Geo-Mar Lett DOI 10.1007/s00367-016-0461-7

ORIGINAL

Spatial and temporal scales of shoreline morphodynamics derived from video camera observations for the island of Sylt, German Wadden Sea Brice Blossier 1

&

Karin R. Bryan 2 & Christopher J. Daly 1,3 & Christian Winter 1

Received: 25 March 2016 / Accepted: 8 August 2016 # Springer-Verlag Berlin Heidelberg 2016

Abstract Spatial and temporal scales of beach morphodynamics were assessed for the island of Sylt, German Wadden Sea, based on continuous video camera monitoring data from 2011 to 2014 along a 1.3 km stretch of sandy beach. They served to quantify, at this location, the amount of shoreline variability covered by beach monitoring schemes, depending on the time interval and alongshore resolution of the surveys. Correlation methods, used to quantify the alongshore spatial scales of shoreline undulations, were combined with semi-empirical modelling and spectral analyses of shoreline temporal fluctuations. The data demonstrate that an alongshore resolution of 150 m and a monthly survey time interval capture 70% of the kilometre-scale shoreline variability over the 2011–2014 study period. An alongshore spacing of 10 m and a survey time interval of 5 days would be required to monitor 95% variance of the shoreline temporal fluctuations with steps of 5% changes in variance over space. Although monitoring strategies such as land or airborne surveying are reliable methods of data collection, video camera deployment remains the cheapest technique providing the high spatiotemporal resolution required to monitor subkilometre-scale morphodynamic processes involving, for example, small- to middle-sized beach nourishment. Responsible editor: B.W. Flemming * Brice Blossier [email protected]

1

MARUM, Center for Marine Environmental Sciences, University of Bremen, Leobener Strasse, 28359 Bremen, Germany

2

Coastal Marine Group, Faculty of Science and Engineering, University of Waikato, 3240, Hamilton, New Zealand

3

University of the West Indies, St. Augustine Campus, St. Augustine, Trinidad & Tobago, West Indies

Introduction Sandy coastal areas constitute valuable interfaces between land and sea, stabilizing sediments via dune and vegetation growth, providing recreation and tourism benefits, and protecting littoral areas against flood hazards (for recent overview, see Barbier et al. 2011). They are amongst the most diverse and dynamic marine environments, continuously adapting to time-varying meteorological and hydrodynamic forcing as well as human impacts. This is reflected in the dynamics of, for example, nearshore sandbars (e.g. Ojeda and Guillén 2008; Splinter et al. 2011; Blossier et al. 2016), beach slopes (e.g. Daly et al. 2015), subaerial dunes (e.g. Durán Vinent and Moore 2015) and coastal cliffs bordering pocket beaches (e.g. Ružić et al. 2014). Particularly, barrier island beaches are influenced by the duration of fair weather conditions, interrupted intermittently by storms. The frequency and chronology of these events are critical for the seaward shore of a barrier beach to accrete and widen (e.g. Lindhorst et al. 2008; Herrling and Winter 2014). The macroscale morphodynamics of the German North Sea coast has attracted increasing attention during the past decade (for overview, see Winter 2011). The barrier island of Sylt (Fig. 1), located at the confluence of the Wadden Sea and the northern German Bight, is known for battling a long history of shoreface erosion with numerous coastal protection measures. After nearly a century of utilising hard protection structures such as groynes and concrete seawalls, the island’s coastal protection policy has evolved towards softer measures (Ahrendt and Köster 1996). Since 1972, Sylt’s shoreline is maintained mainly with regular beach nourishments, amounting to approximately 45 million cubic meters of sand by 2014 (Landesbetrieb für Küsten- und Meeresschutz (LKN), data of 2015).

Geo-Mar Lett

Fig. 1 Geographical setting of the camera installation. a German Bight, SE North Sea (rectangle map in b). b Location of the camera on Sylt (red triangle). Orange dots Locations of Westerland buoy (BSH) and Bunkerhill buoy (HZG). c Closer view of the observation area on

Bunkerhill Beach: georectified image of 14 July 2013 (15:15 CEST) overlying a satellite image (Google Earth, GeoContent, GeoBasis-DE/ BKG). Dashed rectangle Area selected for present study, white arrows local reference frame

Current European and German legislation require a close monitoring of marine systems, such as nearshore environments of high ecosystem value, in order to regulate the implementation and assessment of coastal defence measures and to report on the state of the environment (Winter et al. 2014; Winter et al., Introduction to this special issue). Beach nourishment is seen as a necessary and efficient way of protecting shorelines, and is being increasingly used in Europe (Hanson et al. 2002). As such, the optimisation of the characteristics of nourishments (e.g. cross-shore location, grain size distribution) is an active area of research (Grasso et al. 2011; Huisman et al. 2014). Common assessments of the state of beach systems are typically conducted by performing regular surveys in order to construct digital elevation models (DEM) of the coastline. Such surveys are typically done using terrestrial techniques such as real time kinematics (RTK) GPS, and airborne techniques such as photogrammetry and lidar. Coastline monitoring inherently deals with temporal and spatial scales to establish an optimal design for measurement campaigns. Each monitoring technique can cover a given area with a typical horizontal resolution and vertical accuracy, at a specific frequency (or equivalent design survey time interval). Terrestrial surveys are usually conducted along regularly

