Observations and modelling of shoreline and multiple sandbar behaviour on a high-energy meso-tidal beach

Author’s Accepted Manuscript Observations and Modelling of Shoreline and Multiple Sandbar Behaviour on a High-Energy Meso-Tidal Beach Kristen D. Splinter, Maria V.G. Gonzalez, Joan Oltman-Shay, Jantien Rutten, Robert Holman www.elsevier.com/locate/csr

PII: DOI: Reference:

S0278-4343(17)30587-3 https://doi.org/10.1016/j.csr.2018.03.010 CSR3744

To appear in: Continental Shelf Research Received date: 10 November 2017 Revised date: 23 February 2018 Accepted date: 23 March 2018 Cite this article as: Kristen D. Splinter, Maria V.G. Gonzalez, Joan Oltman-Shay, Jantien Rutten and Robert Holman, Observations and Modelling of Shoreline and Multiple Sandbar Behaviour on a High-Energy Meso-Tidal Beach, Continental Shelf Research, https://doi.org/10.1016/j.csr.2018.03.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Observations and Modelling of Shoreline and Multiple Sandbar Behaviour on a HighEnergy Meso-Tidal Beach Kristen D. Splinter1, Maria V. G. Gonzalez1,2, Joan Oltman-Shay3, Jantien Rutten4, Robert Holman5

1

Water Research Laboratory, School of Civil and Environmental Engineering, UNSW Sydney, Sydney, NSW, Australia 2

Universidade do Estado do Rio de Janeiro, Faculdade de Engenharia Rua São Francisco Xavier, 524, Rio de Janeiro, RJ, Brazil 3

NorthWest Research Associates, Redmond, Washington, USA

4

Universiteit Utrecht, Postbus 80.015, 3508 TA, Utrecht, The Netherlands.

5

College of Earth, Ocean and Atmospheric Sciences, Oregon State University, Corvallis, OR, USA

Corresponding author’s email: [email protected]

Submitted to: Continental Shelf Research, Nov 2017

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Abstract This contribution describes 10 years of observed sandbar and shoreline cross-shore position variability at a meso-tidal, high energy, multiple sandbar beach. To examine relationships between the temporal variability in shoreline/sandbar position with offshore wave forcing, a simple equilibrium model is applied to these data. The analysis presented in this paper shows that the equilibrium model is skilled at predicting the alongshore-averaged, time-varying position of the shoreline (R=0.82) and the outer sandbar position (R=0.75), suggesting that these end members of the nearshore sediment system are most strongly influenced by offshore wave forcing in a predictable, equilibrium-forced manner. The middle and inner bars are hypothesized to act as sediment transport pathways between the shoreline and the outer bar. Prediction of these more transient features by an equilibrium model was less skilful. Model coefficients reveal that these two end members (outer bar and shoreline) in the sediment system act in opposite directions to changes in the annual offshore wave forcing. During high wave events, sediment is removed from the shoreline and deposited in the nearshore sediment system with simultaneous landward retreat of the shoreline and offshore migration of the outer sandbar. While both end member features have cycles at annual and inter-annual scales, their respective equilibrium response factor differs by almost a factor of 10, with the shoreline responding around an inter-annual mean ( = 1000 days) and the outer bar responding around a seasonal mean ( = 170 days). The model accurately predicts shoreline response to both mild (e.g. 2004/05, 2008/09) and extreme (e.g. 2005/06, 2009/10) winter storms, as well as their summer recovery. The more mobile and dynamic outer sandbar is well-modelled during typical winters. Summer onshore sandbar migration of the outer bar in 2005 and 2006 is underpredicted as the system transitioned between a triple (winter) and double (summer) sandbar system. The changing of the number of bars present in the system is something that this simple model cannot predict. Analysis of the data suggests that this multi-bar system adjusts its crossshore seasonal movement when there is a significant change in the sediment supply to the system (e.g., nourishment projects, severe storms).

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Keywords Multiple sandbar system; equilibrium behaviour; high-energy beach; Argus; ShoreFor; Pacific North West.

1 Introduction Sandy coastlines consist of loose sediments arranged into patterns controlled by feedback loops between hydrodynamics and morphology (Wright & Short 1984; Wright et al. 1985; Short 1991; Short 1992; Falques et al. 2000; Coco & Murray 2007). Waves and currents are the main hydrodynamic forcing that drive sediment transport such that sandy beaches erode and accrete in response to changing wave conditions over the timescales of hours to years. The classic example of this was described by Shepard (1950) in relation to the annual cycles of beach profiles along the southern California coastline. Shepard showed that the beach morphology adjusted to the annual variability in wave conditions between two end-member profiles: the classic ‘winter’, or storm profile with an eroded shoreline and an offshore sandbar; and a ‘summer’, or berm profile with an accreted shoreline and berm feature. This behaviour has been documented at a variety of sites in response to both episodic storms and annual wave climate variations (Ruggiero et al. 2009; van de Lageweg et al. 2013; Ludka et al. 2015; Senechal et al. 2015). As described in Hanley et al. (2014), sandbars are a form of natural coastal protection that influence the cross-shore movement of the shoreline (Quartel et al. 2008; Price & Ruessink 2013; van de Lageweg et al. 2013). Larger waves break on the sandbar crests and dissipate most of their energy across the surf zone. At multiple-sandbar sites, waves may repeatedly break and reform as they propagate across a wide surf zone. Consequently the behaviour and alongshore variability of inner bars and the shoreline is often influenced by wave breaking patterns on the outer bars (Ruessink et al. 2009; Almar et al. 2010; Castelle

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et al. 2010; Price & Ruessink 2011; Price & Ruessink 2013). At the multiple bar, meso-tidal Truc Vert beach in France, Almar et al. (2010) found that the outer bar was most influenced by the offshore waves while the inner bar dynamics were most influenced by the tide range. When the outer bar degenerates or undergoes a net offshore migration event (Ruessink et al. 2009; Castelle et al. 2008) it has been shown that the shoreline and inner bar are more exposed to wave energy and vulnerable to subsequent storm erosion (Price & Ruessink 2011; Splinter et al. 2016). Additionally, spatial coupling of the alongshore-variable sandbar and shoreline position has been observed in previous studies (Ruessink et al. 2007; Price & Ruessink 2013; van de Lageweg et al. 2013). The relative coupling of features was found to be spatially and temporally dependent, such that features far apart were non-coupled compared to features closely spaced. Using the simple equilibrium model of Yates et al. (2009), van de Lageweg et al. (2013) were able to model 35% of the alongshore-averaged shoreline variance and 39% of the alongshore-averaged sandbar variance at the single sandbar Tairua Beach, New Zealand. It is yet to be explored if interior sandbars in a multibar system display predictable, equilibrium driven cross-shore behaviour, similar to outer bars (e.g. Plant et al. 1999) and shorelines (e.g. Davidson et al. 2013). The equilibrium beach model states that an exposed beach subjected to steady wave conditions will evolve to an equilibrium state and once this state is reached, no further changes will occur (Dean 1977). However, this state is only an idealized case since natural wave conditions are never steady for extended periods of time. Therefore beaches, sandbars, and shorelines are in constant dynamic equilibrium, with different time scales of morphological response, from intra-wave period to annual, inter-annual and even longer cycles dictated by climate change (Hanley et al. 2014). The concept of an equilibrium state of a beach has been used to model the evolution of beach profiles (Larson & Kraus 1989; Kriebel & Dean 1993; Ludka et al. 2015), nourishment projects (Dean 1991), daily to inter-annual variations in the cross-shore location and alongshore variability of the sandbar (Plant et al. 1999; Plant et al. 2006; Splinter et al. 4

