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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 30, 2016

Relationship between high-frequency sediment-level oscillations in the swash zone and inner surf zone wave characteristics under calm wave conditions

  • Zhiqiang Li EMAIL logo
From the journal Open Geosciences

Abstract

Swash zone topography rapidly responds to the surf zone waves. Understanding how sandy beaches respond to wave action is critical for beach erosion research, and plays a critical role in the design and maintenance of shore protection structures. The main objectives of this study were to detect the relationship between high-frequency beachface oscillations and surf zone wave characteristics under plunging breakers by using Canonical Correlation Analysis (CCA). The study site is located in Houjiangwan Bay, eastern Guangdong. Topography data were sampled at 6 min intervals. The wave characteristic parameters were calculated by spectrum method. During the field work, the beach showed a reflective state and plunging breakers controlled the surf zone. The beach cusp topography was destructed gradually. The analysis provides 4 canonical correlation processes between the beachface variations and surf zone waves, which explained 95.28% of the overall variation in the data. The result shows wave steepness, the irregularity factor and spectral broadness factor had strong impacts on the topography. The wave steepness was the most important factor for beach profile variations. The results of the present study indicate that data-driven statistical analysis, such as CCA, is useful for analyzing profile response to waves if there is strong correlation between the two variables (beach profiles and wave).

1 Introduction

The swash zone is the boundary between the inner surf zone and subaerial beach areas intermittently covered by water and exposed to wave action. The inner surf zone is the surf subsection closest to the shoreline and can be considered as the transition boundary between the wave breaking area and the swash zone [1]. The inner surf zone and the swash zone form the last beach area where waves dissipate or reflect their remaining energy after travelling from the open sea towards the shore [2]. They are characterized by strong unsteady flows, high turbulence levels, large sediment transport rates and rapid morphological changes [1]. The swash action on the beachface consists of two phases: uprush (onshore flow) and backwash (offshore flow). The swash action can move beach materials up and down the beach, which results in the crossshore sediment exchange and beach profile change. Swash zone processes are of considerable importance in determining the susceptibility of coastal properties to wave induced erosion [35], and play a critical role in the design and maintenance of shore protection structures [6].

Since this environment is a part of the constantly changing section of the beach profile, understanding the swash zone topography changes is vital for revealing the beach profile responses to surf zone hydrodynamics. Previous studies on beach-profile changes have focused on changes measured at longer temporal intervals of weeks, days, or hours [7]. However, the time-scale of swash motion varies from seconds to minutes as well. Only several previously published studies focused on high-frequency changes, which include changes measured at intervals approaching the swash period. Waddell measured sediment level at two locations in the upper half of the swash zone after the backwash of each wave [8]. He found significant oscillations of sediment level with periods of 40 seconds and longer and presented evidence that the sediment-level oscillations had some characteristics of sand waves. Discussing the same data, Waddell hypothesized that the bed oscillations were caused by ground-water oscillations of the same frequency [7]. Using the same method as Waddell [7], Sallenger and Richmond [9] found the period of oscillation ranged from between 6 and 15 minutes and decreased landward across the swash zone. They observed that sediment-level oscillations were different than sand waves or other swash-zone bed forms previously described. Li et al. [10] and Li and Chen [11] conducted a similar field experiment at a beach cusp using 1-minute and 6-minute interval sampling periods. They found the daily beachface oscillation tended to correlate with the tides, while the topography oscillations diminished behind the tidal changes. Beach changes at the beach cusp horn were more complex than that of the beach cusp bay.

Studies conducted by Waddell [7], Sallenger and Richmond [9], Li et al. [10], Li and Chen [11] used the mean values (sediment-level heights, wave heights, and periods) to describe links between wave characteristics and beach-face topography changes. Their data analyzing methods omit some important information about how the beach behaves as well as the effects of waves. The interaction between waves and beach profile responses in the nearshore is a highly complicated phenomenon and is characterized by a wide range of spatial and temporal scales [12, 13]. It is often difficult to derive simple, deterministic equations or models to describe the relationship between the waves and the profiles, except in well-defined situations when a few processes control the profile response [14]. Thus, there is a need to employ sophisticated statistical models that reveal the links between the two physical processes. Canonical correlation analysis (CCA) is one such advanced statistical technique that can be used to determine dominant patterns of covariability in two data sets and their relationship [14]. This study will investigate relationships between high-frequency swash zone oscillations and wave characteristics in the inner surf zone using CCA.

