Nonlinear transfer function modelling of beach morphology at Duck, North Carolina

Abstract

This paper presents a simple nonlinear data-based modelling approach for predicting the beach profile volume at Duck, North Carolina, USA. The state-dependent parameter form of the general transfer function (SDP TF) model is used to describe nonlinearity influencing these morphological data in two case examples. Case 1 investigates the nonlinearity associated with the dependency of wave forcing on the preceding beach volume. Case 2 investigates the ability to model the variables within the well known diffusion equation for beach volume using this data-based approach. The results of this study show that the SDP TF approach can be used successfully to develop statistically robust models for describing nonlinearity in beach morphological systems. Furthermore, these models are shown to predict the beach volumes over both short (1 month ahead) and long (2 years ahead) time periods, and thus show great potential for practical applications in coastal zone management and engineering. We thank you and the two reviewers for their constructive comments and suggestions.We have fully taken on board all suggested revisions, we believe these will further improve the manuscript. The following addresses all comments made by the two reviewers in detail. Please note that the revised figures are enclosed within the manuscript as these were generated using Matlab TM , and hence could not be saved separately as image files. Best regards yohamaComments from "Reviewer 1" Specific Comments C1. "Clarify position of profiles along coast (including position of Pier)."We welcome the suggestion of the reviewer. This has been clarified by including a location map (Figure 1) of the beach profiles (Profiles 58, 62, 188 and 190) and the FRF pier at Duck. C2. "Clear explanation of the 'volume' discussed in the paper"We agree with the reviewer and apologise for the confusion. We have clarified that the beach profile volume per unit metre of shoreline were computed by integrating the beach profile data between 75 m and 700 m, which extend well beyond the average position of the depth of closure at Duck (latter is at the 4 m depth at ~410 m crossshore) to the 7 m depth (page 10). C3. "Applying Eq.(6) and a straight and parallel coastline is present, no interaction between the profiles should occur. That calls for equal 'volumes' in the 3 profiles; but the 'volume' depends [see also ii)] e.g. on the position of the reference line. Please clarify this point."Detailed Response to Reviewers 2 Here, is our explanation for this comment, which is summarised in the revised paper (page 10). Although the bathymetric contours at Duck are parallel at times, this is not always the case (Miller et al., 1983;Plant et al., 1996;Miller and Dean, 2007) because of longshore differences in the morphology of profiles on either side of the pier. As seen in Figure 2 of the revised manuscript, alongshore volume differences between northerly and southerly profiles occur, particularly post 1991. Reversed migration directions of the nearshore sand bars on either si...

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