2011), the shoreline (Miller & Dean 2004; Yates et al. 2009; Davidson & Turner 2009; Davidson et al. 2013; Castelle et al. 2014; Splinter et al. 2014; Splinter et al. 2016) and three-dimensional morphology of the inter-tidal beach (Stokes et al. 2015). While these models all use different approaches, the underlying agreement is the definition of some equilibrium state, how that compares to the current state, and some magnitude of forcing to drive the change. Thus, in all models the rate of cross-shore movement of sediment is both a function of disequilibrium and the magnitude of forcing available to move the sand with a time-varying forcing term outside the disequilibrium term (Castelle et al. 2014). Skilful equilibrium-based models have been derived based on the incident wave energy (Plant et al. 1999; Roelvink & Stive 1989; Yates et al. 2009), the incident wave power (Davidson et al. 2013), and the dimensionless fall velocity (Gourlay, 1968, Davidson and Turner, 2009). These models were found to predict changes in state on timescales of seasons to years with reasonable skill. Despite the over-arching conceptual agreement, a model designed for one feature (such as shoreline) is rarely applied to other features in the same sediment system (such as sandbars). However, these features form part of a larger sediment system and the exchange of sand between the dry beach face and the nearshore system is of particular interest. This paper aims to concurrently test the hypothesis that the cross-shore behaviour of multiple features (ie sandbars and shoreline) within a multi-sandbar system respond in a predictable and equilibrium fashion to changes in the wave forcing with the use of the ShoreFor (Davidson et al. 2013; Splinter et al. 2014) equilibrium model. Examining the intersite and temporal variability of the model coefficients, the model is also used to explore changes in the equilibrium state of individual features within the nearshore sediment system over this 10-year period. To the authors’ knowledge, this is the first attempt to model a multibar and shoreline system with a single model. This paper is broken down as follows. Section 2 describes the study site and the data. Observations are summarized in Section 3. Details

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of the model and the results are presented in Section 4 and further discussed in Section 5. Conclusions are presented in Section 6.

2 Site and data description This work utilises 10 years of wave, sandbar, and shoreline data (2004 – 2013) recorded by the Argus Beach Monitoring Station on the 3-km long Benson Beach (NWRA 2014), located just north of the north jetty of the Columbia River (Figure 1) and within the Columbia River Littoral Cell (Ruggiero et al. 2016). The cameras were operational between February 2004 and February 2015. The number of bars can vary both in time and in space. The sandbar system at this site is incredibly dynamic, shifting between 2 and 3 sandbars (Stevens et al. 2012), as well as merging and bifurcating of sandbars (Ojeda et al. 2008) that adds significant alongshore variability in the sediment dynamics at this site. In January 2014, daily images captured a new inner bar forming close to the shoreline at this site and the most offshore bar was no longer detected in the cameras during this net offshore migration and decay (Ruessink et al. 2009; Plant et al. 1999). This marked the start of a new three bar system and is omitted from further analysis. The site is an exposed beach with median grain size (d50) of 0.2 mm. Wave data was obtained from wave buoy NDBC 46029 (Columbia River Bar) located in 145 m of water and gap-filled with NDBC 46041 (Cape Elizabeth) located in 114 m of water as described in Splinter et al. (2014). Benson Beach is meso-tidal with a mean spring tide range (

of

2.3 m. The offshore significant wave height (Hs) is highly seasonal and ranges from 1 m to 13 m and foreshore beach slopes from 0.01 to 0.06 (NWRA 2011). In contrast to the typical notion of flatter nearshore beach slopes in the winter months and a berm in the summer during smaller wave conditions, the inter-tidal beach slope at this meso-tidal site exhibits the opposite behaviour. During winter storms that predominately arrive from the NW, the inner bar is pulled offshore and steep foreshore slopes are formed at the site. During summer,

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when typically waves come from SW, the inner bar attaches to the shoreface and mild foreshore slopes are formed.

Figure 1. Location map of study site, Benson Beach, Washington, USA. The cameras are located in the North Head Lighthouse, looking south along Benson Beach to the jetty. The main wave buoy used in the study (NDBC 46029) is also identified. A total of 298 images were available to extract shoreline and sandbar data for this study. For the purposes of this study, the sandbars are named as follows: Inner Bar (IB); Middle Bar (MB); Outer Bar (OB). An example of the triple bar system is presented in Figure 2. Sandbars frequently merged (e.g. when part of the OB and MB merge to form one bar) during transitional phases. These merged bars (See Fig 2R purple) were omitted from the modelling. Foam produced by waves breaking over the sandbars in the plan-view images is used to locate the position of the sandbar crests and shoreline as described in van Enckevort & Ruessink (2001) on a bi-weekly basis. Sandbar position derived from videobased wave breaking patterns has a cross-shore horizontal accuracy of O(10m) that varies with hydrodynamics, tide and bathymetry (van Enckevort & Ruessink 2001). The mean high water (MHW) shoreline contour was interpolated from the gridded inter-tidal bathymetry 7

generated from the hourly image-derived shoreline contour data during the bi-weekly, spring tide cycle and has a 2 m (horizontal) shoreline measurement error (NWRA 2014). The hourly shoreline contours account for estimates of wave setup and swash amplitudes based on the nearby wave buoy data (NWRA 2014). During the dredging/nourishment campaign of 2010 and the subsequent monitoring program into 2011, shorelines and sandbars were mapped on average once per week (NWRA 2014). The analysis was limited to the alongshore section 850 - 3050 m in the local coordinate system which removed the ~250 m section closest to the jetty. After the sandbars and the shoreline were identified, the alongshoreaveraged position and alongshore standard deviation of each feature was calculated (Figure 3). In all instances, to avoid biasing the alongshore-averaged statistics due to sparse spatial data, first the alongshore-variable shoreline and sandbar positions are made relative to the time-averaged (10-yr) planform shoreline position. Secondly, a spatial minimum of 50% alongshore capture rate for each feature (sandbar or shoreline) was needed to include in the analysis of the alongshore-averaged values. For this analysis, the number of alongshoreaveraged data points available to train/test the model were: shoreline (n=234), outer bar (n=169), middle bar (n=248) and inner bar (n=196).

Figure 2. Example rectified Argus image with mapped sandbars and shoreline. Red – Outer Bar; Blue – Middle Bar; Yellow – Inner Bar; Brown – Shoreline. (Left) Image shows three intact bars and shoreline. (Right) Image also shows a merge between the middle and outer bar (Purple). These intermittent merges are not included in the analysis. Dashed lines represent the previously mapped position of a feature. 8

Figure 3. Observed and modelled shoreline and 3 sandbars. Average alongshore position of all sandbars and shoreline (section 850 m – 3050 m) are shown in the muted colours with vertical bars representing the alongshore standard deviation. The light grey vertical bars represent times when merged sandbar were also present in the data (see Fig 6) indicating a transitional phase. Model results (solid lines) using the full data set to calibrate to are presented in Section 4.