2 Field site and data collection

2.1 Field site

The Houjiangwan beach, located on the eastern Gaungdong coast, is a headland beach in Jieshi Bay (Figure 1). The beach is formed by a 6 km long tombolo between the Shigongliao cape and Zhelang cape. The width of the tombolo is 100~300 m. The beach faces east and is exposed to high energy waves from the South China Sea and locally generated wind-waves, with an annual average wave height andwave period of 1.4 m and 4.0 s, respectively [15]. The beach has a micro-tidal beach with semi-diurnal tidal regime and a mean spring range of 0.8m. The intertidal beach of the surveyed section is relatively steep with a gradient of around 0.085 and the beach is composed of medium quartz sand (D50 ≈0.328 mm). The surf zone of Houjiangwan beach is very narrow and is composed of active bar-trough systems. The depth of the trough ranges from 0.5 to 1 m with incident waves breaking near the shoreline. During the field surveys, it was observed that this beachface is typically characterized by pronounced beach cusp and berm morphologies. The beach is a typical wave dominated beach and exhibits reflective or intermediate beach states.

Figure 1 Location of the study area and instruments deployment.
Figure 1

Location of the study area and instruments deployment.

2.2 Data collection

The field experiment was conducted from 6:40 am to 17:40 pm on 13th October, 2003. During the experiment, incident waves were dominantly of the swell type which came from the NNE direction with wind speeds that were low from 10:30 am to 16:00 pm. Due to different heat capacities of the land and ocean, significant sea breezes(onshore) and land breezes(offshore) occurred in the morning and evening, respectively. In the morning, the sea breeze generated wave component, driven by the local onshore winds, was pronounced.

Wave surface data were collected by a S4ADW wave gauge deployed in the inner surf trough with a sampling frequency of 2 Hz. The wave gauge had a 10 m distance from the shoreline (Figure 1).

In order to collect the swash zone sediment-level oscillations, two transects were established across the beachface, with a spacing of 3.0m. Transects were located in the beach cusp horn (A) and embayment (B) respectively (Figure 1). The spacing between the two transects was 10.0 m (So the cusp spacing was approximate 20.0 m). Both transects consisted of 3 steel pegs (10 mm diameter and 1.2 m in length) which were inserted approximately 0.8 m into the sediment (cf. [9, 1719]).

The height of the exposed pegs was manually measured every 6 min for the duration of the field experiment. Two person synchronously measured peg heights in the horn and embayment, respectively. One person recorded the peg-height data and time. Persons measuring stakes were careful to stand as far as possible away from the stakes. Scour holes caused by persons standing in the swash did not extend to the pegs (cf. [9, 17]). The pegs were of sufficiently small diameter, 10mm, to prevent significant scour around themselves. During our experiment, peg heights were measured after a backwash when the swash zone was subaerial. Because the tide range was small, significant swashes reached the highest pegs during the entire experiment. Although the diurnal tide range for the area is 1.6 m, the range from low to high tide on the day of our experiment was 0.6 m. We also made an accuracy test by taking repeated measurements as in Sallenger [16], Masselink et al. [18]. The accuracy of the technique was ±2mmintheupperswashzone(A2, A3, B2, B3). In the lower swash zone measurements needed to be made rapidly and the base plate tended to sink into the bed more than in the upper swash zone causing the accuracy to be about ±3mm. The accuracy of this technique was sufficient to determine the foreshore morphology variations.

3 Data processing and analysis method

3.1 Sediment-level data processing

Heights of the exposed pegs minus the first measured height value (namely, the initial elevation was regarded as 0), gave variations in the heights of the exposed steel pegs. Taking their opposite numbers, we identified the swash zone sediment-level oscillation processes (Figure 2).

