature, often have physical analogs. The classic bar/berm function identified by Winant et al. (1975) is a prime example. Here it is assumed that at least some of the derived modes represent physical shoreline changes. The hypothesis being tested is that for those modes that do have a physical analog, it should be possible to relate the temporal eigenfunctions to the local conditions through some of the parameters commonly used to characterize the nearshore environment. Although numerous such parameters exist, eight are considered here including the wave energy (E ), the crossshore and longshore wave energy flux (Fx and Fy), the wave steepness (Ho/Lo), the fall velocity parameter (Ω), the profile parameter (P), the surf-similarity parameter (ζ), and a surfzone Froude number (Fr). 2.1. Selected nearshore parameterizations Beaches are complex, which makes any attempt to parameterize the nearshore environment extremely difficult. Even at an intensively studied shoreline such as Duck, data collection limitations combined with an incomplete understanding of the detailed physics in the surfzone, makes understanding and describing this dynamic environment extremely challenging. At a minimum, to adequately describe the nearshore environment some knowledge of the hydrodynamic, morphological, and se-

dimentary characteristics is required. Fortunately, parameters descriptive of these characteristics can be calculated utilizing readily available data at all three sites. Here, the hydrodynamic environment is characterized by wave parameters representing the deep-water (Ho, T, and θo) and breaking wave conditions (Hb, T, and θb). Relevant morphologic and sedimentary characteristics are provided by the nearshore beach slope m, the median sediment diameter d50, and the sediment settling velocity ws. Several dimensional and non-dimensional combinations of these core parameters which are frequently used to characterize the nearshore environment are described below. One of the most obvious arbiters of shoreline change in the coastal environment is the local wave energy. During major storms or winter conditions when the waves reach their maximum, the shoreline would be expected to erode, while accretion should be more likely when calm conditions prevail and wave energy is at a minimum. The wave energy at the edge of the surfzone is given by 1 E ¼ qgHb2 8

ð1Þ

where ρ is the density of water, g is gravity, and Hb is the local breaking wave height. Related to the wave energy is the wave energy flux, F, which describes the intensity or rate at which the energy is supplied to the surfzone. Unlike the wave energy, the wave energy flux is a vector quantity which has both a crossshore and longshore component given by Fx ¼ ECg coshb

ð2Þ

Fy ¼ ECg sinhb

ð3Þ pffiffiffiffiffiffiffi respectively, where Cg is the wave group velocity (¼ ghb using the shallow water approximation) and θb is the breaking wave angle. Although the local wave energy and wave energy flux provide important information about the nearshore conditions, neither takes into account important factors such as wave period, beach slope, or sediment characteristics. One of the simplest, yet most useful parameters which incorporates the wave period is the deep-water wave steepness, Ho/Lo. As early as the 1930s it was recognized that steeper waves typically experienced during storms resulted in beach erosion, while mild conditions, particularly long period swell events, were conducive to beach accretion. A related parameter which is also frequently used to characterize the nearshore environment is the non-dimensional fall velocity parameter, Ω (Gourlay, 1968; Dean, 1973), given by X¼

Hb ws T

ð4Þ

Like the wave steepness, the non-dimensional fall velocity parameter involves a ratio of the wave height to the wave length (through the wave period, T); however it also incorporates a measure of the sediment properties through the inclusion of the fall velocity ws. Physically, Ω is a measure of the ratio of the amount of time a particle with a settling velocity ws remains suspended relative to the wave period, T, when acted upon by a

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wave of height Hb. The basic assumption is that if the particle settles out during the first half of the wave period the net particle displacement will be onshore, consistent with the shoreward directed wave orbital velocities during the initial phase of the wave, while if the particle remains in suspension for longer than half the wave period, the net displacement will be offshore. Kraus et al. (1991) showed that Ω could also be related to the wave energy dissipation within the surfzone, and suggested an alternate physical interpretation, where above some critical value of Ω the sediment is suspended and transported seaward by the near bottom return flow, while below this value wave asymmetry moves the sediment onshore as bedload. Another parameter involving the sediment fall velocity, which has proven to be useful in characterizing the surfzone (particularly in determining the presence of bars), is the socalled surfzone Froude number ws Fr ¼ pffiffiffiffiffiffiffiffi gHb

ð5Þ

Here Hb is related to an upward suspending force, while ws represents a downward settling flux. While Froude numbers are typically thought of in terms of force ratios, an alternate interpretation of Eq. (5) can be made by considering that the bottom term is related to the shallow water phase or group velocity. Therefore Eq. (5) also represents the ratio of the particle settling velocity to the shallow water group or phase speed. Kraus et al. (1991) presented two derivations where the Froude number was shown to be related to both the wave energy dissipation in the surfzone, and the power per unit volume expended by the waves via the bottom shear stress on suspending the sediment. One of the disadvantages of using the surfzone Froude number to characterize the nearshore environment is that while it incorporates measures of both the wave and sediment properties, it does not consider the wave period. The profile parameter, P, developed by Dalrymple (1992) is similar to the surfzone Froude number, in that it has exhibited the ability to distinguish between barred and non-barred profiles; however unlike the Froude number, the profile parameter is a function of the sediment fall velocity as well as both the wave height and period. The profile parameter is defined as P¼

gHo w3s T

ð6Þ

Although originally derived based on the empirical relationships between Ho/Lo and (πws /gT )3/2 and Ho /Lo and (Ho /wsT )3 presented in Kraus and Larson (1988) and Larson and Kraus (1989), the profile parameter can also be shown to be related to the previously defined fall velocity parameter and the surfzone Froude number through the relationship, P = F r− 2Ω. Although derived on the basis of laboratory data, subsequent studies have confirmed the ability of the profile parameter to characterize field data sets as well (Kraus and Mason, 1993). Each of the aforementioned parameters has proven useful in characterizing the nearshore environment; however perhaps none are considered as robust as the surf similarity parameter ζ.

