Cross-shore modelling of multiple nearshore bars at a decadal scale
Introduction
Many wave dominated sandy coastal systems across the world are characterized by the presence of one or more subtidal longshore bars (Larson and Kraus, 1992; Ruessink and Kroon, 1994; Ruessink et al., 2007; Walstra et al., 2012, 2015; Van Enckevort and Ruessink, 2003; Różyński and Lin, 2015; Ruggiero et al., 2016; Bouvier et al., 2017; Aleman et al., 2017; Stwart et al., 2017; Eichentopf et al., 2018). For such systems, models are required for simulating the bar-berm material exchange to reproduce: 1) the seasonal behavior of the beach profile; 2) the effects of the sediment release during storms from the dune and the beach to the subaqueous portion of the profile; and 3) the recovery process of the berm during periods of low-energy, when bars tend to lose volume and migrate onshore (eventually welding to the shore).
In support of coastal engineering and management activities, during the last few decades, a strong demand for sophisticated, robust, and reliable models for simulating coastal evolution over decades to centuries has emerged. The earliest type of long-term coastal evolution models focused on predicting the shoreline evolution in response to the potential sediment transport gradient generated by incident wave energy, following the one-line theory. According to this theory, firstly introduced by Pelnard-Considere (1956) and numerically implemented by numerous authors since then, beach profile moves parallel to itself, maintaining an equilibrium configuration. Thus, one-contour line can be used to describe changes in the beach shape and volume during accretionary and erosional events. Some examples of such models are GENESIS (Hanson, 1988), Unibest CL+ (Deltares, 2011), LITLINE in LITPACK (DHI, 2009a, 2009b, 2017) by DHI (Danish Hydraulic Institute) and LTC (Coelho, 2005). Although, these models can be used at large temporal (annual-decadal) and spatial scales (kilometers), one of their weaknesses has been the simplified representation of the cross-shore (CS) material exchange, where usually CS processes are incorporated through sink or source terms with representative values in time and space.
Profile evolution models, on the other hand, are commonly used to simulate the beach change on a short-term basis (hours to days), for investigating the impact of individual storms in the beach-dune system evolution, as well as the response of beach fills under storm conditions, e.g., SBEACH (Larson and Kraus, 1989), LITPACK (LITPROF) (DHI, 2008), XBEACH (Roelvink et al., 2009), but also on a short-to medium-term (month to year) like Unibest TC by Deltares (Ruessink et al., 2007; Walstra et al., 2012). Nearshore morphology models simulating storm-induced changes have been widely applied for the last decade and demonstrated an acceptable level of accuracy as a result of well-defined cross-shore sediment transport equations, established numerical solutions, and high-quality field and laboratory data (Smith et al., 2017).
Larson et al. (2013) developed a semi-empirical model to simulate the long-term response of longshore bars to incident wave conditions as well as the material exchange between the berm and bar region, through physics-based formulations and simple schematizations of the governing processes. Wijnberg and Kroon (2002) stated that long-term bar behavior results from many storm-recovery sequences and to arrive at these large scales, the integrated effect of short-term storm recovery sequences needs to be considered. Later, Larson et al. (2016) combined this model with modules to calculate dune erosion, overwash, and wind-blown sand (forming a unique-coupled system), in order to simulate the evolution of a schematized profile at a decadal scale.
Following the modelling approach proposed by Larson et al. (2013) and Larson et al. (2016), in this study, efforts are made to expand the theory of the evolution of one single bar to a multi-bar system, where the volume of the individual bars and their response are described, but without regard to the details of the profile/bar shape or how the material may be deposited in or removed from the surf zone. As a first step, a 2-bar model is developed and validated with field data from Duck, North Carolina, where 2 bars (inner and outer) frequently form. The present model was also employed to numerically solve the evolution of offshore mounds through equilibrium equations as they migrate towards the shore and become a part of the beach face. The model was applied to simulate nearshore sand placements at Silver Strand, CA, and Cocoa Beach, FL, where in the latter case natural subtidal bars were not found.
The main objective of the present study is to enhance and validate a numerical approach developed in an equilibrium fashion to predict the subaqueous cross-shore beach profile response, including feeder mounds and multi-barred systems for applications in coastal evolution models, describing processes at the decadal scale. This paper is structured as follows. First, a brief review about the semi-empirical model proposed by Larson et al. (2013) is given, as this form the basis for the theoretical developments of the 2-bar model described in section 2. Selected cases studies are addressed in section 3 through model application and discussion of the numerical results. Final conclusions are drawn in section 4.
Section snippets
Theory for one bar and evolution equation
A subaqueous model developed to simulate bar-berm material exchange is briefly reviewed in this section, since a comprehensive description about the theoretical development is given in Larson et al. (2013, 2016) and Marinho et al. (2017b).
The proposed model assumes that the exchange of material between the bar and the berm takes place under sediment volume conservation, which means that no material is lost offshore. Material needed to supply the bar is mainly taken from the region of the inner
Model application – case studies
In this section, three field data sets collected at 3 different sites in the US coast are employed for model calibration and validation.
Results
The model results were quantitatively evaluated by comparing the computed bar volumes with the values estimated from the surveys. Fig. 13 depicts the time variation in the calculated bar volume, as well as the agreement obtained between the measured and the predicted values during the first year after nourishment operations.
The model prediction is judged to be good by considering the transfer of fill material towards the shore through the most inshore portion of the profile. The obtained error
Discussion
The model application at three different study sites (Duck, Silver Strand, Cocoa Beach) showed that the equilibrium bar model is skilled at predicting the time-varying volume of the outer bar, suggesting that this morphological feature is strongly influenced by offshore wave forcing in a predictable, equilibrium-forced manner (ε = 0.39; NMSE = 0.24). Model skill was lower when predicting the inner bar. It is yet to be explored if the inner bars in a multi-bar sites display predictable,
Conclusions
An extended version of the heuristic model, first introduced by Larson et al. (2013), was developed to reproduce the overall shift in material between the subaerial and subaqueous portions of the profile by taking into account the long-term evolution of multi-bar systems and the response of artificial bars resulted from nearshore nourishment operations. The model is based on simplifications of the governing processes, where bar volume evolution determines the transport direction. The model was
CRediT authorship contribution statement
B. Marinho: Conceptualization, Writing - original draft, Writing - review & editing. C. Coelho: Writing - review & editing. H. Hanson: Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work has been supported by Fundação para a Ciência e Tecnologia through the PhD grant SFRH/BD/95894/2013.
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