Figure 2 Time-series of sediment-level oscillations.
Figure 2

Time-series of sediment-level oscillations.

3.2 Wave data processing

Previous researchers mainly analyzed relationships between the sediment-level height variation and timedomain wave parameters (average or significant height, period, etc.). The surf zone shows strong nonlinear characteristics. It is insufficient to understand and describe the behavior of beach processes just from the average wave parameters. Using the wave spectrum method, researchers can describe the internal energy structure of waves from their frequency domain and can also give the same average wave parameters. The wave spectrum is a very useful method for surf zone studies [2023].

Wave surface recorders sampled by the S4ADW were separated into 110 segments corresponding to the sediment-level height sampling intervals. Essentially, each segment contained 6 min wave surface recorders. Then, the trends of water levels were removed from individual segments. Surface elevation spectra were computed, using the fast Fourier transformation, from pressure records and corrected for frequency dependent depth attenuation using linear wave theory over the frequency range 0–0.5 Hz. The corrected function is:

S(f)=cosh2(kzd)cosh2(dz)Sp(f)(1)

where z is the depth of submergence of the pressure sensor, Kz is the wave number, d is the water depth, Sp (f) is the wave pressure spectrum and s (f) is the wave surface spectrum. Due to amplification of noise at high frequencies, an upper limit frequency cut-off was determined as [24]:

fmax=12gπzHz.(2)

where g is the acceleration due to gravity.

Then several wave parameters were obtained from the spectral analysis [25, 26]:

  1. significant wave height:

    Hmo=4m0(3)
  2. mean wave period

    Tmo2=m0/m2(4)
  3. spectral width factor

    ε4=1m22m0m4=1α2(5)
  4. peakness factor

    Qp = 2m020fs2(f)df(6)
  5. wave steepness:

    Ss = 2πHm0gTm022tanh(kzd)(7)
  6. peak period

    Tp=1/max(s(f))(8)
  7. wave irregularity factor

    α = m2/m0m4(9)
  8. spectral narrowness factor

    ε2=m0m2m121(10)
  9. groupiness parameter

    Ka = 1m00s(f)e2πifTm02df(11)

mn is the nth order spectral moment, given by mn = 0fns(f)df;n=0,1,2...(12)

The wave skewness was computed according to the relation given by Grasso et al. [27].

SK=83/2η3¯Hmo3αHmod2Tm022(12)

where η is wave surface height.

The wave breaking type has influence on the beach sediment transportation and topography variation [28, 29]. The wave breaking types may be parameterized by surf similarity parameter (Iribarren number) [30, 31]:

ξb = tanβ(Hmo /L0)12(13)

where L0 = gT2/2π, βis the beach slope. For ξb>2.0, waves do not break but surge up the beachface; for 0.4<ξb<2.0, plunging waves prevail; and for ξb<0.4, waves break by spilling [31].

In order to investigate the infragravity wave impacts, the water surface elevation time series were low-pass filtered using Fourier technique and a cut-off frequency of 0.05 Hz. The infragravity-wave heights and periods were estimated from low-pass filtered data using formula (3) and (4). Data were proceed by Matlab soft [3234].

3.3 Data analysis method

Field surveys yielded a sediment-level oscillation data matrix of 6×110 and a corresponding wave parameters data matrix of 13×110. CCA was then performed to investigate the presence of any patterns that tend to occur simultaneously in the two data sets and any correlating patterns associated with it [35, 36]. CCA, first introduced by Hotelling (1935) [37], have been used by coastal researchers to find patterns in wave and profile data and to predict the beach profile response due to waves (e.g. Larson et al. [14];Horrillo-Caraballo and Reeve [38]). CCA has also been used to analyze the evolutionary patterns of multiple longshore bars and the interactions between them [39].

The main idea is to form a new set of variables from the original two data sets so that the new variables are linear combinations of the old ones and are maximally correlated. If we have two random variables X and Y of order n × p and n × q respectively and there are correlations among the variables, then CCA will find linear combinations of the Ui and Vi which have maximum correlation with each other and zero correlation for differing indices.