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First introduced by Iribarren and Nogales (1949), but popularized by Battjes (1974), the surf similarity parameter m f ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi Ho =Lo

ð7Þ

has been related to breaker type, breaking index, wave run-up, reflection coefficient, and beach type, to name a just few. Wang and Yang (1980) provided an interesting interpretation of the inverse of the traditional form of the surf similarity parameter as a surfzone interference index, which relates the natural swash period, to the period of the incoming waves. Although numerous other parameter combinations can be used to characterize the nearshore environment, the aforementioned eight have been used successfully in the past, and have sound theoretical and empirical foundations. During the course of the analysis, it became apparent that the eight parameters could be loosely divided into two groups on the basis of the inclusion of the wave period. The first group is independent of the wave period and consists of E, Fx, Fy, and Fr , while the remaining parameters, Hb/Lb, Ω, P, and ζ, are dependent on both the wave height and period. While the group designations are somewhat general, during the analysis it became clear that the inverse dependence on wave period exhibited by parameters in the second group significantly influences the character of the observed relationship between the nearshore conditions and the individual modes of shoreline change. 3. Site descriptions Since each of the three sites selected for this analysis has been described in detail in MD06, only abbreviated descriptions are presented here. A site location map is given in Fig. 1 and a summary of some the relevant site characteristics is presented in Table 1. As described in the table, each site represents a unique coastal environment. 3.1. Duck, NC - USA Duck is one of the most intensively studied coastlines in the world, and is located centrally on the northeast facing section of the North Carolina coastline, approximately 100 km north of Cape Hatteras, NC and 70 km south of Virginia Beach, VA. Since 1980, scientists from the USACOE have been collecting vast amounts of data over an approximately one kilometer stretch of shoreline using a variety of instruments, many of which are accessed from the 560 m long research pier that bisects the site. The nearshore profile at Duck is characterized by the presence of two bars and a fairly mild overall slope, with significant scour often observed adjacent to the pier. Sediment size at the site varies appreciably across the profile, but generally falls in the range d50 = 0.125–0.250 mm, except in the vicinity of the nearshore bar and on the beach face where much larger sediment (d50 N 0.4 mm) is often found. Unfortunately, due to a variety of reasons (see MD06 for an expanded discussion), the Duck shoreline behaves somewhat atypically compared to others in the region.

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Fig. 1. Site location map.

Supplementing the bathymetric surveys at Duck is an extensive set of hydrodynamic data which is collected by a combination of pier mounted and offshore gauges. The wave data used in this study was obtained primarily from a series of non-directional gauges located in approximately 8 m of water. The local wave field as recorded by an offshore buoy in 17 m of water reflects the highly seasonal wave climate, and is characterized by a mean significant wave height of 1.1 m with an associated period of 8.7 s. The mean wave direction for the period 1986–1999 reported at the 8 m directional array is approximately 77°. The tidal gauge located at the end of the research pier records a semi-diurnal tide with a mean range on the order of 1 m. Table 1 Relevant site characteristics

Location Latitude Longitude Shoreline data Temporal resolution (days) Spatial resolution (m) Wave data Primary gauge Secondary gauge Depth at primary gauge (m) Mean Hs (m) Associated T (second) Sediment data Median grain size (mm) Settling velocity (cm/s) Tide data Range (m) s

Summer wave conditions. Winter wave conditions.

w

Duck

Pacific Northwest Gold Coast

36.18°N 75.75°W

46.65°N 124.05°W

27.97°S 153.42°E

30 Variable

Variable Variable

1 5

FRF

NOAA-46029 CDIP-036 128 1.25–1.75s 2.0–3.0w 5.0–10.0s 10.0–20.0w

QEPA-23 QEPA-13 16 1.1

8 1.1 8.7

9.2

0.125–0.250 0.15–0.20 1.4–3.2 1.8–2.5

0.25–0.30 3.2–4.0

1.1

1.8

2.7

3.2. Pacific Northwest - USA The Pacific Northwest data set consists of shoreline and wave information obtained near the Washington–Oregon border, and is typical of the high-energy, headland dominated coastlines of the Pacific Coast of the United States. The available shoreline data were collected by the U.S. Geological Survey and the Washington State Department of Ecology as a part of an ongoing study of the Columbia River Littoral Cell (CRLC). Detailed discussions of this excellent, but largely unknown data set are given in Kaminsky et al. (1998), Ruggiero et al. (1999), Ruggiero and Voigt (2000), and Ruggiero et al. (2005) among others. Natural headlands and navigational entrances subdivide the CRLC into subcells ranging in length from 30 to 45 km. Beginning in Oregon and proceeding north into Washington State, the four coastal segments are the Clatsop Plains, Long Beach, Grayland Plains, and North Beach subcells. Initially the shoreline information was recorded biannually, however the surveying frequency was increased to quarterly in the Fall of 1998. The sediment within the subcell typically exhibits a fining trend with distance from its primary source at the Columbia River, with most falling in the 0.15–0.20 mm diameter range. The Pacific Northwest wave data were obtained from a combination of offshore buoys maintained by the National Oceanic and Atmospheric Administration (NOAA) and Scripps Institution of Oceanography. The primary gauge is a directional wave buoy (NOAA Buoy 46029), located just offshore of the Columbia River bar in 128 m of water. Where necessary, a second directional buoy (Scripps, CDIP 036) located 1 km southwest of the entrance to Grays Harbor, WA was used to supplement the primary data set. The severity of the wave climate in the Pacific Northwest is well documented. Tillotson and Komar (1997) found mean deep-water significant wave heights in the region ranging from 1.25 to 1.75 m during the