3 Observations 3.1 Observed sandbar and shoreline behaviour All data presented in this section is for alongshore-averaged sandbar and shoreline positions. From the time series plots in Figure 3 it is observed that both the alongshoreaveraged position of the shoreline and sandbars have an annual signal, suggesting the cross-shore movement of sediment between the shoreline and sandbars at annual scale. The annual signal is most noticeable (significant at the 95% level, Table 1, bottom row) in the alongshore-averaged position of the outer bar and shoreline that move in opposing directions. The alongshore-averaged position of the middle bar also displays an annual signal that is significant at the 95% level. The alongshore-averaged positions of the inner and middle sandbars also have cycles less than a year (9.6 months and 6 months, Table 1), while the outer bar also oscillates at cycles just over a year. The shoreline and inner bar

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oscillate bi-annually. Each feature also has at least one longer-term cycle of 5 - 10 years, highlighting the inter-annual variability in the system. As an indication of the complexity of this site, the average alongshore standard deviation of the sandbar/shoreline ranged from 13  4.5 m to 35  15.6 m (Table 1). Over the 10-year period, 47% of the bi-weekly images recorded at least 1 merged sandbar in the study area (Figure 3, grey vertical lines and Figure 5 B-C). These merged portions of the sandbars are not included in the modelling. The outer bar is most responsive to the annual wave climate (winter – summer) as defined by its temporal cross-shore range and any long-term trends of the waves, while the shoreline is the most stable feature (Table 1). Interestingly, over the 10year period, the alongshore-averaged position of the shoreline and inner bar both had landward trends in their position, while the middle and offshore bar had offshore trends (Figure 3, Table 1). These observations suggest that the beach is experiencing a net erosion trend over the decadal timescale in this study. The middle bar is positively correlated to the outer bar (R=0.58) in terms of its annual to multi-year behaviour, while the inner bar is weakly positively correlated to the shoreline with a bi-annual cycle and similar long-term trend (R=0.3, Figure 4, Table 1). The inner and middle bar (R=0.73, Figure 4) also display similar patterns of alongshore-averaged cross-shore migration at cycles of 0.8 and 0.5 years (Table 1), while the inner and outer bars are weakly negatively correlated (R=-0.15).

Table 1. Sandbar and shoreline characteristics. Spectral analysis is done using the LombScargle periodogram for non-uniformly-spaced data.

Temporal range (m) Temporal std of the alongshore avg feature (m) Trend (m/yr) Temporal mean of the alongshore std (m) Temporal std of the alongshore std (m) Spectral peaks (years,

Shoreline 40

Inner Bar 100

Middle Bar 120

Outer Bar 250

18

37

55

104

-2.2

-2.3

5.5

20.4

13

29

35

35

4.5

14.0

14.9

15.6

1, 2.3, 5

0.5, 0.8, 2.2,

0.5, 0.8, 1, 5

1, 1.2, 1.5,

10

significant at 0.95)

5, 10

10

The winter of 2005/2006 was the severest winter at Benson Beach in the 10-year study, resulting in the erosion of grass dunes behind the beach. This was followed by two years of seasonally varying shoreline position and a general erosion trend, shifting the MHW shoreline landward, and the north jetty foot was weakened. Between 2004 and 2008 the sandbar system oscillated between a 3 bar (winter) and 2 bar (summer) system (see Figure 3, summers of 2005 and 2006). Two beach nourishment projects were carried out during the monitoring period; the first in 2008 when 96,000 m3 of dredge material was placed along the jetty and the second in 2010 when 281,000 m3 of sediments were placed on the beach (Stevens et al. 2012). Post - 2008 a 3-bar system was present throughout most of the year.

Figure 4. XY plots comparing the correlation between shoreline (Shore), Inner Bar (IB), Middle Bar (MB), and Outer Bar (OB). Each feature has been demeaned using the timeaveraged position of the respective feature. With the exception of IB:OB, all correlations (R) are significant at the 95% level. Blue lines represent the regression equation given in each subplot.

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3.2 Temporal variability in the sediment system Changes in the equilibrium state of a sediment system can come about through natural changes (e.g., sediment loss/supply, wave climate) and/or man-made influences (e.g., construction of jetties, harbours, groins, nourishment projects). Qualitative analysis of the sandbars at Benson Beach suggests that this multi-bar system adjusts its cross-shore seasonal movement when there is significant change in the sediment supply to the system (e.g., nourishment projects, severe storms) and can transition between a double and triple sandbar system as a result. Prior to nourishments in 2008 and 2010, it is hypothesized that the nearshore system had an inadequate volume of sand to maintain a triple sandbar system and was therefore not in an equilibrium state. Following winter storms in 2004/05 and 2005/06, a weak outer bar degraded as it moved back onshore and fed the middle and inner bars as well as the shoreface (Figure 5, Figure 6). Similar behaviour has been reported by Ruessink et al. (2009) at the Gold Coast, Australia. It is clear from the images that by summer’s end (Figure 5D: Aug 21, 2005) the bars were disjointed and weak as indicated by the lack of consistent and wide breaking compared to earlier in the year (Figure 5B: May 08, 2005). This weak sandbar system left the beach more vulnerable to impending fall/winter storms (Price & Ruessink 2013; Splinter et al. 2016).

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Figure 5. Temporal evolution of the bar system in 2005 showing the degradation and merging of bars. Red – Outer bar; Blue – middle bar; Yellow – inner bar; brown – shoreline. Green indicates a merge of the middle (blue) and inner (yellow) bar. Dashed lines indicate previous measured position. (A) Mar 17, 2005; (B) May 08, 2005; (C) Jun 6, 2005; (D) Aug 21, 2005. The winter of 2005/06 was the severest in this 10-year study and significantly eroded the back dunes above the MHW (2.0 m) contour. This erosion added significant amounts of sediment from the dune system to the nearshore subaqueous sandbar system that had been previously unavailable. At the same time this severe winter destroyed the outer bar. In January 2006, a double/triple bar system was present (Figure 6A). At the southern end near the jetty, there was a visible double-bar system and the outer bar moved onshore (Mar 13, 2006, Figure 6B). The northern section of the outer bar was left stranded offshore and eventually degraded (not shown) as the outer bar merged with the middle bar at the northern end. The southern end of the middle bar merged with the inner bar as the bars moved onshore (Green lines: Jun 19, 2006, Figure 6C). Bars continued to move onshore, degrade

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and merge as the summer progressed under low wave conditions. By August 23, 2006 (Figure 6D), a salient was visible at the shoreline and mirrored in the inner bar (Argus alongshore 1800 m – 2500 m). It is hypothesized that the sediment available to form this salient was due to the influx of sediment into the nearshore that was eroded from the dunes almost 10 months prior. The shoreline salient was a distinct feature (Figure 7) that appeared in 2006 (light blue bold line) following the recovery of the severe storms in winter 2005/06 and again in 2010 (yellow bold line) following the 281,000 m3 of sand placed on the beach (Stevens et al. 2012).

