Shoreline Undulations Research Articles

Long‐term erosional hot spots in the southern Brazilian coast

The southern Brazilian coast is a sandy barrier adorned by subtle shoreline perturbations widespread in a rhythmical pattern. Previous works indicated that short‐ and long‐term shoreline changes are not alongshore uniform. They are based on coastline position monitoring, geomorphological evidences, historical cartographic documents, and aerial photography. Moreover, these studies associated the main observed erosional sites with high rates of sediment drift and energy focusing due to wave refraction. Nevertheless, the role of the highly oblique incident waves in driving shoreline changes was not considered. A recently derived sediment diffusion equation showed the possibility of coastal instability induced by incident waves with high obliqueness, as opposed to the traditional approach. Therefore, this paper applied these concepts to wave climate and performed coastal instability analysis to explain shoreline changes at an undulating littoral. Calculations showed wave climate yielding a negative instability index (−0.13) when using a 42‐month‐long time series of wave parameters obtained from a forecasting numerical model. Also, the calculated direction asymmetry on wave climate revealed a net littoral drift. Consequently, the sites between troughs and updrift flanks of shoreline undulations are expected to exhibit erosive processes. This is the case in the most conspicuous long‐term erosional hot spots at the southern Brazilian coast, which was pointed out in earlier studies. Therefore, coastal instability and littoral sediment drift analysis explained the main morphodynamic processes governing shoreline changes at the study area.

Statistical analysis of coastal morphological data sets over seasonal to decadal time scales

Statistical analysis of long-term morphological data on coastal sedimentary features provides important information on the processes governing these features and their evolution in space and time. In this paper, seasonal, yearly and decadal (i.e. long-term) behavior of coastal morphological features is derived from field data by using both simple and advanced statistical techniques. The sedimentary features which we are especially focusing on are a) nearshore bars, and b) large-scale shoreline undulations, for example, longshore sand waves and nesses. High-quality bathymetric field data of regularly sampled cross-shore profiles and shorelines were the basis of the available data sets at Noordwijk beach (The Netherlands), Duck, North Carolina (USA), Sylt (Germany), Lubiatowo (Poland) and Winterton (UK). Additional data sets from Argus video-images (see [Holman, R.A., Stanley, J., 2007. The history, capabilities and future of Argus. Coastal Engineering Special Issue of the CoastView project. doi:10.1016/j.coastaleng.2007.01.003]) and aerial photographs were used to increase the temporal and spatial resolution of the data sets where possible. The statistical methods applied include some linear and non-linear techniques described by Larson et al. [Larson, M., Capobianco, M., Jansen, H., Rózyński, G., Southgate, H.N., Stive, M., Wijnberg, K.M., Hulscher, S., 2003. Analysis and modeling of field data on coastal morphological evolution over yearly and decadal time scales. Part 1: background and linear techniques. Journal of Coastal Research, 19-4, 760–775] and Southgate et al. [Southgate, H.N., Wijnberg, K.M., Larson, M., Capobianco, M., Jansen, H., 2003. Analysis of field data of coastal morphological evolution over yearly to decadal timescales. Part 2: non-linear techniques. Journal of Coastal Research, 19-4, 776–789]. The methods proved to be useful for extracting characteristics of the coastal sedimentary features concerning length scales (e.g., spacing and rhythmicity) and temporal scales (e.g., migration rates and evolutionary patterns). However, the success of the statistical analysis strongly depends on the total size of the data set characterized by the specific spatial coverage, spatial resolution, temporal resolution, and overall length in time. Recent data sets from remote sensing video systems like Argus often meet these requirements and are of major importance for the formulation of conceptual behavior models.

Reply to comment by M. Ortega‐Sánchez et al. on “High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes”

[1] We would like to thank Ortega-Sanchez et al. for highlighting Carchuna beach (southern Spain) [OrtegaSanchez et al., 2003] as another natural example where large-scale cuspate shoreline features are coincident with a wave climate dominated by high-angle waves, providing an independent test of the hypothesis presented by Ashton et al. [2001] and Ashton and Murray [2006a, 2006b]. OrtegaSanchez et al. discuss a series of large-scale cuspate shoreline features and also demonstrate the apparent formation of smaller-scale shoreline undulations along a relatively straight portion of the coast, suggesting that a straight coast in this subregion may also be responding to the high-anglewave instability. In model simulations, cuspate features are not completely regular, with variations in the spatial wavelength of up to a factor of two, and some portions of the coast can temporarily attain fairly straight configurations between cuspate features (see Figure 9 and auxiliary material in the work of Ashton and Murray [2006a]). The selforganization mechanism can explain both variation in wavelength and the appearance of different quasi-rhythmic features at distinctly different scales—both observed at Carchuna beach. [2] As discussed in detail by Ashton and Murray [2006a] and investigated by others [Falques and Calvete, 2005], we agree that the assumptions underlying our numerical model become less appropriate at spatial scales much less than a kilometer (for an open-ocean coast). When the scale of shoreline features is not much greater than the storm surf zone [Ortega-Sanchez et al., 2004], breaking-wave dynamics, local hydrodynamics, and deviations from shore-parallel contours, factors not captured by the exploratory model, become increasingly important in morphologic evolution. Many other factors not included in this simple model will influence the specific evolution and shape of a natural coast, including the geologic framework, preexisting coastline configurations, and the external supply of sediment. Direct comparison between the model results and a natural example should be performed with care, as the objective of the described exploratory model [Murray, 2003] is to investigate the range of shoreline behaviors resulting from the simple interactions considered, and not to reproduce in detail the evolution of any particular coastline. [3] We also urge caution in the interpretation of the figures demonstrating how model behaviors change with variation in the model parameters A, the fraction of waves approaching from the right (the asymmetry), and U, the fraction of unstable, high-angle waves [Ashton and Murray, 2006a, Figure 9a]. A and U are model-specific parameters used to determine the wave climate in the numerical experiments [e.g., Ashton and Murray, 2006a, Figure 8], and should not be directly related to a natural wave climate with the expectation of a quantitatively accurate comparison. Ashton and Murray [2006b] present a methodology for more rigorously analyzing and characterizing a wave climate, introducing a stability parameter, G. Approximate values of this stability parameter can be computed using wave energy roses such as those presented in the comment by Ortega-Sanchez et al. [2008], and its computation should be more straightforward than approximations of the model parameter H.