spaced cross-shore transects and are 1 to 3 cm accurate vertically (Lee et al. 2013). Airborne methods provide highresolution topographic measurements over large areas (spatial resolution typically at the sub-metre scale) with a vertical accuracy that can reach 10 cm (Sallenger et al. 2003; Casella et al. 2016). Terrestrial and airborne surveys both require human supervision, which implies certain costs. Although GPS equipment can be mounted on vehicles for rapid surveys (Harley et al. 2011), the mobilization costs for terrestrial surveys limit their frequency and increase the alongshore spacing between transects if large areas of beach are to be covered. While a kilometre of beach can be monitored with a horizontal resolution of a few meters within a day (Harley et al. 2011), long beaches of tens of kilometres—such as Sylt’s shoreline— are usually monitored with a spacing of a few hundred meters every few weeks, months or annually (e.g. the Dutch Annual Coastal Measurements, JARKUS, started in 1965 in The Netherlands, supervised by the Ministry of Infrastructure and the Environment, Rijkswaterstaat). Airborne surveys are more competitive than terrestrial surveys over large scales (tens of kilometres); however, the mobilization costs are much higher compared to terrestrial surveys, quickly becoming restrictive and thereby limiting their temporal frequency.

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Video camera systems are increasingly becoming a common tool for coastal observation and monitoring on the kilometre scale (Holman and Stanley 2007). They offer a limited vertical accuracy above 10 cm (Plant et al. 2007) but a high spatial resolution (from sub-metre near the camera to a few metres at 1 km distance) and, even more importantly, a high temporal resolution with data collected every daylight hour every day for months to years. They require only periodic maintenance—hence, they are low-cost monitoring solutions compared to terrestrial and airborne survey methods. Pioneer work dates back to the late 1980s with the seminal studies of Lippmann and Holman (1990) and Holman et al. (1991), focusing on nearshore sandbars and beach profiles in North Carolina (USA) respectively. More recently at Barcelona (Spain), Ojeda and Guillén (2008) and SanchoGarcía et al. (2013) characterised the response of embayed beaches to storm events, artificial beach nourishment and the construction of breakwaters, and Turki et al. (2015) evaluated the relaxation time of shoreline rotation. At Biscarosse (France), Sénéchal et al. (2015) related cross-shore migrations to seasonal events and showed the singularity of specific events such as storm clusters. At Tairua (New Zealand), van de Lageweg et al. (2013) and Blossier et al. (2016) studied the behaviour of the shoreline and subtidal bar, and Bryan et al. (2013) compared Tairua’s behaviour with that of a neighbouring beach at Pauanui. Within this context, the present study assesses the natural spatiotemporal variability of the upper shoreface of Bunkerhill Beach on the south-western coast of Sylt (Fig. 1), employing a prototype video camera monitoring system to survey a 1.3 km beach sector over 3.5 years from 2011 to 2014. The upper shoreline is defined by the mean high water (MHW) level, located 1 m above mean sea level (MSL). First, the representativity of single-transect surveys is assessed. Then, combining numerical modelling and spectral analysis, the interannual to daily timescales of cross-shore position fluctuations are quantified. The modelling approach evaluates response times, i.e. the time needed to observe a significant response of the shoreline to given environmental forcing conditions. The spectral analysis decomposes the shoreline signal into a sum of harmonic frequency signals. Such data can serve to gauge the performance of other terrestrial and airborne monitoring techniques.

a rail track built in 1927, and since then demarcating (from north to south) the Lister Tief and Hörnum Tief backbarrier tidal basins (Fig. 1b). To the west, Sylt is bordered by a 38 km long, continuous sandy beach stretching from the southern (Vortrapp - Hörnum Tief) to the northern tidal inlet (Lister Tief). Whereas the central sector is urbanized and partly protected by an 800 m long seawall, the beach is backed by a wide coastal dune system along the northern and southern spits. The northern spit, wide between Kampen and List (width between 1.7 and 7 km), connects at the north of List to a 7 km long hooked spit via a 300 m wide hinge. The width of the southern spit varies between 600 m near Rantum and 1.5 km near Hörnum. The beach consists of medium to coarse sand, and commonly exhibits a double-barred profile (Ahrendt and Köster 1996; Ahrendt 2001). Ahrendt and Köster (1996) report that a subtidal bar located between 300 and 500 m from the shoreline shows crescentic features with a typical wavelength of 700 to 1,400 m alongshore. An intertidal bar extends from the shoreline up to approximately 150 m offshore. This bar regularly exhibits rip channels with a spacing ranging from one to a few hundred metres. Measurements of beach profiles in the study area with lidar (source: LKN) in November 2013, and with RTK GPS in June 2014, October 2015 and April 2016 showed that the slope βf of the upper shoreface (0–2 m above MSL) varies between 0.11 and 0.16, with most values around 0.13. This value is selected for βf in subsequent analyses. The surf similarity parameter (Iribarren number, Battjes 1974) ξ is expressed as:

Study area

with g the gravitational acceleration and Tm the mean wave period.

