Sandbar Behavior Research Articles

A Novel GIS-Based Approach for Automated Detection of Nearshore Sandbar Morphological Characteristics in Optical Satellite Imagery

Satellite remote sensing is a valuable tool for coastal management, enabling the possibility to repeatedly observe nearshore sandbars. However, a lack of methodological approaches for sandbar detection prevents the wider use of satellite data in sandbar studies. In this paper, a novel fully automated approach to extract nearshore sandbars in high–medium-resolution satellite imagery using a GIS-based algorithm is proposed. The method is composed of a multi-step workflow providing a wide range of data with morphological nearshore characteristics, which include nearshore local relief, extracted sandbars, their crests and shoreline. The proposed processing chain involves a combination of spectral indices, ISODATA unsupervised classification, multi-scale Relative Bathymetric Position Index (RBPI), criteria-based selection operations, spatial statistics and filtering. The algorithm has been tested with 145 dates of PlanetScope and RapidEye imagery using a case study of the complex multiple sandbar system on the Curonian Spit coast, Baltic Sea. The comparison of results against 4 years of in situ bathymetric surveys shows a strong agreement between measured and derived sandbar crest positions (R2 = 0.999 and 0.997) with an average RMSE of 5.8 and 7 m for PlanetScope and RapidEye sensors, respectively. The accuracy of the proposed approach implies its feasibility to study inter-annual and seasonal sandbar behaviour and short-term changes related to high-impact events. Algorithm-provided outputs enable the possibility to evaluate a range of sandbar characteristics such as distance from shoreline, length, width, count or shape at a relevant spatiotemporal scale. The design of the method determines its compatibility with most sandbar morphologies and suitability to other sandy nearshores. Tests of the described technique with Sentinel-2 MSI and Landsat-8 OLI data show that it can be applied to publicly available medium resolution satellite imagery of other sensors.

Observations on decadal sandbar behaviour along a large‐scale curved shoreline

AbstractNearshore sandbars are characteristic features of sandy surf zones and have been observed with a variety of geometries in cross‐shore (e.g. location) and longshore direction (e.g. planform). Although the behaviour of sandbars has been studied extensively on spatial scales up to kilometres and timescales up to years, it remains challenging to observe and explain their behaviour on larger spatial and temporal scales, especially in locations where coastline curvature can be prominent. In this paper, we study a data set with 38 years of coastal profiles, collected with alongshore intervals of 50 m, along the 34 km‐long curved sandy shoreline of Sylt island, Germany. Sylt's shoreline has an orientation difference of ~20° between the northern and southern half of the island. We found that the decadal coastal profiles on the southern half show features of a low‐tide terrace and a sandbar located further from the shoreline (~441 m). On the nothern half, the sandbar was located closer to the shoreline (~267 m) and was less pronounced, while the profiles show transverse bar and rip features. The alongshore planform also differed systematically and significantly along the two island sides. The sandbar on the southern island half, with alongshore periodicity on a larger length scale (~2240 m), was coupled out‐of‐phase to the shoreline, while no phase coupling was observed for the sandbar with periodicity on a shorter length scale (~670 m) on the northern half. We related the observed geometric differences of the sandbars to the difference in the local wave climate along Sylt, imposed by the shoreline shape. Our observations imply that small alongshore variations in wave climate, due to the increasing shoreline curvature on larger spatial scales, can lead to significant alongshore differences in the decadal evolution of coastal profiles, sandbars and shorelines. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd

Modeling the Impact of the Implementation of a Submerged Structure on Surf Zone Sandbar Dynamics

Coastal defense strategies based on structures are increasingly unpopular as they are costly, leave lasting scars on the landscape, and sometimes have limited effectiveness or even adverse impacts. While a clear improvement concerning aesthetic considerations using soft submerged breakwater is undeniable, their design has often focused on wave transmission processes across the crest of the structure, overlooking short- to medium-term morphodynamic responses. In this study, we used a time- and depth-averaged morphodynamic model to investigate the impact of the implementation of a submerged breakwater on surf zone sandbar dynamics at the beach of Sète, SE France. The hydrodynamic module was calibrated with data collected during a field experiment using three current profilers deployed to capture rip-cell circulation at the edge of the structure. The model showed good agreement with measurements, particularly for the longshore component of the flow (RMSE = 0.07 m/s). Results showed that alongshore differential wave breaking at the edge of the submerged breakwater drove an intense (0.4 m/s) two-dimensional circulation for low- to moderate-energy waves. Simulations indicated that inner-bar rip channel development, which was observed prior to the submerged reef implementation, was inhibited in the lee of the structure as rip-cell circulation across the inner bar disappeared owing to persistently low-energy breaking waves. The cross-shore sandbar dynamics in the lee of the structure were also impacted due to the drastic decrease of the offshore-directed flow over the inner-bar during energetic events. This paper highlights that implementation of a submerged breakwater results in larges changes in nearshore hydrodynamics that, in turn, can affect overall surf zone sandbar behavior.