Figure 6. Temporal evolution of the bar system in 2006 showing the development and degradation of sandbars and a shoreline salient. Colours as described in Figure 5. Purple indicates the merge of an outer (red) and middle (blue) bar. Dashed lines indicate previous measured position. (A) Jan 26, 2006; (B) Mar 13, 2006; (C) Jun 19, 2006; (D) Aug 23, 2006.

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Figure 7. 2.0m NAVD88 Shorelines. September months are bold for inter-annual comparison. A salient appears ~ alongshore 2000-2400m in 2006 (light blue) and 2010 (yellow). Early fall storms in October 2010 removed the shoreline salient (nourishment) and placed the sand in the nearshore system, but this does not appear to be enough to maintain a triplebar system (Figure 8). The outer bar was frequently only visible in the northern half of the study site (Argus alongshore coordinates < 2000 m) away from the nourishment and was not visible (by wave breaking patterns) during the summer months, re-emerging in the images in September as the northern half of the middle bar (Figure 8C). Detailed topographic and bathymetric surveys of this beach during this time period, as described in Stevens et al. (2012) indicate that substantial volumes of sand were lost from the outer bar region due to the

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. During the first fall storm in late 2011, 3 bars close to shore were detected (Figure 8D), but the outer bar was short-lived (as evident in Figure 3 by the 2 isolated data points for the outer bar).

Figure 8. Examples of the 2011 sandbar evolution. Colours as described in Figures 6 and 7. (A) Dec 22, 2010; (B) Mar 23, 2011; (C) Sep 02, 2011; (D) Oct 4, 2011.

4 Equilibrium modelling of sandbar and shoreline behaviour In order to better understand this multi-bar system and to test the hypothesis that the shoreline and sandbars within a multi-bar system exhibit equilibrium behaviour, the ShoreFor equilibrium model was applied.

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4.1 Model description ShoreFor is a simple equilibrium shoreline model first presented by Davidson et al. (2013). The model has been shown to successfully reproduce weekly to annual shoreline variability at a wide range of beaches around the world, including the present study site (Davidson et al. 2013; Castelle et al. 2014; Splinter et al. 2014). The conceptual model has also been successfully applied to examine the time-varying inter-tidal beach morphology (Stokes et al. 2015), suggesting that this equilibrium approach may also be suitable to examine equilibrium behaviour of other nearshore features, such as sandbars.

For a

complete model description the reader is referred to Davidson et al. (2013) and Splinter et al. (2014). Briefly, the cross-shore displacement of a feature (dx/dt, units: m/s) takes the following form, according to Splinter et al. (2014):

(1)

(

where F+ and F- (units: N0.5s-0.5) represent the accretive (+) and erosive (-) forcing response, b (units: m/s) is the linear trend component; and c (units: mN-0.5s-0.5) is the response rate and is dependent on the magnitude of wave energy flux and the observed response in the shoreline/sandbar. The erosion ratio, r (dimensionless) is determined within the model based on the balance between F+ and F-. The forcing term is defined as:

(2)

where P is the wave power (P = ECg) and is a function of the wave energy (E) and group velocity (Cg). The degree of disequilibrium ( background dimensionless fall velocity (

) is described by the difference between a and the instantaneous value (Ω = Hsb/wTp),

where Hsb is the significant wave height at breaking, w is the sediment fall velocity and Tp is 17

the peak wave period.

is normalized by the standard deviation

. The degree of

disequilibrium is defined as:

(3) where

(4) [∑

]

∑

The response factor ( , days) is indicative of ‘memory decay’ and indicates the dominant time scales of sediment exchange. In the present form of the model, only 1 timescale of equilibrium is included (dictated by

, but this does not necessarily preclude the model from

being able to capture inter-annual cycles and trends in the waves/shoreline/sandbar as well as shorter (storm to seasonal) scale response. Small

values indicate a system more

responsive to individual storms, while larger values indicate a system that varies predominately with the annual variation in wave conditions (Splinter et al. 2014). For assessing the skill of the model, three definitions are used: correlation coefficient (R) between the measured and modelled position, the Brier Skill Score (BSS) and the normalized mean square error (NMSE). Normalized mean square error is defined as:

∑( ∑(

) ̅̅̅̅

(5)

where xp is the predicted position and xm is the measured position of the feature and the overbar represents the time mean. As described in Splinter et al. (2013) and Miller and Dean (2004) a NMSE = 0 indicates the model perfectly captures all data points, while a NMSE = 1 indicates that model mean square error is equivalent to the measured variance. General skill assessment can be made by: NMSE < 0.3 (Excellent); 0.3 < NMSE < 0.6 (Good); 0.6 < NMSE < 0.8 (Reasonable); and 0.8 < NMSE < 1.0 (Poor). The presence of only a few

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outliers can significantly affect the NMSE and result in high errors for an otherwise good model. As such, the Brier Skill Score is another useful tool and is defined as:

∑(|

|

)

(6)

∑( According to van Rijn et al. (2003), the BSS coefficient can be classified as ‘excellent’ (1.0 – 0.8), ‘good’ (0.8 – 0.6), ‘reasonable/fair’ (0.6 – 0.3), ‘poor’ (0.3 – 0.0) and ‘bad’ (< 0.0). The baseline condition (xb) used in the BSS is a simple linear trend (in time) of the data as done in similar analysis (Davidson et al. 2013). Measurement error in the shoreline/sandbar measurements, as well as the uncertainty due to the alongshore variability in the shoreline/sandbar (as measured by the time-varying, alongshore standard deviation of the feature) is captured in x. Multi-year erosion or accretion may be captured in the model through both the wave-driven component (first term on RHS eq. 1) or a long-term trend (second term on RHS eq. 1). The formation or disappearance of features (such as a new bar or bar degradation) cannot be captured.

4.2 Full alongshore average For this first section, the ShoreFor equilibrium model was run on each individual feature for the 10-year period (Table 1). Overall, the model performed well with a Brier Skill Score (BSS) considered as ‘good’ (BSS > 0.6) for the three sandbars and the shoreline. Model skill was highest for the shoreline (R = 0.82, NMSE = 0.32), followed by the outer bar (R = 0.75, NMSE = 0.44). Model skill was significantly lower for the inner (R = 0.23, NMSE = 0.95) and middle (R = 0.38, NMSE = 0.86) sandbars (Table 2), suggesting these features are not forced by equilibrium behaviour and that incident wave energy is not a single dominant driver of cross-shore sandbar movement in multiple sandbar systems. Model coefficients highlight broad similarities between features. For example, the inner bar and shoreline have similar rate coefficients (c, Table 2) of the same sign. This indicates their alongshore-averaged cross-shore migration is loosely positively correlated (as in Figure 4),

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with onshore migration/shoreline erosion during high waves and offshore migration/shoreline progradation during small waves. This is in contrast to the middle and outer bar (negative c) that move offshore with large waves and onshore during smaller waves (Figure 3 and Figure 4). The magnitude of the response rate (c) indicates the level of cross-shore migration for a given wave height. As the model for each feature is driven by offshore wave data, the outer bar, which is the most exposed feature, is the most responsive, (c = -1.78E-7) while the inner bar is the least responsive (c = 1.71E-8). The erosion ratio (r, equation 1) is also slightly larger for the outer bars (Table 2), indicating these features are more responsive to an increase in waves than the more sheltered inner sandbar/shoreline. Due to the wave sheltering by the outer and middle bar, the inner sandbar and shoreline respond more to the annual variation in the wave climate ( > 360 days), and exhibit modelled spectral peaks in cross-shore sandbar position at 1, and ~4.5 years. The modelled alongshore-averaged shoreline also showed a significant peak at ~2 years. The alongshore-averaged position of the middle and outer bar, which are more exposed to variations in the wave climate, have model best fit response factor coefficients that indicate that the equilibrium response of these features is more influenced by shorter term fluctuations in wave climate (

days ).