βf ξ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi H 0 =L0

ð1Þ

with H0 and L0 the offshore wave height and wave length respectively. ξ falls between 0.55 and 1.3 (5 and 95% percentiles respectively), corresponding to intermediate beach slopes where waves are mostly plunging rather than surging, collapsing (steeper profiles) or spilling (gentler profiles). In this paper, H0 is equivalent to the significant wave height offshore of the subtidal bar crest (Hs) at the location of the Bunkerhill buoy at 7 m depth (see Fig. 1c). The offshore wave length is computed using deep water linear wave theory: L0 ¼

gT 2m 2π

ð2Þ

Physical characteristics Environmental conditions Sylt is the northernmost German barrier island separating the North Sea from the Wadden Sea (Fig. 1a). To the east, the island is bordered by extensive salt marshes and tidal flats. It is connected to the mainland by a 10 km long dike supporting

The Sylt coastline is microtidal, exposed to semidiurnal tides with a tidal range between 1.8 and 2 m during neap and spring tide respectively. Westerly winds dominate, generating waves

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with an average significant wave height Hs of 0.9 m originating from directions varying mainly between 247.5 and 315° (Ahrendt 2001). Tidal data used in this study were collected at Hörnum (see Fig. 1b) and provided by the Federal Administration of Waterways and Navigation (Wasserund Schifffahrtsverwaltung des Bundes, WSV) and the German Federal Institute of Hydrology (BfG). The wave data have four different sources. Data collected by the Bunkerhill wave buoy deployed by the HelmholtzZentrum Geesthacht (HZG), approximately 700 m offshore of the beach beyond the subtidal bar at 7 m depth, constituted the basis of the wave dataset (see Fig. 1b, c). Data gaps were filled with wave data collected by the Westerland wave buoy located further offshore, 18 km to the northwest at 14 m depth, and maintained by the Federal Maritime and Hydrographic Agency (BSH; see Fig. 1b). R2 coefficients of 0.96 and 0.71 were found for Hs and Tm, with corresponding root mean square errors (RMSEs) of 14 cm and 0.5 s respectively. Further missing sequences were filled with modelled wave data. Wave heights were extracted from the Deutscher Wetterdienst (DWD) model, and wave periods from a model developed within the HZG COSYNA project (BCoastal Observation Systems in the North Sea and Arctic^). This choice was made according to the R2 coefficients and RMSE values found between the model data and the Bunkerhill buoy data. R 2 =0.84 and RMSE=0.27 m were obtained for the DWD model wave heights, and R2=0.49 and RMSE=1 s for the COSYNA model wave periods. The reconstituted wave dataset extends from the end of 2010 to mid-2014, and largely agrees with the findings of Ahrendt (2001) with an average Hs=0.95 m. The maximum wave height that occurred during the observation period, 8.3 m, is close to the value of 9 m found by Ahrendt (2001) between 1986 and 1997. Mean wave periods were usually short with an average of 4 s over the 3.5 years of observations.

Materials and methods Video monitoring system A prototype video camera system was installed at Bunkerhill Beach in December 2010 (Fig. 1b). The camera is mounted approximately 25 m above MSL on top of a measuring station provided by the HZG, in which electric power for computing equipment and internet connection allows for remote monitoring of the station. The camera has a sensor size of 1/3 inch (6.0×4.8 mm) and a 16 mm fixed focal length mounted lens. Every hour, 1,080 images are acquired at 1 Hz over 18 minutes. This frequency ensures adequate resolution of shoreline

water level variability induced by incoming wave run-up and run-down, as well as wave group-induced surf beat. The average water level observed at the shoreline corresponds to the superimposition of the tidal level, the water level setup induced by wave breaking in the surf zone, and the swashinduced run-up (Plant et al. 2007). In this analysis, only the images corresponding to an overall water level between 0.8 and 1.2 m above MSL are selected, corresponding to MHW±0.2 m. This interval was chosen because first, at these water levels, the intertidal bar is not visible and second, it has proven satisfactory for representing the overall behaviour of sandy beaches in similar applications (van de Lageweg et al. 2013; Castelle et al. 2014; Sénéchal et al. 2015). In the present case, therefore, the shoreline is always located along the upper shoreface of slope βf. The image selection range of 0.4 m thus results in a maximum horizontal deviation of ±2 m from the considered shoreline located at MHW. The overall water level setup due to waves (setup and swash run-up) at Sylt was evaluated as the 2% exceedence water level R2 computed using the empirical formula of Stockdon et al. (2006) for intermediate beaches (0.3<ξ<1.25): 0

   1 = 1 2 2 H L 0:563β þ 0:004 0 0 f = A R2 ¼ 1:1@0:35β f ðH 0 L0 Þ 2 þ 2 1

ð3Þ Images for which Hs was above 1 m were excluded to decrease the error in wave setup evaluation. Averaged images were first corrected for lens distortion following methods in Heikkila and Silven (1997). Then, the computed water level served to georectify the averaged images with a grid spacing of Δx=Δy=0.5 m. While the horizontal pixel footprint remains below 0.5 m up to a distance of 430 m from the camera, it increases gradually up to 1 m in the cross-shore direction and 18 m in the alongshore direction at 1.6 km distance. Further away, the data were ignored as the accuracy would further decrease and the overall reliability would need further investigation. Shorelines were extracted automatically based on the ratio of red to blue colours at each pixel of the georectified image (Smith and Bryan 2007). Manual digitization was used when the algorithm failed, usually due to low image quality related to weather conditions. In total, 627 digitized shorelines corresponding to MHW±0.2 m were selected, i.e. 0.7 image per day (ignoring data gaps longer than 20 days). A 6-day moving average (using on average six shorelines for each averaged shoreline) served to reduce further the error related to the water level selection range. The resulting horizontal error (standard deviation), based on the moving-averaged water levels including tide and wave contributions, was estimated as 60 cm.