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summer and increasing to between 2.0 and 3.0 m during the winter. The associated wave periods also exhibit a strong seasonal variation, increasing from between 5.0 and 10.0 s during the summer to between 10.0 and 20.0 s during the winter. Recent evidence also indicates that on average wave heights in the region are increasing by approximately 0.024 m/year, while extreme waves are increasing at an even faster rate of 0.108 m/ year (Allan and Komar, 2000, 2002). A tide gauge at the site near the entrance to Willapa Bay reports a spring tidal range of over 2.5 m. 3.3. Gold Coast - Australia The Gold Coast data set consists of wave information obtained from a combination of two offshore buoys and an extremely dense shoreline record extracted from a video monitoring system installed as a part of the Northern Gold Coast Beach Protection Strategy (Boak et al., 2000). The Gold Coast is located approximately 100 km south of Brisbane along the central portion of Australia's east coast. An ARGUS (Holman et al., 1993) system installed to monitor the impacts of a nearby beach nourishment and offshore reef construction project has provided near continuous shoreline observations along 4.5 km of coastline since 1999. For the purposes of this study, only data from the southernmost 1.5 km of the site (updrift of the reef) were utilized. Daily shoreline observations were extracted from the video record at 5 m intervals using the technique described in Turner and Leyden (2000) and Turner (2003). The characteristic grain size of the beach sediment at the site is approximately 0.25–0.30 mm. Wave information for the region was obtained from two offshore buoys maintained by the Queensland Government Environmental Protection Agency. Buoy number 23 located just offshore of the site in 16 m of water was used to obtain the wave heights and periods, while buoy number 13 was used to provide directional information. The mean significant wave height and peak period recorded by buoy 23 are 1.1 m and 9.2 s, respectively; however waves as large as 14.3 m have been measured during extreme storms. Tides measured at the site are semidiurnal with a spring tide range of approximately 1.8 m. 4. Methodology The relationship between the individual modes of shoreline variability identified by the EOF analysis and the nearshore conditions is explored by considering the correlation between the temporal eigenfunctions, ck(t), and corresponding time series of the nearshore parameters. Each of the eight parameters is composed of a combination of core variables, H, T, θ, m, d50, and ws, where the wave conditions correspond to either deepwater or breaking. The only variables that are assumed constant are d50 and ws, as all of the remaining information can be derived from the available wave data. Starting with the measured wave characteristics (H, T, and θ) in intermediate depth, linear theory can be used to determine both the deep-water (Ho and θo) and breaking (Hb and θb) characteristics. Depth limited breaking is assumed to occur when the wave height reaches 80% of the local water depth. At Duck, where a portion of the

137

wave data is directionless, non-directional waves are assumed to approach from the median wave direction of 77° reported in USACOE statistical summaries. The directionless nearshore wave data at the Gold Coast are supplemented with directional information derived from the nearby offshore gauge. Snell's Law is used to estimate the amount of refraction that occurs between the deep-water directional buoy and the local nearshore buoy. The complete nearshore data set consists of the measured nearshore conditions supplemented with the derived wave angle. Typically, the local beach slope (m) is taken as a constant, particularly in cases where complete profile data is sparse. Since no consensus exists on where exactly to measure the beach slope in most instances, a non-traditional approach was used to define a time varying nearshore slope in terms of the local sediment characteristics, and the time varying wave properties, for the present study. The active surfzone is assumed to extend a distance W⁎ out to the breakpoint defined by Hb = κhb, where κ is the depth limited breaking coefficient (taken as 0.8). The time varying surfzone slope is then defined in terms of the active surfzone width and breaking depth as m(t) = hb(t) / W⁎(t). With the additional assumption of depth limited breaking on an equilibrium beach profile (h = Ay2/3), the time varying “hydrodynamic beach slope” is given by m(t) = A1.5κ0.5 / Hb(t)0.5, where A is the sediment scale parameter of Moore (1982). From these core variables, time series of the nearshore parameters discussed in the previous section can be calculated. Correlation analyses are then used to examine the relationship between the nearshore parameter data sets, and the temporal coefficients ck(t) identified by the EOF analysis and discussed in detail in MD06. The correlation coefficient, rxy, measures the linear association between two data sets, and is given by

rxy ¼

1 n

n P

ðxi −¯xÞð yi −¯yÞ

i¼1

sx sy

−1V rxy V1

ð8Þ

where x and y are the data sets being correlated, sx and sy are the standard deviations of x and y, and overbars denote mean values. Correlation coefficients of ± 1 indicate a perfect correlation (negative values indicate that the variables change inversely to one another), while a value of 0 indicates the absence of a linear relationship. In the case of uniformly sampled data (such as the Duck and Gold Coast data sets used here), a lagged correlation coefficient can be calculated by systematically shifting one data set with respect to the other and calculating the correlation. The lag quantifies the phase relationship of two data sets, where for example, shoreline changes might be expected to lag the changes in the nearshore conditions. The 95% significance level, r95%, is used to check the statistical reliability of the results; however due to the extensive length of several of the data sets, the significance criterion can be quite low. In order to distinguish the strongest correlations, a more stringent, subjective, well-correlated criterion, rwc, was also defined. Typically wave measurements are available on an hourly basis; therefore each of the eight nearshore parameters can be

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calculated with the same resolution. The frequency of the shoreline measurements (and thus the temporal eigenfunctions) on the other hand, ranges from daily at the Gold Coast, to approximately quarterly in the Pacific Northwest. In order to compare the two time series using the correlation coefficient however, both data sets must be sampled consistently. As the shoreline response is not expected to be instantaneous, different averaging windows were applied to the parameter time series. Each window is applied such that the average represents the typical conditions during the period prior to each shoreline measurement. In addition, the maximum and minimum values of the parameters within each window were also recorded, such that a correlation analysis could be performed using the extremes as well. 5. Results Potential relationships between the local nearshore conditions and the individual modes of shoreline change identified by the EOF analyses were explored by comparing the correlation between each of the nearshore parameters and the temporal eigenfunctions ck(t). Due to space limitations, the individual modes which are presented and discussed in detail in MD06 are not given here, rather the reader is referred to the original paper for a detailed discussion of the EOF analyses. At the two sites where lagged correlation coefficients can be calculated (Duck and the Gold Coast), a series of plots similar to those shown in Fig. 2 are generated for each parameter set and averaging window. According to the convention used in generating the

Table 2 Summary of correlation criteria used in the analysis Data Set

Duck ytot yls ycs Pacific Northwest Clatsop Plains Long Beach Grayland Plains North Beach Australia Gold Coast