Despite being more responsive to sub-annual fluctuations in the wave climate, these features have spectral peaks of the modelled alongshore-averaged cross-shore position at 1 year, ~5 years, >10 years. All modelled features also had a peak longer than the record length and no model showed a significant (at the 95% level) peak at a frequency shorter than 1 year. The observed shorter term (less than 1 year) cross-shore movement of the inner and middle bar (Table 1) is not reproduced at the 95% significance level in the model (Table 2) and may be one reason for the lower model skill of these two features. Table 2. ShoreFor results for the full (800-3050 m) alongshore average. Calibration period 2004-2013.

Number of points (n) Offset (m) Trend (b, m/yr)

Shoreline

Inner Bar

Middle Bar

Outer Bar

234 3 0.27

196 189 -3.01

248 325 3.48

169 548 11.46

20

Response rate (c, mN-0.5s-0.5) Erosion: Accretion ratio (r) Response factor (φ, days) Correlation coefficient (R) Brier Skills Score (BSS) Normalized Mean Square (NMSE)

Error

3.10E-08 0.33 1000 0.82 0.66

1.71E-08 0.32 380 0.23 0.65

-5.17E-08 0.37 160 0.38 0.65

-1.78E-07 0.37 170 0.75 0.74

0.32

0.95

0.86

0.44

1, 4.65, >10yrs

1, 4.9, >10yrs

1, 4.9, >10yrs

1, 2.2, Spectral peaks of modelled feature 4.4, (years, significant at 0.95) >10yrs

During the summers of 2005 and 2006 and late fall 2007, the outer bar model does not predict the full magnitude of the onshore migration of the sandbar (Figure 3). These time periods correspond to when the system was oscillating between a double bar (summer) and triple bar (winter) system and merges in sandbars (grey lines, Figure 3) were frequently occurring. It is not expected that the simple equilibrium model used here would be able to capture these transitions if it was trained on a stable triple bar system as well. Like the outer bar, the middle bar is observed to move further onshore than the model predicts during these time periods and enters the cross-shore space of the inner bar. This temporal dependency of the nearshore sediment system is further explored in Section 4.3.

4.3 Temporal variability It is clear from the alongshore-averaged model results (Figure 3) that the model is more skilful during certain time periods than others. To examine if 2 timeframes of different equilibrium behaviour exist due to changes in sediment supply, the data was divided into two time periods defined as pre- and post- nourishment: Jan 2004 – Jul 2008; Jul 2008 – Dec 2014. This roughly defines the transition between a 2/3 bar system (pre-2008) and a more continuous 3 bar system (post-2008). Model BSS was considered to be ‘good’ to ‘excellent’ for both time periods of the outer bar (Table 3) and visually appears to be capturing a greater extent of the cross-shore variability in the first half of the data set (Figure 9) than when calibrated to the full data set (Figure 3). To account for this larger cross-shore variability observed, the response factor is larger in the first half of the data set (c = -2.08E-7) than in the second half (c = - 1.61E-07), 21

while the timescales of oscillation (denoted by ) do not change significantly between the 2 time periods. The trend term (b) also varies significantly between the 2 time periods, highlighting the potential sensitivity of model calibration to data length (Splinter et al. 2013) as well as model best fit between wave-driven processes captured by the model and unresolved processes (in the form of the linear trend) over the shorter timescales. The middle bar shows significant deviations in model coefficients between the two time periods (Table 2). Similar to the outer bar, the trend term (b) varies in sign and magnitude. The time scales of equilibrium oscillation differ between the two time periods, with the first half suggesting the bar moves around the time mean (=∞) compared to the latter half with a response time similar to the outer bar (=130 days). This change in  may be related to changes in sediment supply, with more sediment and a more continuous outer bar influencing the equilibrium behaviour of the inner and middle bar. However, the middle bar does not show a significant temporal dependence on its rate parameter (c) as was found for the outer bar. The skill of the model for the middle bar for both time periods is similar and ranked as ‘good’ on the BSS scale.

Figure 9. Model results for two separate calibration periods (04-08 and 08-14). Observed data as described in Figure 3.

22

Table 3. ShoreFor results for analysing temporal variability

OB

MB

IB

Shore

Time Period (yr)

n

b (m/yr)

c (mN-0.5s-0.5)

Φ (days)

r

R

BSS

NMSE

2004 2008

-

85

-15.03

-2.08E-07

180

0.36

0.70

0.83

0.51

2008 2014 2004 2008 2008 2014 2004 2008 2008 2014 2004 2008 2008 2014

-

84

12.97

-1.61E-07

190

0.34

0.57

0.69

0.68

-

97

-19.49

-6.31E-08

∞

0.31

0.44

0.70

0.81

-

151

11.99

-6.05E-08

130

0.36

0.42

0.64

0.83

-

57

-15.95

1.98E-07

1

0.78

0.40

0.64

0.84

-

139

3.24

1.20E-08

370

0.32

0.19

0.67

0.96

-

101

-6.01

2.54E-08

700

0.33

0.89

0.43

0.21

-

133

5.32

2.92E-08

∞

0.31

0.81

0.49

0.34

The model skill is lower at predicting the time-varying alongshore-averaged position of the inner bar, suggesting that this feature does not respond in an equilibrium fashion to the incident offshore waves. The lack of coherent behaviour is further evidenced by the widely varying optimized coefficients between the two time periods. The inner bar is quite intermittent in the first half of the data (n=57, Table 3), appearing predominately in the winter months. This will skew model skill, but more importantly model coefficients. This is in contrast to the second half of the data when the inner bar is present throughout all seasons (n=139, Table 3) The shoreline also shows variability in model coefficients between the two time periods (Table 3). Similar to the sandbars, the linear trend term (b) changes sign and magnitude. While the response rate (c) and response factor () also vary between the two time periods, this variability is not expected to overly impact the model behaviour. In particular, the response factor that dictates the filtering timescale is sufficiently large in both cases as to not significantly alter the equilibrium condition.