Ui = ai1X1 + ai2X2 + . . .+aipXp = aiX(14)
Vi = bi1Y1 + bi2Y2 + . . . + biqYq = biY(15)

where Ui and Vi are canonical variates; the columns of pandqcorrespond to variables and the row n corresponds to experimental units. In the present analysis, X is the swash zone sediment-level oscillation matrix and Yis the wave parameters matrix. The statistical P-value can be used to test the significance of canonical variate pairs. Usually, the significant level is set as P < 0.05. The further details may be found in Różyński [39], Johnson and Wichern [40]. Ui and Vi are linear functions, therefore the magnititude of aip and biq represent the relative importance of a factor’s influence on the crosponding canonical variate.

4 Results

4.1 Hydrodynamics

The hydrodynamic changes observed in thesurfzone can be principally attributed to the progressive addition of obliquely incident, locally generated wind waves to the shore-normal, background swell wave field [19]. Figure 3 is the spectral graph of wave surface spectra. Spectral graphs display incident waves which had a relatively narrow band with significant peak of incident swell energy. The wind wavesgenerated by the sea breeze were first noticeable approximately 10:00 am with a period of 2.5 s. A small amount of infragravity energy was only present in the early portion of the experiment. The average Hm0 was 0.33 m and the average Tp was 11.0 s.

Using the mean value of each segment of wave surface recorders, the tidal water level process is displayed in Figure 4n. The experiment was run for approximately one tide cycle. Before 09: 00, the flood tide was coming in and the water reached high tide by noon. Sea level fell from 12: 40 to 14:40 and the low tide occurred at 14:40. After 14:40 pm, the water rose again. The water level fluctuation range was about 0.6 m during the experiment. The change of wave heights and water level has the same trend as observed by many studies (e.g. Thornton and Guza [41]; Wright et al. [? ]; Sallenger and Howd [17]; Horn [43]).

Figure 3 Frequency-time plot of water surface elevation.
Figure 3

Frequency-time plot of water surface elevation.

4.2 Swash zone sediment-level oscillation

The swash zone sediment-level oscillation processes are shown in Figure 2. The sediment-level heights at the same layer have a similar oscillation trend. Except for the heights at A1 and B1, which had a rapidly falling trend at 16:00, most of the heights have positive values. Therefore, Houjiangwan beach was experiencing an accretionary trend during the field experiment. Corresponding to the tidal level falling, the lower beach (A1 and B1) was eroded drastically at the end of the experiment. Sediment-level oscillation variances at the six pegs are 23.75(A1), 18.10(A2), 5.84(A3), 31.44(B1), 7.40(B2), and 4.45(B3), respectively. So the sediment oscillation at the lower beach and beach cusp embayment is more active than at the upper beach and beach cusp horn. Waddell describes the sediment-level oscillation as sand waves that are migrating on to the beachface [8]. Oscillations measured by Waddell [8] had periods on the order of a minute and oscillations measured by Sallenger and Richmond [9] had periods of 6–15 min [8]. In this study periods were not clear or were very long and there is no distinct evidence that showed the sand wave movement in this experiment. Oscillation amplitudes were also larger than that observed by Waddell [8] and Sallenger and Richmond [9].

The correlation coefficients between the oscillations of the six pegs were calculated (Table 1). There was a significant relationship between A1 and B1;A2 and A3, B2, B3; A3 and B2, B3. This indicated that horn divergence occurred on the beachface. Horn divergent swash motion is characterized by the deflection of the wave up-rush from the horn to the embayment. The backwash was concentrated in the embayment while, the sediments were transported from the beach horn to the embayment.

Table 1

Correlation coefficients between sediment-levels at six pegs.

A1A2A3B1B2B3
A110.09050.06240.8202−0.1439−0.0549
A210.71180.09760.74060.8073
A310.05640.46590.6517
B11−0.0761−0.0320
B210.7431
B31

4.3 Beach morphodynamic state, swash type and wave breaking type

The surf-scaling parameter [44] is computed to distinguish the morphodynamic state of the beach.