DOF⁎

Daily

Weekly

Monthly

r95%

rwc

r95%

rwc

r95%

rwc

254 254 254

0.123 0.123 0.123

0.195 0.150 0.125

0.123 0.123 0.123

0.250 0.200 0.150

0.123 0.123 0.123

0.300 0.250 0.150

15 16 15 15

0.482 0.468 0.482 0.482

0.482 0.468 0.482 0.482

0.482 0.468 0.482 0.482

0.482 0.468 0.482 0.482

0.482 0.468 0.482 0.482

0.482 0.468 0.482 0.482

963

0.063

0.250

0.063

0.300

0.063

0.400

⁎DOF recorded is the DOF associated with zero lag for sites where lagged correlation analyses were performed.

plots, negative lags imply the nearshore parameter time series leads ck(t). The three lines in each plot represent the results of the correlation analysis performed using the average (blue solid line), minimum (magenta dotted line), and maximum (red dashdotted line) values of each parameter within the daily/monthly window. Horizontal lines representing the 95% significance level (r95%) as well as the more stringent, subjective wellcorrelated (rwc) criterion are also given. A summary of r95% and rwc values is provided in Table 2. The results at each site are summarized in plots similar to Fig. 3, where each bar represents the maximum (in terms of magnitude) correlation coefficient for

Fig. 2. Results of lagged correlation analysis between ck(t) and average wave energy (E) from the preceding day at Duck, NC.

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139

Fig. 3. Summary of the results of the lagged correlation between ck(t) and the average of select nearshore parameters over the preceding day at Duck, NC.

the indicated combination of the nearshore parameter and ck(t). The different colored bars in Fig. 3 correspond to the correlations calculated using the mean (blue), maximum (green), and minimum (red) values of each parameter (i.e. each bar identifies the maximum of one of the three lines in Fig. 2). The number adjacent to each bar denotes the lag at which the maximum correlation occurs, and similar to the previous plot, a dashed horizontal line is used to identify rwc. Since lagged correlations cannot be calculated for the Pacific Northwest data sets due to the inconsistent sampling interval, only standard correlations are calculated for this dataset. Results of the correlation analyses are summarized in tables such as Table 3, where the highlighted cells identify correlations exceeding the well-correlated criterion. 5.1. Duck, NC - USA In MD06, the Duck shoreline data were decomposed into longshore (yls) and cross-shore (ycs) components; however due to the limited amount of information gleaned from the EOF analyses of the component data sets, only the complete data set (ytot) is discussed here. The primary mode of variability, or mean shoreline function, identified at Duck describes a longterm accretional trend, where the shoreline changes north of the pier tend to be larger. Based on a spectral analysis of the temporal component of the mean shoreline function, this longterm accretion is accompanied by a low frequency oscillation with a period of approximately 3.6 years. The lack of a

significant annual signal in c1(t) corresponding to the strong seasonal wave variability is not surprising, as several previous studies have also documented this behavior (Plant and Holman, 1996; Lee et al., 1998; Birkemeier et al., 1999). As indicated in the upper left hand panel of Fig. 3, none of the parameters are well correlated to c1(t) when the daily averages are considered. In fact, as shown in Fig. 2, the correlation between c1(t) and most of the parameters is approximately zero for most lags. If the averaging window is expanded to include the entire month preceding each survey, the correlations increase slightly as shown in Fig. 4; however only E, Fx, Fy, and Ω approach the well-correlated criterion. Although typically variations in the average nearshore conditions might be expected to be closely related to variations in c1(t), this is not the case at Duck. As explained in MD06, and mentioned briefly in Section 3, a number of factors combine to make Duck somewhat atypical. Together these outside factors strongly influence the long-term profile variability at Duck, such that the simple wave-based relationships considered here are unable to explain the longterm shoreline variability described by c1(t). The second mode identified by the EOF analysis at Duck describes a longshore periodic feature with a wavelength of approximately 1500 m centered near the pier. The temporal eigenfunction associated with this sandwave-like feature contains a number of low frequency oscillations in addition to a strong annual signal. Since the seasonality of the wave climate is well-documented, it is not surprising to find strong correlations between c2(t) and several of the nearshore

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Table 3 Correlation between ck(t) and the daily averages of each nearshore parameter at the Pacific Northwest site

Highlighted values identify correlations exceeding rwc.

parameters. When the conditions from the previous day are averaged, only Ho/Lo, Ω, Fr, P, and ζ are well correlated to c2 (t); however if the monthly average conditions are considered instead, all of the parameters (with the exception of Fy) are well correlated for at least some lags. This emphasizes the importance of incorporating the wave period in the description of the local conditions, particularly when shorter averaging windows are applied, as four of the five well-correlated daily average parameters are functions of both wave height and period. The synergistic nature of the relationship between the annual signal in c2(t) and the seasonal wave climate is evident in lagged correlation plots such as Fig. 2. Peaks in the correlation coefficient at lags of 0, ± 12 months, ± 24 months, etc. reflect the fact that both data sets contain annual signals which are in phase with one another. Interestingly, the lagged correlation corresponding to the minimum (or the maximum for those that have an inverse dependence on H) of each parameter over the specified window does not exhibit the same periodic characteristics as the average and the maximum. This is potentially related to the fact that calm conditions (lower wave heights, hence smaller values for most of the parameters) are more likely to be evenly distributed throughout the year than extreme events. Similar to mode two, mode three also represents a rhythmic feature, however the wavelength of e3(x), is much smaller (600 m) than that associated with e2(x) (1500 m). Spectral analysis highlights not only the obvious long period (N 2 years) oscillations in c3(t), but also several smaller, more obscure signals including a seasonal fluctuation. As indicated in Fig. 3, although none of the monthly average parameters meet the stringent well-correlated criterion, all of the nearshore parameters