Geo-Mar Lett

Combining errors related to water level selection range and pixel footprint resulted in a potential crossshore error of 1.1 m close to the camera and 1.6 m at 1.6 km distance. The alongshore averaging of the shoreline position (cf. below) results in an error of 1.3 m. For comparison, an RTK GPS survey conducted in June 2014 enabled to evaluate the differences between measured and digitized control points using a 1.5×1.5 m target in the field. On average over the whole observation domain, position errors were 1.5 m horizontally and 0.15 m vertically. Within the local reference frame, the camera location is the origin. The x-axis is directed northwards, parallel to the average orientation of the southern coastline of Sylt (3.2° east of north). The y-axis is oriented seawards, perpendicular to the coast (Fig. 1c). Semi-empirical modelling Semi-empirical models have been developed to simulate the cross-shore migration of shorelines (Miller and Dean 2004; Yates et al. 2009; Davidson et al. 2010). They are based on the definition of a theoretical equilibrium shoreline position ys,eq for certain boundary conditions, and vice versa. At any point in time, a first-order response characterizes the evolution of the cross-shore position ys towards ys,eq. This means that the instantaneous shoreline migration rate is proportional to the difference between the current position of the shoreline and its theoretical equilibrium position (i.e. quicker for large differences and slower for small differences). The analysis below uses the model developed by Yates et al. (2009) where the environmental parameter controlling the shoreline equilibrium position is the wave energy E: E eq ¼ ays þ b

ð4Þ

shoreline erodes and C– is used. The model can be rewritten in terms of equilibrium shoreline position: E−b a  dys 1  ¼ − ys −ys;eq dt τ 1 pffiffiffiffi τ ¼− C a E

ys;eq ¼

ð6Þ ð7Þ ð8Þ

where τ is the instantaneous response time in days. Semiempirical models may be applied to assess the response times of a shoreline as they relate migration rates to forcing conditions. Generally, response times (also named characteristic times) quantify the time duration needed for a forced system to respond significantly to an external forcing. In the present case, in the approximation of constant wave energy conditions valid for a short period of time, the temporal evolution of the cross-shore shoreline position ys obeys a first-order linear differential equation (Eq. 7). Accordingly, 95% of the response of ys towards its equilibrium position ys,eq is achieved within three times the response time τ.

Results Shoreline observations In order to obtain a better visualisation of the morphodynamics occurring in the study area, the temporal average of the shoreline position in the 1,325 m long local reference frame was removed. This time-averaged shoreline is presented in Fig. 2 (black line). Very low-amplitude shoreline undulations, especially between x=275 m and x=900 m, were removed using a moving average over 150 m (red dashed line). This value was chosen as the

and pffiffiffiffi  dys ¼ −C  E E−Eeq dt

ð5Þ

with Eeq the equilibrium wave energy, C+ the accretion rate coefficient, C– the erosion rate coefficient, and a and b the equilibrium slope and y intercept respectively. In this study, the wave energy E is equivalent to the squared significant wave height Hs2. C+, C–, a and b are calibrated using a particle swarm algorithm (Ebbesen et al. 2012). Equations 4 and 5 describe the model in terms of equilibrium energy Eeq rather than equilibrium position ys,eq. Therefore, instead of ys,eq defined as a function of E as mentioned above, the formulation of Yates et al. (2009) defines equivalently an equilibrium energy Eeq depending on ys so that, if (EEeq), then the

Fig. 2 Time-averaged shoreline cross-shore position averaged over observation period (December 2010 to June 2014, black line) and its alongshore moving average over 150 m (red line): x-axis values increase northwards, y-axis values increase seawards (see Fig. 1c)

Geo-Mar Lett

minimum value removing these remnant shoreline undulations of small amplitude (below 5 m). According to the time-averaged shoreline shape, the beach is narrower close to the camera (300
2012) with an average of 4.5 m. The wavelength of these undulations varies between 200 m (January to May 2011) and 600 m (January to May 2012). The crests of these undulations exhibit a complex behaviour with merging events (May–August 2011, x=600–900 m) and splitting events (June 2012). The upper beach shoreface is also observed to reset, meaning that wave events lead to a complete reorganisation of the rip channels in, for instance, winter 2012 (erosional event) and April 2014 (accretive event). Large-scale seasonal variations are evident in the crossshore dimension (Fig. 3a). Alternation of summer and winter type profiles is indicated by seaward shoreline locations in summer (particularly July and August every year) and landward shoreline locations in winter (January 2012, November 2012 to January 2013, November 2013 to February 2014). Moreover, rip channels tend to migrate northwards during winters (+200 m in winter 2012–13, +300 m in winter 2013–14) and southwards during summers (–300 m in summer 2011, –200 m in summer 2013). In addition, the data

Fig. 3 a Temporal evolution of shoreline cross-shore position S(x, t) relative to its time-averaged position between December 2010 and June 2014, plotted as a function of time t (horizontal axis) and alongshore position x (vertical axis). N North, S south, white areas no data. For more information, see main text. b Significant wave height offshore of Bunkerhill Beach. c Alongshore-averaged shoreline cross-

shore position < S(x, t) > (black dots) and corresponding standard deviation (gray shading), outcome of semi-empirical model of Yates et al. (2009) calibrated over the full 3.5-year dataset (red line), and aggregated outcome of semi-empirical model calibrated for yearly time periods (blue line; see Table 1)

Geo-Mar Lett

show the effect of nourishment at the south of the beach in July 2013 (275
corresponding to all possible spacings δ from 0.5 to 1,325 m (distance between the first and last transect). Related equations are:

Spatial scales

~ C i; j ¼ ρi; j C ¼ S~t S;