ε=4π2Hb/gT2tanβ(16)

where Hb is the incident breaking wave height. The model classifies beach states into 3 basic types: (1) dissipative state (ε>2.0), (2) intermediate state (2.5<ε<25) and (3) reflective state (ε<2.5). During the experiment, ε<1.0, the beach is in a reflective state (Figure 4j).

Baldock et al. [45] suggested there are generally two approaches to describing swash motions on natural beaches: (1) swash flows resulting from the collapse of high-frequency bores (f>0.05 Hz) on the beachface; and (2) swash flows characterized by standing, low-frequency (f<0.05 Hz) motions [46]. The type of swash motion that is prevalent depends on the incident-wave conditions and the beach morphology, which can be predicted using the surf similarity parameter ε[44]. Values of ε>20 indicate dissipative conditions (swash characterized by standing long-wave motion), whereas ε<2.5 is indicative of reflective conditions (swash dominated by incident-wave bores) [47]. In this study ε<1.0, swash processes were mainly driven by incident-wave bores (Figure 4j).

The surf similarity parameter, ξb<1.0 (Figure 4o), indicates plunging breakers dominated in the inner surf zone.

The beach morphodynamic state, swash type, and wave breaking type can clearly describe the dynamic processes. Houjiangwan is a typical reflective beachface where breaking, plunging type waves mainly occur near the shoreline in the inner surf zone. The plunging breaker produced an overturning of the wave [48, 49]. This wave deformation traps air pockets which leads to large quantities of air being entrained [29]. As a result, turbulent aerated bores propagated and dissipated over the beachface from the initial impact point to the maximum extent of run-up.

Figure 4 Time-series of morphodynamic parameters in the surf zone.
Figure 4

Time-series of morphodynamic parameters in the surf zone.

4.4 Canonical variates

Before the CCA, matrixes of sediment-level oscillations and wave characteristics (Figure 4) were standardized. Six canonical variate pairs were derived by the CCA (Figure 5). The cumulative variance contribution percentage of the first 4 principal components has reached 95.28% and their test statistic P<0.05 (Table 2). So there are 4 significant canonical variate pairs. Variation trends of U1V1, U2V2, U3V3, U4V4 are illustrated in Figure (5). Correlation coefficients between U1 and V1,U2 and V2, U3 and V3, U4 and V4 are 0.8247, 0.7385, 0.5940, and 0.5326, respectively (Table 2).

Table 2

Eigenvalues, correlation coefficients and P test values of the 6 canonical correlation variables.

Canonical variate pairEigenvaluesPercent variance explainedCorrelation coefficientsP test values
13.3210.55360.82470
21.80600.30100.73850
30.36670.06110.59400
40.22220.03700.53260.0133
50.17350.02890.32330.6142
60.10980.01830.19330.8243

The first sample canonical variate pair is

U1=0.0287X1+0.0620X20.0053X30.0900X4 + 0.1506X5 + 0.1314X6(17)
V1=44.2319Y11.3295Y20.89113Y3+395.4263Y4+3.05414Y572.3465Y6+3.6145Y768.3324Y80.8341Y91.5511Y102.9432Y11+0.0232Y12+0.4638Y13(18)

The first canonical variate pair explained 55.36% of the total variance. According to the coefficients (Table 3), variables of B2 and B3 are positive values and have the maximum weights in U1. The variable coefficient of A2 is positive, while the coefficient of A3 is a very small negative value. Therefore, the first canonical mode represents the depositional process of the swash zone. Because accretion in the beach cusp embayment was quicker than in the beach cusp horn, and the upper part of the horn had slight erosion, the beach cusp was destructed gradually and the beachface became flatter. In the canonical variate of V1, variables of wave steepness (Ss), wave irregularity factor (α) and spectral width factor (ε4) have the larger loadings of 359.4263, −72.3465 and −68.3324, respectively (Table 4). The cumulative loading contribution percentage of the first 3 variables reached 90.10%. Among the three coefficients, Ss has a positive coefficient, whilst α and ε4 have negative coefficients (Table 4). These show that the steepness factor has a positive correlation with the sediment deposition on the beachface and the wave irregularity factor and the spectral width factor have a negative relationship with onshore sediment transportation.