with the exception of Fy are well correlated with c3(t) when the daily average is used. In Fig. 2, it is clear that the consistent periodic trend indicative of the relationship between the seasonal variations of c2(t) and the local wave climate, is more subdued for mode three. In general, the peak correlations which occur in the vicinity of zero lag are much sharper for mode three, corresponding to a much narrower range of strong correlations. Interestingly, the rhythmic feature described by mode three tends to be less well correlated to the offshore wave climate (as described by Ho/Lo, P and ζ) than to the nearshore breaking wave conditions (as parameterized by E, Fx, Fy, Ω, and Fr). The fourth mode represents only a relatively small amount (b2%) of the total variability of the Duck shoreline, and describes another longshore periodic feature with a wavelength of approximately 450 m. Unlike each of the previous two modes, no distinguishable relationship exists between c4(t) and the nearshore parameters. In fact, the correlation between c4(t) and most of the parameters (using either window) falls considerably short of the well-correlated criterion for most lags. When compared to the daily average, most parameters struggle to meet even the much less stringent significantly correlated criterion. Given the relatively small amount of variability described by mode four, the fact that none of the parameters appear to have a strong linear relationship to c4(t) is not surprising. 5.2. Pacific Northwest - USA The Pacific Northwest site differs from the Duck and Gold Coast sites primarily due to the spatial scales involved. While the shoreline data from both Duck and the Gold Coast represent

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less than 2 km of coastline, each subcell within the Pacific Northwest data set is at least 25 km long. The most notable trait identified by the EOF analyses of the Pacific Northwest data sets was the pronounced influence of the site boundaries on the resulting shoreline variability. In terms of the temporal scales, the Pacific Northwest data are surveyed quarterly, however due to the somewhat irregular surveying interval and the large shoreline changes occurring between surveys, the shoreline data were not interpolated prior to analysis like the Duck and Gold Coast data sets. Due to the irregular surveying frequency spectral analyses and lagged correlation analyses were not performed on the Pacific Northwest data sets. 5.2.1. Clatsop Plains, OR - USA EOF analysis of the Clatsop Plains data identifies the presence of a dominant longshore uniform seasonal shoreline translation which is modified adjacent to the subcell boundaries. While the majority of the site has experienced considerable erosion since the initial survey, the region immediately adjacent to the Columbia River entrance has experienced up to 40 m of accretion. As indicated in Tables 3–6, the dominant seasonal shoreline transition is well correlated with several of the nearshore parameters when c1(t) is compared to monthly averaged data. Given the well-documented seasonal variability of the local wave climate, this result is not surprising. Significant correlations are obtained between c1(t) and the monthly averages of E, Fx, Fy and Fr. The fact that c1(t) is not strongly correlated with any of the daily averaged parameter

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sets reflects the fact that mode one represents a mean condition, which is more closely linked to the average wave conditions than the instantaneous wave conditions. Given the strong correlations, it is likely that the shoreline change pattern associated with mode one is related to the strong seasonal variations in the local wave climate. The spatial variability described by mode two is very similar to mode one, in that e2(x) also describes a uniform shoreline translation. Unlike mode one however, it is adjacent to the southern boundary rather than the northern boundary where the shoreline changes are amplified compared to the rest of the site. The temporal variability of mode two is dominated by the presence of a 3.5 year oscillation, although a shorter annual signal is also evident. Once again, c2(t) was not well correlated with any of the daily average parameter sets; however when compared with the monthly averaged data, c2(t) was found to be strongly correlated with several of the parameters (E, Fx, Fy, Ω, Fr, and P). Interestingly, the maximum (minimum in the case of Fr due to its inverse dependence on H) value of each parameter over the same interval is also well correlated to c2(t), and in most cases the correlation is slightly stronger. This suggests that mode two may be more closely related to extreme conditions rather than the average conditions. Given the significance of the 3.5 year signal in c2(t), and the strong correlations observed between c2(t) and several of the nearshore parameters, mode two may also be related to several recent El Niño events, which have displayed a similar recurrence interval.

Fig. 4. Summary of the results of the lagged correlation between ck(t) and the average of select nearshore parameters over the preceding month at Duck, NC.

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Table 4 Correlation between ck(t) and the daily extremes of each nearshore parameter at the Pacific Northwest site

Highlighted values identify correlations exceeding rwc.

In contrast to the previous two modes which describe longshore uniform shoreline translations, mode three is decidedly non-uniform. Spatial eigenfunction e3(x) contains a nodal point separating two regions across which the shoreline changes are out of phase with one another. As discussed in MD06, there is also some evidence suggesting that mode three describes a series of migratory features which move from south to north within the subcell. The dominant temporal signal in mode three is a somewhat consistent 2.5 year oscillation. In contrast to modes one and two, c3(t) is only well correlated to parameters obtained using the daily averaging window. As expected, the mean, maximum, and minimum values over the daily interval are closely related; therefore strong correlations exist for each data type. The fact that c3(t) is more strongly correlated with the daily average parameter sets than the monthly averaged data, suggests that mode three has a shorter response timescale compared to modes one and two.

Similar to mode three, the fourth mode also contains several prominent features which appear to be migrate to the north. Spatial eigenfunction e4(x) is characterized by an alternating pattern of shoreline “bumps” and “indentations”, which according to c4(t), vary both annually and at an undetermined lower frequency. Once again, none of the monthly averaged parameter sets is well correlated with c4(t); however, the minimum deepwater wave steepness and average, maximum, and minimum surf-similarity parameter over the previous day are well correlated with c4(t). While these results suggest that mode four may represent a short-term response to variations in wave steepness, the likelihood that e4(x) is related to a physical mode of variability is considered low, due to the relatively small amount of variability described by the mode. 5.2.2. Long Beach, WA - USA The results of the EOF analysis of the Long Beach shoreline data are consistent with those at Clatsop Plains, in that the

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Table 5 Correlation between ck(t) and the monthly averages of each nearshore parameter at the Pacific Northwest site

Highlighted values identify correlations exceeding rwc.

