A simple new shoreline change model
Introduction
Coastal engineers and scientists routinely address a wide variety of coastal problems. How will proposed structures affect adjacent shorelines? How long will a beach nourishment project last? What will be the effects of altering an existing inlet? Despite our ability to answer a number of challenging questions such as these, we are still unable to adequately answer a much more basic question. Where will the shoreline be tomorrow? Next week? Next year? In a decade? The reasons for our inability to address this question in a satisfactory manner are numerous. The many factors that make beaches and the entire nearshore environment so fascinating to study make them extremely difficult to model accurately. Beaches are extraordinarily complex, dynamic systems, experiencing changes on a variety of different temporal and spatial scales. These changes range from small-scale fluctuations due to the formation of beach cusps to large-scale changes caused by longshore migrating sand waves, episodic storm events or seasonal weather patterns. The paucity of frequent, high-quality surveys encompassing the entire nearshore system only makes the task of describing and predicting profile changes that much more challenging. Despite the significant strides made in our understanding of nearshore processes in the last decade, describing shoreline changes over the full range of relevant temporal and spatial scales remains a daunting task.
The monumental task of modeling the shoreline over the entire spectrum of temporal and spatial scales can be simplified somewhat if only a subset of relevant scales is considered. Fortunately, space and time scales are related, with large-scale shoreline changes generally occurring with longer time scales. The so-called engineering time scale is arguably the most relevant time scale, and hence the focus of this paper. The engineering time scale refers to the range of shoreline changes expected to impact a structure during its lifetime. This range generally encompasses everything from storm-induced changes with time scales on the order of hours, up to long-term changes with decadal time scales. Due to our present inability to predict long-term changes adequately using a generally applicable shoreline change model, many developers, engineers and coastal managers continue to rely upon outdated, rudimentary extrapolations of some best-fit trend line to predict future shoreline changes. A more complete method for predicting future shoreline migration must account for shoreline changes on a variety of time scales including both the seasonal and storm time scales. Although periodic trends such as seasonal fluctuations or El Niño related phenomena are much easier to predict than storm-induced changes, both have significant impacts on the shoreline and must be included in any complete model. The aperiodic nature of storm events, and the uncertainty of future weather conditions, argues for the use of some statistical simulation procedure such as a Monte Carlo technique. Utilizing such a procedure, the probabilities associated with various magnitudes of shoreline change may be calculated based upon the statistical characteristics of the forcing parameters.
The prediction of shoreline migration can be simplified even further by separating the changes due to longshore processes and largely responsible for long-term changes from those caused by cross-shore processes and tending to operate on much shorter time scales. A notable exception to this generalization is the shoreline change related to long-term sea-level variability which results in a readjustment of the profile to the new water levels and is a cross-shore response. This separation procedure is commonly applied and leads to two broad categories of morphological models: coastal area or longshore models and profile or cross-shore models. Although several highly detailed process-based morphological models exist, these models tend to be computationally intensive and their accuracy near the shoreline over a broad spectrum of relevant time scales has not been demonstrated. Additionally, the complexity and computational costs involved in applying these detailed models to the nearshore region, over long time scales, makes them inefficient at the present time for long-term shoreline studies.
The objective of this paper is to present a new shoreline change model capable of reproducing the shoreline response to cross-shore forcing over a variety of temporal scales. Simplicity and efficiency, while maintaining a sufficient level of accuracy thus ensuring the widest possible range of applicability, were primary considerations. Historical shoreline data from the locations depicted in Fig. 1 have been used to calibrate and evaluate the model. The temporal density of the available shoreline data allows for the skill of the model to be evaluated over a variety of time scales ranging from biweekly to multidecadal. The geographical diversity of the data sets provides an interesting platform for examining the natural variability in the nearshore system and for evaluating the model over a wide range of beach conditions. As more data become available, additional sites will be incorporated into the analysis in order to test the robustness of the model.