23

4.4 Intra-site variability The alongshore variability of a sandbar at this site can be considerable, as indicated by the alongshore standard deviation represented by the vertical coloured bars in Figure 3. Bar merges and bifurcations occur approximately 50% of the time, with the north and south end of the beach displaying different temporal variability, and at times a different number of sandbars (e.g., Figure 5, Figure 6 and Figure 8). After running the model for the full alongshore average and obtaining the results given in Section 4.2, the length of the domain was subdivided into three sections to examine intra-site variability. This allowed for better understanding of the behaviour of the sandbars from north-south and how the north jetty and the localised nourishment may influence the movement of the sandbars and shoreline over the 10-year period. For all three sandbars, the southern area closest to the jetty (2300 – 3050 m) responded differently (Table 4) than the two northern sections. For the outer bar, the model skill (0.73 ≤ R ≤ 0.79) was comparable to the full alongshore average (R=0.75), and the linear trend term (b) increased from north to south, as did the response factor (), while the rate coefficient was largest in the north (c = -2.32E-7). Response factors () varied considerably alongshore between 140 and 220 days for the outer bar. For the middle bar, the model was less skilful (0.40 ≤ R ≤ 0.44). The response rate (c) increased to the south (closer to the jetty and nourishment) while the response factor () decreased, which is opposite to the outer bar. Like the outer bar, the response factor for the southernmost section is distinctly different from the northern two sections (Table 4), which may indicate a localized influence of the jetty and/or nourishment on sediment transport/mobility. Table 4. ShoreFor results for analysing intra-site variability. Alongshore location (m) OB

800 - 1550

n 186

b (m/yr) 3.01

c (mN-0.5s-0.5) -2.32E-7

24

Φ (days ) 140

NMSE r

R

BSS

0.38

0.73

0.64

0.46

MB

IB

Shore

1550 - 2300

175

12.18

-1.88E-7

160

0.37

0.73

0.58

0.47

2300 - 3050

132

17.93

-1.70E-7

220

0.35

0.79

0.62

0.37

800 - 1550

259

2.64

-6.70E-8

160

0.37

0.44

0.53

0.81

1550 - 2300

249

3.97

-6.70E-8

150

0.37

0.4

0.49

0.84

2300 - 3050

224

7.87

-1.99E-7

15

0.48

0.40

0.43

0.84

800 - 1550

213

1.25

1.33E-7

4

0.58

0.21

0.49

0.95

1550 - 2300 2300 - 3050

199 184

-4.35 -1.80

1.35E-7 -2.12E-7

1 7

0.78 0.53

0.26 0.33

0.54 0.52

0.93 0.89

800 - 1550 1550 - 2300 2300 - 3050

234 234 234

-2.61 0.45 2.97

1.82E-8 3.32E-8 4.15E-8

1000 1000 1000

0.33 0.33 0.33

0.81 0.7 0.74

0.76 0.82 0.84

0.35 0.42 0.46

For the inner bar, the correlation coefficient varied alongshore as well (0.21 ≤ R ≤ 0.33). For the inner bar, the intra-site variability in the model coefficients includes a sign change in the rate parameter (c) from north to south, indicating that the model best fit would have the inner bar moving in the same direction as the middle bar in some locations (negative c) and moving in the same direction as the shoreline in other alongshore locations (positive c). Again, the most southern section, closest to the jetty and the nourishments displayed distinctly different behaviour than the northern sites. This change in sign reinforces again the complexity of the inner bar feature at this site. Response factors were quite small and showed minimal intra-site variability for the inner bar (1 ≤ φ ≤ 7 days). For the shoreline, similar to splitting the data into two time periods, the linear trend term (b) shows alongshore variability, including a sign change from north to south. This may be due to the local influence of the nourishment close to the jetty (section 2300-2050m) or a build-up of sand at the jetty due to longshore transport processes which dominate the decadal scale shoreline evolution on this stretch of coastline (Ruggiero et al. 2016). The rate coefficient (c) also varies from north to south by a factor of 2. This indicates that the shoreline near the jetty is more responsive to changes in wave heights (higher c) than areas further away.

25

5 Discussion 5.1 Modelling Equilibrium Behaviour Modelling cross-shore movement of sandbars is not new (e.g. Plant et al. 1999; Plant et al. 2006; Pape et al. 2007; Splinter et al. 2011) and has been shown to be skilful at intermediate beaches such as Duck, NC, USA and Palm Beach, NSW, Australia. To the authors knowledge, this is the first attempt to model a multi-bar and shoreline system with a single model. The equilibrium model here was most skilful at predicting the equilibrium behaviour of the end members; namely the shoreline and the outer bar. While the model was able to capture the equilibrium behaviour of the middle bar, the lower skill in the modelled alongshore-averaged time-varying position of the middle and inner bar was expected as these are influenced by the outer bar (e.g. Ruessink et al. 2007; Price & Ruessink 2011; Almar et al. 2010), shoreline (Price & Ruessink 2013; van de Lageweg et al. 2013), as well as the tide range (Almar et al. 2010) and have complex inter-dependencies between adjacent features not captured in the simple equilibrium model used in this study. At the multiple bar, meso-tidal Truc Vert beach in France, Almar et al. (2010) found that the inner bar dynamics were most influenced by the tide range. Tide range was not considered in this present study. For example, Ruessink et al. (2007) showed that on the double-bar system of the Gold Coast, Australia, the three-dimensional patterns (not examined here) of the inner and outer bars was temporally dependant. After a large wave event where the sandbars were ‘reset’ their initial growth in alongshore variability was non-coupled. However, as the outer bar moved onshore and became more three-dimensional, it began to influence the inner-bar morphology that began to couple with the outer bar morphology. Price and Ruessink (2013) extended this work to show that the type of coupling also varied and that five distinct morphological coupling (of the three-dimensional morphology) states between sandbars and the shoreline existed at the Gold Coast.

The coupling of sandbars with respect to the

26

alongshore variable planform may influence their cross-shore migrations (Splinter et al. 2011) but was not explored here. Observations of a single bar – shoreline system at an embayed beach Tairua Beach, New Zealand by van de Lageweg et al. (2013) also showed varied amounts of coupling between the sandbar and the shoreline as a function of cross-shore distance between the two features. Coupling here was defined as spatial similarities in the alongshore variability of the shoreline/sandbar position rather than the temporal correlation of the alongshoreaveraged position as done in this work. Using the simple equilibrium model of Yates et al. (2009), van de Lageweg et al. (2013) were able to model 35% of the alongshore-averaged shoreline variance and 39% of the alongshore-averaged sandbar variance at the singlebarred beach of Tairua. Results generated by ShoreFor (Table 2) suggest that the two end-members, namely the outer sandbar and shoreline, exhibit predictable and opposing equilibrium-driven behaviour as part of the complex seasonal to multi-year cross-shore sediment exchange at Benson Beach. As described elsewhere in the literature (e.g. Shepard 1950), the triple bar system of Benson Beach undergoes a constant cross-shore exchange of sediment between the nearshore and the subaerial beach, dominated by the annual change in wave conditions. During high wave energy events, sand is stripped from the eroding shoreline/inner bar and placed in the nearshore bar system as the sandbars move offshore. During the milder summer months, the sandbars migrate back onshore and sand is transported back on to the accreting shoreline and forms low tide terraces. The alongshore-averaged positions of the middle and inner bar, which display less cross-shore movement due to the annual (winter-summer) changes in wave climate and lower model skill (Table 2), are hypothesized to act as intermediary features and subannual/seasonal transient sediment pathways between the two end member states. The modelled alongshore-averaged middle bar displays weak equilibrium behaviour at the