dominant modes of shoreline variability tend to be longshore uniform. The first EOF mode at Long Beach describes a persistent accretional trend, with the shoreline in some places advancing as much as 150 m over the course of the study. The temporal eigenfunction c1(t) reflects this persistent trend, and contains no apparent periodic fluctuations. Since none of the nearshore parameter sets contains a corresponding long-term trend, it is not surprising to find that c1(t) is not well correlated with any of the parameters. While this does not necessarily eliminate the possibility that mode one represents a physical mode of shoreline variability, it does suggest that factors not considered in this analysis, such as local sea level trends and non-linear relationships, may be responsible for the observed shoreline behavior. The second mode at Long Beach is also longshore uniform; however unlike mode one, the shoreline changes described by e2(x) vary considerably adjacent to the site boundaries. Near Willapa Bay, the magnitude of e2(x) decreases significantly and even reverses direction compared to the rest of the site, while the region just north of the Columbia River entrance experiences similar, but increased variability. The associated temporal eigenfunction c2(t) contains a pronounced annual signal, which suggests that mode two represents a mostly uniform seasonal shoreline translation. As might be expected, the monthly averages of several parameters (E, Fx, Fy, Fr, Ω and P) are well correlated with c2(t) due to the synergistic relationship between the annual signals in each data set. This relationship is apparent even when the shorter, daily averaging window is applied to E and Fx. While the correlation analysis does not definitively establish mode two as a physical mode of

shoreline variability, it does suggest that e2(x) and c2(t) are closely related to seasonal variations in the wave climate. Although mode three represents over 5% of the total variability within the Long Beach data set, the majority of this variability is limited to an extremely narrow region adjacent to the entrance to Willapa Bay. As indicated in Tables 3–6, none of the nearshore parameters are well correlated with c3(t), which contains a dominant 3–4 year oscillation. Although the period of this oscillation is roughly consistent with recent El Niño events, the results of the correlation analyses suggest that mode three is either unrelated to these events, or that a more complicated relationship exists. Each of the remaining modes at Long Beach describes less than 1% of the overall shoreline variability; therefore the discussion of the results of the correlation analyses is limited to the first three modes. 5.2.3. Grayland Plains, WA - USA The EOF analysis of the Grayland Plains data set does not identify the types of longshore uniform modes which are common throughout the rest of the Pacific Northwest data sets. The first mode at Grayland Plains describes an irregular pattern of shoreline change, which is dominated by an extensive accretional deposit just north of the entrance to Willapa Bay. The related temporal eigenfunction c1(t) contains a consistent long-term trend which overshadows several smaller, short-term fluctuations. Surprisingly the daily maximum wave steepness and minimum surfsimilarity parameters are well correlated with c1(t), in spite of the dominant linear trend. None of the monthly average parameters are significantly correlated to c1(t), suggesting that the linear trend

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Table 6 Correlation between ck(t) and the monthly extremes of each nearshore parameter at the Pacific Northwest site

Highlighted values identify correlations exceeding rwc.

and short period fluctuations exhibited by c1(t) are not directly related to corresponding changes in the monthly average nearshore conditions. The second mode accounts for nearly all of the remaining shoreline variability at Grayland Plains, and similar to mode one, it is dominated by the variability adjacent to the site boundaries. Based on c2(t), these boundary influenced shoreline changes tend to occur with 3–4 year return periods. Based on the results in Tables 3–6, c2(t) appears to be more closely related to short-term variations in the nearshore conditions, as significant correlations were limited to the daily average and daily extreme parameter sets. In terms of average, c2(t) is strongly correlated with Ho/Lo, Ω, and P, while in terms of the extremes, c2(t) is well correlated with the maximum values of Ho/Lo, Ω, and P, and the minimum values of Ω, P, and ζ. While the low frequency signal in c2(t) suggests mode two might be linked to the occurrence of recent El Niños, the lack of a significant correlation between c2(t) and any of the monthly

averaged parameter sets suggests otherwise. El Niño induced variations in the local wave climate would be expected to be reflected in the monthly averages; therefore mode two might actually be more closely related to localized events with shorter response timescales. Due to the relatively small amount of variance described by the remaining modes (less than 1%), the discussion of the results of the correlation analyses at Grayland Plains is limited to the first two modes. 5.2.4. North Beach, WA - USA The mean shoreline function at North Beach reflects the relatively consistent longshore uniform behavior exhibited within the northernmost subcell of the CRLC. The pattern of spatial variability described by e1(x) consists of a long uniform central section, bounded by two regions where the shoreline changes are qualitatively similar but exaggerated. Similar to most of the Pacific Northwest sites, c1(t) is characterized by a significant long term trend upon which a seasonal oscillation is superimposed. In

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large part due to the presence of the strong annual signal, c1(t) is well correlated with several of the nearshore parameters (E, Fx, Ω, Fr, and P) using either averaging window. Although, the monthly average longshore wave energy flux is also well correlated to c1(t), the daily average is not, due to the dramatic changes that can occur when nearly perpendicular waves change direction (Fy switches signs). These results suggest an obvious link between the longshore uniform shoreline changes described by mode one, and the distinctly seasonal local wave climate. Mode two is similar to mode one in that the shoreline changes it describes are predominantly longshore uniform. Unlike mode one however, the shoreline changes adjacent to the site boundaries are out of phase with those at the center of the site. According to c2(t), these fluctuations typically have longer periods, although a seasonal oscillation is also apparent. In contrast with the primary mode where multiple strong correlations were found using both averaging windows, only E and Fx are well correlated to c2(t), and only using the daily window. The lack of significant correlations using the longer monthly window suggests that mode two represents a rapid response to the local conditions as embodied by the averages of E and Fx over the previous day. If modes one and two both represent physical modes of variability that are distinct from one another, mode two can be thought of as representing a local (in both time and space) modifier to the large scale seasonal shoreline fluctuations described by mode one. Modes three and four combine to account for just over 5% of the total variability in the North Beach data set; however as

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indicated in Tables 3–6, no significant correlations were found between any of the nearshore parameters and either c3(t) or c4(t). As described in MD06, mode three was found to be consistent with a seasonal beach rotation scenario, while mode four describes a longshore uniform beach translation, where the shoreline changes adjacent to the site boundaries are out of phase with the rest of the site. While c3(t) was found to contain both annual and 3–4 year oscillations, no consistent pattern was apparent in c4(t). In comparison with the results obtained at other sites, it is surprising that none of the nearshore parameters are well correlated with mode three given the seasonal variability exhibited by both c3(t) and the local wave climate. One possible explanation for this is that the nearshore parameters and c3(t) are slightly out of phase with one another implying a lag between the potential forcing and a mode three shoreline response. The lack of a relationship between c4(t) and the nearshore parameters on the other hand is more readily understandable, given the absence of any apparent trends in c4(t). 5.3. Gold Coast - Australia The Gold Cost site differs from both Duck and the Pacific Northwest in that it represents a fairly natural open coastline, free from the types of shore-perpendicular littoral barriers which were found to have a profound influence on both the Duck and Pacific Northwest shorelines. The density of the Gold Coast shoreline data (Δt = 1 day and Δx = 5 m) also makes it unique. The mean shoreline function, e1(x), which reflects the

Fig. 5. Results of lagged correlation analysis between ck(t) and average wave energy (E) from the preceding day at the Gold Coast, Australia.