The representativity of single cross-shore transects is a critical parameter when beach morphology is monitored by means of transect-based surveys. Shoreline undulations can hinder the recognition of large-scale temporal fluctuations when considering a single cross-shore transect (constant x value). For instance, winter erosion could be hidden by the forming crest of an undulation, such as in February 2012 (x=1,200 m), or similarly by an alongshore migrating crest (cf. Fig. 3a). This would appear as an accretion event, which is not representative of the average shoreline behaviour. This aspect was assessed based on two analyses whereby the shoreline dataset was split into Δx=0.5 m alongshore-spaced transects spanning the 3.5 years of observations. The first analysis gauges the correlation between shoreline position time signals along two single transects as a function of the inter-transect alongshore distance. If the shoreline were alongshore uniform, then the correlation would be 1 for all alongshore spacings. The second analysis assesses the influence of transect spacing on the calculation of a kilometre-scale averaged shoreline position. The reference signal is set as the original alongshoreaveraged shoreline signal based on the full dataset. Shoreline transects are selected with a spacing ranging from 0.5 to 1,000 m. Selected transects are alongshore-averaged, resulting in a temporal signal that is compared to the reference signal (Δx=0.5 m spacing).

M ¼ C⊙C; M i; j ¼ R2i; j

Single transect representativity The alongshore extent of the representativity of single transects was assessed based on linear correlation analysis between the cross-shore position time series of two given transects separated by a distance δ. These linear correlations are evaluated for all possible couples of transects in the dataset, by computing the covariance matrix C of the shoreline signal S~ ðx; t Þ normalized in time. A covariance matrix element Ci,j corresponds to the correlation coefficient ρi,j between transects i and j with values of 1 along the diagonal (i=j). This matrix is squared element-wise (symbol ⊙) to obtain a matrix M with Mi,j=R2i,j. R2i,j at row i and column j corresponds to the R2 coefficient between the shoreline position signals at transects i and j separated by an alongshore spacing δ = (j–i)Δ x . Therefore, the alongshore spacing is constant along diagonals of M since these correspond to constant values of (j–i). M is averaged along its diagonals to obtain representative averaged < R2(δ) > values and associated standard deviations σR2 ðδÞ

< R2 ðδÞ >

¼

ð9Þ ð10Þ

1

X

δ N− Δx

ði; jÞ; ð j−iÞΔx ¼δ

0 1 σR 2 ð δ Þ ¼ @ N − Δδx

X

ð11Þ

M i; j

h

R2i; j −

i2

11 =

2

< R ðδ Þ > A 2

ði; jÞ; ð j−iÞΔx ¼ δ

ð12Þ with N the number of shoreline transects (N=2,651) and t S~ the ~ Statistical results < R2(δ) >, σR2 ðδÞ and extrema transpose of S. are plotted in Fig. 4a, as a function of δ. A conservative F test (conservative because not accounting for ensemble averaging) shows that R2 below 0.18 is not significant at the 95% level. This means that transects separated by more than 70 m are weakly correlated (< R2 > − σR2 =0.18) and, above 105 m, they are not significantly correlated (< R2 >=0.18). For the observed section of the Sylt beach, a transect spacing below 70 m therefore appears as a minimum to satisfactorily account for beach morphodynamics below the kilometre scale. Transect spacing and averaging Evaluating the influence of shoreline morphodynamics on the calculation of kilometre-averaged shoreline positions enables the assessment of the amount of shoreline temporal variability that, at this scale, is captured by common land surveys based on cross-shore transects. The reference signal was set as the full-resolution alongshore-averaged temporal signal < S(x, t) > (see Fig. 3c, black dots). Then, using different alongshore spacing δsub varying between Δx=0.5 m and 1,000 m, the dataset was subsampled into subsets S δsub ;k ðx; t Þ. For each spacing δsub, k subsets were built with k = δsub/Δx–1. These subsets were alongshore-averaged (< S δsub ;k ðx; t Þ > ) and the R2 coefficients with the reference signal computed. In Fig. 4b, the results show a significant correlation (< R2 > − σR2 >0.18) between the subsampled and reference shoreline signals down to a spacing of 900 m (i.e. two transects). A better representation of shoreline temporal fluctuations at a kilometre scale in the present study area requires spacings of 150 m (< R2 > >0.95) or 100 m (< R2 > >0.99). Temporal scales For sandy beaches, the response times of shoreline cross-shore position to variations in incident wave energy (cf. Wright and

Geo-Mar Lett

Fig. 4 a R2 coefficients for interrelationship between temporal signals of cross-shore shoreline positions at two locations separated by the distance given along the horizontal axis: solid line average value, dashed lines standard deviation, dotted lines extrema. Significant values above 0.18. b R2 coefficients for interrelationship between the alongshore-averaged

position of the shoreline using all cross-shore transects and the alongshore-averaged position of the shoreline based on a limited number of transects using the alongshore spacing given along the horizontal axis. Lines As in a. Significant values above 0.18

Short 1984) has been found to range from days (storm conditions) to months (fair weather conditions; Miller and Dean 2006; Yates et al. 2009). In the present case, this aspect was evaluated by (1) computation based on the semi-empirical model described by Eqs. 6, 7 and 8 (cf. Miller and Dean 2006; Yates et al. 2009) and (2) computing the power spectrum of temporal fluctuations in shoreline position.

The model successfully hindcasts the shoreline positions within less than one standard deviation compared to < S(x, t) >. The model skills are fair, with an RMSE of 2.2 m close to the shoreline signal standard deviation (2.4 m). The R2 value of 0.23 is slightly above the significance level (0.18), and the Brier skill score (Bss) of 0.18 confirms that the model is able to partly simulate the shoreline behaviour. More reliable model coefficients were obtained by calibrating the model of Yates et al. (2009) over yearly periods. These are defined with a 6-month overlap, so that six segments were obtained (see Table 1). Overlapping model outcomes are averaged in Fig. 3c. Model skills and coefficients (Table 1) are significantly better, with average values of 1.5 m, 0.56 and 0.53 for the RMSE, R2 and Bss respectively.