Impact of River Improvement on Sand-Bar Behavior and Stream Regime in the Shirakawa River

Impact of River Improvement on Sand-Bar Behavior and Stream Regime in the Shirakawa River

Behaviour of subtidal sandbars in response to nourishments

The behaviour of subtidal sandbars can be strongly influenced by the introduction of sand nourishments in the coastal system. This study focuses on the impact of nourishments on subtidal bar behaviour at spatio-temporal scales beyond a single nourishment project. It aims to determine the long-term behaviour of subtidal sandbars along an entire coastal cell, taking into account both the unnourished and nourished regime, and covering various types of nourishments. The analysis is based on over 50 years of sandbar evolution along the Delfland coast, a 17-km long coastal cell at the Dutch North Sea coastline protected by groynes and maintained with frequent sand nourishments. Observations reveal clearly different sandbar behaviour during the unnourished (first 20 years) and nourished periods of the dataset. Introduction of the first beach nourishments (nourished sand primarily placed at the subaerial beach) was found to stimulate sandbar development along previously unbarred sections of the coast. Shoreface nourishments (nourished sand placed at the seaward face of the pre-existing subtidal sandbar) tended to migrate shoreward rapidly at a rate of 20 to 60 m/year at this coast, thereby forcing the pre-existing sandbar to weld to the dry beach. An abrupt transition of sandbar dynamics was observed following a major nourishment operation (∼ 37.5 Mm3 of nourished sand) that covered the entire coastal cell. A new, shallow sandbar formed with a degree of alongshore variability that was unprecedented at the Delfland coast over the full study period. These results imply that individual nourishments can influence the formation and migration of individual sandbars, while continued nourishments can fundamentally change long-term sandbar dynamics along an entire coastal cell.

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

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 (ϕ = 1000 days) and the outer bar responding around a seasonal mean (ϕ = 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 under-predicted 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 cross-shore seasonal movement when there is a significant change in the sediment supply to the system (e.g., nourishment projects, severe storms).

Observations on sandbar behaviour along a man‐made curved coast

AbstractSandbars, submerged ridges of sand parallel to the shoreline, affect surfzone circulation, beach topography and beach width. Under time‐varying wave forcing, sandbars may migrate onshore and offshore, referred to as two‐dimensional (2D) behaviour, and vary in planshape from alongshore uniform ridges to alongshore non‐uniform ridges through the growth and decay of three‐dimensional (3D) patterns, referred to as 3D behaviour. Although 2D and 3D sandbar behaviour is reasonably well understood along straight coasts, this is not the case for curved coasts, where the curvature can invoke spatial variability in wave forcing. Here, we analyse sandbar behaviour along the ∼3000 m man‐made curved coastline of the Sand Engine, Netherlands, and determine the wave conditions governing this behaviour. 2D and 3D behaviour was quantified within a box north and west of the Sand Engine's tip, respectively, using a 2.4‐year dataset of daily low‐tide video images and a sparser bathymetric dataset. The northern and western sides behaved similarly in terms of 2D behaviour, with seasonal onshore and offshore migration, resulting in a stable position on inter‐annual timescales. However, both sandbar geometry and 3D behaviour differed substantially between both sides. The geometric differences (bar shape, bar crest depth and wavelength of 3D patterns) are consistent with computed alongshore differences in breaker height due to refraction. The differences in the timing in growth, decay and morphological coupling of 3D patterns in the sandbar and shoreline are likely related to differences in the local wave angle, imposed by the curved coast. Similar dependency of bar behaviour on local wave height and angle may be expected elsewhere along curved coasts, e.g. shoreline sandwaves, cuspate forelands or embayed beaches. Copyright © 2017 John Wiley & Sons, Ltd.