High‐angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes

Contrary to traditional findings, the deepwater angle of wave approach strongly affects plan view coastal evolution, giving rise to an antidiffusional “high wave angle” instability for sufficiently oblique deepwater waves (with angles between wave crests and the shoreline trend larger than the value that maximizes alongshore sediment transport, ∼45°). A one‐contour‐line numerical model shows that a predominance of high‐angle waves can cause a shoreline to self‐organize into regular, quasiperiodic shapes similar to those found along many natural coasts at scales ranging from kilometers to hundreds of kilometers. The numerical model has been updated from a previous version to include a formulation for the widening of an overly thin barrier by the process of barrier overwash, which is assumed to maintain a minimum barrier width. Systematic analysis shows that the wave climate determines the form of coastal response. For nearly symmetric wave climates (small net alongshore sediment transport), cuspate coasts develop that exhibit increasing relative cross‐shore amplitude and pointier tips as the proportion of high‐angle waves is increased. For asymmetrical wave climates, shoreline features migrate in the downdrift direction, either as subtle alongshore sand waves or as offshore‐extending “flying spits,” depending on the proportion of high‐angle waves. Numerical analyses further show that the rate that the alongshore scale of model features increases through merging follows a diffusional temporal scale over several orders of magnitude, a rate that is insensitive to the proportion of high‐angle waves. The proportion of high‐angle waves determines the offshore versus alongshore aspect ratio of self‐organized shoreline undulations.

How does underlying geology affect coastline change? An initial modeling investigation

Conceptual geologic framework models predict that areas of the coast underlain by a weak or very fine grained lithology retreat landward faster than adjacent, more resistant or coarser‐grained segments. These apparently commonsense predictions seem inconsistent with observations that sandy coastlines underlain by heterogeneous lithology remain fairly smooth. We have developed a numerical model to explore the interaction between shoreface lithology effects and alongshore transport processes on scales greater than years and kilometers. Shoreline indentations, or sections of the coast that are slightly landward of adjacent sections, tend to form in the model where the shoreface weathers more rapidly or is composed of finer‐grained material. However, alongshore transport tends to fill in these indentations, slowing the weathering rates there while increasing them in adjacent areas where mobile sediment is preferentially removed. Over the long term this leads to an alongshore uniform retreat rate. Subtle shoreline undulations reflecting the heterogeneous geologic framework exist in the model, but their amplitude reaches a steady state rather than increasing with time. Compositional heterogeneities determine the morphology of the coast while weathering rate heterogeneities control the thickness of sediment on the shoreface. Thus indentations can form in sections composed of harder (less erodible) rocks if they are finer grained.

Reversing storm hotspots on sandy beaches: Spatial and temporal characteristics

Coastal erosion hotspots are defined as sections of coast that exhibit significantly higher rates of erosion than adjacent areas. This paper describes the spatial and temporal characteristics of a recently identified type of coastal erosion hotspot, which forms in response to storms on uninterrupted sandy coasts largely free from human intervention. These are referred to here as reversing storm hotspots because the erosion is reversed by accretion of a similar magnitude to the storm-induced erosion. The accretion occurs within a few days or weeks of fair weather after the storm. Reversing storm hotspots observed here, on two US east coast beaches, have a longshore length averaging 3.86 km, a cross-shore excursion (magnitude of erosion or accretion) averaging 15.4 m, and a time scale of days to weeks associated with individual storm events. These spatial and temporal scales clearly distinguish reversing storm hotspots from previously described forms of longshore variability in erosion, including those attributed to several types of shoreline undulations and hotspots associated with long-term shoreline change.

Rhythmic Landforms seen in the Beach Areas and Offshore Sea Bottom

Recently, rhythmic land forms such as shoreline waves, rhythmic system of arcuate bars, and the meandering of the longshore current along beaches have been pointed out by means of accurate hydrographic survey and aerial photographic interpretation. On the other hand, rhythmic patterns on the sea bottom such as sand waves are found in the areas with strong current and sandy bottom. The author recognized some resemblances in the configurations, composing materials and their movements between the shoreline undulations and sand waves. On the offshore bottom with the more depth, the water and the sand particles are able to move vertically to the sea bottom. While, on the nearshore bottom with little depth, the water and the sand particles are able to move horizontally to the shoreline. Both the shoreline undulations and submarine sand waves are facing the cape like cusp or crest perpendicular to the direction of the nearshore and offshore currents. Accordingly, the relations between movements of water and sand particles and these rhythmic topographies are very close to each other.From these reasons the author assumed that there is a similar mechanism on the origin of the both rhythmic topographies.He, then, presented hypothesis that the shoreline undulation and submarine sand wave were formed by the water circulations or vortices resulted from the meandering of currents caused by the occasional disturbance of currents.