Semi-empirical model calibration The semi-empirical model of Yates et al. (2009) was calibrated in terms of the alongshore-averaged position of the shoreline < S(x, t) > covering the full 3.5-year study period (Fig. 3c). Daily wave height data presented in Fig. 3b were used as model input. Model coefficients and model skills are given in Table 1. Model outcomes are depicted in Fig. 3c (red line). The model accounts for seasonal effects and the impact of storms—the winter shoreline retreat is fairly well reproduced in 2012, 2013 and 2014. The equilibrium shoreline position ys,eq,0 for E=0, equal to –b/a (see Eq. 6), is 2.4 m. This realistic value is slightly below the most seaward measured shoreline position (5 m).

Table 1

Model skills and coefficients

Time

C+ C– a (m day–1/m3) (m)

Dec. 2010–Jun. 2014 Dec. 2010–Dec. 2011 Jun. 2011–Jun. 2012 Dec. 2011–Dec. 2012 Jun. 2012–Jun. 2013 Dec. 2012–Dec. 2013 Jun. 2013–Jun. 2014

3.587 0.005 0.183 0.504 0.719 0.592 7.334

0.04 3.12 0.02 0.06 0.10 0.03 0.04

–0.13 –0.25 –0.17 –0.24 –0.18 –0.10 –0.14

b RMSE R2 (m2) (m)

Bss

0.31 9.29 0.87 0.24 0.39 0.45 0.33

0.18 0.50 0.39 0.59 0.62 0.54 0.53

2.2 1.4 2.1 1.4 1.3 1.4 1.2

0.23 0.52 0.49 0.63 0.63 0.56 0.54

Derived response times The shoreline response times defined by Eq. 8 were evaluated based on the calibrated model coefficients. The value of the equilibrium wave energy Eeq (Eq. 4), necessary to determine whether C+ or C– should be used, was taken from the model outcome. Response times τ were first calculated for the model calibrated over the full 3.5-year time period (Fig. 5, thin black line). Then, they were similarly evaluated using interpolated values for coefficients C+, C–, a and b, and the modelled equilibrium wave energy corresponding to each yearly segment (averaged for overlapping segments). The distribution of τ values is presented in Fig. 5 in terms of exceedence probability Pmod. For a general first-order system, 95% of the total response to an external forcing occurs within a timeframe of 3τ. This means that surveying a shoreline with a design period Tsurvey (or frequency fsurvey) allows for the dynamics of a response with response time τ=Tsurvey to be caught, and that of any slower response with τ>Tsurvey. Therefore, Fig. 5 enables the calculation of how much of the beach temporal dynamics are

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period exceedence probability Pspec(T>Tc), with T the time period of a random harmonic fluctuation of the shoreline. The minimum survey design time interval required to monitor fluctuations of time period Tc is Tsurvey=Tc/2. Therefore, the probability that shoreline fluctuations of time period T can be measured with a survey design time interval Tsurvey is Pspec(T>2Tsurvey) = Pspec(T/2>Tsurvey). The corresponding curve showing Tsurvey as a function of Pspec(T/2>Tsurvey) is presented in Fig. 5, averaged over all the transects (thick red line) with an indication of the standard deviation (dashed red lines). The same curve corresponding to the Lomb-Scargle spectrum of the alongshore-averaged shoreline position < S(x, t) > is given in blue. For instance, covering 50% of the shoreline dynamics requires surveying every 11 weeks according to the red line, or every 45 days according to the blue line.

Discussion Shoreline surveying

Fig. 5 Exceedence probability curves of shoreline response times τ and shoreline fluctuation time periods T. Black lines Pmod(τ>Tsurvey) evaluated for modelled response times τ computed using interpolated semiempirical model coefficients calibrated for yearly periods (thick line) and for the entire 3.5-year period (thin line). Red and blue lines Pspec(T/ 2>Tsurvey) corresponding to measured shoreline fluctuation time periods T, thick red line average for all cross-shore transects, dashed red lines corresponding standard deviation, blue line alongshore-averaged shoreline (cf. black dots in Fig. 3c)

covered for a given survey frequency fsurvey (or design time interval Tsurvey) by providing the exceedence probability Pmod(τ>Tsurvey). For instance, according to the thick black line, surveying every year (Tsurvey=365 days) gives access to ca. Pmod(τ>Tsurvey)=15% of the shoreline dynamics; surveying every fortnight gives access to ca. 85%.