Process-based modeling of cross-shore sandbar behavior

A coupled wave–current–sediment transport beach profile model is used to simulate cross-shore sandbar evolution on the time scale from days to months comprising both rapid offshore and slow onshore migrations. The discrimination of four modes of sediment transport driven by velocity and acceleration skewness, mean currents and slope effects allows addressing the dominant hydrodynamic processes governing cross-shore sandbar behavior. Acceleration–skewness-induced transport systematically results in a slow onshore sandbar migration together with a slow bar growth. Velocity–skewness-induced transport can drive onshore and offshore bar migrations with substantially larger rates. Mean–current-induced sediment transport systematically drives an offshore bar migration with either bar growth or decay. Slope effects essentially act as a damping term. The water level above the sandbar crest mainly influences the sandbar migration direction, while wave obliquity regulates the magnitude of the migration rates and is crucial to accurately simulate offshore sandbar migration during energetic obliquely incident waves. The inclusion of acceleration skewness is a necessary requirement to accurately reproduce the onshore migration of shallow sandbars. Detailed inter-site comparison of best-fit model parameters shows large differences meaning that free parameters attempt to compensate some mispecifications of the physics in the model. Although this also applies to other existing beach profile models, this suggests that this model needs further improvements including, for instance, the contribution of the injection of breaking wave turbulence onto the bed to sand stirring.

Data-based methods and algorithms for the analysis of sandbar behavior with exogenous variables

Sandbars are natural features generated in the nearshore zones by the interaction between the sea and the coast. The short-term processes that drive sandbar behavior are waves and sediment transport. The interaction between waves and the coast is highly nonlinear and, traditionally, process-based models (e.g., evolution models) have been used for modelling and analyzing sandbar behavior in the short term. However, medium- to long-term predictions are not always possible with these models due to their exponential error accumulation. Data-driven models emerge as an alternative to process-based models as they do not need insight on the physical knowledge of the model, but they extract knowledge from patterns found in the data. In this paper, we apply the data-driven techniques: EMD (empirical mode decomposition) method and ARNN (autoregressive neural networks) on sandbar and wave time series from the coast of Cartagena de Indias, Colombia. The former is used for analyzing the relationship between sandbar and wave conditions in a graphical way; and the latter is used for deriving nonlinear simple/partial cross/auto-correlation coefficients. Evidence of nonlinear dependencies is detected between the present state of sandbar location and the past states of wave conditions.

Input reduction for long-term morphodynamic simulations in wave-dominated coastal settings

Input reduction is imperative to long-term (>years) morphodynamic simulations to avoid excessive computation times. Here, we introduce an input-reduction framework for wave-dominated coastal settings. Our framework comprises 4 steps, viz. (1) the selection of the duration of the original (full) time series of wave forcing, (2) the selection of the representative wave conditions, (3) the sequencing of these conditions, and (4) the time span after which the sequence is repeated. In step (2), the chronology of the original series is retained, while that is no longer the case in steps (3) and (4). We apply the framework to two different sites (Noordwijk, Netherlands and Hasaki, Japan) with multiple nearshore sandbars but contrasting long-term offshore-directed behavior: at Noordwijk the offshore migration is gradual and not coupled to individual storms, while at Hasaki the offshore migration is more episodic, and wave chronology appears to control long-term evolution. The performance of the model with reduced wave climates is referenced to a simulation with the actual (full) wave-forcing series. We demonstrate that input reduction can dramatically affect long-term predictions, even to such an extent that the main characteristics of the offshore bar cycle are no longer reproduced. This was particularly the case at Hasaki, where all synthetic series that no longer capture the initial chronology (steps 3 and 4) lead to rather unrealistic long-term simulations. At Noordwijk, synthetic series can result in realistic behavior, provided that the time span after which the sequence is repeated is not too large; the reduction of this time span has the same positive effect on the simulation as increasing the number of selected conditions in step 2. We further demonstrate that, although storms result in the largest morphological change, conditions with low to intermediate wave energy must be retained to obtain realistic long-term sandbar behavior. Our input-reduction framework must be applied in an iterative fashion as to obtain a reduced wave climate that simulates long-term sandbar sufficiently accurately within an acceptable computation time. Given its potentially huge impact on the actual simulation, we believe it is imperative to consider input reduction as an intrinsic part of model set-up, calibration and validation.