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Fig. 6. Results of lagged correlation analysis between ck(t) and average wave steepness (Ho/Lo) from the preceding day at the Gold Coast, Australia.

Fig. 7. Results of lagged correlation analysis between ck(t) and the average non-dimensional fall velocity parameter (Ω) from the preceding day at the Gold Coast, Australia.

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predominantly longshore uniform nature of the shoreline changes at the site, was found to represent an overwhelming amount (N 94%) of the total shoreline variability. Spectral analysis of the associated temporal eigenfunction c1(t), indicates that these longshore uniform changes occur over fairly uniform intervals ranging from 1 to 2 years. The results of the lagged correlation analyses performed at the Gold Coast follow three distinct patterns. As shown in Fig. 5, the correlation between c1 (t) and each of the wave-height-only dependent parameters peaks near zero lag. E, Fx, and Fr are all strongly correlated with c1(t) using either the monthly or daily averaging window. Slightly different results are obtained when c1(t) is correlated with Ho/Lo and ζ as indicated in Fig. 6. For both parameters the maximum correlation occurs at a large positive lag, indicating that c1(t) leads both parameter time series. This is counterintuitive, as according to the convention adopted, this implies that the potential shoreline response embodied by c1(t) actually leads the potential forcing (Ho/Lo and ζ). The two remaining parameters, Ω and P, follow yet another pattern similar to that depicted in Fig. 7, where the correlation is fairly constant for lags between − 100 and 0. Although the patterns displayed in each lagged correlation plot are different for each mode, the characteristics of each plot within each group ({E, Fx, Fy, Fr}, {Ho/Lo, ζ}, and {Ω, P}) are similar. Figs. 8 and 9 summarize these results without reproducing the details of each individual lagged correlation plot. The strong correlation between c1(t) and E, Fx, and Fr suggests that the seasonal shoreline translation described by mode one is closely linked to corresponding

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changes in the wave climate, particularly in the wave energy. A similar result was found by Turner (2004) based on data from 2001–2004; however a subsequent analysis including data through 2006 (Turner, 2006) has shown this seasonal trend has decreased in significance subsequent to a strong storm in October 2004. The pervasiveness of fairly strong correlations between these parameters (and also Ω and P) and c1(t) over considerable negative lags reflects the fact that the antecedent nearshore conditions are also significant. In contrast, the strong correlations between c1(t) and Ho/Lo, Ω, P, and ζ at large positive lags are much less well understood. The meaning of this result is not immediately clear, as it implies a strong linear relationship between fluctuations in the mean shoreline and nearshore conditions that will occur up to 2 months later. One possible explanation is that the lagged correlation appears to be somewhat periodic, therefore another correlation peak may be expected to occur at a lag of − 150 days, which suggest that Ho/Lo, Ω, P, and ζ are out of phase by approximately 6 months. The second mode which accounts for nearly 40% of the remaining variability contains two sets of rhythmic features, with wavelengths of approximately 160 m and 2000 m. These rhythmic features tend to vary periodically in time as well, as c2(t) contains a strong annual signal. As described in MD06, the combined eigenfunction suggests that the shoreline features described by e2(x) migrate to the north at a rate of between 2 and 5 m/day. As shown in Figs. 5–7, the lagged correlation plots between most of the nearshore parameters and c2(t) are qualitatively very similar to those of mode one. This is most

Fig. 8. Summary of the results of the lagged correlation between ck(t) and the average of select nearshore parameters over the preceding day at the Gold Coast, Australia.

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Fig. 9. Summary of the results of the lagged correlation between ck(t) and the average of select nearshore parameters over the preceding month at the Gold Coast, Australia.

likely due to the commonality between the dominant low frequency fluctuations in c1(t) and c2(t). Quantitatively, c2(t) is not as strongly correlated with the nearshore parameters, especially when the daily averaging is used. As indicated in Figs. 8 and 9, all of the nearshore parameters with the exception of Fy are well correlated with c2(t) for at least some lags when the monthly averaging window is applied; however only Ho/Lo, Ω, Fr, and ζ are well correlated when the daily averages are compared to c2(t). The strong correlations which occur at approximately zero lag suggest that the rhythmic features described by mode two are also closely related to the seasonal changes in the wave climate. As discussed in MD06, there is strong evidence that modes three and four may be linked; therefore the results of the correlation analyses will be discussed collectively. The characteristic spatial variations described by e3(x) and e4(x) are very similar, as both describe rhythmic features with wavelengths of between 400 m and 600 m. Spectral analysis of the corresponding temporal eigenfunctions, c3(t) and c4(t), reveals the dominance of low frequency oscillations with periods of between 0.5 and 2.75 years. Similar to mode two, modes three and four together describe a series of rhythmic features which appear to migrate to the north at a rate of approximately 2–3 m/day. As shown in Figs. 5–7, the character of the lagged correlation plots for modes three and four is much different than that associated with the first two modes. Although several parameters are well correlated with either c3(t) or c4(t),

none of these strong correlations occur at zero lag. As was the case for modes one and two, the lagged correlations seem to be somewhat periodic, suggesting that maximum correlations at positive lags, may also be accompanied by slightly weaker correlation peaks at larger negative lags. This implies that the shoreline changes described by modes 3 and 4, although potentially related to the nearshore conditions, are out of phase with the nearshore parameter data sets. 6. Conclusions As described in MD06, EOF analysis was used to identify the dominant modes of shoreline variability in data sets from Duck, North Carolina, the Gold Coast, Australia, and the Pacific Northwest coast of the United States. Each mode consists of a linear combination of a characteristic spatial pattern given by ek(x), and an associated time history or chronology represented by ck(t). Although these modes are extracted purely on the basis of statistical merit, oftentimes they have physical analogs such as the bar/berm function described by Winant et al. (1975). One of the keys to identifying these physical analogs lies in interpreting the results in the broader physical context from which they were derived. The objective here is to do this by relating the individual modes to the local conditions through correlating the derived ck(t) to select parameterizations of the nearshore environment. While strong correlations do not necessarily confirm the physicality of the derived modes, they