Power spectrum A power spectrum enables characterizing temporal variance exceedence levels, i.e. defining for which frequency fc (or time period Tc) a given percentage of the total variance is reached. The power spectrum of unevenly spaced data can be evaluated using the Lomb-Scargle method (Press et al. 1992). In the present study, Lomb-Scargle spectra of the shoreline crossshore position were computed and normalized for each alongshore location. Then, the power spectrum cumulative distribution was computed by integrating the power spectrum from f=0 to fc for each frequency fc. Finally, frequencies were converted to periods, resulting in the shoreline fluctuation time

Depending on their objectives, coastal monitoring programs vary strongly in the degree they track detailed spatiotemporal trends in beach morphodynamics. In the present test case of the island of Sylt, observations cover shoreline morphodynamics from a metre to kilometre scale. The results of spatiotemporal analyses show that the design time interval of a survey as well as its spatial resolution strongly control the amount of information gained. In this regard, the dataset enables the evaluation of the relation between the resolution of a survey in time and space, the amount of shoreline variability captured, and the representativity of kilometre-averaged morphological parameters such as shoreline position. According to Fig. 4, a 10 m spacing of survey transects captures shoreline dynamics with an alongshore resolution of 5% temporal variability (95% of the variance of the shoreline position signal is shared at two alongshore locations spaced 10 m apart, i.e. R2=0.95). In terms of design survey time periods, 5 days cover 95% of shoreline dynamics, 15 days cover more than 80%, monthly surveys cover 70% and quarterly surveys (every 3 months) still cover 45% (Fig. 5, red line). Only few technologies can provide this level of spatiotemporal resolution (airborne technologies using lidar or photogrammetry, video camera systems, and terrestrial vehiclemounted GPS units), and the required frequency of surveys would always induce very high costs for those involving human supervision and remobilization of equipment. Video camera systems do not suffer from this disadvantage (see Introduction). They also enable cost-effective monitoring of kilometre-scale beach sectors for which the constraints on survey spatial resolution are less restrictive. Based on the present results, a spacing of 150 m is sufficient to capture 95% of

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the temporal variability in kilometre-scale cross-shore morphodynamics, and 250 m would still capture 80% (Fig. 4b). The requirements in terms of survey time intervals remain stringent, as mentioned above. The analyses in the present work are based on a 3.5-year dataset of a small beach sector of the island of Sylt. Accordingly, the results cannot reliably account for longterm morphological fluctuations with periods exceeding 1 year. Rather, they relate to the dynamics of extreme events (e.g. storms or storm clusters) and subkilometre-scale morphological features (e.g. rip channels, shoreline undulations, sandbars related to beach nourishment). Validity and limitations Combining the semi-empirical modelling approach with the spectral analysis of the shoreline data strengthens the validity of the results on temporal scales. Indeed, while the two methods are strongly independent, the results agree fairly well, as shown by the good fit between the solid lines in Fig. 5. Modelled erosion and accretion rates The response time distributions (cf. black lines in Fig. 5) depend on the calibrated coefficients of the semi-empirical model (Table 1). This calibration was first performed on the 3.5year measured, alongshore-averaged shoreline position < S(x, t) >. The limited skills of the resulting calibrated model motivated the use of a second method where the model was calibrated for six overlapping yearly time segments. Model skills improved significantly. Coefficients a and b are quite stable for the different calibration methods, with a ratio –b/a (corresponding to the equilibrium shoreline position ys,eq,0 for E=0) falling between 1 and 5.2 m. Only for the first time segment (December 2010–2011) did this ratio reach 37 m due to a high value of b. C+ is mostly one order of magnitude larger than C–, being two orders of magnitude larger than C– for the 3.5-year calibration period and the last time segment (June 2013–2014). The opposite occurs for the first time segment where C+ is three orders of magnitude smaller than C–. Larger values of C+ indicate that, for equivalent incident wave energy E, the shoreline accretes more rapidly than it erodes. Whereas Yates et al. (2009) found similar values for C+ and C–, Davidson et al. (2013) also found larger values for C+ using a similar semi-empirical model. Therefore, strong shoreline erosion in winter is not due to erosion outweighing accretion but rather to storm intensity decreasing the response time (E½ at the denominator, Eq. 8) coupled with the large difference between the incident wave energy E and the equilibrium wave energy Eeq. In other words, large differences between observed positions of the shoreline ys and its equilibrium position ys,eq result in increased shoreline migration rates (Eqs. 5 and 7). For this reason, similarly high shoreline migration rates can occur under both

eroding (November–December 2011) and accreting conditions (January–February 2012). The large value of b for the time period December 2010– 2011 resulting in ys,eq,0=37 m indicates a strong tendency for the beach to accrete, even though the larger C– value shows that strong accretion is partly compensated by increased erosion in the model. The tendency of the beach to accrete appears in the measured data where the most seaward value ys of the entire dataset, 5 m, is reached successively in May, July and August 2011 (Fig. 3c). However, this accretion is potentially overemphasized by the large shoreline undulation crest identified at the north of the study area between February and September 2011. This undulation may not have been well resolved by the coverage of the camera, i.e. a compensating undulation trough may have occurred northwards. In addition, given the location at the most seaward boundary of the timeaveraged shoreline (Fig. 2), the strong accretion here may also be related to longshore processes. The results revealed a disparity between model coefficients and skills depending on the duration of the calibration period (Table 1), whereby there was a significant difference in the exceedence probability of shoreline response times Pmod(τ>Tsurvey) between the model calibrated for 3.5 years (Fig. 5, thin black line) and the aggregated yearly calibrations (thick black line). In Fig. 5, the flatter the curves, the more corresponding response times were computed by the model. Thus, interannual and monthly response times are simulated more frequently with the 3.5 years calibrated model. The reverse is the case for annual, biannual and weekly response times. The overestimation of interannual response times by the 3.5 years calibrated model can be related to its limited skills. While it provides a good representation of winter erosion events and consecutive recovery periods, it suffers from an underestimation of other events occurring the rest of the year. For this reason, yearly calibrated models with better skills are preferable in investigating shoreline response times. Timescale assessment The probability of exceedence of shoreline response times Pmod(τ>Tsurvey) (thick black line in Fig. 5) can be directly related to the probability of exceedence of shoreline fluctuation time periods Pspec(T/2>Tsurvey) (blue line). Indeed, they are both based on the alongshore-averaged shoreline position < S(x, t) >. Even though the two curves in Fig. 5 fit reasonably well at the interannual timescale, the shoreline variance found between the annual and quarterly timescales with the spectral approach (blue line) is significantly less (steeper slope) than what is expected from the response time distribution (black line, gentler slope). In contrast, more variance is found for periods shorter than a fortnight. The reason could be related to the limited skills of the model in simulating shoreline fluctuations with time periods shorter than a month (see Fig. 3c). These