On the impact of an offshore bathymetric anomaly on surf zone rip channels

We use a nonlinear morphodynamic model to demonstrate that the presence of a single persistent offshore bathymetric anomaly strongly affects the formation, nonlinear evolution and saturation of surf zone rip channels. In the case of an offshore bump or trough and waves with oblique incidence, a rip channel shoreward of the anomaly is enforced by the more seaward alongshore variability in depth. The degree of rip channel enforcement is controlled by the strength of the rotational nature of surf zone rip current circulations, which is, in turn, driven by differential broken wave energy dissipation induced by wave refraction across the offshore bathymetric anomaly. The alongshore location of this forced rip channel is more stable with increasing offshore anomaly amplitude, decreasing offshore wave obliquity and decreasing bathymetric anomaly distance to the shore. Simulations show that rip channel behavior downdrift and updrift of the offshore perturbation are different. In our numerical experiments, downdrift rip channels have systematically larger alongshore scales, smaller alongshore migration rates and more erosive megacusps than those updrift. Rip channels therefore self‐organize into patterns of different alongshore scales and migration rates as a result of an alongshore perturbation in the wave forcing enforced by wave refraction across an offshore bathymetric anomaly. These simulations are qualitatively corroborated by video observations of sandbar behavior during a down‐state sequence at a site with a persistent offshore trough.

Neural-network predictability experiments for nearshore sandbar migration

Cross-shore migratory behavior of nearshore sandbars is commonly studied with nearshore bathymetric-evolution models that represent underlying processes of hydrodynamics and sediment transport. These models, however, struggle to reproduce natural cross-shore sandbar behavior on timescales of a few days to weeks and have uncertain skill on longer scales of months to years. One particular concern for the use of models on prediction timescales that far exceed the timescale of the modeled processes is the exponential accumulation of errors in the nonlinear model equations. The relation between cross-shore sandbar migration, sandbar location and wave height has previously been demonstrated to be weakly nonlinear on timescales of several days, but it is unknown how this nonlinearity affects the predictability of long-term (months to years) cross-shore sandbar behavior. Here we study the role of nonlinearity in the predictability of sandbar behavior on timescales of a few days to several months with data-driven neural network models. Our analyses are based on over 5600 daily-observed cross-shore sandbar locations and daily-averaged wave forcings from the Gold Coast, Australia, and Hasaki, Japan. We find that neural network models are able to hindcast many aspects of cross-shore sandbar behavior, such as rapid offshore migration during storms, slower onshore return during quiet periods, seasonal cycles and annual to interannual offshore-directed trends. Although the relation between sandbar migration, sandbar location and wave height is nonlinear, sandbar behavior can be hindcasted accurately over the entire lifespan of the sandbars at the Gold Coast. Contrastingly, it is difficult to hindcast the long-term offshore-directed trends in sandbar behavior at Hasaki because of exponential accumulation of errors over time. Our results further reveal that during periods with low-wave conditions it becomes increasingly difficult to predict sandbar locations, while during high waves predictions become increasingly accurate.

Models and scales for cross‐shore sandbar migration

We investigate the long‐term (months to years) predictability of cross‐shore sandbar migration with two models that operate on different abstraction levels: (1) a coupled, cross‐shore waves‐currents‐bathymetric evolution model and (2) two data‐driven neural network models, based on simplified cross‐shore profile representations and daily averaged wave properties. For model calibration, training, and validation, we use a high‐resolution 15 yearlong profile data set collected at the Hasaki Oceanographic Research Station in Japan. Sandbar behavior at this field site is characterized by cycles of net‐offshore migration with a duration of 1–4 years. We find that all models can produce several general features of sandbar behavior at the studied field site, such as rapid offshore migration, slower onshore return, and net‐offshore migration. However, it is difficult to quantitatively predict the offshore‐directed trends in sandbar location over time scales of months to years. While simple linear models outperform more detailed nonlinear models, for all models it is difficult to predict long‐term sandbar behavior, because of error accumulation in the model's processes over time. Representing processes on a more abstract level (scale aggregation) alleviates error accumulation but does not completely overcome this problem.

Seasonal-scale nearshore morphological evolution: Field observations and numerical modeling

A coupled waves–currents-bathymetric evolution model (DELFT-3D) is compared with field measurements to test hypotheses regarding the processes responsible for alongshore varying nearshore morphological changes at seasonal time scales. A 2001 field experiment, along the beaches adjacent to Grays Harbor, Washington, USA, captured the transition between the high-energy erosive conditions of winter and the low-energy beach-building conditions typical of summer. The experiment documented shoreline progradation on the order of 10–20 m and on average approximately 70 m of onshore sandbar migration during a four-month period. Significant alongshore variability was observed in the morphological response of the sandbar over a 4 km reach of coast with sandbar movement ranging from 20 m of offshore migration to over 175 m of onshore bar migration, the largest seasonal-scale onshore migration event observed in a natural setting. Both observations and model results suggest that, in the case investigated here, alongshore variations in initial bathymetry are primarily responsible for the observed alongshore variable morphological changes. Alongshore varying incident hydrodynamic forcing, occasionally significant in this region due to a tidal inlet and associated ebb-tidal delta, was relatively minor during the study period and appears to play an insignificant role in the observed alongshore variability in sandbar behavior at kilometer-scale. The role of fully three-dimensional cell circulation patterns in explaining the observed morphological variability also appears to be minor, at least in the case investigated here.