27

annual (winter-summer) time scale, while the inner bar sometimes migrates with the sandbars and at other times it migrates in sync with the shoreline (Table 4). These results agree with those presented by Ludka et al. (2015) where equilibrium behaviour was most evident in the end-member states (i.e. shoreline and offshore sandbars) and less skilful in the inner surf zone. The outer bar is the most responsive to changes in wave power arriving along the coast in agreement with previous literature (e.g. Almar et al. 2010). This is expected as this feature dissipates most of the energy that comes from the waves and is highlighted by the large values in the response rate (c) in the model calibration coefficients, compared to the middle and inner bar, as well as the shoreline (Table 1). As the model is forced purely by the offshore wave conditions, the reduced response rate values for the middle bar, inner bar and shoreline compared to the outer bar is expected as the model attempts to account for missing physics, such as damped cross-shore component of wave energy flux (due to wave breaking over the outer bar(s)) not accounted for in this simple model. A wave transformation model that could account for the dissipation on the outer bars might improve model skill, but would require detailed bathymetric surveys and is beyond the scope of this present work. While all modelled features have a spectral peak around the annual signal, the difference in the response factor ( ) between the outer bar (

days) and the shoreline (

= 1000

days) indicates the equilibrium response of these two features occurs at different timescales and that the cross-shore movement of the more-exposed outer bar is more influenced by recent storms and the seasonality of the waves, whereas the cross-shore movement of the shoreline, which is protected by a double/triple sandbar system is dominated by the annual fluctuation in the average wave climate. To provide a more rigorous assessment of the model’s predictive capacity the model was calibrated to the period 2004 - 2010 and then run on 2004 - 2014. Model BSS was

28

considered ‘good’ with values between 0.59 and 0.73, indicating the model is capable of predicting unseen behaviour. As expected, highest skill was for the shoreline (R = 0.82) and the outer bar (R = 0.73) capturing the general inter-annual behaviour of the sediment system. Model results were sensitive to the calibration data set chosen, similar to previous findings (Miller & Dean 2004; Yates et al. 2009; Yates et al. 2011; Davidson et al. 2013; Splinter et al. 2013; Splinter et al. 2016; Davidson et al. 2017) highlighting the sensitivity to non-equilibrium time periods and temporal variability in linear trends.

5.2 Role of sediment availability Sandbars play a key role in the overall stability and evolution of the shoreline in the nearshore sediment system and provide a means for the temporary storage of sand during high wave events. Shoreline recovery on wave-dominated coastlines has been linked to the cross-shore location and presence of sandbars (Angnuureng et al. 2017; Phillips et al. 2017), while the lack of, or reduction in the number of sandbars has been linked to subsequent increased shoreline erosion (Price & Ruessink 2013; Splinter et al. 2016). The net offshore migration of sandbars (e.g. Wijnberg & Terwindt 1995), as is present in the region of this study site (Ruggiero et al. 2016; Di Leonardo & Ruggiero 2015), may also contribute to sediment loss due to offshore sandbar decay (Ruessink et al. 2009; Stevens et al. 2012; Walstra et al. 2012). In the context of this present study, the temporal variability in the number of sandbars present, nourishments, and engineering structures led to temporal and spatial variability in model best-fit coefficients in the equilibrium model (Table 3 and Table 4). Several studies have examined the influence of nearshore or shoreface nourishments to sandbar and shoreline behaviour. Stevens et al. (2012) documented the initial morphological response to the 281,000 m3 shoreface nourishment at the southern end of this site (Benson Beach) in 2010. During the nourishment period (July – September 2010) the sandbars behaved typical of low-energy conditions and onshore bar migration. The outer bar moved onshore and decreased in height, while the middle bar was more variable both in its height 29

and cross-shore movement. Stevens et al. (2012) noted that the middle bar was largest offshore of the nourishment area. With the onset of winter higher waves, the majority of the nourishment was transported offshore by cross-shore sediment transport into the inner and middle sandbars. A triple sandbar system developed during this time accompanied by offshore sandbar migration. Between December 2010 and September 2011 several morphological surveys documented net erosion, as well as net accretion of the subaerial beach and the loss/decay of the outer bar and the system transferring to a single bar system. The decay of the outer bar was associated with longshore transport process, as described elsewhere (Aagaard et al. 2010). Net accretion of the subaerial beach over the summer months was notable at the southern end near the north jetty, just south of the original nourishment site. Stevens et al. (2012) concluded that despite the initial rapid erosion of the shoreface nourishment at Benson Beach, the nourishment likely had a positive buffering effect and reduced upper beach erosion during the higher winter waves. The nourishment may have also contributed to enhanced recovery during the following summer. Within the context of this larger 10-year study at the same site, the nourishment may have contributed to a more stable (less cross-shore dynamic outer sandbar) as evidenced in Table 3 (c coefficient) in the latter portion of the study period. This more stable outer bar may have in turn influenced the equilibrium cross-shore behaviour of the middle bar as evidenced in Table 4( coefficient) in the latter portion of the study period. Similarly, regions closest to engineering control structures and nourishments displayed different model best-fit coeffients compared to the other 2 regions in this study (Table 4). Grunnet and Ruessink (2005) reported on a 2M m3 nourishment along the meso-tidal Dutch coastline where net offshore bar migration is continuously present with cycles on the order of 12 years. Unlike the upper shoreface nourishment described by Stevens et al. (2012) at Benson Beach, the Terschelling nourishment was placed in the surfzone between the middle and outer bar, filling the trough. The nourishment had a significant stabilizing effect on the local beach for a period of 6-7 years. This included a shoreline advance of ~ 15m/yr

30

(compared to pre-nourishment at -3m/yr), distinct development of a three-dimensional sandbar system and the temporary stoppage of the offshore migration of sandbars. Ojeda and Ruessink (2008) reported on a similar 1.7M m3 nourishment at Noordwijk, the Netherlands. In this instance, the nourishment was placed offshore of the outer bar and slowly moved onshore over the subsequent 4 years. During this time, the sandbars did become discontinuous and showed signs of merging and bi-furcating as seen at Benson Beach (this study). Like the nourishment described by Grunnet and Ruessink (2005), the Noordwijk nourishment halted the net offshore migration cycle. However, this nourishment placed offshore of the outer bar did not influence the shoreline variability or the alongshore three-dimensionality of the sandbars. These large-scale nourishments on the Dutch coastline are an order of magnitude greater than what was placed on Benson Beach and may be one reason why the nourishment responses were more pronounced in terms of shoreline and sandbar stability at Terschelling and Noordwijk. Severe storms, like the extreme winters described here, as well as other events observed around the world (Masselink, Scott, et al. 2016; Masselink, Castelle, et al. 2016; Castelle et al. 2015; Harley et al. 2017) describe the erosion of sand from the subaerial beach and dune system and subsequent deposition of large amounts of sediment into the nearshore sandbars. Observations of recovery are less available, but several studies have shown that even after these large wave events where 100-200 m3/m of sand can be removed from the dry beach and dune system, the lower dry beach has shown significant recovery within 1 – 2 years on sandy coastlines (Scott et al. 2016; Phillips et al. 2017; Castelle et al. 2017). These observations agree with those presented in this study where no longterm effect on the stability of the sandbars and shoreline were observed due to the severe winter storms.