Table 3

Correlation coefficients between significant canonical correlation variables and beachface heights.

Peg codeU1U2U3U4
X1(A1)−0.0287−0 04040.02900.0706
X2(A2)0.0620−0.0830−0.3337−0.2099
X3(A3)−0.0053−0.10380.3150−0.4092
X4(B1)−0.0900−0.10200.02500.0105
X5(B2)0.1506−0.02210.55850.0377
X6(B3)0.13140.0032−0.32540.8400
Table 4

Correlation coefficients between significant canonical correlation variables and wave dynamic factors.

MorphodynamicsV1V2V3V4
Y1(Hm0)−44.2319−15.010021.4925−58.4484
Y2(Tm02)−1.3295−0.05212.439914.2522
Y3(Tp)−0.891130.1693−0.4416−0.1689
Y4(Ss)395.4263−71.2806163.2987−1053.6700
Y5(Ka)3.05414−10.4555−12.1454−7.5970
Y6(α)−72.3465−148.915078.5262−16.5378
Y7(ε2)3.6145−3.444226.428338.9526
Y8(ε4)−68.3324−147.56205.1024−127.7800
Y9(Qp)−0.83414.14236.97852.060472
Y10(ξ)−1.551115.0144−19.178053.7156
Y11(Hinf)−2.9432−12.807815.45913.9341
Y12(Tinf)0.02320.00580.0034−0.0778
Y13(SK)0.4638−0.02080.2911−0.0324

The second canonical variate pair is

U2 = - 0.0404X10.0830X2 - 0.1038X30.1020X40.0221X5+0.0032X6(19)
V2=15.0100Y10.0521Y2 + 0.1693Y371.2806Y410.4555Y5148.9150Y63.4442Y7147.5620Y8+4.1423Y9+15.0144Y1012.8078Y11+0.0058Y120.0208Y13(20)

with a 30.10% explanation of the total variances.

According to the coefficients (Table 3), U2 represents the beachface eroding process. Pegs of A3, B1, A2 eroded more quickly, so the beachface is flattened. The wave steepness (Ss), wave irregularity factor (α) and spectral width factor (ε4) also have the larger loadings in V2 (Table 4). The loading contribution percentage of the three factors reached 85.92%.

The third canonical variate pair is

U3=0.0290X10.3337X2+0.3150X3+0.0250X4+0.5585X50.3254X6(21)
V3=21.4925Y1+2.4399Y20.4416Y3+163.2987Y412.1454Y5+78.5262Y6+26.4283Y7+5.1024Y8+6.9785Y919.1780Y10+15.4591Y11+0.0034Y12+0.2911Y13(22)

The third canonical variate pair explained 6.11% of the total variance. In the canonical variate U3, variables of A2, A3, B2 and B3 have significant loadings with B2 having the largest positive loading (0.5585). Variables of A1, A3, B1 and B2 are positive, while A2 and B3 are negative (Table 3). According to the coefficients, U1 suggests a process of sediment deposition on the upper portion of the beach cusp while the lower portion of the beach cusp is destructing. The beach cusp had retreated to the upper level of the beachface. In the canonical variate V3, Hm0, Ss, α and 2 have the larger loadings (Table 4). The four factors contributed 82.55% of the total loading. The relationship between wave height (Hm0) and water level might give an explanation about this canonical variate pair. Figure 4 shows that wave heights (Hmo) and water levels have a strong linear correlation as observed by Thorn and Guza [34], Wright et al. [42], Horn [43], and Masselink and Hegge [18]. Therefore, the third canonical variate pair indicated the beach cusp moved on to the beachface with the water level variations. Coco et al.’s filed measurements also found that tides modulate the height and cross-shore position of the beach cusps [50]. Beach cusps extended farther offshore during falling tide and contracting onshore during rising tide.