Seasonal Changes of Sandbar Behavior in Nanwan Beach, South China

Frequent leveling data of beach profiles is collected from Nanwan Beach, which is characterized by a large seasonal variation in wave climate. Variability of the bar crest position obtained from the data of measured profiles is examined to quantify seasonal changes of the sandbar by empirical orthogonal function (EOF) analysis. The first eigenfunction showed that a rhythmic bar is a common feature of the beach all year round. The second eigenfunction effectively indicated that the two-dimensional variability of the bar behavior is of seasonal changes. The cross-shore bar movement ranged −30∼40 and −2∼60 m in summer and in winter, respectively. The next two eigenfunctions represented three-dimensional components of the bar behavior with a range of −21∼21 and −30∼21 m in summer and in winter, respectively.

Multivariate analysis of nonlinearity in sandbar behavior

Abstract. Alongshore sandbars are often present in the nearshore zones of storm-dominated micro- to mesotidal coasts. Sandbar migration is the result of a large number of small-scale physical processes that are generated by the incoming waves and the interaction between the wave-generated processes and the morphology. The presence of nonlinearity in a sandbar system is an important factor determining its predictability. However, not all nonlinearities in the underlying system are equally expressed in the time-series of sandbar observations. Detecting the presence of nonlinearity in sandbar data is complicated by the dependence of sandbar migration on the external wave forcings. Here, a method for detecting nonlinearity in multivariate time-series data is introduced that can reveal the nonlinear nature of the dependencies between system state and forcing variables. First, this method is applied to four synthetic datasets to demonstrate its ability to qualify nonlinearity for all possible combinations of linear and nonlinear relations between two variables. Next, the method is applied to three sandbar datasets consisting of daily-observed cross-shore sandbar positions and hydrodynamic forcings, spanning between 5 and 9 years. Our analysis reveals the presence of nonlinearity in the time-series of sandbar and wave data, and the relative importance of nonlinearity for each variable. The relation between the results of each sandbar case and patterns in bar behavior are discussed, together with the effects of noise. The small effect of nonlinearity implies that long-term prediction of sandbar positions based on wave forcings might not require sophisticated nonlinear models.

Modeling cross‐shore sandbar behavior on the timescale of weeks

We compare predictions of a coupled, wave‐averaged, cross‐shore waves‐currents‐bathymetric evolution model to observations of onshore and offshore nearshore sandbar migration. The observations span a 10‐ and 44‐day period with onshore/offshore bar migration at Duck, North Carolina, and at Hasaki, Kashima Coast, Japan, respectively, a 3.5‐month period of onshore bar migration at Duck, and a 22‐day period of offshore bar migration at Egmond, Netherlands. With best fit parameter values the modeled temporal evolution of the cross‐shore bed profiles agrees well with the observations. Model skill, defined as 1 minus the ratio of prediction to no‐change error variances, ranges from 0.50 at Egmond to 0.88 for the prolonged onshore bar migration at Duck. Localized (in time and space) reductions in model skill coincide with alongshore variations in the observed morphology. Consistent with earlier observations, simulated offshore bar migration takes place during storms when large waves break on the bar and is due to the feedback between waves, undertow, suspended sediment transport, and the sandbar. Simulated onshore bar migration is predicted for energetic, weakly to nonbreaking conditions and is due to the feedback between near‐bed wave skewness, bedload transport, and the sandbar, with negligible to small effects of bound infragravity waves and near‐bed streaming. Under small waves and conditions, when breaking and nonbreaking conditions alternate with the tide, the sandbar is predicted to remain stationary. The intersite differences in the optimum parameter values are, at least partly, induced by insensitivity to parameter variations, parameter interdependence, and errors in the offshore wave forcing.