5.3 Limitations of this study One of the challenges in attempting to understand and predict multi-bar behaviour is the book-keeping of individual sandbars. The methodology employed here was to label their location compared to other bars present in the same image and historical tracking. This was 31

possible because of the high temporal resolution of the Argus system; hourly images were acquired during daylight hours, 365 days a year and were used to track each sandbar. This temporal resolution was critically important. On occasion, when large waves and weather masked the images, the identity of a sandbar was in question. However, its identity was eventually resolved by tracking its subsequent behaviour. Several iterations of sandbar identity of the continuous 10-year study period was required to obtain the final data set used here. It is appreciated that there could be spurious errors in sand bar identity and therefore outliers in sandbar position. During the mild summer conditions in 2005 and 2006, the 2 sandbars present were identified as the outer and middle bar despite their cross-shore location being within the long-term temporal variability of the middle and inner sandbars (Figure 3). When attempting to model discrete sandbar movement based on equilibrium theory, these outlier points (defined as greater than +/- 2 standard deviations of the mean) were not well modelled by their respective sandbar model but their observed cross-shore position was correctly estimated by the next inner bar model (i.e. the outer bar position was now correctly modelled by the middle bar model). This still suggests that the time varying position of sandbars based on equilibrium theory could be predicted by these simple discrete models. Data points considered to be outliers (greater than +/- 2 standard deviations of the mean) were removed from the data set to determine if model skill could be improved. These points were often identified as rapid onshore movement of a bar to the position of the next inshore bar. The intention behind this was to see how the model was able to capture the dominant equilibrium signal, rather than the transitional phases and bar merges. Removing these points, however, did not improve the model skill. No attempt was made to reassign bars (for example from outer bar to middle bar) when the outliers fell within the cross-shore variability of another bar. Modelling is complicated in a multi-bar system when bars merge and bifurcate both in time and alongshore. Merges are more common during transitional phases before and after winter and summer seasons, and they are most often located in the north and south ends of 32

this site. Elsewhere (Ojeda et al. 2008), bar merging and bifurcating has been linked to nourishment projects. It was expected that the presence of merges would impact bar behaviour; however, model skill was not significantly higher in areas where merges did not exist. The equilibrium model treats each bar as a discrete entity, with no input or feedback from adjacent features. However, coupling of nearshore features has been observed in the field (Castelle et al. 2010; Price & Ruessink 2013; van de Lageweg et al. 2013; Rutten et al. 2017) and likely influences the cross-shore migration of individual bars but is not captured in the present model. Despite this, the model was able to reveal equilibrium behaviour along three features in this multi-bar/shoreline system. With the exception of the inter-tidal inner bar, the model showed reasonable skill at predicting the inter-annual variability of the alongshore-averaged position of both sandbars and shorelines, suggesting this modelling approach could be more widely applied to other beaches to explore equilibrium sandbar/shoreline behaviour. Calibrating the model to different time periods and different alongshore sections revealed the sensitivity of model best-fit coefficients to the training data. This is most relevant when attempting to forecast shoreline and/or sandbar positions into the future. At long forecast ranges (10-50 years), the linear trend term in the model may dominate the predicted response. This term informs the modeller about the unknown portion of variability not captured in the wave driven component of the present model formulation. For example, comparing the observed linear trend in the data (Section 4.1) to the model best fit coefficients (Table 2), the model captures 78% of the decadal-scale shoreline trend in the wave driven component (first term on RHS of eq. 1). In contrast, only 43% of the linear trend in the observed offshore bar migration is captured by the wave-driven component of the model. Accounting for additional physics in this simple model, particularly at longer timescales is a focus of future research.

33

6 Conclusions A 10-year data set (2003 - 2014) of bi-weekly shorelines and sandbar measurements derived from time-averaged video images were used to explore seasonal to inter-annual behaviour of the nearshore sediment system at Benson Beach, a high-energy meso-tidal site with a multi-sandbar system. During the study period, the nearshore sediment system responded to losses and gains of sediment by transitioning between a double and triple bar system and exhibited complex three-dimensionality as sandbars merged and bifurcated. Severe winter storms weakened the sandbar system and resulted in greater cross-shore migration of the outer bars.

On the decadal timescale, the sediment system appears to be

in an erosive state as the sandbars move offshore and the shoreline erodes. The application of a simple equilibrium shoreline model (ShoreFor), to an exposed highenergy meso-tidal beach with a multi-sandbar system indicates that equilibrium theory is skilful at predicting the wave-driven cross-shore movement of discrete sandbars and the shoreline at seasonal to decadal timescales. Over a 10-year period analysed in this study, equilibrium behaviour is strongest on the end-member states: the outer sandbar (R = 0.75) and the shoreline (R = 0.82). The shoreline model is able to capture both extreme and mild years. While the outer bar model was skilful, it under-estimated the cross-shore displacement of the bar when the system transitioned between a double (summer) and triple (winter) sandbar system. The sandbars located in between the shoreline and the offshore bar, particularly the inner bar, are hypothesized to play a role of sediment transport pathways between these two features and are less well-modelled by a simple-equilibrium approach. Temporal and spatial variability in model coefficients suggest this nearshore sediment system evolves due to changes in sediment supply and is influenced by engineering structures at the southern end of the site. Acknowledgments The authors would like to acknowledge the contribution of the Brazilian government and governmental organization CNPq (Program Ciência sem Fronteiras / Science without 34

Borders) for giving financial support for the student Maria V.G. Gonzalez on her exchange to UNSW Sydney that led on to her participation on this present research project. Wave data was downloaded from the NOAA National Data Buoy Center (http://www.ndbc.noaa.gov/). Shoreline and sandbar position analysis were provided with funding to NorthWest Research Associates (NWRA) from the US Army Corps of Engineers, Portland District. A special thanks to Hans R. Moritz (USACE NWP) for his visionary championing of long-term data collection at the Mouth of the Columbia River. Shoreline and sandbar data are available from the corresponding author. The authors wish to thank the two reviewers who provided insightful feedback that improved the quality of this paper. References Aagaard, T. et al., 2010. Observations of offshore bar decay: Sediment budgets and the role of lower shoreface processes. Continental Shelf Research, 30(14), pp.1497–1510. Almar, R. et al., 2010. Two- and three-dimensional double-sandbar system behaviour under intense wave forcing and a meso-macro tidal range. Continental Shelf Research, 30(7), pp.781–792. Angnuureng, D.B. et al., 2017. Shoreline resilience to individual storms and storm clusters on a meso-macrotidal, barred beach. Geomorphology, 290, pp.256–276. Castelle, B. et al., 2008. Can the Gold Coast beaches withstand extreme events. GeoMarine Letters, 28(1), pp.23–30. Castelle, B. et al., 2010. Coupling mechanisms in double sandbar systems. Part 1: Patterns and physical explanation. Earth Surface Processes and Landforms, 35(4), pp.476–486. Castelle, B. et al., 2014. Equilibrium shoreline modelling of a high-energy meso-macrotidal multiple-barred beach. Marine Geology, 347, pp.84–94. Castelle, B. et al., 2017. Foredune morphological changes and beach recovery from the

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Highlights: • The sandbar system at Benson Beach, WA displays a high degree of spatial and temporal variability • Equilibrium behavior of the end-member states (offshore bar and shoreline) is predictable and reproduced by a simple empirical model • Modelling reveals that the outer 2 bars are loosely coupled, while the inner bar is more coupled to the shoreline • Sandbar systems can oscillate between the number of bars present based on seasonal wave climate

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