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do add credence to these physical interpretations. Strong correlations can also be used to help identify the types of nearshore conditions responsible for each individual mode of shoreline response. The eight nearshore parameters considered here include the wave energy, E, the cross-shore and longshore wave energy fluxes, Fx and Fy, the wave steepness, Ho/Lo, the nondimensional fall velocity parameter, Ω, the profile parameter, P, the surf similarity parameter, ζ, and a surfzone Froude number, Fr. Correlations were calculated between ck(t) and the mean, maximum, and minimum values of each parameter over the preceding day, week, and month. Typically, the strongest correlations were obtained using the mean values of the parameters; however the difference between the results is minimal when the shorter daily window is considered. Although the results varied from site to site, typically the “mean shoreline” function (mode one) for each data set was well correlated with the monthly average of several of the nearshore parameters. This is consistent with the physical interpretation of e1(x) as a quasi-stationary mean shoreline condition representing the low frequency shoreline response to corresponding variations in the local nearshore conditions. The results of the correlation analysis at Duck suggest that, unlike both of the other sites, seasonal variations in the local wave climate do not play the primary role in controlling the shoreline morphology. The surprisingly longshore uniform “mean shoreline function” identified by mode one was not found to be strongly related to any of the nearshore parameter data sets. This result is consistent with several previous studies which have shown that several factors which were not considered in this analysis significantly influence the long-term shoreline evolution at Duck. Significant correlations were observed however between some of the lower modes (e2(x)–e6(x)) related to longshore periodic shoreline features and the local nearshore conditions. The second mode describing a 1500 m sand wave like feature was found to be well correlated with nearly all of the nearshore parameters. Periodic correlation peaks at lags of 0, ±12 months, and ±24 months suggest that a significant portion of this relationship can be attributed to the synergistic annual variation between the local wave climate and c2(t). Mode three, which was found to describe a smaller rhythmic feature with a wavelength of approximately 600 m, was also well correlated with several of the nearshore parameters, although only using the shorter daily averaging window. This suggests that mode three may represent a more localized shoreline response with a shorter timescale. Finally, although modes four through six also display longshore periodic characteristics, little or no correlation was found between c4(t), c5(t), and c6(t) and the local conditions. Due to the vast spatial scales involved, the Pacific Northwest data was divided into four smaller subsets representing the Clatsop Plains, Long Beach, Grayland Plains, and North Beach, littoral subcells. As interpolation of these data sets to consistent time intervals was not possible, only traditional (non-lagged) correlation analyses were performed on the Pacific Northwest data. Within each subcell, two distinct regions could be identified; one sufficiently far and uninfluenced by the boundaries of the subcell, and another immediately adjacent to and severely impacted by the boundary. EOF analyses identified at least one

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longshore uniform mode at each site (with the exception of the Grayland Plains subcell), which was typically well correlated with the monthly average of several of the nearshore parameters. These modes represent the shoreline response to seasonal variations in the wave climate. Distinct differences in the strength of the correlation between individual modes and the daily and monthly parameter sets suggest that each mode has its own response timescale. Rarely were both the monthly and daily averages well correlated to the same mode. Poor correlations tended to be caused by one of two reasons. Modes representing persistent long-term shoreline trends, were typically not well correlated with any of the nearshore parameters, as corresponding long-term trends in the forcing conditions (over the length of the study) were not observed. Poor correlations were also obtained between the local conditions and those modes describing changes confined to narrow regions, representing primarily localized responses. Shoreline variations at the Gold Coast tend to be dominated by a single longshore uniform mode, which is well correlated with seasonal variations in the nearshore conditions. Lagged correlation analyses show that many of these strong correlations persist over periods of several months, reflecting the importance of antecedent conditions. Two migrating rhythmic features (with wavelengths of 160 m and 2000 m) represented by mode two were also found to be well correlated with seasonal variations in the nearshore parameters. In some cases, periodic variations in the lagged correlations suggest that a significant phase difference exists between the forcing encompassed in the parameters, and the resulting shoreline changes described by the individual modes. Interestingly, the results of the correlation analyses from the Gold Coast, fall into three distinct categories. Correlations between ck(t) and each of the wave-height-only parameters behave in a similar manner, while correlations with the wave-height-and-period dependent parameters fall into two distinct groups, {Ho/Lo, ζ} and {Ω, P}. The reason for this clear distinction is uncertain. Acknowledgements The authors would like to acknowledge the hard work of those responsible for collecting and disseminating the data used in this report. Public access to high-quality data sets, such as these provides both the means and the inspiration to advance the field of coastal science. In particular we would like to thank Ian Turner for compiling the Gold Coast shoreline data and providing it in a very user friendly format. Finally, the first author wishes to thank the staff at Davidson Laboratory for providing a supportive environment, which allowed for the continuation of this work. References Allan, J.C., Komar, P.D., 2000. Are ocean wave heights increasing in the eastern North Pacific. EOS, Transactions of the American Geophysical Union 81, 561–567. Allan, J.C., Komar, P.D., 2002. Extreme Storms on the Pacific Northwest Coast During the 1997–98 El Nino and 1998–99 La Nina. Journal of Coastal Research 18 (1), 175–193.

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