Recurrent neural network modeling of nearshore sandbar behavior

The temporal evolution of nearshore sandbars (alongshore ridges of sand fringing coasts in water depths less than 10 m and of paramount importance for coastal safety) is commonly predicted using process-based models. These models are autoregressive and require offshore wave characteristics as input, properties that find their neural network equivalent in the NARX (Nonlinear AutoRegressive model with eXogenous input) architecture. Earlier literature results suggest that the evolution of sandbars depends nonlinearly on the wave forcing and that the sandbar position at a specific moment contains 'memory', that is, time-series of sandbar positions show dependencies spanning several days. Using observations of an outer sandbar collected daily for over seven years at the double-barred Surfers Paradise, Gold Coast, Australia several data-driven models are compared. Nonlinear and linear models as well as recurrent and nonrecurrent parameter estimation methods are applied to investigate the claims about nonlinear and long-term dependencies. We find a small performance increase for long-term predictions (>40 days) with nonlinear models, indicating that nonlinear effects expose themselves for larger prediction horizons, and no significant difference between nonrecurrent and recurrent methods meaning that the effects of dependencies spanning several days are of no importance.

An investigation of the multi-scale temporal variability of beach profiles at Duck using wavelet packet transforms

In an earlier paper a particular discrete wavelet transform (DWT) was used to study the complex variation of beach profile changes. However, use of the DWT requires that the sequence of spatial and temporal resolution is fixed as a dyadic sequence, which means that the variability over longer intervals is not characterised well. Here we introduce the discrete wavelet packet transform (DWPT) that uses an adaptive scaling to partition the data variance, according to an entropy cost function. The advantages of this approach are demonstrated by its application to the study of temporal variability of a 22 year record of beach profile data from the Field Research Facility (FRF) at Duck, North Carolina, USA. Time series of beach elevations at three locations across a particular profile are investigated in detail. We conclude that the DWPT provides a superior analysis of non-stationary time series to that of the DWT, with improved resolution of the scale intervals of the variability. The beach elevation around the shoreline is shown to respond at both sub-annual and interannual scales, but variability at an annual scale is weak. Moving seaward into deeper water, the variance is partitioned into fewer and longer scales. It is confirmed that elevation changes around the inner bar at Duck exhibit a strong interannual variation consistent with Plant et al. (Plant, N.G., Holman, R.A. and Freilich, M.H., 1999. A simple model for interannual sandbar behaviour. Journal of Geophysical Research 104(C7), 15755–15776). Around 23% of the variance around the inner bar is explained at the temporal scale of 64–128 months, which is consistent with the bar behaviour of 6 years found by Ruessink et al. (Ruessink, B. G., Wijnberg, K. M., Holman, R. A., Kuriyama, Y. and Van Enckevort, I. M. J., 2003. Intersite comparison of interannual nearshore bar behaviour. Journal of Geophysical Research, 108 (C8): 1–12). A significant new finding is, however, that about 26% of the variance is attributable to temporal scales of 16–21.3 months. Reconstruction of the wavelet packet components for individual temporal scales is shown to provide a means for identifying the impact and scale of non-stationary events, such as storms, on the beach response. This provides further information that can be used to interpret the morphological changes in terms of the forcing processes and also serves to inform morphodynamic modelling.

Non-linear principal component analysis of nearshore bathymetry

Spatially and temporally extensive nearshore bathymetric datasets have recently been analyzed with complex principal component analysis (CPCA) to extract propagating spatial patterns that constitute most to the dominant lower-dimensional structure in the datasets. CPCA assumes this structure to be linear, which may be an oversimplification of the true structure as the nearshore is a strongly non-linear system. Here we investigate whether a neural network-based circular non-linear principal component analysis (NLPCA.cir) provides a more representative approximation of the underlying lower-dimensional structure of nearshore depth data than possible with CPCA. To that end, NLPCA.cir was applied to three datasets characterized by interannual offshore-directed sandbar behavior, coming from Egmond (The Netherlands), Hasaki Coast (Japan) and Duck (North Carolina, USA). The main difference between these datasets is the temporal variation in sandbar amplitude, which is smallest at Egmond and largest at Duck. We find that the first NLPCA.cir mode 1 at Egmond and Hasaki leads to a more complete characterization of the lower-dimensional data structure than possible with CPCA (i.e. the underlying low-dimensional structure of bathymetric data at Egmond and Hasaki is indeed non-linear). This is not the case at Duck, where the temporal variations in sandbar amplitude are so large that the non-linear lower-dimensional structure in the data, should it exist, is no longer visually apparent and can no longer be detected by NLPCA.cir. This suggests that a simple visual check of the data suffices to decide whether one should resort to NLPCA.cir or to the more simple and computationally quicker CPCA.