The fourth third canonical variate pair is

U4=0.0706X10.2099X20.4092X3+0.0105X4+0.0377X5+0.8400X6(23)
V4=58.4484Y1+142522Y20.1689Y31053.6700Y47.5970Y516.5378Y6+38.9526Y7127.7800Y8+2.060472Y9+53.7156Y10+3.9341Y110.0778Y120.0324Y13(24)

The fourth mode explained 30.10%of the total variance. In canonical variate U4, variables in the beach cusp embayment are positive values (Table 3). Variables of A2 and A3 are negative, while the variable A1 is a small positive value. These values show that this mode represents the beach cusp eroding. Sediments quickly deposited on the upper part of the beach cusp embayment. In the canonical variate V4, Ss, Hm0 and ε4 contribute 90.04% of the total loading and are significant variables (Table 4).

Figure 5 canonical variate pairs.
Figure 5

canonical variate pairs.

5 Discussion

Surf zone hydrodynamics govern swash zone sediment transport and are of considerable importance in determining the susceptibility of coastal properties to wave induced erosion [35]. These factors play a critical role in the design and maintenance of shore protection structures (e.g., van der Meer and Stam [6]). The prediction of sediment transport due to wave action is of major concern to the coastal scientific and engineering communities [27]. However, most of the simplest models for predicting sediment fluxes are generally based on an “energetic” approach [5153] for which the energy expended by steady flows for transporting sediment is proportional to the total dissipation. Topography models are established by an integral method based on sediment transport models. When mean currents have been strong (typically under storm conditions), models based on this assumption (e.g. Thornton [54]; Gallagher et al. [55]) have been able to predict observed morphological change with a reasonable degree of accuracy. However, under calm conditions, these same models perform poorly and generally cannot predict onshore sediment movement [5557]. Exploring wave characteristics and the sediment transporting relationship is a basic approach to improve the accuracy for modeling. Surf zone waves are complex, nonlinear phenomena. Discussing the relationship between the wave characteristic and sediment transport from time-domain might omit some important information. The spectrum method is a good way to reveal the wave energy structure and can also give the time-domain wave parameters.

Many factors control sediment transport on the beach-face and associated beach profile adjustment, as a response to changes in the wave conditions. Recently, some studies have recognized the wave steepness as a useful parameter to link the wave actions and beach profile responses for the gravel beach. Sherman [58] studied the daily morphological response of two coarse-gravel (D=5–200 mm and 4–64 mm) beaches over a 10-day period with maximum significant wave heights up to 2.5 m and wave periods of 10 to11sec. Wave steepness was found to play the key role in controlling onshore (H0/L0 <0.007) versus offshore (H0/L0>0.01) sediment transport. Masselink et al. [59] collected morphodynamic data from a finegravel beach (D = 2–10 mm) under a range of wave-tide conditions (Hs = 0.5–1 m, Ts = 4–8 s) and highlighted that the upper beach experienced accretion and berm formation during tides with low steepness swell waves (H0L0<0.01), and underwent erosion during tides dominated by high steepness wind waves (H0/L0>0.01). Poate et al. [60] found small intertidal beach volume losses occurred under high steepness waves (H0/L0>0.01) at a fine gravel barrier (D50 = 3.5 mm) under energetic wave conditions. During the experiment, Houjiangwan bay was dominated by swells with mean wave heights of 0.33 m and mean peak periods of 11.0 s. The wave steepness ranged from 0.007 to 0.016 with a mean value of 0.0115 (Figure 4d). Other than the difference in the sediment size (D50 = 0.328 mm), the study had similar conditions as Masselink et al. [59]. In this paper, the wave steepness accounted for 66.45% of total coefficients in the U1 and it is a significant factor in the other canonical variate. This makes the wave steepness a key parameter to describe the sediment-level response to the impact of waves in the swash zone. The wave height is only a relatively larger coefficient in the third canonical variate. This means that the wave steepness is more related to changes in the profile than the wave height. The results underpin Pedrozo-Acuńa et al.’s hypothesis that greater wave steepness is associated with larger impact pressures on the gravel beach [24]. Pedrozo-Acuńa et al. [29] and Karunarathnan et al. [61, 62] concluded this result indirectly by investigating the relationship between beach profiles and wave empirical probability density functions. In this paper, we arrive at this intuitive conclusion by calculating the wave steepness directly.