The efficiency of the model makes it particularly useful for long-term studies ranging from the prediction of seasonal shoreline changes to the prediction of decadal shoreline migration patterns for coastal management applications. The simplicity of the proposed model makes it ideal for representing the shoreline response to cross-shore processes in a simple one-line model, similar to the approach of Hanson and Larson (1998). A cross-shore model requiring minimal input would be an improvement over the parameterizations used to represent cross-shore processes in their original model. Given the modest amount of data required to drive the model, and the general availability of this data, the model could also be applied in a real-time sense to provide first-approximation predictions of the erosive potential of approaching storms.
Section snippets
Background
Although many significant advancements have been made in the science of hydrodynamics and sediment transport in the past decade, these advancements have yet to yield accurate shoreline change models applicable over the full spectrum of time scales of engineering relevance (storms, seasonal and decadal). The complexity involved in modeling the extremely dynamic nearshore region has led to the development of a number of different approaches. Roelvink and Broker (1993) and van Rijn et al. (2003)
Theoretical development
Traditionally, models have been grouped into one of three categories, empirical, analytical or numerical based upon the character and complexity of the equations involved and the solution technique. The new shoreline change model presented here utilizes a combination of these traditional approaches. An analytical equation suggested by empirical evidence is solved numerically and is then calibrated using historical shoreline data. Laboratory investigations by Swart (1974), along with previous
Field site description
In order to test the robustness of the model, 10 different sites representing a variety of different coastal environments were used to calibrate and evaluate the model. These sites are depicted in Fig. 1 and include both beaches typical of the high-energy, rocky headland-dominated Pacific coastline, as well as those representative of the low-lying barrier island topography found along much of the Atlantic coast. Although there may appear to be a bias towards East Coast data, this is purely a
Summary of results
A summary of the model results is presented in Table 3. At each site, five different forms of the rate parameter were evaluated according to:
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Case 1: k constant, average Hb used to define yeq,
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Case 2: k constant, significant Hb used to define yeq,
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Case 3: k proportional to Ω, significant Hb used to define yeq,
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Case 4: k proportional to Hb2, significant Hb used to define yeq, and
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Case 5: k proportional to Hb3, significant Hb used to define yeq.
Conclusions
A simple new shoreline change model has been proposed, calibrated and evaluated at a number of sites. The model is based upon previous numerical and experimental results that indicate a shoreline approaches an equilibrium state with a form that is approximately exponential with time. The equilibrium or linear relaxation equation suggested by these observations has proved useful in other areas of coastal engineering, and is utilized successfully here, to model shoreline changes associated with
Acknowledgements
The authors would like to thank the National Defense Science and Engineering Graduate Fellowship Program and the American Society for Engineering Education, as well as the Fulbright Fellowship Program, for providing the funding for this project. The authors would also like to thank those who either contributed significant data sets or aided in the interpretation of the available data including Bill Birkemeier and Cliff Barron of the FRF, Stewart Farrell and Chris Constantino of Richard Stockton
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2023, Coastal EngineeringCitation Excerpt :Metrics of wave disequilibrium used in these models include wave energy (Yates et al., 2009) and the dimensionless fall velocity (Davidson et al., 2013; Splinter et al., 2014). When calibrated, reduced-complexity equilibrium shoreline models have been shown to successfully simulate wave-driven shoreline changes for many coastlines (Davidson et al., 2013; Ibaceta et al., 2020; Miller and Dean, 2004; Muir et al., 2020; Splinter et al., 2014; Robinet et al., 2017, 2018; Schepper et al., 2021; Tran and Barthélemy, 2020;Vitousek and Barnard, 2015; Vitousek et al., 2017). While full morphological models account for water level changes explicitly (Lesser et al., 2004; Roelvink et al., 2009), reduced complexity shoreline models generally do not take into account water level variations, and thus any shoreline movement affected by water level changes are effectively aliased into the wave forcing terms in the models.