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fluctuations can be due to the development of shoreline undulations not taken into account by the model or to environmental parameters ignored by the model, such as the tides. As a result, lower frequencies could be overestimated in the model response time distribution and higher frequencies underestimated. On the contrary, the noise contained in the shoreline data due to the water level selection range (Eq. 3), as well as errors in the digitization process have potentially introduced high-frequency noise in signal that would lead to an overestimation of short-term fluctuations and, therefore, to an underestimation of lower-frequency fluctuations. It is likely that these two aspects influenced the results. The spectral approach based on the alongshore averaging of the spectral distributions computed at each of the 2,651 alongshore locations of the dataset (Fig. 5, red line) is much more robust to noise than that based on the sole alongshoreaveraged shoreline position (Fig. 5, blue line). Interestingly, the red curve falls in between the thick black curve, based on yearly aggregated model response times, and the blue curve, showing intermediate amounts of variance between annual and quarterly timescales and periods shorter than a fortnight. The robustness of the method, and the good agreement of its outcomes with the model-based and spectral-based results (both utilizing the alongshore-averaged shoreline position < S(x, t) >) encourage selecting the red curve in Fig. 5 as the reference line to evaluate the surveyed temporal shoreline variability corresponding to a given survey time interval Tsurvey.

Scales of beach nourishment Part of a nourishment carried out in July 2013 can be seen in the data collected by the camera (Fig. 3a) at the southern end of the beach. At the time, 51,805 m3 of sediment were distributed over 350 m of shoreline, the observations showing only the northernmost 200 m. At first glance, the intermediate scale of the nourishment (in terms of cross-shore extent) makes it appear as a natural shoreline undulation. The influence of the nourished sand on the morphology can be recognized when looking at the alongshore-averaged position of the shoreline (Fig. 3c). After the nourishment, a 5 m seaward displacement of the shoreline is observed, and the alongshore variability of the shoreline increases from 2 to 6 m (standard deviation). These values fall within the range of natural variability (maximum observed is 8 m). The shoreline undulation caused by the nourishment migrated rapidly alongshore while possibly decaying. It is difficult to fully interpret the record because of the partial coverage of the area by the video system. While it seems that a substantial part of the sand migrated southwards out of the camera field of view, the data show that some of it may have merged with an existing undulation crest located to the north (600
eroded by several storms, the nourished sand had moved away from the area of initial deposition.

Conclusions A high-resolution shoreline dataset was derived from nearshore observations acquired by a video camera system at Bunkerhill Beach on Sylt, Germany. Relevant spatial and temporal scales of shoreline morphodynamics were assessed from statistical, spectral and modelling analyses of the shoreline evolution. Spatial scales reveal that common transect-based RTK GPS surveys with cross-shore transect spacings of 10 and 150 m cover the overall and kilometre-scale dynamics of the shoreline respectively. In both cases, these spacings need to be associated with a survey time interval of 5 days to cover 95% of the shoreline variability. To investigate the detailed behaviour of beach systems under natural boundary conditions, video camera systems are today the only inexpensive option to monitor the spatiotemporal scales related to subkilometre beach processes at daily or weekly frequency. Such processes include the beach response to short extreme events, but also the dynamics of middle-size morphological features, whether these are natural (e.g. sandbars, rip channels) or related to human intervention (e.g. beach nourishments). Current large-scale monitoring schemes are commonly based on surveys performed with time intervals of 1–3 months. Such schemes still cover 70% and 45% of the shoreline variability respectively. For kilometre-scale shoreline fluctuations, the present work showed that missing data within such intervals could be partly simulated by numerical models. However, on the interannual timescale, shoreline fluctuations could neither be well modelled, nor reliably studied due to the yet limited 3.5-year observation time. Therefore, further investigations based on longer datasets and incorporating neighbouring locations are needed to better assess the larger spatiotemporal scales of Sylt’s shoreline dynamics. Acknowledgements This study was funded through the DFGResearch Center for Marine Environmental Sciences MARUM. C. Daly acknowledges funding from the Hanse-Wissenschaftskolleg as a Junior Fellow in the project WIMO (Wissenschaftliche Monitoringkonzepte für die Deutsche Bucht). The authors gratefully acknowledge the HelmholtzZentrum Geesthacht (HZG) for hosting the video camera system and for graciously providing wave buoy and wave model data via the COSYNA project (Coastal Observation Systems in the North Sea and Arctic, http://www.hzg.de/institutes_platforms/cosyna). Additional wave buoy data were provided by the Federal Maritime and Hydrographic Agency (BSH), and additional wave model data originate from the Deutscher Wetterdienst DWD model. Tidal data were provided by the Federal Administration of Waterways and Navigation (Wasser- und Schifffahrtsverwaltung des Bundes, WSV) and the German Federal Institute of Hydrology (BfG). The authors would like to thank two anonymous reviewers whose comments helped clarifying this manuscript. Conflict of interest The authors declare that there is no conflict of interest with third parties.

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