The other two important factors are the spectral width factor and wave irregularity factor. Negative signs of the two factors’ coefficients hinted at negative feedback between the sediment transport and spectral width factor and wave irregularity factor, i.e. onshore sediment transport will occur under the narrow-spectrum or regular wave (e.g. swells) conditions and offshore sediment transportation will take place under the broad-spectrum or irregular wave conditions (e.g. wind waves and storms).

Beach cusps are rhythmic shoreline features formed by swash action. In this study, pegs were arranged in the beach cusp horn and embayment. The sediment-level oscillations gave a window to investigate the beach cusp morphodynamics. Masselink et al. [18, 19] proposed a threshold to describe the beach cusp development with the surf similarity parameter. When ξb<1.2, that beach cusp is planed off, whereas cusp morphology is enhanced when ξb>1•2. In the present study, ξb<1.0, therefore the beach cusps were destructive features. The morphology adjustments were shown in the first, second and fourth canonical variate pairs. The subsequent 16-day period observation also verified this process [63]. Correlation coefficients between the oscillations of six pegs (Table 1) showed that horn divergence occurred. The beachface had more accretion on the cusp horn while the beach cusp eroded.

Although many studies have been done, it is currently difficult to derive simple, deterministic equations or models to describe the relationship between the waves and the profiles except in well-defined situations when a few processes control the profile response [14]. CCA method provides a way to identify patterns and structures in the data that can be linked to these physical processes. Larson et al. [14] used this method to detect patterns in the wave and profile data and to predict the profile response due to waves. Horrillo-Caraballo and Reeve used CCA to investigate the sensitivity of the quality of predictions on the choice of the distribution function used to describe the wave heights [31]. Horrillo-Caraballo and Reeve also used CCA to investigate patterns of beach evolution in the vicinity of a seawall [64]. In addition, Różyński used the CCA method to analyze the evolution patterns of multiple longshore bars and their interactions [39]. All studies show the CCA method is useful for analyzing profile responses to waves. In the present paper, by analyzing the relationship between swash zone morphology changes and wave parameters, the usefulness of the CCA method is clear. Thus, CCA has a potential advantage in coastal engineering and coastal management for forecasting beach profile responses to the waves.

6 Conclusions

In this paper, sediment-level oscillations of the swash zone were surveyed with 6 min intervals on the beach cusp horn and embayment (2 transects with 3 pegs, respectively). The inner surf zone wave parameters were computed using the spectral method. Relationships between the swash zone sediment-level oscillations and inner surf zone wave characteristics were analyzed with the CCA method. The observed transects were with 6 pegs. On the basis of the detailed analysis, the following conclusions are drawn:

  1. The beach, Houjiangwan, investigated in the present study was in a reflective state (ε<1.0) during the field experiment. Plunging breakers prevailed in the surf zone (ξ<1.0). Sediments were transported onshore under the swells and the beach showed accretionary features. The beach cusp was destructed under the swash circulations of horn divergence (ξ<1.0).

  2. Using CCA method, 4 significant canonical variate pairs are found. Each canonical variate pair was attributed to a specific process.

  3. The sediment-level oscillations are mostly driven by wave steepness, the spectral width factor, and the wave irregularity factor. The wave steepness was shown to have the greatest impact on sediment-level oscillations.

  4. CCA method is useful for analyzing profile responses to waves and has potential for application in coastal engineering and coastal management.

Acknowledgements

This work was jointly funded by the National Science Foundation of China under contract 41676079 and Guangdong Ocean University Science Foundation for Young Group under contract C1212157. My thanks are expressed to Zachary J. Westfall, from the Department of Geology, University of South Florida, for his tremendous help in improving this manuscript.

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Received: 2016-4-13
Accepted: 2016-10-3
Published Online: 2016-12-30
Published in Print: 2016-1-1

© 2016 Zhiqiang Li, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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